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+The Project Gutenberg EBook of Instructions on Modern American Bridge
+Building, by G. B. N. Tower
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: Instructions on Modern American Bridge Building
+
+Author: G. B. N. Tower
+
+Release Date: February 2, 2005 [EBook #14873]
+
+Language: English
+
+Character set encoding: ISO-8859-1
+
+*** START OF THIS PROJECT GUTENBERG EBOOK AMERICAN BRIDGE BUILDING ***
+
+
+
+
+Produced by Curtis Weyant, Ronald Holder and the PG Online Distributed
+Proofreading Team.
+
+
+
+
+
+
+INSTRUCTIONS
+
+ON
+
+MODERN AMERICAN
+
+BRIDGE BUILDING.
+
+WITH
+
+PRACTICAL APPLICATIONS AND EXAMPLES,
+
+ESTIMATES OF QUANTITIES, AND
+VALUABLE TABLES.
+
+Illustrated by four Plates and Thirty Figures.
+
+BY G.B.N. TOWER,
+
+CIVIL AND MECHANICAL ENGINEER,
+
+_Formerly Chief Engineer U.S. Navy, and late Chandler Instructor in Civil_
+_Engineering at Dartmouth College._
+
+BOSTON:
+
+A. WILLIAMS & COMPANY,
+
+135 WASHINGTON STREET.
+
+1874.
+
+  Entered according to act of Congress, in the year 1874, by
+  A. WILLIAMS & CO.,
+ in the office of the Librarian of Congress, at Washington, D.C.
+
+
+
+
+PREFACE.
+
+
+This little treatise was written for the purpose of supplying a want
+felt by the author while giving instruction upon the subject. It was
+intended for an aid to the young Engineer, and is not to be considered
+as a complete substitute for the more elaborate works on the subject.
+
+The first portion of this work mentions the various strains to which
+beams are subjected, and gives the formulĉ used in determining the
+amount of those strains, together with a few examples to illustrate
+their application, and also the method of calculating a simple truss.
+
+The second portion names and explains the various members of a Bridge
+Truss, and, by means of examples, shows the method of calculating the
+strains upon the various timbers, bolts, etc., as well as their proper
+dimensions; and gives, in addition, several useful tables.
+
+The explanatory plates, which are referred to freely throughout the
+work, are believed to be amply sufficient for the purpose intended.
+
+So much has been written on this subject that it is next to impossible
+to be wholly original, and no claim of that nature is preferred. It is
+simply an arrangement of ideas, gleaned from the various works of
+standard authorities, and modified by the author's practice, embodied
+in book form. To give a correct list of all the books consulted would
+be simply impossible;--but it is well to state that the Hand-book of
+Railroad Construction, by Prof. G.L. Vose, under whom the author
+served as an Engineer, has been used as authority in many cases where
+there has been a difference of opinions among other authors. Some
+parts have been quoted entirely; but due credit has been given, it is
+believed, wherever such is the case.
+
+It is not claimed that this little work covers the whole ground, but
+it is intended to describe, and explain thoroughly, three or four of
+the more prominent styles of Truss, leaving the other forms of Wooden
+Bridges to a subsequent volume.
+
+Abutments and Piers, as well as Box and Arch Culverts, belonging more
+properly to masonry, will be treated of hereafter under that head.
+
+Iron Bridges form a distinct class, and may be mentioned separately at
+some future period.
+
+If this small volume should lead the student of Engineering to examine
+carefully the best Bridges of modern practice, and study the larger
+scientific works on this art, the author will feel satisfied that his
+efforts have not been entirely in vain.
+
+_Cambridge, February 23, 1874._
+
+
+
+
+TOWER'S
+
+Modern American Bridge Building.
+
+
+
+
+BRIDGE BUILDING
+
+
+The simplest bridge that can be built, is a single beam, or stick of
+timber, spanning the opening between the abutments--but this is only
+of very limited application--(only for spans of 20 feet and less)
+owing to the rapid increase in sectional dimensions which is required
+as the span becomes greater.
+
+Next comes the single beam supported by an inclined piece from each
+abutment meeting each other at the middle point of the under side of
+the beam--or, another arrangement, of two braces footing securely on
+the beam and meeting at a point above the middle point of the beam,
+which is suspended from the apex of the triangle formed by them, by
+means of an iron rod--These arrangements may be used up to 50 feet.
+For any span beyond 50 feet, modifications of this arrangement are
+used which will be described hereafter. Now let us investigate shortly
+the different strains that the various parts of a bridge have to
+bear--and the strength of the materials used. The theory of strains in
+bridge trusses is merely that of the Composition and Resolution of
+Forces. The various strains, to which the materials of a bridge are
+subjected--are compression, extension and detrusion.
+
+Wood and Iron are the materials more generally employed in bridge
+construction--and in this pamphlet we shall take the following as the
+working strength of the materials--per square inch of section.
+
+             Tension.  Compression.  Detrusion.
+
+Wood,          2000       1000          150
+
+Wro't Iron,   15000      11000
+
+Cast Iron,     4500      25000
+
+
+=Tension.= If a weight of 2000 lbs. were hung to the lowest end of a
+vertical beam, so that the line of action of the weight and axis of
+the beam formed one and the same straight line--the tension on the
+beam would be 2000 lbs. But, if the beam were inclined, and the force
+acted in a vertical direction, then the strain would be increased in
+the ratio of the increase of the diagonal of inclination over the
+vertical;--suppose the beam is 20 ft. long and inclined at an angle of
+45°--and let 2000 lbs., as before, be suspended from its lower end.
+Now the diagonal being 20°,--the vertical will be 14.014 ft.--and the
+strain will be found as follows,--
+
+  14.014 : 20 :: 2000 : 2854--lbs.
+
+The greater the angle of inclination from the horizontal, the less the
+strain from a given load--and when the beam is vertical the weight
+causes the least strain.
+
+
+=Compression.= If we load a vertical post with a weight of 2000 lbs.,
+the strain of compression exerted upon the post will be 2000 lbs. Now,
+if we incline the post--the strain will be increased, as we have shown
+above under the head of tension, and in like manner, dependent upon
+the inclination.
+
+But when wood, iron, or any other material is used for a pillar or
+strut, it has not only to resist a crushing force, but also a force
+tending to bend or bulge it laterally.
+
+A post of circular section with a length of 7 or 8 diameters will not
+bulge with any force applied longitudinally, but will split. But if
+the length exceeds this limit--it will be destroyed by an action
+similar to that of a transverse strain.
+
+A cast iron column of thirty diameters in length, is fractured by
+bending; when the length is less than this ratio--by bending and
+splitting off of wedge shaped pieces. But by casting the column
+hollow, and swelling it in the middle, its strength is greatly
+increased.
+
+Barlow's formula for finding the weight that can be sustained by any
+beam, acting as a pillar or strut, before bending, is:--
+
+  WL²                    bd³ x 80 E
+  ---- = bd³, whence W = -----------
+  80 E                       L²
+
+[TeX: $\frac{WL^2}{80 E} = {bd^3}$, whence $W = \frac{{bd^3} x 80 E}{L^2}$]
+
+now, having the weight given, and assuming the dimensions of
+the cross-section--we shall have
+
+          -----
+         / WL²              WL²
+  d =  ³/ -----,  and b = ------
+      \/  80 Eb           80 Ed³
+
+[TeX: $d = \sqrt[3]{\frac{WL^2}{80 EB}}$, and $b = \frac{WL^2}{80 ED^3}$]
+
+in the above formulĉ,
+
+  W = weight in pounds.
+  L = length in feet.
+  E = a constant.
+  b = breadth in inches.
+  d = depth in inches.
+
+
+=Transverse Strains.= The strain caused by any weight, applied
+transversely, to a beam supported at both ends, is directly as the
+breadth, and square of the depth, and inversely as the length. It
+causes the beam to be depressed towards the middle of its length,
+forming a curve, concave to the horizontal and below it. In assuming
+this form--the fibres of the upper part of the beam are compressed,
+and those of the lower part are extended--consequently there must be
+some line situated between the upper and lower surfaces of the beam
+where the fibers are subjected to neither of these two forces, this
+line is called the _neutral axis_.
+
+These two strains of compression and extension must be equal in
+amount--and upon the relative strength of the material to resist these
+strains, as well as its form and position, the situation of this axis
+depends. If wood resists a compression of 1000 lbs. per square inch of
+section, and a tension of 2000 lbs. the axis will be twice as far from
+the top as from the bottom in a rectangular beam.
+
+The following table by Mr. G.L. Vose gives, with sufficient accuracy
+for practice, the relative resisting powers of wood, wrought, and cast
+iron, with the corresponding positions of the axis.
+
+                                                 Dist. of axis
+               Resistance  Resistance            from top in
+                   to          to                frac's of
+  Material.    Extension.  Compression.  Ratio.  the depth.
+
+  Wrought Iron,    90          66        90/66   90/156, or 0.58.
+
+  Cast Iron,       20         111       20/111   20/131, or 0.15.
+
+  Wood,             2           1          2/1    2/3, or 0.66.
+
+
+Thus we see that the resistance of a beam to a cross strain, as well
+as to tension and compression, is affected by the incompressibility
+and inextensibility of the material.
+
+The formula for the dimensions of any beam to support a strain
+transversely is
+
+      4 bd²
+  S = ----
+       l
+
+[TeX: $S = \frac{4 bd^2}{l}$]
+
+  S = the ultimate strength in lbs.
+  b = the breadth in inches.
+  d = the depth in inches.
+  l = the length in inches.
+
+
+=Detrusion.= Detrusion is the crushing against some fixed point, such
+as obtains where a brace abuts against a chord, or where a bridge
+rests on a bolster; and the shearing of pins, bolts and rivets, also
+comes under this head.
+
+
+=General Abstract.= The resistance to the above mentioned strains
+varies as the area of the cross section; so that by doubling the area
+we double the strength. Any material will bear a much greater strain
+for a short time than for a long one. The working strength of materials,
+or the weight which does not injure them enough, to render them unsafe,
+is a mooted point, and varies, according to the authority, from 1-3
+to 1-10 of the ultimate strength. The ratio of the ultimate strength
+to the working strength is called the _factor of safety_.
+
+The following is a table of ultimate and working strengths of
+materials, and factors of safety:
+
+  Weight                Ult.    Ult.   Working Strengths Factor  Safety.
+  in lbs.  Materials.   Ext.    Comp.  Exten.    Comp.   Tension  Comp.
+
+    30    Wood.        14,000   7,000   2,000    1,000      7      7
+   480    Wrou't Iron. 60,000  64,000  15,000   12,000      4      5.33
+   450    Cast Iron.   18,000 100,000   4,500   25,000      4      4
+
+
+=Lateral Adhesion.= Lateral adhesion is the resistance offered by the
+fibres to sliding past each other in the direction of the grain, as
+when a brace is notched into a chord, or tie beam, at its foot, it is
+prevented by the lateral adhesion of the fibres from crowding off the
+piece, to the depth of the notch, against which it toes. Barlow's
+experiments give the lateral adhesion of fir as 600 lbs. per square
+inch, and the factor of safety employed varies in practice from 4 to
+6, giving a working strength of from 150 to 100 lbs. per square inch.
+
+
+=TABLE OF COMPRESSIVE RESISTANCE OF TIMBER.=
+
+  Length      Safety       Length    Safety     Length    Safety
+  given in    Weig't in   given in   Wt. in    given in   Wt. in
+  Diameters.  Pounds.    Diameters.  Pounds.  Diameters.  Pounds.
+
+     6         1000         24         440       42         203
+     8          960         26         394       44         185
+    10          910         28         358       46         169
+    12          860         30         328       48         155
+    14          810         32         299       50         143
+    16          760         34         276       52         132
+    18          710         36         258       54         122
+    20          660         38         239       56         114
+    22          570         40         224       58         106
+                                                 60          99
+
+In tensional strains, the length of the beam does not affect the
+strength; but in the beams submitted to compression, the length is a
+most important element, and in the table given above, the safety
+strains to which beams may be subjected, without crushing or bending,
+has been given for lengths, varying from 6 to 60 diameters.
+
+
+PRACTICAL RULES.
+
+=Tensional Strain.=
+
+  Let T = whole tensional strain.
+  "   S = strength per square inch.
+  "   a = sectional area in inches.
+  Then we have T = Sa.
+
+Now to find the necessary sectional area for resisting any strain, we
+have the following general formula:
+
+       T
+  a = ---
+       S
+
+[TeX: $a = \frac{T}{S}$]
+
+or, by substituting the working strengths for the various materials in
+the formula, we have for wood,
+
+                  a = T/2000
+
+  Wrought Iron,   a = T/1500
+
+  Cast Iron,      a = T/4500
+
+But, in practice, cast iron is seldom used except to resist
+compression.
+
+=Strains of Compression.= Allowing the same letters to denote the
+same things as above, we have for
+
+  Wood, a = T/1000
+
+  Wrought Iron, a = T/12000
+
+  Cast Iron, a = T/25000
+
+As this pamphlet has to do with wooden bridges only, nothing will be
+said of the proper relative dimensions of cast-iron columns to sustain
+the strains to which they may be subjected, but a table of the
+strength of columns will be found further on.
+
+=Transverse Strains.=
+
+  Let W = breaking weight in lbs.
+   "  s = constant in table.
+   "  b = breadth in inches.
+   "  d = depth in inches.
+   "  L = length in inches.
+
+Then, for the power of a beam to resist a transverse strain, we shall
+have,
+
+      4 sbd²
+  W = ------
+        L
+
+[TeX: $W = \frac{4 sbd^2}{L}$]
+
+This formula has been derived from experiments made by the most
+reliable authorities.
+
+The constant, 1250, adopted for wood in the following formula, is an
+average constant, derived from the table, of those woods more commonly
+used.
+
+Now to reduce the formula to the most convenient shape for use, we
+substitute the value of s, and we have
+
+      4 x 1250 bd²
+  W = ------------,
+           L
+
+[TeX: $W = \frac{4 \times 1250 bd^2}{L}$]
+
+or
+
+      5000 bd²
+  W = --------.
+          L
+
+
+[TeX: $W = \frac{5000 bd^2}{L}$]
+
+But, to reduce the load to the proper working strain, we must divide
+this equivalent by 4, the factor of safety, and we shall have
+
+      5000 bd²
+  W = --------.
+         4L
+
+[TeX: $W = \frac{5000 bd^2}{4 L}$]
+
+Let us apply the formula--
+
+  Case I. Given a span of 14 feet,
+                a breadth of 8 inches,
+                a depth of 14 inches.
+
+Required the safe load.
+
+                  5000 bd²
+  The formula W = --------
+                     4L
+
+[TeX: $W = \frac{5000 bd^2}{4 L}$]
+
+becomes, by substitution,
+
+      5000 x 8 x 196
+  W = -------------- = 11.666 lbs.
+          4 x 8
+
+[TeX: $W = \frac{5000 \times 8 \times 196}{4 \times 168} = 11,666$ lbs.]
+
+  Case II. Given the safety load 18000 lbs.
+                 the breadth 9 inches,
+                 the length 14 feet.
+
+Required the depth.
+From the above formula we have
+
+         -------
+        / W X 4L
+  d =  /  ------
+     \/   5000 b
+
+
+[TeX: $d = \sqrt{\frac{w \times 4L}{5000 b}}$]
+
+substituting
+
+         ----------------
+        / 18000 x 168 x 4      ------
+  d =  /  --------------- =   / 268.8 = 16, inches nearly.
+     \/      5000 x 9       \/
+
+
+[TeX: $d = \sqrt{\frac{1800 \times 168 \times 4}{5000 \times 9}}
+ = \sqrt{268.8} = 16$]
+
+  Case III. Given the safety load 22,400 lbs.
+  the depth 18 inches.
+  the length 14 feet.
+
+Required the breadth.
+Deriving b from the foregoing, we have,
+
+        W x 4L
+  b = ----------
+      5000 x d²
+
+[TeX: $b = \frac{W \times 4L}{5000 \times d^2}$]
+
+substituting
+
+      22400 x 4 x 168
+  b = --------------- = 9.3 inches nearly.
+        5000 x 324
+
+[TeX: $b = \frac{22400 \times 4 \times 168}{5000 \times 324} = 9.3$]
+
+For a cast iron beam or girder--Mr. Hodgkinson found from numerous
+carefully conducted experiments that, by arranging the material in the
+form of an inverted T--thus creating a small top flange as well as the
+larger bottom one, the resistance was increased, per unit of section,
+over that of a rectangular beam, in the ratio of 40 to 23.
+
+In this beam the areas of the top and bottom flanges are inversely
+proportional to the power of the iron to resist compression and
+extension. Mr. Hodgkinson's formula for the dimensions of his girder,
+is
+
+       26 ad
+  W = ------
+         L
+
+[TeX: $W = \frac{26 ad}{L}$]
+
+The factor of safety being 6 for cast iron beams--the formula for the
+working load will be,
+
+       26 ad
+  W = ------
+        6 L
+
+[TeX: $W = \frac{26 ad}{6 L}$]
+
+and, to find area of lower flange, we shall have
+
+      6 WL
+  a = ----
+      26 d
+
+[TeX: $a = \frac{6 WL}{26 d}$]
+
+The general proportions of his girders are as follows:
+
+  Length,             16
+  Height,              1
+  Area Top Flange,     1.0
+  Area Bottom Flange,  6.1
+
+In the above formula for cast iron beams,
+
+  W = weight in tons.
+  a = area in square inches of bottom flange.
+  d = depth in inches.
+  h = length in inches.
+
+The web uniting the two flanges must be made solid--as any opening, by
+causing irregularity in cooling, would seriously affect the strength
+of the beam.
+
+_Example._--Required the dimensions of a Hodgkinson girder--for a span
+of 60 feet--with a load of 10 tons in the centre.
+
+      6 x 10 x 60 x 12
+  a = ---------------- = 37 inches nearly.
+            60 x 12
+       26 x -------
+              16
+
+[TeX: $a = \frac{6 \times 10 \times 60 \times 12}{26 \times \frac{60
+\times 12}{16}} = 37$]
+
+and the area of the top flange will be,
+
+  37
+  -- = 6.16 inches--
+  6
+
+[TeX: $\frac{37}{6} = 6.16$]
+
+so that our dimensions will be as follows:
+
+  Length,              30 feet.
+  Depth,               45 inches.
+  Area Top Flange,      6.16 inches.
+  Area Bottom Flange,  37 inches.
+
+[Illustration: Pl. 1.]
+
+The thickness of web is usually a little greater at the bottom than
+at the top, and varies from 1/14 to 1/24 of the depth of the girder.
+The bottom rib is usually made from six to eight times as wide as it
+is thick, and the top rib from three to six times as wide as thick, so
+that, in the example above given, we could have as dimensions for the
+parts
+
+  Top Flange,     4 1/4 x 1 1/2 inches nearly.
+  Bottom Flange,  6 x 2 1/2 inches nearly.
+  Web,            1 1/2 inches thick.
+
+The simplest bridge, consisting of a single stick, to span openings of
+20 feet and under, is calculated according to the formula
+
+          ------
+         /  4WL
+  d =   / ------ --
+      \/  5000 b
+
+
+[TeX: $d = \sqrt{\frac{4 WL}{5000 b}}$]
+
+_Example._--The depth of a beam, of 12 feet span and 12
+feet wide, to support a load of 22400 lbs. will be
+
+          ------       --------------------
+         / 4WL        / 4 X 22400 x 12 x 12      -------
+  d =   / ------ =   /  ------------------- =   / 215.04 = 15 in. nearly
+      \/  5000 b   \/        5000 x 12        \/
+
+
+[TeX: $d = \sqrt\frac{4 WL}{5000 b}} = \sqrt\frac{4 \times 22400
+\times 12 \times 12}{5000 \times 12} = \sqrt{215.04} = 15$]
+
+The following Table was calculated by the above rule--and the
+dimensions altered according to the actual practice of the writer.
+
+  Span.  Breadth.  Depth.
+
+    4       10       12
+    6       10       12
+    8       12       12
+   10       12       13
+   12       12       15
+   16       12       18
+   18       12       20
+   20       12       22
+
+These dimensions will give ample strength and stiffness. Fig. 1, Plate
+I. gives an illustration of this kind of bridge--in which a, a, are
+the bolsters or wall plates, shown in section, to which the bridge
+beams are notched and bolted. Fig. 1, A, Plate I, shows the method of
+diagonally bracing these beams by planks, dimensions of which in
+general use are 6 to 8 by 2 to 3 inches. The track should rest on
+ties, about 6 inches by 8 or 10 inches--the same bolt confining the
+ends of the ties and diagonal braces when practicable. These ties
+should be notched on the string pieces 2 or 3 inches--without cutting
+the stringers. Below is a table giving general dimensions, in inches,
+of the several parts of a bridge of this description.
+
+  Span.  Bolsters.  Stringers.   Ties.   Braces.   Diameter of Bolts.
+
+    4     12 x 12    10 x 12     6 x 8    2 x 8         1 inch.
+   10     12 x 12    12 x 13     6 x 8    2 x 8         1  "
+   16     14 x 14    12 x 18     6 x 8    2 x 8         1  "
+   20     14 x 14    12 x 22     6 x 8    2 x 8         1  "
+
+
+Each bolt must have a washer under the head, and also under the nut.
+For a span of from 15 to 30 feet, we can use the combination shown in
+Plate II, Fig. 3. The piece A F must have the same dimensions as a
+simple string piece of a length A B--so that it may not yield between
+B and either of the points A or D. The two braces D F and E F must be
+stiff enough to support the load coming upon them. Suppose the weight
+on a pair of drivers of a Locomotive to be 10 tons, then each side
+must bear 5 tons, and each brace 2-1/2 tons = 2-1/2 x 2240 = 5600 lbs.
+Now, to allow for sudden or extra strains, call 8000 lbs. the strain
+to be supported by each brace, and, accordingly, 8 square inches of
+sectional area would be sufficient for compression only; but, as the
+brace is inclined, the strain is increased. Let the vertical distance
+from A to D be 10 ft., and, calling the span 30 ft.--A B will be 15
+ft.--from whence D F must be 18 ft., then we shall have the proportion
+
+  10 : 18 :: 8000 : 14400 lbs.
+
+which would require an area of about 15 square inches of section to
+resist compression, or a piece 3x5 inches. Now, as this stick is more
+than 6 or 8 diameters in length, it will yield by bending--and
+consequently its area must be increased. The load, which a piece of
+wood acting as a post or strut will safely sustain, is found by the
+formula already given.
+
+      2240 bd³
+  W = --------
+         L²
+
+[TeX: $W = \frac{2240 bd^3}{L^2}$]
+
+Now substituting 3 for b, and 5 for d, we have
+
+      2240 x 3 x 125   840000
+  W = -------------- = ------ = 2592 lbs.
+           324           324
+
+[TeX: $W=\frac{2240 \times 3 \times 125}{324}=\frac{840000}{324}=2592$]
+
+which is not enough. Using 6 for b and 8 for d, we have
+
+      2240 x 6 x 512
+  W = -------------- = 21238 lbs.
+            324
+
+[TeX: $W = \frac{2240 \times 6 \times 512}{324} = 21238$]
+
+which is something larger than is actually required, but it is no
+harm to have an excess of strength. Now in many cases this arrangement
+would be objectionable, as not affording sufficient head room on
+account of the braces--and we can as well use the form of structure
+given in Pl. I. Fig. 3, since it is evidently immaterial whether the
+point B be supported on F or suspended from it, provided we can
+prevent motion in the feet of the braces, which is done by notching
+them into the stringer at that point. This of course creates a
+tensional strain along the stringer, which is found as
+follows:--Representing the applied weight by F B, Pl. II, Fig. 2, draw
+B D parallel to F C, also D H parallel to A C--D H is the tension.
+This is the graphical construction, and is near enough for practice.
+Geometrically we have the two similar triangles A F B and D F H,
+whence
+
+  A F : D F :: A B : D H
+
+            D F x A B
+  and D H = ---------
+               A F
+
+[TeX: $DH = \frac{DF \times AB}{AF}$]
+
+This style of structure may be used up to 50 feet, but it is not
+employed for spans exceeding 30 feet in length. It is very customary
+to make the braces in pairs so as to use smaller scantling, and gain
+in lateral stiffness--the two pieces forming one brace by being
+properly blocked and bolted together. Below is given a table of
+dimensions for the various parts of this style of structure:
+
+  Span.    Rise.    Bolster.    Stringer.     Braces.     Rod.
+                                                         No. Size.
+
+   15        6      12 x 12     12 x 12       2--5 x 6    1-1/8
+   20        7      14 x 14     12 x 13       2--5 x 8    1-3/8
+   25        8      14 x 14     12 x 15       2--6 x 8    1-1/2
+   30       10      14 x 14     12 x 18       2--6 x 9    1-5/8
+
+Single Beams under each rail firmly braced laterally, and trussed by
+an iron rod, (or preferably by two iron rods,) and a post on the under
+side of the beam. The deflection of the rod is usually taken at 1\8 of
+the span. Pl. II., Fig. 1, represents this style of trussing a
+beam--which is generally used for spans of from 15 to 30 ft. Below is
+a table of dimensions for this truss with single and double rods; if
+double rods are used only half the given section will be necessary for
+each one of the pair.
+
+  Span.     Rise.      Stringer.    Post.      Rod.           Rods.
+  Feet.    In Feet.                          (single.)      (double.)
+
+   15       1-7/8      12 x 12      6 x 8    2-1/8 diam. or 1-1/2 diam.
+   20       2-1/2      12 x 14      7 x 8    2-1/2   "      1-3/4   "
+   25       3-1/8      12 x 16      8 x 8    2-3/4   "      2       "
+   30       3-3/4      13 x 18      9 x 9    3       "      2-1/8   "
+
+It is as well to tenon the post into the beam, and also strap it
+firmly with iron plates--and the end should be shod with iron to form
+a saddle for the rods to bear upon.
+
+Now if we should make a bridge, on the plan of Fig. 3, Pl. I., 75 or
+100 feet, or perhaps more, in length, the braces A F and F C, would
+not only be very long but very large and heavy, and one chief
+requisite in a good bridge is, to have all the beams so proportioned
+that they will resist all the strains acting upon them, without being
+unnecessarily large. It now becomes necessary to have a different
+arrangement of the parts of the truss in order to obtain increased
+length of span.
+
+Suppose we have a span, of 40 feet, as represented in Fig 2, Pl. I.
+Now instead of running the braces from A C until they meet in a point,
+as before we stop them at a, and c, and place the straining beam, a c,
+between them to prevent those points from approaching, suspend the
+points B and D from them, and start the braces B b and D b--and, if
+the truss were longer, would continue on in the same manner as far as
+needful. To prevent the. truss from altering its form, as shown by the
+dotted lines A' b C', and A E C, by any passing load, we insert the
+counter braces marked R.
+
+The braces A a and C c, must support all of the weight of the bridge
+and its load within the parallelogram B a c D--and the next set of
+braces, B b and D b, sustain that part of the load which comes over
+the centre of the bridge. Consequently the braces must increase in
+size from the centre towards the abutments. The rods resist the same
+pressure in amount as their braces--but being vertical, do not need
+the increase, given to the braces on account of their inclination--but
+increase simply with the strain upon them, from the centre to the ends
+of the truss.
+
+There are many forms of small bridges differing from those enumerated,
+in various minor details, but sufficient has been said to give the
+reader a fair idea of the strains upon the different parts, and how to
+arrange and proportion the materials to resist them.
+
+
+
+
+PRACTICAL RULES AND EXAMPLES IN WOODEN BRIDGE BUILDING.
+
+
+In any case that may arise, we must determine approximately the gross
+weight of the bridge and its load--as a basis, and then we can proceed
+as follows--in case of a Howe, Pratt, or Arch Brace Truss.
+
+
+=To find the dimensions of the Lower Chord.=
+
+The tension at the centre of the Lower Chord is found by _dividing the_
+_product of the weight of the whole bridge and load by the span_, by
+sight times the height--or letting T=tension in lbs., W=weight of
+bridge and load in lbs., S=span in feet, and h=rise or height--we have
+
+      W x S
+  T = ----- --.
+       8 h
+
+[TeX: $T = \frac{W \times S}{8 h}$]
+
+In this case we have taken the rise at 1/8 of the span, which is
+evidently the best ratio between those dimensions, as it equalizes
+the vertical and horizontal forces. As to the proportions of the
+_bays_ or _panels_, (or that portion of the truss bounded by two
+adjacent verticals, as struts or ties, and the chords,) the ratio of
+the rise (or the vertical distance between the centre lines of the two
+chords,) and the length on the chord should be such, that the diagonal
+truss members may make an angle of about 50° with the chords; as the
+size of the timbers is increased by decreasing the angle, and, if the
+angle is increased, there are more timbers required.
+
+Mr. G.L. Vose, in his admirable work on R.R. Construction, observes
+very truly that "The braces, at the end of a long span, may be nearer
+the vertical than those near the centre, as they have more work to do.
+If the end panel be made twice as high as long, and the centre panel
+square, the intermediates varying as their distance from the end, a
+good architectural effect is produced."
+
+Now it is necessary for us to have some data from which to determine
+the approximate weight of the bridge, and also its load. These can be
+found by comparing weights of bridges in common use, as obtained from
+reports. In a small bridge of short span, the weight of the structure
+itself may be entirely neglected, because of. the very small
+proportion the strains caused by it bear to those due to the
+load;--but, in long spans, the weight becomes a very important element
+in the calculations for strength and safety--inasmuch as it may exceed
+the weight of the load.
+
+In all Bridges of 120 ft. span, about 1/3 of a ton, per foot run, will
+be the weight of each truss for a single track, including floor
+timbers--transverse bracing, &c. If the bridge were loaded with
+Locomotives only, the greatest load would be, on the whole bridge--160
+tons = 1.33 tons per ft. run of the bridge or .666 tons per ft. run of
+each truss. Now if we make the rise of the bridge 15 ft., and divide
+the span into 12 panels of 10 ft. each, we shall have for total weight
+of bridge and load 240 tons, or for a single truss 10 tons to each
+panel.
+
+
+=Lower Chords.= Now to find the tension on the Lower Chords,
+
+      W x S
+  T = ----- and supplying values, we have
+       8 h
+
+[TeX: $T = \frac{W \times S}{8 h}$]
+
+      240 x 120
+  T = --------- = 240 tons, or 537600 lbs.,
+        8 x 15
+
+[TeX: $T = \frac{240 \times 120}{8 \times 15 = 240$}
+
+for the two Lower Chords, and 1/2 of this, or 268800 lbs. for one
+chord. The Tensional Strength of timber for safety may be taken at
+2000 lbs. per square inch of section, and hence the area of timber
+required to sustain the above strain will be
+
+  268800
+  ------ = 134.4 sq. inches.
+   2000
+
+[TeX: $\frac{268800}{2000} = 134.4$]
+
+But this chord has also to sustain the transverse strains arising from
+the weights passing over it, and, as in the case of a Locomotive, the
+weight of 20 tons on 2 pair of drivers, (or 10 tons for one truss,)
+may be concentrated on the middle point of a panel--the chord must be
+so proportioned as to safely bear, as a horizontal beam, this weight.
+Suppose we take three sticks of 8" x 12", to form the chord (the
+greater dimension being the depth,) we shall have 3 x 8" x l2" = 288
+square inches area of section, and
+
+   allowing for splicing     72 square inches,
+     "      "  foot blocks, 24   "       "
+     "      "  bolts,       24   "       "
+     "      "  washers,      8   "       "
+
+we shall have after deducting allowances (288-128) 160 square inches
+area, giving an excess over 134.4, the area demanded, sufficient to
+cover allowances for any accidental strain.
+
+
+=Upper Chords.= The upper chords are compressed as forcibly as the
+lower ones suffer tension--owing to the action and reaction of the
+diagonals. In this case the compression is 268800 lbs., and as 1
+square inch of section will safely bear 1000 lbs., we have for the
+
+                 268800
+  area required, ------ = 268.8
+                  1000
+
+[TeX: $\frac{268800}{1000} = 268.8$]
+
+square inches,--three pieces 8" x 11" will give 264 square inches and
+this area will require no reduction, as the whole chord presses
+together when properly framed and is not weakened by splicing. So far,
+the calculations made would apply to either of the three Bridges
+mentioned, as well as to a Warren Truss. But now, to obtain the
+dimensions of the web members, so called, of the Truss, it is
+necessary to decide upon the specific variety. The form of Bridge in
+more general use in the United States is called the Howe Truss, from
+its inventor, and in spans of 150 feet, and under, is very reliable;
+for spans exceeding 150 ft. it should be strengthened either by Arch
+Braces or by the addition of Arches, as the heavy strains from the
+weight of bridge and load bearing on the feet of the braces near the
+abutments, tend to cripple and distort the truss by sagging, although
+the Baltimore Bridge Co. have built a Wooden Howe Bridge of two
+Trusses of 300 ft. span, 30 ft. rise, and 26 ft. wide, without any
+arch, but it has a wrought iron lower chord, and is only proportioned
+for a moving load of 1000 lbs. per ft. run. [Vide Vose on R.R.
+construction.]
+
+In order to ensure uniformity in strength in the chords--but one joint
+should be allowed in a panel--and that should come at the centre of
+the panel length--but in long spans this cannot always be done.
+
+
+=Web Members.= We will now proceed to calculate the web members of a
+Howe Truss of the foregoing dimensions, when subjected to the strains
+above mentioned.
+
+=Braces.= The end braces must evidently support the whole weight of
+the bridge and load, which for one end of one truss will be 134400
+lbs., and as these braces are in pairs,--67200 lbs. will be the strain
+vertically on the stick--but as this stick is a diagonal--whose
+vertical is 15 ft., and horizontal 10 ft., we shall have for its
+length 18 ft. in round numbers, whence the strain along the diagonal
+will be found from the proportion 15 : 18 :: 67200 : 80640 lbs.,
+whence we have an area of 80 inches required for compression, or a
+stick of 8" x 10". Now, to ascertain if this is stiff enough for
+flexure, we will substitute these values in the equation
+
+      2240 bd³
+  W = --------, and we have
+         L²
+
+[TeX: $W = \frac{2240 \times bd^3}{L^2}$]
+
+      2240 x 8 x 1000
+  W = ---------------, or reducing, W=55308 lbs.
+            324
+
+[TeX: $W = \frac{2240 \times 8 \times 1000}{324} = 55308$]
+
+Now, these proportions will give ample strength for both flexure and
+compression, for if we block the two sticks composing the end brace
+together, and firmly connect them by bolts, we shall have a built beam
+
+                           2240 x 24 x 1000
+  of 24" x 10"--whence W = ---------------- = 165925 lbs.,
+                                 324
+
+[TeX: $W = \frac{2240 \times 24 \times 1000}{324} = 165925$]
+
+and as 134400 lbs. was all that the conditions demand, we really have
+an excess of strength. The next set of braces supports the weight of
+the rectangle included between the upper ends of the braces and the
+two chords, and the dimensions of the sticks are calculated in the
+same manner. We find, as we approach the centre of the bridge, that
+the strains on the braces become less, and consequently their
+scantling should be reduced, but in ordinary practice this is seldom
+done.
+
+=Rods.= The next thing is to ascertain the dimensions of the various
+tie rods. It is evident that the same weight comes upon the first set
+of rods, as on the first set of braces--which will give for the rods
+at one end of one truss, 134400 lbs.; and as there are two of these
+rods, each will sustain a strain of 67200 lbs.--and, at 15,000 lbs.
+per square inch, will have an area of 4.48 sq. inches, and, by Vose's
+Tables, must have a diameter of 2-1/2 inches. The sizes of the rods in
+each set will decrease towards the centre of the bridge as the weight
+becomes less.
+
+[Illustration: Pl. II. with Fig. 1., Fig. 2., Fig. 3., Fig. 4.]
+
+
+=Counterbraces.= Now, as to the necessity of Counterbracing, there are
+various opinions. The object of it is to stiffen the truss and check
+vibrations. If a load be placed over any panel point, it causes that
+portion of the truss to sink, and produces an elevation of the
+corresponding panel point at the other end of the truss--thus
+producing a distortion, which change of form is resisted by proper
+counterbraces. The strain to which this timber is subjected is caused
+by the moving load on one panel only--and requires only scantling of
+the size of the middle braces. These counterbraces should not be
+pinned or bolted to the braces where the cross--as their action is
+thereby entirely altered--but it is well to so confine them as to
+prevent vertical or lateral motion.
+
+
+=Shoes.= Formerly it was the custom to foot the braces and counters on
+hard wood blocks on one side of the chord, the vertical rods passing
+through and screwing against a block on the other side--thus the whole
+strain tended to crush the chord across its fibres. This is now
+remedied by the use of cast iron blocks, bearing on one side of the
+chord, but having tubes extending through to the other side, where the
+washer plate for the bolts fits firmly on their ends, forming a
+complete protection, as all the crushing strain is received on the
+block itself.
+
+
+=Width.= It now becomes necessary to determine upon the width between
+the two trusses. For a single track bridge for a railroad, 14 ft. is
+the usual width adopted, and for a highway bridge, from 12 to 16 ft.
+When a double track is required, three trusses are usually employed,
+with a width for each roadway of 14 ft. for railroads.
+
+
+=Bolsters.= Large timbers 12 x 12, or thereabouts, are laid on the
+bridge seats of the abutments to support the ends of the trusses, one
+of these should be directly under each of the extreme panel points. A
+panel point is the intersection of the centre line of a brace
+produced, with the centre line of a chord. The rise of a truss is the
+vertical distance between the centre lines of the upper and lower
+chords.
+
+=Camber.= Were a bridge to be framed with its chords perfectly
+horizontal, it would be found to fall below the horizontal line on
+being placed in its proper position, owing to the closing up of the
+joints in the upper parts of the structure, and opening of joints in
+the lower parts, as well as to the compression of the parts. To
+obviate this defect, it is usual to curve the chords slightly in a
+vertical direction, by elongating the upper chord, so that the bays or
+panels are no longer rectangular but of a trapezoidal form--and, as a
+consequence, the inclined web members are slightly lengthened, and the
+verticals become radii of the curve. The amount of deviation from a
+horizontal line is called the Camber.
+
+A table of Cambers for different spans will be found further on, as
+also a table of multipliers, by which to multiply the camber in order
+to find the elongation of the upper chord. Part of the Camber table is
+taken from Trautwine's Engineer's Pocket-Book, (which should be the
+inseparable companion of every engineer,) and part was calculated for
+this pamphlet, according to Trautwine's rules. The table of
+multipliers is Trautwine's.
+
+=Diagonal Bracing.= In order to stiffen a bridge, it should have the
+two Trusses braced together at the Lower Chords always, at the Upper
+Chords when practicable--and in case of a deck bridge, where the
+roadway is supported on the upper chords, it is as well to have rods
+for vertical diagonal braces, their planes being perpendicular to the
+axis of the bridge. The more usual form is similar to the web members
+of the Howe Truss--the rods from 3/4" to 1" in diameter, and the
+braces of 6" x 7" scantling, footed on wooden blocks, usually. It is
+more usual to have the tie rods of the horizontal diagonal bracing,
+and the braces themselves, meet in a point about midway of a Truss
+panel on the centre line, nearly, of the chord. This will generally
+give a half panel of diagonal bracing near each end of the truss--and
+it is very usual to have the diagonals foot at their intersection
+there against a cross timber interposed between the trusses, while the
+tie rod prevents any spreading.
+
+
+=Floor Timbers.= The general dimensions of the transverse floor beams,
+when about 3 feet apart, from centre te centre, are 8" x 14", the
+largest dimension being the depth. The stringers should be notched to
+the floor beams about 1" or 2", and should be about 10" or 12" x 14".
+The cross ties should be 18" to 24" apart, from centre to centre, and
+be 3-1/2" x 6".
+
+Large, heavy bridges require no fastening to connect them with their
+seats, but light bridges should be fastened, as the spring on the
+sudden removal of a load, (as when the last car of a train has
+passed,) may move it from its proper position.
+
+
+=Splices.= As the upper and lower chords have to be made in several
+lengths, securely fastened to each other, and, in order to weaken the
+built beam as little as possible, it is necessary to adopt some form
+of splicing whereby the greatest amount of tensional strength may be
+retained in the chord with the least amount of cutting, and yet have a
+secure joint. Such a splice is shown in Pl. II, Fig. 4, and below is a
+table from Vose's Hand-book, giving reliable dimensions.
+
+        Span.    A C     B B      C D
+        Feet.   Feet.  Inches.   Feet.
+          50    1.00    1-1/2    1.50
+         100    1.25      2      2.00
+         150    1.75    2-1/2    2.25
+         200    2.00      3      2.75
+
+This manner of splicing requires the back of the splice block to be
+let into the chord stick, against which it lies, about 3/4 of an inch.
+To show how the various Engineers differ, as to their estimates of the
+sizes of the several parts of bridges, I subjoin two Tables--one by
+Prof. G.L. Vose, a well known Engineer, and one by Jno. C. Trautwine,
+an Engineer of note also--and I would premise that a bridge built
+according to either would be amply strong.
+
+
+TABLE FOR DIMENSIONING A HOWE TRUSS BRIDGE.
+G.L. VOSE.
+
+                                      End    Centre           Centre
+      Span. Rise. Panel.  Chords.    Braces. Braces. End Rods. Rods.
+       50    10     7    2--8 x 10   7 x  7   5 x 5  1--1-1/8  2--1
+       75    12     9    2--8 x 10   8 x  8   5 x 5  2--1-1/2  2--1
+      100    15    11    2--8 x 10   8 x  9   6 x 6  2--1-3/4  2--1
+      150    20    13    4--8 x 12  10 x 10   6 x 7    3--2    3--1
+      200    25    15    4--8 x 16  12 x 12   7 x 7    5--2    5--1
+
+
+TABLE FOR DIMENSIONING A HOWE TRUSS BRIDGE.
+JNO. C. TRAUTWINE, C.E.
+
+       |    |    |An Upper | A Lower |  An End |A Centre|        |   End     |  Centre
+  Clear|    | No.| Chord.  |  Chord. |  Brace. |  Brace.|Counter.|   Rod.    |   Rod.
+  Span |Rise| of |---------|---------|---------|--------|--------|-----------|-----------
+   in  | in |Pan-| No|     | No|     | No.|    | No|    | No|    | No.|      | No.|
+  feet.|feet|els.|Pcs|Size.|Pcs|Size.|Pcs.|Size|Pcs|Size|Pcs|Size|Rods|Size. |Rods|Size.
+  -----|----|----|---|-----|---|-----|----|----|---|----|---|----|----|------|----|-----
+    25 |  6 |  8 | 3 | 4x5 | 3 | 4x10|  2 |4x6 | 2 |5x5 | 1 |4x5 |  2 |1-5/16|  2 |  7/8
+    50 |  9 |  9 | 3 | 6x7 | 3 | 6x10|  2 |6x7 | 2 |5x6 | 1 |5x6 |  2 |1-5/8 |  2 |1-1/16
+    75 | 12 | 10 | 3 | 6x9 | 3 | 6x11|  2 |6x8 | 2 |6x6 | 1 |6x6 |  2 |1-7/8 |  2 |1-3/16
+   100 | 15 | 11 | 3 | 6x10| 3 | 6x12|  2 |8x9 | 2 |6x8 | 1 |6x8 |  2 |2-3/16|  2 |1-5/16
+   125 | 18 | 12 | 4 | 6x10| 4 | 6x13|  2 |8x10| 2 |6x9 | 1 |6x9 |  2 |2-5/8 |  2 |1-3/8
+   150 | 21 | 13 | 4 | 8x10| 4 | 8x14|  3 |9x10| 3 |6x9 | 2 |6x9 |  3 |2-3/8 |  3 |1-3/16
+   175 | 24 | 14 | 4 |10x12| 4 |10x15|  3 |9x11| 3 |8x8 | 2 |8x8 |  3 |2-5/8 |  3 |1-1/4
+   200 | 27 | 15 | 4 |12x12| 4 |12x16|  3 |9x12| 3 |8x10| 2 |8x10|  3 |2-7/8 |  3 |1-3/8
+
+Both of these tables were calculated for a single Railroad track, and
+would answer equally well for a double Highway Bridge. In the bridge
+according to Trautwine's Table, each lower chord is supposed to have a
+piece of plank, half as thick as one of the chord pieces, and as long
+as three panels, firmly bolted on each of its sides, in the middle of
+its length.
+
+       *       *       *       *       *
+
+
+=PRATT'S BRIDGE.=
+
+This is opposite in arrangement of parts to a Howe Bridge, as the
+diagonals are rods, and sustain tension, and the verticals are posts,
+and suffer compression:
+
+  _Example._--Span                  = 100 feet.
+              Rise                  =  12   "
+              Panel                 =  10   "
+              Weight per lineal ft. = 3000 lbs.
+
+The tension on the lower, or compression on the upper chord, will be
+
+  300000 x 100
+  ------------ = 3333333 lbs.
+       96
+
+[TeX: $\frac{300000 \times 100}{96} = 3333333$]
+
+The dimensions of the chord and splicing would be found in the same
+manner as for a Howe Truss.
+
+
+=Suspension Rods.= Fig. 1, Pl. III., represents an elevation of a
+Pratt Bridge. Now, it is evident that the first sets of rods must
+support the weight of the whole bridge and its load, which we have
+found to be 300000 lbs. Each truss will have to sustain 150,000 lbs.,
+and each end set of rods 75,000 lbs. Now, if there are two rods in
+each set,--each rod will have to bear a strain of 37500 lbs., and this
+will have an increase due to its inclination, so that the strain on it
+must be found by the following proportion:
+
+    Height : diagonal :: W : W' or
+
+    12 : 15.8 :: 37500 : 49375 lbs.
+
+Referring to the Table for bolts, we find that 2-1/8 gives a strength
+a little in excess, and will be the proper size. The next set of rods
+bear the weight of the whole load, less that due to the two end
+panels, and so on. Fig. 2, Pl. III, shows the manner of applying the
+rods. The bevel block should be so fitted to the chord that it will
+not have a crushing action.
+
+
+=Counters.= Top and bottom chords are always used in this bridge, and
+consequently the counter rods have only to sustain the movable load on
+one panel. The weight of the moving load cannot be more than 2000 lbs.
+per lineal foot which, for a panel of 10 ft., gives 20000 lbs., or
+10,000 lbs. for each set, and if we have two rods in a set, the strain
+on each rod will be 5000 lbs., increasing this for inclination, we
+shall have,
+
+  12 : 15.8 :: 5000 : 6585 lbs.,
+
+requiring a rod of 3/4 of an inch diameter. The posts in this bridge
+correspond to the braces of the Howe Truss, but being vertical, are
+not so large.
+
+Subjoined are two Tables, one by Prof. G.L. Vose, and one by Mr.
+Trautwine, giving principal dimensions for bridges of different spans
+of the Pratt type of Truss.
+
+
+TABLE OF DIMENSIONS OF A PRATT TRUSS.
+
+PROF. G. L. VOSE.
+
+                          End   Centre    End     Centre  Counter
+  Span. Rise. Chords.    Post.   Post.    Rod.     Rod.     Rod.
+
+    50   10   2--8x10   5 x  5   4 x 4  2--1-3/8   2--1   1--1-1/2
+    75   12   2--8x10   6 x  6   5 x 5  2--1-5/8   2--1   1--1-1/2
+   100   15   3--8x10   7 x  7   6 x 6  2--1-3/4   2--1   2--1-1/8
+   125   18   3--8x10   8 x  8   6 x 6  3--1-7/8   3--1   2--1-1/3
+   150   21   4--8x12   9 x  9   6 x 6  3--2-1/8   3--1   8--1-1/8
+   200   24   4--8x16  10 x 10   6 x 6  5--1-7/8   5--1   3--1-1/8
+
+
+TABLE OF DIMENSIONS OF A PRATT'S TRUSS.
+
+       |    |    | Upper   |  Lower  |  Main Brace Rods.  |  Counter  |   |     |          |
+  Clear|    | No.| Chord.  |  Chord. |                    |   Rods.   |   |     |  Posts.  |
+  Span |Rise| of |---------|---------|--------------------|-----------|   |     |----------|
+   in  | in |Pan-|No.|     |No.|     |No.| Size |No.|Size.|Num|       |No.| Size|No.|Size. |
+  feet.|feet|els.|Pcs|Size.|Pcs|Size.|Ctr|Centre|End| End.|ber| Size. |End| End.|Ctr|Centre|
+  -----|----|----|---|-----|---|-----|---|------|---|-----|---|-------|---|-----|---|------|
+    25 |  6 |  8 | 3 | 4x5 | 3 | 4x10| 2 |1     | 2 |1-3/8| 1 |1-7/16 | 3 | 4x5 | 3 |  4x4 |
+    50 |  9 |  9 | 3 | 6x7 | 3 | 6x10| 2 |1-3/16| 2 |1-1/8| 1 |1-5/8  | 3 | 6x6 | 3 |  6x5 |
+    75 | 12 | 10 | 3 | 6x9 | 3 | 6x11| 2 |1-5/16| 2 |2-1/2| 1 |1-7/8  | 3 | 6x7 | 3 |  6x5 |
+   100 | 15 | 11 | 3 | 6x10| 3 | 6x12| 2 |1-7/16| 2 |2-7/8| 1 |2      | 3 | 6x9 | 3 |  6x7 |
+   125 | 18 | 12 | 4 | 6x10| 4 | 6x13| 2 |1-1/2 | 2 |2-3/8| 1 |2-1/8  | 4 | 6x9 | 4 |  6x7 |
+   150 | 21 | 13 | 4 | 8x10| 4 | 8x14| 3 |1-5/16| 3 |2-1/2| 2 |1-5/8  | 4 | 8x8 | 4 |  8x7 |
+   175 | 24 | 14 | 4 |10x12| 4 |10x15| 3 |1-5/8 | 3 |2-3/4| 2 |1-11/16| 4 |10x10| 4 | 10x8 |
+   200 | 27 | 15 | 4 |12x12| 4 |12x16| 3 |1-1/2 | 3 |3-1/8| 2 |1-13/16| 4 |12x10| 4 | 10x8 |
+
+This table is partly given in Trautwine's Engineer's Pocket Book, and
+partly made up from directions therein given.
+
+
+TABLE OF DIMENSIONS FOR SMALL SINGLE TRACK PRATT TRUSSES.
+
+                                 At centre   At end    Centre      End
+  Clear Chords  Centre    End    of truss,  of truss,  Counter,  Counter,
+  Span, each,    Post,   Posts,  Diam. of   Diam. of   Diameter, Diameter,
+  Ft.   Ins.     Ins.     Ins.     Rods.     Rods.      Ins.      Ins.
+
+   30    9 x 11  4 x 9    7 x 9    1         1-5/8      1-3/8      1
+   40   10 x 12  4 x 10   8 x 10   1-1/8     1-7/8      1-5/8      1
+   50   10 x 14  5 x 10   9 x 10   1-1/4     2-1/8      1-3/4      1
+   60   12 x 15  5 x 12   9 x 12   1-3/8     2-3/8      2          1
+   70   12 x 17  6 x 12  11 x 12   1-1/2     2-1/2      2-1/8      1
+
+This bridge possesses an advantage over the Howe Truss, for the panel
+diagonals can be tightened up by screws, so that every part of the
+truss can be forced to perform its work. In Howe's bridge the
+adjustments must be made by wedging the braces and counters.
+
+Below are given the dimensions of a Howe bridge on the Vermont Central
+R.R., at South Royalton, (single track, deck.)
+
+              No. of     Upper        Lower
+  Span. Rise. Panels.    Chord.       Chord.      Braces.   Counters.
+  150    20    12     4--6-1/2 x 13 4--6-1/2 x 13 2--8 x 9  1--8 x 9
+
+    Rods.    Transverse Bracing.
+              Braces.    Rods.
+  3--1-1/4"   6 x 8      7/8
+
+The bridge over the White River, on the Passumpsic R.R., is a Howe
+Truss, strengthened by an arch. The verticals are of wood, and the
+diagonals foot on steps formed by enlarging the ends of the verticals.
+The counters are in two lengths, and are adjusted by wedges at the
+points where they intersect the braces. The bridge is in two spans,
+and has a double track, and consequently three trusses. There are two
+timber arches to each truss, and the truss is supported on them by
+connecting them to the verticals by short cross pieces notched into
+the posts, and resting on the upper surface of the arches. It is a
+very stiff bridge, and similar to the one at Bellows Falls, both
+having their axis oblique to the channel of the stream they cross. The
+timbers could hardly be procured now, except at great expense.
+
+       No.
+       of        Upper     Lower
+  Span Pan- Rods Chord     Chord     Braces   Counters  Uprights Arches
+       els
+  182   14   21  2--8 x16  2--8 x17, 1--21 x8 1--8 x10  21 x11   2--8 x9
+                 1--5 x16  2--4 x17,
+                           1--5 x17,
+
+Diagonals 6 x 8, Rods 7/8. Floor timbers suspended both from
+arches and truss, 9 x 13; stringers 10 x 14.
+
+In the Cheshire Bridge, the braces are only 20x8, and the span is only
+175 feet, the number of Panels being 14, as in the W.R. Bridge--the
+other dimensions are the same. Below are given the dimensions of a
+Howe Truss of 108 ft. span, weight to be borne on upper chord.
+
+               No.
+               of    Upper    Lower                        E.        Floor
+  Rise  Camber Pan-  Chord    Chord    Braces    Counters  Rods     Timbers
+   Ft.   Ins.  els    Ins.     Ins.     Ins.       Ins.    Ins.      Ins.
+
+  13-1/2  3     12   8--3 x12 8--3 x12 2--8 x10  1--7 x10  2--2-1/8  9 x16
+
+As plank is used for the chords, the pieces must be bolted thoroughly
+with 5/8 bolts.
+
+
+A form of bridge that has been used to some extent on the Baltimore
+and Ohio Railroad, by Mr. Latrobe, is the Arch Brace Truss. In this
+form of Truss the braces lead directly from the abutments to the head
+of each vertical; thus the load is transferred at once to the
+abutments, without passing through a series of web members. The
+counterbracing is effected by means of a light lattice,--and is
+applied to both sides of the chords, and the intersections of the
+diagonals are fastened while the bridge is strained by a load--thus
+preventing recoil--so that the effect of a moving load is to lighten
+the strain on the lattice--without otherwise affecting the Truss.
+
+[Illustration: Pl. III. with Fig. 1., Fig. 2., Fig. 3., Fig. 4., Fig. 5.]
+
+There are two models of this style of bridge, to my knowledge; one
+built by Prof. G.L. Vose, on a scale of 1/2 an inch to the foot,
+and representing a span of 150 feet, which supported 2,500 lbs. at
+the centre, and a movable load of 150 lbs., proving itself to be
+strong and rigid enough for any thing. The other, on a scale of 1
+inch to the foot, and representing a span of 76 feet, was built by
+the Class of '73, of the Thayer Engineering School, under the
+writer's direction, and though bearing very heavy weights, has never
+been thoroughly tested--it has, however, been subjected to the
+sudden shock of 1040 lbs. falling 20 inches, without injury, several
+times. Subjoined are the dimensions of the models mentioned.
+
+DIMENSIONS OF A MODEL OF AN ARCH BRACE TRUSS.
+
+                  G.L. VOSE.
+
+        Length,  7 feet.
+        Height,  1 foot.
+        Width,   1 foot.
+        Chords,  4--1/4 x 1/2  inch.
+        Braces   4--1/4 x 1/8   "
+        Lattice,    1/4 x 1/16  "
+
+This represented a span of 150 ft, a rise of 20 feet, and a panel
+of 15 ft. Weight, per running foot of bridge and load, was taken
+at 3000 lbs.
+
+The method of calculating the dimensions of this truss, from the
+foregoing data, is as follows. The half number of panels is 5, and the
+lengths of the corresponding diagonals (neglecting fractions) are
+
+     ---------
+    /20² + 15² = 25 feet. [TeX: $\root{20^2 + 15^2} = 25$]
+  \/
+
+     ---------
+    /20² + 30² = 37  "    [TeX: $\root{20^2 + 30^2} = 37$]
+  \/
+
+     ---------
+    /20² + 45² = 49  "    [TeX: $\root{20^2 + 45^2} = 49$]
+  \/
+
+     ---------
+    /20² + 60² = 64  "    [TeX: $\root{20^2 + 60^2} = 64$]
+  \/
+
+     ---------
+    /20² + 75² = 78  "    [TeX: $\root{20^2 + 75^2} = 78$]
+  \/
+
+The weight upon each set of braces is that due to one panel, or 3000
+x 15 = 45000 lbs., half of this, or 22500 lbs., is the weight for one
+truss only--and, as there is a brace under each of the 4 chord sticks,
+we divide by 4, and have 5625 lbs. per stick of the brace;--now,
+correcting for inclination, we shall have
+
+  20 : 25 :: 5625 :  7031 lbs.
+  20 : 37 :: 5625 : 10406 lbs.
+  20 : 49 :: 5625 : 13781 lbs.
+  20 : 64 :: 5625 : 18000 lbs.
+  20 : 78 :: 5625 : 21937 lbs.
+
+The weights fouud show the compressional strains on the several
+braces;--and, were the pieces to be proportioned for compression
+only, their Scantling would be quite small--but on account
+of their elasticity, they require larger dimensions.
+
+These braces should not be fastened to the verticals,--but
+should be confined both laterally and vertically, where they pass
+them. The length of beam, for which we have to guard agains
+flexure, is the length between verticals in any panel.
+
+  In panel No. 1, it will be 25 feet,
+       "    "  2,    "   "   18  "
+       "    "  3,    "   "   17  "
+       "    "  4,    "   "   16  "
+       "    "  5,    "   "   16  "
+
+Now, using the formula
+
+  2240 b d³
+  --------- = W,
+      L²
+
+[TeX: $\frac{2240 bd^3}{L^2} = W$]
+
+we shall have, in round numbers, the following dimensions:
+
+  For the 1st panel, 25 feet long, 8 x 10
+     "    2d   "     37   "    "   8 x 10
+     "    3d   "     49   "    "   8 x 10
+     "    4th  "     64   "    "   8 x 10
+     "    5th  "     78   "    "   8 x 10
+
+For the lattice work, a double course on each side of each truss, in
+long spans; and a single course, in shorter spans, of 3 x 6, or 2 x 9
+plank, bolted at intersections, is sufficient.
+
+
+GENERAL TABLE OF DIMENSIONS FOR ARCH BRACE TRUSS.
+
+                    G.L. VOSE.
+
+  Span.  Rise.   Chords.     Ties.      Braces.     Lattice.
+    50    10    2--8 x 10   1--8 x 10   2--6 x 6
+    75    12    2--8 x 10   1--8 x 10   2--6 x 6     2 x 9
+   100    15    3--8 x 10   2--8 x 10   3--6 x 6      or
+   150    20    4--8 x l2   3--8 x 10   4--6 x 8     3 x 6
+   200    25    4--8 x 16   3--8 x 10   4--6 x 9
+
+The arch braces must all foot on an iron thrust block, of which a view
+is given in Fig. 4, Pl. III; and the centre of pressure of the braces
+must be directly over a bolster, to prevent crippling.
+
+The several sticks forming a brace must be blocked together at
+intervals, and When they are spliced,--a butt joint Should be
+used--and it should come in the centre of a panel. Below are given the
+dimensions of the Thayer Engineering School model.
+
+  Height Ins.    12
+  No. Panels      8
+  Chords Ins.    2--1 x 1/2
+  Posts Ins.     1--2/3 x 5/6
+  Braces Ins.    2--1/2 x 1/2
+  Lattice Ins.   1/4 x 1/2
+  Width Ins.     13
+
+There are several other forms of Bridge, the most notable among which
+are the Whipple, McCallum's, Post's, Towne's, Haupt's, and Burr's. But
+enough has been said to give the student an idea of the general
+arrangement of the different parts of a Truss, and to enable him to
+determine the strains to which the various members are subjected.
+Nothing will be said in regard to Wooden Arches, as our space is too
+limited.
+
+
+=Pile Bridging.= A bridge of this description is useful in crossing
+marshes, or in shallow water. Fig. 5, Pl. III, gives a good example of
+this kind of bridge, under 20 feet in height. If on a curve, there
+must be extra bracing on the convex side.
+
+
+=Trestle Work.= This is a combination of posts, caps, and braces; and
+is used for both temporary and permanent works. Plate IV, Figs. 1, 2,
+3 and 4, give some of the best varieties in use. Figs. 1 and 2, may be
+used up to 15 feet in height; Fig. 4, up to 20 feet; and Fig. 3, to 30
+ft. The distance apart of the various bents should not exceed 10 or 12
+ft., unless bracing is introduced between them, and the bents should
+always be raised above the ground a few feet on a solid masonry
+foundation. Want of space forbids any mention of abutments and piers,
+which really come more properly under the head of masonry.
+
+Iron Bridging is gradually working its way into favor, and Will
+probably eventually supersede wooden trusses;--but in many cases wood
+is the only material at hand--and therefore some knowledge of Wooden
+Bridging is desirable. It is intended to follow this pamphlet with a
+portfolio of sheets containing working drawings of several kinds of
+Wooden Bridges, taken from actual measurements of some of the best
+specimens of the different styles of Truss in use.
+
+       *       *       *       *       *
+
+
+=PRACTICAL NOTES.=
+
+
+When putting a truss together in its proper position, on the
+abutments, 'false works' must first be erected to support the parts
+until they are so joined together as to form a complete
+self-sustaining truss. The bottom chords are first laid as level as
+possible on the false works, then the top chords are raised on
+temporary supports, sustained by those of the lower chord, and are
+placed a few inches higher at first than their proper position, in
+order that the web members may be slipped into place. When this is
+done the top chords are gradually lowered into place. The screws are
+then gradually tightened, (beginning at the centre and working towards
+both ends,) to bring the surfaces of the joints into proper contact,
+and by this method, the camber forms itself, and lifts the lower
+chords clear of the false works, leaving the truss resting only upon
+its proper supports. The subjoined Table will be found useful in
+estimating the strains on a truss when proportioning a bridge for any
+moving load.
+
+Table of weights per running foot of a bridge, (either of wood or
+iron,) including weights of floor, lateral bracing, &c., complete, for
+a single track.
+
+  Clear      Weight of
+  Span.       Bridge.
+            Tons.  lbs.
+
+   25       .266    596
+   30       .281    629
+   40       .313    701
+   50       .343    768
+   60       .374    838
+   70       .404    905
+   80       .434    972
+   90       .464   1039
+  100       .494   1106
+  120       .554   1241
+  140       .614   1375
+  150       .643   1440
+  160       .673   1507
+  170       .703   1575
+  180       .733   1642
+  200       .792   1774
+  225       .867   1942
+  250       .940   2105
+  275      1.013   2269
+  300      1.087   2435
+
+
+The weight of a single track railway bridge may be taken as equal to
+that of a double track highway bridge,--and the trusses that will be
+large enough for one will be large enough for the other.
+
+The greatest load that a highway bridge can be subjected to is 120
+lbs. to the square foot of surface.
+
+
+TABLE OF CAMBERS FOR BRIDGE TRUSSES.
+
+  Span.   Camber.   Span.   Camber.   Span.   Camber.   Span.   Camber.
+  feet.   Inches.   Feet.   Inches.   Feet.   Inches.   Feet.   Inches.
+
+   25       0.8      75      2.5      175       5.8     275      9.2
+   30       1.0     100      3.3      200       6.7     300      10.0
+   50       1.7     120      4.0      225       7.5     325      10.8
+   60       2.0     150      5.0      250       8.3     350      11.7
+
+
+TRAUTWINE'S TABLE FOR FINDING INCREASE IN
+LENGTH OF UPPER CHORD BEYOND THE
+LOWER CHORD ON ACCOUNT OF THE CAMBER.
+
+             Multiply               Multiply
+  Depth of   Camber      Depth of   Camber
+   Truss.      by         Truss.      by
+
+  1-4 span    2.00      1-12 span    .666
+  1-5  "      1.60      1-13  "      .614
+  1-6  "      1.33      1-14  "      .571
+  1-7  "      1.15      1-15  "      .533
+  1-8  "      1.00      1-16  "      .500
+  1-9  "      .888      1-17  "      .470
+  1-10 "      .800      1-18  "      .444
+  1-11 "      .727      1-20  "      .400
+
+
+
+TABLE OF AMERICAN WOODS.
+
+                   Weight per   Resistance in lbs. per
+     Kind.         cubic foot        square inch.         Value of s.
+                   in pounds.   Extension  Compression.
+
+  White Pine.          26         12,000       6000          1229
+  Yellow Pine.         31         12,000       6000          1185
+  Pitch Pine.          46         12,000       6000          1727
+  Red Pine.            35         12,000       6000          1527
+  Virginia Pine.       37         12,000       6000          1456
+  Spruce.              48         12,000       6000          1036
+  Tamarack.            26         12,000       6000           907
+  Canada Balsam.       34         12,000       6000          1123
+  White Oak.           48         15,000       7500          1743
+  Red Oak.             41         15,000       7600          1687
+  Birch.               44         15,000       7000          1928
+  Ash.                 38         16,000       8100          1795
+  Hickory.             51         15,000       7200          2129
+  Elm.                 45         16,000       8011          1970
+
+
+The above table is compiled from a much fuller one in Vose's Treatise
+on R.R. Construction.
+
+
+TABLE OF BOLTS AND NUTS CALCULATED FOR A
+WORKING STRAIN OF 15,000 LBS. PER
+SQUARE INCH OF SECTION.
+
+  Diameter.  Area.    Strength in Weight per           Thick's  No. thr's
+  Inches.  Sq. inches.  Pounds      Foot.  Square nut.  of nut. per inch.
+
+    1/2      .19635        2940     0.66     1-1/4 in    3/4 in    12
+    5/8      .30680        4602     1.03     1-3/8       3/4       10
+    3/4      .44179        6630     1.49     1-1/2       7/8       10
+    7/8      .60132        9019     2.03     1-3/4     1            9
+  1          .78540       11775     2.65     2         1            8
+  1-1/8      .99402       14910     3.36     2         1-1/8        7
+  1-1/4     1.2272        18405     4.17     2-1/4     1-1/4        7
+  1-3/8     1.4849        22260     5.02     2-1/2     1-3/8        6
+  1-1/2     1.7671        25505     5.97     2-3/4     1-1/2        6
+  1-5/8     2.0739        31095     7.01     2-7/8     1-5/8        5
+  1-3/4     2.4053        36075     8.13     3         1-3/4        5
+  1-7/8     2.7612        41415     9.33     3-1/4     1-7/8        4-1/2
+  2         3.1416        47130    10.62     3-1/2     2            4-1/2
+  2-1/8     3.5166        53190    12.00     3-3/4     2-1/8        4
+  2-1/4     3.9761        59640    13.40     4         2-1/4        4
+  2-3/8     4.4301        66450    15.00     4-1/8     2-3/8        4
+  2-1/2     4.9087        73620    16.70     4-1/4     2-1/2        3-1/2
+  2-5/8     5.4119        81178    18.20     4-1/2     2-5/8        3-1/2
+  2-3/4     5.9396        89094    20.00     4-3/4     2-3/4        3-1/2
+  2-7/8     6.4918        97377    21.90     5         2-7/8        3
+  3         7.0686       106029    23.80     5-1/4     3            3
+  3-1/4     8.2958       124437    27.90     5-3/4     3-1/4        3
+  3-1/2     9.6211       144316    32.40     6         3-1/2        2-1/2
+
+
+TABLE OF SAFE WORKING LOAD IN LBS., FOR HOLLOW CAST-IRON COLUMNS.
+
+[_G.L. Vose._]
+
+   Outside             Length or height in Feet              Metal
+   Diameter                                                 Thickness
+  in inches.  6      8      10     12     15     18     20  in inches.
+
+       3    16000  14000  13000  11000   9000   7000   6000    3/8
+       4    30000  29000  26000  24000  22000  18000  16000    1/2
+       5    50000  37000  45000  42000  39000  37000  31000    5/8
+       6    59000  57000  55000  52000  49000  44000  41000    3/4
+       7   101000  99000  96000  92000  88000  81000  76000   13/16
+       8   131000 129000 126000 122000 118000 109000 105000    7/8
+       9   169000 167000 164000 160000 156000 146000 141000   1
+      10   210000 200000 200000 200000 190000 180000 180000   1-1/8
+      11   250000 250000 240000 240000 240000 230000 220000   1-1/4
+      12   300000 300000 290000 290000 290000 270000 270000   1-1/2
+      14   450000 430000 410000 380000 370000 350000 330000   1-3/4
+      16   520000 500000 480000 460000 440000 420000 400000   2
+      18   650000 630000 610000 590000 560000 520000 470000   2-1/2
+      20   800000 760000 740000 690009 650000 590000 540000   3
+
+
+[Illustration: Pl. IV. with Fig. 1., Fig. 2., Fig. 3., Fig. 4.]
+
+
+
+
+Transcriber's Notes:
+
+DISCLAIMER: This document should NOT be used to engineer any bridge
+projects! Many typesetting errors were found, and it is possible that
+there are further errors in the information that were not caught.
+
+Formulas have been provided both as ASCII and TeX following in brackets.
+Bold headings are handled with equal signs before and after the bold text.
+Italicised text uses the standard underlines before and after the text.
+Fractions are expressed in the format: 2-1/4 means two and one quarter.
+
+The page numbers listed below are project page numbers.
+(The original book used Roman numerals to number the pages.)
+
+Note that the book uses the "long" ton equal to 2,240 pounds.
+
+CORRECTIONS MADE:
+
+   1. Page 8--the formula for "d" must use a cube root, which is how it
+      is shown here, but the '3' to indicate a cube root is not found in
+      the original document.
+   2. Page 8--typo in word 'sectien'--changed to 'section'.
+   3. Page 10--Value for working comp. strength of cast iron in the
+      table had a typo (25,v00). Since other values use round numbers,
+      it is assumed the value should be 25,000.
+   4. Page 10--Two other typos. Changed 'the the' to 'the', and in
+      table heading, original word was 'detrution', changed to correct
+      spelling of 'detrusion'.
+   5. Page 12--changed 'woooden' to 'wooden'.
+   6. Page 13--Example II--In the calculations, the intermediate value
+      in the book was printed as the square root of 67.2. The left part
+      is correct, but reduces to the square root of 268.8, and that is
+      ~16.395. So I have corrected the intermediate value.
+   7. Page 13--Because the original page scan cut off the text on the
+      right edge, I have made assumptions on what text was missing.
+      Because the scans came from an outside source, I could not get
+      the missing information, which was the words at the end of Example
+      II, and words in the last paragraph of the page.
+   8. Page 14--Three typos found: 'dimensiens' for 'dimensions', 'betng'
+      for 'being', and 'ars' for 'are'.
+   9. Page 17--a value in a formula was printed as 6000, but in the
+      context of the other information, particularly the example
+      immediately following, the value was believed to be incorrect, and
+      was changed to 5000.
+  10. Page 23--The value of 388 sq. inches at the top of the page in the
+      book is incorrect; 3 x 8 x 12 = 288, so has been corrected.
+  11. Page 24--Rods section, numerical value appeared to be 15.000 in
+      the book, but from context, must be 15,000 instead.
+  12. Page 28--Typos: changed 'Trautwine's Edgineer's Pocket-Bood' to
+      Trautwine's Engineer's Pocket-Book'; corrected  'af' to 'as',
+      'bracas' to 'braces'.
+  13. Page 30--Apparent typo in the table at the bottom of page.  Value
+      for Center Brace size for 200' span was shown as '8 x 1', believed
+      from context of table to be '8 x 10'.
+  14. Page 33--table of dimensions of a Pratt Truss, last column, row
+      starting with 150, the original says 8--1-1/8, this is believed to
+      be, and has been changed to, 3--1-1/8.
+  15. Page 37--The five formulas with square roots were incorrectly
+      printed in the book, multiplying the terms inside the square root
+      instead of adding them, which is obviously incorrect per the
+      Pythagorean theorem of right triangles.
+  16. Page 38: The fifth ratio in the group of five near the top of the
+      page must start with 20, not 10 as in the book
+  17. Page 38--The equation for W as printed on this page is not
+      consistent with that found on pages 18 to 24, so has been corrected
+      from 'bd^2' to 'bd^3'.
+  18. Page 39--arch brace truss table heading typo-changed 'FOE' to 'FOR'.
+
+
+
+
+
+
+End of the Project Gutenberg EBook of Instructions on Modern American Bridge
+Building, by G. B. N. Tower
+
+*** END OF THIS PROJECT GUTENBERG EBOOK AMERICAN BRIDGE BUILDING ***
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+
+<html xmlns="http://www.w3.org/1999/xhtml">
+  <head>
+    <title>
+      The Project Gutenberg eBook of Instructions on Modern American Bridge Building, by G.B.N. Tower.
+    </title>
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+<pre>
+
+The Project Gutenberg EBook of Instructions on Modern American Bridge
+Building, by G. B. N. Tower
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: Instructions on Modern American Bridge Building
+
+Author: G. B. N. Tower
+
+Release Date: February 2, 2005 [EBook #14873]
+
+Language: English
+
+Character set encoding: ISO-8859-1
+
+*** START OF THIS PROJECT GUTENBERG EBOOK AMERICAN BRIDGE BUILDING ***
+
+
+
+
+Produced by Curtis Weyant, Ronald Holder and the PG Online Distributed
+Proofreading Team.
+
+
+
+
+
+
+</pre>
+
+
+<h3>INSTRUCTIONS</h3>
+
+<h4>ON</h4>
+
+<h2>MODERN AMERICAN</h2>
+
+<h2>BRIDGE BUILDING.</h2>
+
+<h4>WITH</h4>
+
+<h3>PRACTICAL APPLICATIONS AND EXAMPLES,</h3>
+
+<h3>ESTIMATES OF QUANTITIES, AND<br />
+VALUABLE TABLES.</h3>
+
+<h3><i>Illustrated by four Plates and Thirty figures.</i></h3>
+
+<h2>BY G.B.N. TOWER,</h2>
+
+<p class="center">CIVIL AND MECHANICAL ENGINEER,</p>
+
+<p class="center"><i>Formerly Chief Engineer U.S. Navy, and late Chandler Instructor in Civil<br />
+Engineering at Dartmouth College.</i></p>
+
+<hr style="width: 35%;" />
+
+<p class="center">BOSTON:</p>
+
+<p class="center">A. WILLIAMS &amp; COMPANY,</p>
+
+<p class="center">135 WASHINGTON STREET.</p>
+
+<p class="center">1874.</p>
+
+<p>&nbsp;</p>
+<p>&nbsp;</p>
+<p>&nbsp;</p>
+
+<hr style="width: 85%;" />
+<p class="center">Entered according to act of Congress, in the year 1874, by</p>
+<p class="center">A. WILLIAMS &amp; CO.,</p>
+<p class="center">in the office of the Librarian of Congress, at Washington, D.C.</p>
+<hr style="width: 85%;" />
+
+<p>&nbsp;</p>
+<p>&nbsp;</p>
+<p>&nbsp;</p>
+
+
+<p class="heading">PREFACE.</p>
+<hr style="width: 10%;" />
+
+<p>This little treatise was written for the purpose of supplying a
+want felt by the author while giving instruction upon the subject.
+It was intended for an aid to the young Engineer, and is not to be
+considered as a complete substitute for the more elaborate works
+on the subject.</p>
+
+<p>The first portion of this work mentions the various strains to
+which beams are subjected, and gives the formul&aelig; used in determining
+the amount of those strains, together with a few examples
+to illustrate their application, and also the method of calculating
+a simple truss.</p>
+
+<p>The second portion names and explains the various members
+of a Bridge Truss, and, by means of examples, shows the method
+of calculating the strains upon the various timbers, bolts, etc., as
+well as their proper dimensions; and gives, in addition, several
+useful tables.</p>
+
+<p>The explanatory plates, which are referred to freely throughout
+the work, are believed to be amply sufficient for the purpose intended.</p>
+
+<p>So much has been written on this subject that it is next to
+impossible to be wholly original, and no claim of that nature is
+preferred. It is simply an arrangement of ideas, gleaned from the
+various works of standard authorities, and modified by the author's
+practice, embodied in book form.</p>
+
+<p>To give a correct list of all the books consulted would be
+simply impossible;&mdash;but it is well to state that the Hand-book of
+Railroad Construction, by Prof. G.L. Vose, under whom the author
+served as an Engineer, has been used as authority in many cases
+where there has been a difference of opinions among other authors.
+Some parts have been quoted entirely; but due credit has been
+given, it is believed, wherever such is the case.</p>
+
+<p>It is not claimed that this little work covers the whole ground,
+but it is intended to describe, and explain thoroughly, three or four
+of the more prominent styles of Truss, leaving the other forms of
+Wooden Bridges to a subsequent volume.</p>
+
+<p>Abutments and Piers, as well as Box and Arch Culverts, belonging
+more properly to masonry, will be treated of hereafter under that
+head.</p>
+
+<p>Iron Bridges form a distinct class, and may be mentioned
+separately at some future period.</p>
+
+<p>If this small volume should lead the student of Engineering
+to examine carefully the best Bridges of modern practice, and study
+the larger scientific works on this art, the author will feel satisfied
+that his efforts have not been entirely in vain.</p>
+
+<p><i>Cambridge, February 23, 1874.</i></p>
+<p>&nbsp;</p>
+
+
+<hr style="width: 65%;" />
+<p>&nbsp;</p>
+
+<p class="heading">TOWER'S</p>
+
+<p class="heading">Modern American Bridge Building.</p>
+<p>&nbsp;</p>
+
+<hr style="width: 65%;" />
+<p>&nbsp;</p>
+
+
+<p class="heading">BRIDGE BUILDING.</p>
+<hr style="width: 15%;" />
+
+<p>The simplest bridge that can be built, is a single beam, or
+stick of timber, spanning the opening between the abutments&mdash;but
+this is only of very limited application&mdash;(only for spans of
+20 feet and less) owing to the rapid increase in sectional dimensions
+which is required as the span becomes greater.</p>
+
+<p>Next comes the single beam supported by an inclined piece
+from each abutment meeting each other at the middle point of
+the under side of the beam&mdash;or, another arrangement, of two
+braces footing securely on the beam and meeting at a point
+above the middle point of the beam, which is suspended from
+the apex of the triangle formed by them, by means of an iron
+rod&mdash;These arrangements may be used up to 50 feet. For any
+span beyond 50 feet, modifications of this arrangement are used
+which will be described hereafter. Now let us investigate shortly
+the different strains that the various parts of a bridge have
+to bear&mdash;and the strength of the materials used. The theory
+of strains in bridge trusses is merely that of the Composition
+and Resolution of Forces. The various strains, to which the
+materials of a bridge are subjected&mdash;are compression, extension
+and detrusion.</p>
+
+<p>Wood and Iron are the materials more generally employed
+in bridge construction&mdash;and in this pamphlet we shall take the
+following as the working strength of the materials&mdash;per square
+inch of section.</p>
+
+<table cellspacing="0" cellpadding="4" border="0"
+summary="Working strength of materials">
+<tr>
+	<th>&nbsp;</th> <th>Tension.</th> <th>Compression.</th> <th>Detrusion.</th>
+</tr>
+<tr>
+	<td>Wood, </td> <td align="right">2000 &nbsp; </td> <td align="right">1000 &nbsp; </td> <td align="right">150 &nbsp; </td>
+</tr>
+<tr>
+	<td>Wro't Iron,</td> <td align="right">15000 &nbsp; </td> <td align="right">11000 &nbsp; </td> <td align="right">&nbsp;</td>
+</tr>
+<tr>
+	<td>Cast Iron,</td> <td align="right">4500 &nbsp; </td> <td align="right">25000 &nbsp; </td> <td align="right">&nbsp;</td>
+</tr>
+</table>
+<p>&nbsp;</p>
+
+<p><span class="boldhead">Tension.</span> If a weight of 2000 lbs. were hung to the
+lowest end of a vertical beam, so that the line of action of the
+weight and axis of the beam formed one and the same straight
+line&mdash;the tension on the beam would be 2000 lbs. But, if the
+beam were inclined, and the force acted in a vertical direction,
+then the strain would be increased in the ratio of the increase
+of the diagonal of inclination over the vertical;&mdash;suppose the
+beam is 20 ft. long and inclined at an angle of 45&deg;&mdash;and let
+2000 lbs., as before, be suspended from its lower end. Now the
+diagonal being 20,&mdash;the vertical will be 14.014 ft.&mdash;and the
+strain will be found as follows,&mdash;</p>
+
+<p class="center">
+14.014 : 20 :: 2000 : 2854&mdash;lbs.<br />
+</p>
+
+
+<p>The greater the angle of inclination from the horizontal,
+the less the strain from a given load&mdash;and when the beam is
+vertical the weight causes the least strain.<br />&nbsp;</p>
+
+<p><span class="boldhead">Compression.</span> If we load a vertical post with
+a weight of 2000 lbs., the strain of compression exerted upon the
+post will be 2000 lbs. Now, if we incline the post&mdash;the strain
+will be increased, as we have shown above under the head of
+tension, and in like manner, dependent upon the inclination.</p>
+
+<p>But when wood, iron, or any other material is used for a
+pillar or strut, it has not only to resist a crushing force, but also
+a force tending to bend or bulge it laterally.</p>
+
+<p>A post of circular section with a length of 7 or 8 diameters
+will not bulge with any force applied longitudinally, but will
+split. But if the length exceeds this limit&mdash;it will be destroyed
+by an action similar to that of a transverse strain.</p>
+
+<p>A cast iron column of thirty diameters in length, is fractured
+by bending; when the length is less than this ratio&mdash;by
+bending and splitting off of wedge shaped pieces. But by casting
+the column hollow, and swelling it in the middle, its strength
+is greatly increased.</p>
+
+<p>Barlow's formula for finding the weight that can be sustained
+by any beam, acting as a pillar or strut, before bending,
+is:&mdash;</p>
+
+<p class="center">
+<img src="images/p8_eq1.gif" width="91" height="45" align="middle" alt="Equation: WL^2/80E = bd^3" title="Equation: WL^2/80E = bd^3" />, whence
+<img src="images/p8_eq2.gif" width="119" height="46" align="middle" alt="Equation: W=bd^3 x 80E/L^2" title="Equation: W=bd^3 x 80E/L^2" />
+</p>
+
+<p>now, having the weight given, and assuming the dimensions of
+the cross-section&mdash;we shall have</p>
+
+<p class="center">
+<img src="images/p8_eq3.gif" width="99" height="60" align="middle" alt="Equation: d=(cube root of)(WL^2/80 EB)" title="Equation: d=(cube root of)(WL^2/80 EB)" />
+and
+<img src="images/p8_eq4.gif" width="87" height="45" align="middle" alt="Equation: b=WL^2/80 Ed^3" title="Equation: b=WL^2/80 Ed^3" />
+</p>
+
+<p>in the above formul&aelig;,</p>
+
+<p class="ind30">
+W = weight in pounds.<br />
+L = length in feet.<br />
+E = a constant.<br />
+b = breadth in inches.<br />
+d = depth in inches.<br />
+&nbsp;</p>
+
+
+<p><span class="boldhead">Transverse Strains.</span> The strain caused by
+any weight, applied transversely, to a beam supported at both
+ends, is directly as the breadth, and square of the depth, and
+inversely as the length. It causes the beam to be depressed
+towards the middle of its length, forming a curve, concave to
+the horizontal and below it. In assuming this form&mdash;the fibres
+of the upper part of the beam are compressed, and those of the
+lower part are extended&mdash;consequently there must be some line
+situated between the upper and lower surfaces of the beam
+where the fibers are subjected to neither of these two forces,
+this line is called the <i>neutral axis</i>.</p>
+
+<p>These two strains of compression and extension must be
+equal in amount&mdash;and upon the relative strength of the material
+to resist these strains, as well as its form and position, the
+situation of this axis depends. If wood resists a compression
+of 1000 lbs. per square inch of section, and a tension of 2000
+lbs. the axis will be twice as far from the top as from the bottom
+in a rectangular beam.</p>
+
+<p>The following table by Mr. G.L. Vose gives, with sufficient
+accuracy for practice, the relative resisting powers of wood,
+wrought, and cast iron, with the corresponding positions of the
+axis.</p>
+
+
+<table cellspacing="0" cellpadding="6" border="0"
+summary="Resisting power of materials">
+<tr>
+	<th>Material.</th> 	<th>Resistance to <br />Extension.</th>
+	<th>Resistance to <br />Compression.</th> <th>Ratio.</th>
+	<th>Dist. of axis from top <br />in frac's of the depth.</th>
+</tr>
+<tr>
+	<td>Wrought Iron, </td> <td align="center">90</td> <td align="center">66 </td>
+	<td align="center">90 / 66 </td> <td align="center">90 / 156, or 0.58</td>
+</tr>
+<tr>
+	<td>Cast Iron,</td> <td align="center">20</td> <td align="center">111</td> <td align="center">20 / 111</td>
+	<td align="center">20 / 131, or 0.15.</td>
+</tr>
+<tr>
+	<td>Wood, </td> <td align="center">2 </td> <td align="center">1 </td> <td align="center">2 / 1</td>
+	<td align="center">2 / 3, or 0.66.</td>
+</tr>
+</table>
+<p>&nbsp;</p>
+
+<p>Thus we see that the resistance of a beam to a cross strain,
+as well as to tension and compression, is affected by the incompressibility
+and inextensibility of the material.</p>
+
+<p>The formula for the dimensions of any beam to support a
+strain transversely is</p>
+
+<p class="center">
+<img src="images/p9_eq1.gif" width="75" height="46" alt="Equation; S=4bd^2/l" title="Equation; S=4bd^2/l" />
+</p>
+
+<p class="ind30">
+S = the ultimate strength in lbs.<br />
+b = the breadth in inches.<br />
+d = the depth in inches.<br />
+l = the length in inches.<br />
+<br /></p>
+
+
+<p><span class="boldhead">Detrusion.</span> Detrusion is the crushing against
+some fixed point, such as obtains where a brace abuts against a
+chord, or where a bridge rests on a bolster; and the shearing
+of pins, bolts and rivets, also comes under this head.<br />&nbsp;</p>
+
+<p><span class="boldhead">General Abstract.</span> The resistance to the
+above mentioned strains varies as the the area of the cross section;
+so that by doubling the area we double the strength.
+Any material will bear a much greater strain for a short time
+than for a long one. The working strength of materials, or
+the weight which does not injure them enough to render them
+unsafe, is a mooted point, and varies, according to the authority,
+from 1-3 to 1-10 of the ultimate strength. The ratio of the
+ultimate strength to the working strength is called the <i>factor
+of safety</i>.</p>
+
+<p>The following is a table of ultimate and working strengths
+of materials, and factors of safety:</p>
+
+<table cellspacing="0" cellpadding="4" border="1" summary="Working and Ultimate strengths of materials">
+<tr>
+	<th>Weight </th> <th>Materials.</th>
+	<th>Ult. Ext.</th> <th>Ult. Comp.</th>
+	<th colspan="2">Working Strengths.</th>
+	<th colspan="2">Factor of Safety.</th>
+</tr>
+<tr>
+	<td>in lbs.</td> <td>&nbsp;</td> <td>&nbsp;</td> <td>&nbsp;</td>
+	<td>Exten.</td> <td>Comp.</td> <td>Tension</td> <td>Comp.</td>
+</tr>
+<tr>
+	<td align="center">30</td> <td>Wood.</td> <td align="center">14,000</td> <td align="center">7,000</td>
+	<td align="center">2,000</td> <td align="center">1,000</td> <td align="center">7</td> <td align="center">7</td>
+</tr>
+<tr>
+	<td align="center">480</td> <td>Wro't Iron.</td> <td align="center">60,000</td> <td align="center">64,000</td>
+	<td align="center">15,000</td> <td align="center">12,000</td> <td align="center">4</td> <td align="center">5.33</td>
+</tr>
+<tr>
+	<td align="center">450</td> <td>Cast Iron.</td> <td align="center">18,000</td> <td align="center">100,000</td>
+	<td align="center">4,500</td> <td align="center">25,000</td> <td align="center">4</td> <td align="center">4</td>
+</tr>
+</table>
+<p>&nbsp;</p>
+
+<p><span class="boldhead">Lateral Adhesion.</span> Lateral adhesion is the
+resistance offered by the fibres to sliding past each other in the
+direction of the grain, as when a brace is notched into a chord,
+or tie beam, at its foot, it is prevented by the lateral adhesion
+of the fibres from crowding off the piece, to the depth of the notch,
+against which it toes. Barlow's experiments give the lateral
+adhesion of fir as 600 lbs. per square inch, and the factor of
+safety employed varies in practice from 4 to 6, giving a working
+strength of from 150 to 100 lbs. per square inch.</p>
+
+<p class="heading">TABLE OF COMPRESSIVE RESISTANCE OF TIMBER.</p>
+
+<table cellspacing="0" cellpadding="4" border="1"
+summary="Compressive resistance of timber">
+<tr>
+	<td align="center">Length given <br />in Diameters.</td>	<td align="center">Safety Weig't <br />in Pounds.</td>
+	<td align="center">Length given <br />in Diameters.</td>	<td align="center">Safety Weig't <br />in Pounds.</td>
+	<td align="center">Length given <br />in Diameters.</td>	<td align="center">Safety Weig't <br />in Pounds.</td>
+</tr>
+<tr>
+	<td align="center">6</td> <td align="center">1000</td> <td align="center">24</td> <td align="center">440</td>
+	<td align="center">42</td> <td align="center">203</td>
+</tr>
+<tr>
+	<td align="center">8</td> 	<td align="center">960</td> <td align="center">26</td> <td align="center">394</td>
+	<td align="center">44</td> <td align="center">185</td>
+</tr>
+<tr>
+	<td align="center">10</td> <td align="center">910</td> <td align="center">28</td> <td align="center">358</td>
+	<td align="center">46</td> <td align="center">169</td>
+</tr>
+<tr>
+	<td align="center">12</td> <td align="center">860</td> <td align="center">30</td> <td align="center">328</td>
+	<td align="center">48</td> <td align="center">155</td>
+</tr>
+<tr>
+	<td align="center">14</td> <td align="center">810</td> <td align="center">32</td> <td align="center">299</td>
+	<td align="center">50</td> <td align="center">143</td>
+</tr>
+<tr>
+	<td align="center">16</td> <td align="center">760</td> <td align="center">34</td> <td align="center">276</td>
+	<td align="center">52</td> <td align="center">132</td>
+</tr>
+<tr>
+	<td align="center">18</td> <td align="center">710</td> <td align="center">36</td> <td align="center">258</td>
+	<td align="center">54</td> <td align="center">122</td>
+</tr>
+<tr>
+	<td align="center">20</td> <td align="center">660</td> <td align="center">38</td> <td align="center">239</td>
+	<td align="center">56</td> <td align="center">114</td>
+</tr>
+<tr>
+	<td align="center">22</td> <td align="center">570</td> <td align="center">40</td> <td align="center">224</td>
+	<td align="center">58</td> <td align="center">106</td>
+</tr>
+<tr>
+	<td>&nbsp;</td> <td>&nbsp;</td> <td>&nbsp;</td> <td>&nbsp;</td> <td align="center">60</td> <td align="center">99</td>
+</tr>
+</table>
+<p>&nbsp;</p>
+
+<p>In tensional strains, the length of the beam does not affect
+the strength; but in the beams submitted to compression, the
+length is a most important element, and in the table given
+above, the safety strains to which beams may be subjected,
+without crushing or bending, has been given for lengths, varying
+from 6 to 60 diameters.</p>
+<p>&nbsp;</p>
+
+<p class="heading">PRACTICAL RULES.</p>
+
+<p class="boldhead">Tensional Strain.</p>
+
+<p class="ind30">
+Let T = whole tensional strain.<br />
+&nbsp; &quot;  &nbsp; S = strength per square inch.<br />
+&nbsp; &quot;  &nbsp; a = sectional area in inches.<br />
+Then we have T = Sa.<br />
+</p>
+
+<p>Now to find the necessary sectional area for resisting any
+strain, we have the following general formula:</p>
+
+<p class="center">
+a = T &divide; S<br />
+</p>
+
+<p>or, by substituting the working strenths for the various materials
+in the formula, we have for wood,</p>
+
+<p class="center">a = T &divide; 2000</p>
+
+<p>Wrought Iron,</p>
+
+<p class="center">a = T &divide; 1500</p>
+
+<p>Cast Iron, </p>
+
+<p class="center">a = T &divide; 4500</p>
+
+
+<p>But, in practice, cast iron is seldom used except to resist
+compression.</p>
+<p>&nbsp;</p>
+
+<p><span class="boldhead">Strains of Compression.</span> Allowing the
+same letters to denote the same things as above, we have for</p>
+
+
+<p>Wood,</p>
+
+<p class="center">a = T &divide;1000</p>
+
+<p>Wrought Iron, </p>
+
+<p class="center">a = T &divide; 12000</p>
+
+<p>Cast Iron,    </p>
+
+<p class="center">a = T &divide; 25000</p>
+
+
+<p>As this pamphlet has to do with wooden bridges only,
+nothing will be said of the proper relative dimensions of cast-iron
+columns to sustain the strains to which they may be subjected,
+but a table of the strength of columns will be found
+further on.</p>
+<p>&nbsp;</p>
+
+<p><span class="boldhead">Transverse Strains.</span></p>
+
+<p class="ind30">Let W = breaking weight in lbs.<br />
+&nbsp; &quot; &nbsp; s = constant in table.<br />
+&nbsp; &quot; &nbsp; b = breadth in inches.<br />
+&nbsp; &quot; &nbsp; d = depth in inches.<br />
+&nbsp; &quot; &nbsp; L = length in inches.</p>
+
+<p>Then, for the power of a beam to resist a transverse strain,
+we shall have,</p>
+
+<p class="center">
+<img src="images/p12_eq1.gif" width="93" height="45" alt="Equation: W = 4sbd^2/L" title="Equation: W = 4sbd^2/L" />
+</p>
+
+<p>This formula has been derived from experiments made by
+the most reliable authorities.</p>
+
+<p>The constant, 1250, adopted for wood in the following
+formula, is an average constant, derived from the table, of
+those woods more commonly used.</p>
+
+<p>Now to reduce the formula to the most convenient shape
+for use, we substitute the value of s, and we have</p>
+
+<p class="center">
+<img src="images/p12_eq2.gif" width="139" height="47" alt="Equation: W = 4 x 1250bd^2/L" title="Equation: W = 4 x 1250bd^2/L" />
+</p>
+
+<p>or</p>
+
+<p class="center">
+<img src="images/p12_eq3.gif" width="115" height="49" alt="Equation: W = 5000bd^2/L" title="Equation: W = 5000bd^2/L" />
+</p>
+
+<p>But, to reduce the load to the proper working strain, we
+must divide this equivalent by 4, the factor of safety, and we
+shall have</p>
+
+<p class="center">
+<img src="images/p13_eq1.gif" width="114" height="48" align="middle" alt="Equation: W = 5000 bd^2/4L" title="Equation: W = 5000 bd^2/4L" />
+ .</p>
+
+<p>Let us apply the formula&mdash;</p>
+
+<p class="ind20">Case I. Given a span of 14 feet,<br />
+a breadth of 8 inches,<br />
+a depth of 14 inches.</p>
+
+<p>Required the safe load.</p>
+
+<p>The formula
+<img src="images/p13_eq1.gif" width="114" height="48" align="middle"
+alt="Equation: W = 5000 bd^2/4L" title="Equation: W = 5000 bd^2/4L" />
+becomes, by substitution,</p>
+
+<p class="center">
+<img src="images/p13_eq2.gif" width="149" height="47" align="middle"
+alt="Equation: W =  5000 x 8 x 196 / 4 x 168 " title="Equation: W =  5000 x 8 x 196 / 4 x 168 " />
+ = 11,666 lbs.</p>
+<p>&nbsp;</p>
+
+<p class="ind20">Case II. Given the safety load 18000 lbs.,<br />
+the breadth 9 inches,<br />
+the length 14 feet.</p>
+
+<p>Required the depth.</p>
+
+<p>From the above formula we have</p>
+
+<p class="center">
+<img src="images/p13_eq3.gif" width="109" height="58"
+alt="Equation: d = (sqrt)(w x 4L / 5000 b)" title="Equation: d = (sqrt)(w x 4L / 5000 b)" />
+</p>
+
+<p>substituting</p>
+
+<p class="center">
+<img src="images/p13_eq04.gif" width="237" height="54" align="middle"
+alt="Equation: d = (sqrt)(18000 x 168 x 4 / 5000 x 9) = (sqrt)268.8"
+title="Equation: d = (sqrt)(18000 x 168 x 4 / 5000 x 9) = (sqrt)268.8" />
+ = 16 inches nearly.</p>
+<p>&nbsp;</p>
+
+<p class="ind20">Case III. Given the safety load 22,400 lbs.,<br />
+the depth 18 inches,<br />
+the length 14 feet.</p>
+
+<p>Required the breadth.</p>
+
+<p>Deriving b from the foregoing, we have,</p>
+
+<p class="center">
+<img src="images/p13_eq5.gif" width="110" height="46"
+alt="Equation: B = w x 4L / 5000 x d^2" title="Equation: B = w x 4L / 5000 x d^2" />
+</p>
+
+<p>substituting</p>
+
+<p class="center">
+<img src="images/p13_eq6.gif" width="155" height="46"  align="middle"
+alt="Equation: B = 22400 x 4 x 168 / 5000 x 324" title="Equation: B = 22400 x 4 x 168 / 5000 x 324" />
+ = 9.3 inches nearly.<br />
+</p>
+
+<p>For a cast iron beam or girder&mdash;Mr. Hodgkinson
+from numerous carefully conducted experiments that,
+by arranging the material in the form of an inverted T&mdash;thus
+creating a small top flange as well as the larger bottom one,
+the resistance was increased, per unit of section, over that of a
+rectangular beam, in the ratio of 40 to 23.</p>
+
+<p>In this beam the areas of the top and bottom flanges are inversely
+proportional to the power of the iron to resist compression
+and extension. Mr. Hodgkinson's formula for the dimensions
+of his girder, is</p>
+
+<p class="center">
+<img src="images/p14_eq1.gif" width="88" height="48" alt="Equation: W = 26 ad / L" title="Equation: W = 26 ad / L" />
+</p>
+
+<p>The factor of safety being 6 for cast iron beams&mdash;the formula
+for the working load will be,</p>
+
+<p class="center">
+<img src="images/p14_eq2.gif" width="90" height="49" alt="Equation: W = 26 ad / 6 L" title="Equation: W = 26 ad / 6 L" />
+</p>
+
+<p>and, to find area of lower flange, we shall have</p>
+
+<p class="center">
+<img src="images/p14_eq3.gif" width="81" height="47" alt="Equation: a= 6 WL / 26 d" title="Equation: a= 6 WL / 26 d" />
+</p>
+
+<p>The general proportions of his girders are as follows:</p>
+
+<p class="ind20">
+Length,             16<br />
+Height,              1<br />
+Area Top Flange,     1.0<br />
+Area Bottom Flange,  6.1<br />
+In the above formula for cast iron beams,<br />
+&nbsp; W = weight in tons.<br />
+&nbsp; a = area in square inches of bottom flange.<br />
+&nbsp; d = depth in inches.<br />
+&nbsp; h = length in inches.<br />
+</p>
+
+
+<p>The web uniting the two flanges must be made solid&mdash;as
+any opening, by causing irregularity in cooling, would seriously
+affect the strength of the beam.</p>
+
+<p><i>Example.</i>&mdash;Required the dimensions of a Hodgkinson girder&mdash;for
+a span of 60 feet&mdash;with a load of 10 tons in the centre.</p>
+
+<p class="center">
+<img src="images/p14_eq4.gif" width="147" height="69" align="middle"
+alt="Equation: a = 6 x 10 x 60 x 12 / (26 x (60 x 12) / 16)"
+title="Equation: a = 6 x 10 x 60 x 12 / (26 x (60 x 12) / 16)" />
+ = 37 inches nearly.</p>
+
+<p>and the area of the top flange will be,</p>
+
+<p class="center">37 &divide; 6 = 6.16 inches&mdash;</p>
+
+<p>so that our dimensions will be as follows:</p>
+
+<p class="ind20">
+Length,              30 feet.<br />
+Depth,               45 inches.<br />
+Area Top Flange,      6.16 inches.<br />
+Area Bottom Flange,  37 inches.<br />
+</p>
+
+<p>&nbsp;</p>
+
+<div class="figcenter">
+<img src="images/plate-i.gif" width="457" height="635" alt="Plate 1" title="Plate1" />
+</div>
+
+<p>&nbsp;</p>
+
+<p>The thickness of web is usually a little greater at the bottom
+than at the top, and varies from 1/14 to 1/24 of the depth of the
+girder. The bottom rib is usually made from six to eight times
+as wide as it is thick, and the top rib from three to six times as
+wide as thick, so that, in the example above given, we could
+have as dimensions for the parts</p>
+
+<p class="ind20">
+Top Flange,     4&frac14; X 1&frac12; inches nearly.<br />
+Bottom Flange,  6 X 2&frac12; inches nearly.<br />
+Web,            1&frac12; inches thick.<br />
+</p>
+
+<p>The simplest bridge, consisting of a single stick, to span
+openings of 20 feet and under, is calculated according to the formula</p>
+
+<p class="center">
+<img src="images/p17_eq1.gif" width="125" height="62" alt="Equation: d = (sqrt)4 WL / 5000 b"
+title="Equation: d = (sqrt)4 WL / 5000 b" />
+</p>
+
+<p><i>Example.</i>&mdash;The depth of a beam, of 12 feet span and 12
+feet wide, to support a load of 22400 lbs. will be</p>
+
+<p class="center">
+<img src="images/p17_eq2.gif" width="354" height="58" align="middle"
+alt="Equation: d = (sqrt)4 WL / 5000 b = (sqrt) 4 x 22400 x 12 / 500 x 12 = (sqrt)215.04"
+title="Equation: d = (sqrt)4 WL / 5000 b = (sqrt) 4 x 22400 x 12 / 500 x 12 = (sqrt)215.04" />
+ = 15 in. nearly.</p>
+
+<p>The following Table was calculated by the above rule&mdash;and
+the dimensions altered according to the actual practice of the writer.</p>
+<table align="center" cellspacing="0" cellpadding="4" border="0" summary="Sizing for different spans">
+<tr>
+	<th align="center">Span.</th> <th align="center">Breadth.</th> <th align="center">Depth.</th>
+</tr>
+<tr>
+	<td align="center">4</td> <td align="center">10</td> <td align="center">12</td>
+</tr>
+<tr>
+	<td align="center">6</td> <td align="center">10</td> <td align="center">12</td>
+</tr>
+<tr>
+	<td align="center">8</td> <td align="center">12</td><td align="center">12</td>
+</tr>
+<tr>
+	<td align="center">10</td> <td align="center">12</td> <td align="center">13</td>
+</tr>
+<tr>
+	<td align="center">12</td> <td align="center">12</td> <td align="center">15</td>
+</tr>
+<tr>
+	<td align="center">16</td> <td align="center">12</td> <td align="center">18</td>
+</tr>
+<tr>
+	<td align="center">18</td> <td align="center">12</td> <td align="center">20</td>
+</tr>
+<tr>
+	<td align="center">20</td> <td align="center">12</td> <td align="center">22</td>
+</tr>
+</table>
+
+
+<p>&nbsp;<br />These dimensions will give ample strength and stiffness.
+Fig. 1, Plate I. gives an illustration of this kind of bridge&mdash;in
+which a, a, are the bolsters or wall plates, shown in section, to
+which the bridge beams are notched and bolted. Fig. 1, A, Plate
+I, shows the method of diagonally bracing these beams by
+planks, dimensions of which in general use are 6 to 8 by 2 to 3
+inches. The track should rest on ties, about 6 inches by 8 or 10
+inches&mdash;the same bolt confining the ends of the ties and diagonal
+braces when practicable. These ties should be notched on
+the string pieces 2 or 3 inches&mdash;without cutting the stringers.
+Below is a table giving general dimensions, in inches, of the
+several parts of a bridge of this description.</p>
+
+<table cellspacing="0" cellpadding="4" border="0" summary="Sizing for different spans">
+<tr>
+	<th align="center">Span.</th> <th align="center">Bolsters.</th> <th align="center">Ties.</th>
+	<th align="center">Ties.</th> <th align="center">Braces.</th> <th align="center">Diameter of Bolts.</th>
+</tr>
+<tr>
+	<td align="center">4</td> <td align="center">12 x 12</td> <td align="center">10 x 12</td>
+	<td align="center">6 x 8</td> <td align="center">2 x 8</td> <td align="center">1 inch.</td>
+</tr>
+<tr>
+	<td align="center">10</td> <td align="center">12 x 12</td> <td align="center">12 x 13</td>
+	<td align="center">6 x 8</td> <td align="center">2 x 8</td> <td align="center">1 &nbsp;&quot;</td>
+</tr>
+<tr>
+	<td align="center">16</td> <td align="center">14 x 14</td> <td align="center">12 x 18</td>
+	<td align="center">6 x 8</td> <td align="center">2 x 8</td> <td align="center">1 &nbsp;&quot;</td>
+</tr>
+<tr>
+	<td align="center">20</td> <td align="center">14 x 14</td> <td align="center">12 x 22</td>
+	<td align="center">6 x 8</td> <td align="center">2 x 8</td> <td align="center">1 &nbsp;&quot;</td>
+</tr>
+</table>
+
+
+<p>&nbsp;<br />Each bolt must have a washer under the head, and also under
+the nut. For a span of from 15 to 30 feet, we can use the combination
+shown in Plate II, Fig. 3. The piece A F must have
+the same dimensions as a simple string piece of a length A B&mdash;so
+that it may not yield between B and either of the points A
+or D. The two braces DF and EF must be stiff enough to support
+the load coming upon them. Suppose the weight on a
+pair of drivers of a Locomotive to be 10 tons, then each side
+must bear 5 tons, and each brace 2&frac12; tons = 2&frac12; x 2240 = 5600 lbs.</p>
+
+<p>Now, to allow for sudden or extra strains, call 8000 lbs. the
+strain to be supported by each brace, and, accordingly, 8 square
+inches of sectional area would be sufficient for compression only;
+but, as the brace is inclined, the strain is increased. Let the
+vertical distance from A to D be 10 ft., and, calling the span 30
+ft.&mdash;A B will be 15 ft.&mdash;from whence D F must be 18 ft., then
+we shall have the proportion</p>
+
+<p class="center">
+10:18::8000:14400 lbs.<br />
+</p>
+
+<p>which would require an area of about 15 square inches of section
+to resist compression, or a piece 3x5 inches. Now, as this
+stick is more than 6 or 8 diameters in length, it will yield by
+bending&mdash;and consequently its area must be increased. The
+load, which a piece of wood acting as a post or strut will safely
+sustain, is found by the formula already given.</p>
+
+<p class="center">
+<img src="images/p18_eq1.gif" width="109" height="46"
+alt="Equation: W = 2240 bd^3 / L^2" title="Equation: W = 2240 bd^3 / L^2" />
+</p>
+
+<p>Now substituting 3 for b, and 5 for d, we have</p>
+
+<p class="center">
+<img src="images/p18_eq2.gif" width="226" height="46" align="middle"
+alt="Equation: W = 2240 x 3 x 125 / 324 = 840000 / 324"
+title="Equation: W = 2240 x 3 x 125 / 324 = 840000 / 324" />
+ = 2592 lbs.</p>
+
+<p>which is not enough. Using 6 for b and 8 for d, we have</p>
+
+<p class="center">
+<img src="images/p18_eq3.gif" width="149" height="42" align="middle"
+alt="Equation: W = 2240 x 6 x 512 / 324"
+title="Equation: W = 2240 x 6 x 512 / 324" />
+ = 21238 lbs.</p>
+
+<p>which is something larger than is actually required, but it is no
+harm to have an excess of strength. Now in many cases this
+arrangement would be objectionable, as not affording sufficient
+head room on account of the braces&mdash;and we can as well use the
+form of structure given in Pl. I. Fig. 3, since it is evidently
+immaterial whether the point B be supported on F or suspended
+from it, provided we can prevent motion in the feet of the braces,
+which is done by notching them into the stringer at that
+point. This of course creates a tensional strain along the
+stringer, which is found as follows:&mdash;Representing the applied
+weight by FB, Pl. II, Fig. 2, draw BD parallel to FC, also
+DH parallel to AC&mdash;DH is the tension. This is the graphical
+construction, and is near enough for practice. Geometrically
+we have the two similar triangles AFB and DFH,
+whence</p>
+
+<p class="center">AF: DF:: AB: DH</p>
+
+<p class="center">and
+<img src="images/p18_eq4.gif" width="124" height="46" align="middle"
+alt="Equation: DH = DF x AB / AF"
+title="Equation: DH = DF x AB / AF" />
+</p>
+
+<p>This style of structure may be used up to 50 feet, but it is not
+employed for spans exceeding 30 feet in length. It is very customary
+to make the braces in pairs so as to use smaller scantling,
+and gain in lateral stiffness&mdash;the two pieces forming one
+brace by being properly blocked and bolted together. Below is
+given a table of dimensions for the various parts of this style of
+structure:</p>
+
+<table cellspacing="0" cellpadding="4" border="0" summary="Sizing for different spans">
+<tr>
+	<th align="center">Span.</th> <th align="center">Rise.</th> <th align="center">Bolster.</th>
+	<th align="center">Stringer.</th> <th colspan="2" align="center">Braces.</th> <th align="center">Rod.</th>
+</tr>
+<tr>
+	<td>&nbsp;</td> <td>&nbsp;</td> <td>&nbsp;</td>
+	<td>&nbsp;</td> <th align="center">No.</th> <th align="center">Size.</th>
+	<td>&nbsp;</td>
+</tr>
+<tr>
+	<td align="center">15</td> <td align="center">6</td> <td align="center">12 x 12</td> <td align="center">12 x 12</td>
+	<td align="center">2</td> <td align="center">5 x 6</td> <td align="center">1&#8539;</td>
+</tr>
+<tr>
+	<td align="center">20</td> <td align="center">7</td> <td align="center">14 x 14</td> <td align="center">12 x 13</td>
+	<td align="center">2</td> <td align="center">5 x 8</td> <td align="center">1&#8540;</td>
+</tr>
+<tr>
+	<td align="center">25</td> <td align="center">8</td> <td align="center">14 x 14</td> <td align="center">12 x 15</td>
+	<td align="center">2</td> <td align="center">6 x 8</td> <td align="center">1&frac12;</td>
+</tr>
+<tr>
+	<td align="center">30</td> <td align="center">10</td> <td align="center">14 x 14</td> <td align="center">12 x 18</td>
+	<td align="center">2</td> <td align="center">6 x 9</td> <td align="center">1&#8541;</td>
+</tr>
+</table>
+
+<p>&nbsp;<br />Single Beams under each rail firmly braced laterally, and trussed
+by an iron rod, (or preferably by two iron rods,) and a post
+on the under side of the beam. The deflection of the rod is
+usually taken at 1/8 of the span. Pl. II., Fig. 1, represents this
+style of trussing a beam&mdash;which is generally used for spans of
+from 15 to 30 ft. Below is a table of dimensions for this truss
+with single and double rods; if double rods are used only half
+the given section will be necessary for each one of the pair.</p>
+
+<table cellspacing="0" cellpadding="4" border="0" summary="Sizing for different spans">
+<tr>
+	<th align="center">Span.<br />Feet.</th> <th align="center">Rise.<br /> In Feet. </th>
+	<th align="center">Stringer.<br />&nbsp;</th> <th align="center">Post.<br />&nbsp;</th>
+	<th align="center">Rod.<br />(single.) </th> <th align="center">Rods.<br />(double.)</th>
+</tr>
+<tr>
+	<td align="center">15</td> <td align="center">1&#8542;</td> <td align="center">12 x 12</td>
+	<td align="center">6 x 8</td> <td align="center">2&#8539; diam.</td> <td align="center">or 1&frac12; diam.</td>
+</tr>
+<tr>
+	<td align="center">20</td> <td align="center">2&frac12;</td> <td align="center">12 x 14</td>
+	<td align="center">7 x 8</td> <td align="center">2&frac12;&nbsp;  &quot;</td> <td align="center">1&frac34;&nbsp;  &quot;</td>
+</tr>
+<tr>
+	<td align="center">25</td> <td align="center">3&#8539;</td> <td align="center">12 x 16</td>
+	<td align="center">8 x 8</td> <td align="center">2&frac34;&nbsp;  &quot;</td> <td align="center">2&nbsp; &nbsp;  &quot;</td>
+</tr>
+<tr>
+	<td align="center">30</td> <td align="center">3&frac34;</td> <td align="center">13 x 18</td>
+	<td align="center">9 x 9</td> <td align="center">3&nbsp; &nbsp;  &quot;</td> <td align="center">2&#8539;&nbsp;  &quot;</td>
+</tr>
+</table>
+
+
+<p>&nbsp;<br />It is as well to tenon the post into the beam, and also strap it
+firmly with iron plates&mdash;and the end should be shod with iron
+to form a saddle for the rods to bear upon.</p>
+
+<p>Now if we should make a bridge, on the plan of Fig. 3, Pl. I.,
+75 or 100 feet, or perhaps more, in length, the braces AF
+and FC, would not only be very long but very large and heavy,
+and one chief requisite in a good bridge is, to have all the
+beams so proportioned that they will resist all the strains acting
+upon them, without being unnecessarily large. It now becomes
+necessary to have a different arrangement of the parts of the
+truss in order to obtain increased length of span.</p>
+
+<p>Suppose we have a span, of 40 feet, as represented in Fig 2, Pl. I.
+Now instead of running the braces from AC until
+they meet in a point, as before we stop them at a, and c, and
+place the straining beam, ac, between them to prevent those
+points from approaching, suspend the points B and D from
+them, and start the braces Bb and Db&mdash;and, if the truss were
+longer, would continue on in the same manner as far as needful.</p>
+
+<p>To prevent the truss from altering its form, as shown by the
+dotted lines A'bC', and AEC, by any passing load, we insert
+the counter braces marked R.</p>
+
+<p>The braces Aa and Cc, must support all of tho weight of
+the bridge and its load within the parallelogram BacD&mdash;and
+the next set of braces, Bb and Db, sustain that part of the load
+which comes over the centre of the bridge. Consequently the
+braces must increase in size from the centre towards the abutments.
+The rods resist the same pressure in amount as their
+braces&mdash;but being vertical, do not need the increase, given to
+the braces on account of their inclination&mdash;but increase simply
+with the strain upon them, from the centre to the ends of the
+truss.</p>
+
+<p>There are many forms of small bridges differing from those
+enumerated, in various minor details, but sufficient has been
+said to give the reader a fair idea of the strains upon the
+different parts, and how to arrange and proportion the materials to
+resist them.</p>
+<p>&nbsp;</p>
+<p>&nbsp;</p>
+
+
+<p class="heading">PRACTICAL RULES AND EXAMPLES IN WOODEN BRIDGE BUILDING.</p>
+
+<p>In any case that may arise, we must determine approximately
+the gross weight of the bridge and its load&mdash;as a basis,
+and then we can proceed as follows&mdash;in case of a Howe, Pratt,
+or Arch Brace Truss.<br />&nbsp;</p>
+
+
+<p class="boldhead">To find the dimensions of the Lower Chord.</p>
+
+<p>The tension at the centre of the Lower Chord is found by
+<i>dividing the product of the weight of the whole bridge and load
+by the span</i>, by eight times the height&mdash;or letting T=tension
+in lbs., W=weight of bridge and load in lbs., S=span in
+feet, and h=rise or height&mdash;we have
+<img src="images/p21_eq1.gif" width="85" height="44" align="middle"
+alt="Equation: T = W x S / 8h" title="Equation: T = W x S / 8h" />&mdash;.
+In this case we have taken the rise at &#8539; of the span, which is evidently
+the best ratio between those dimensions, as it equalizes the vertical
+and horizontal forces. As to the proportions of the <i>bays</i> or
+<i>panels</i>, (or that portion of the truss bounded by two adjacent
+verticals, as struts or ties, and the chords,) the ratio of the rise
+(or the vertical distance between the centre lines of the two
+chords,) and the length on the chord should be such, that the
+diagonal truss members may make an angle of about 50&deg; with
+the chords; as the size of the timbers is increased by decreasing
+the angle, and, if the angle is increased, there are more timbers
+required.</p>
+
+<p>Mr. G.L. Vose, in his admirable work on R.R. Construction,
+observes very truly that &quot;The braces, at the end of a long
+span, may be nearer the vertical than those near the centre, as
+they have more work to do. If the end panel be made twice as
+high as long, and the centre panel square, the intermediates varying
+as their distance from the end, a good architectural effect
+is produced.&quot;</p>
+
+<p>Now it is necessary for us to have some data from which to
+determine the approximate weight of the bridge, and also its
+load. These can be found by comparing weights of bridges in
+common use, as obtained from reports. In a small bridge of
+short span, the weight of the structure itself may be entirely
+neglected, because of the very small proportion the strains
+caused by it bear to those due to the load;&mdash;but, in long spans,
+the weight becomes a very important element in the calculations
+for strength and safety&mdash;inasmuch as it may exceed the weight
+of the load.</p>
+
+<p>In all Bridges of 120 ft. span, about &#8531; of a ton, per foot run,
+will be the weight of each truss for a single track, including
+floor timbers&mdash;transverse bracing, &amp;c. If the bridge were
+loaded with Locomotives only, the greatest load would be, on
+the whole bridge&mdash;160 tons = 1.33 tons per ft. run of the bridge
+or .666 tons per ft. run of each truss. Now if we make the rise
+of the bridge 15 ft., and divide the span into 12 panels of 10 ft.
+each, we shall have for total weight of bridge and load 240
+tons, or for a single truss 10 tons to each panel.</p>
+
+
+<p><span class="boldhead">Lower Chords.</span> Now to find the tension on the Lower Chords,
+<img src="images/p21_eq1.gif" width="85" height="44" align="middle"
+alt="Equation: T = W x S / 8h" title="Equation: T = W x S / 8h" />
+and supplying values, we have
+<img src="images/p22_eq1.gif" width="111" height="43" align="middle"
+alt="Equation: T = 240 x 120 / 8 x 15" title="Equation: T = 240 x 120 / 8 x 15" />
+= 240 tons, or 537600 lbs., for the two Lower Chords, and &frac12; of this,
+or 268800 lbs. for one chord. The Tensional Strength of timber for safety
+may be taken at 2000 lbs. per square inch of section, and hence the area of timber
+required to sustain the above strain will be 268800 &divide; 2000 = 134.4 sq. inches.
+But this chord has also to sustain the transverse strains arising
+from the weights passing over it, and, as in the case of a Locomotive,
+the weight of 20 tons on 2 pair of drivers, (or 10 tons for one truss,)
+may be concentrated on the middle point of a panel&mdash;the chord
+must be so proportioned as to safely bear, as a horizontal beam, this weight.
+Suppose we take three sticks of 8&quot; x 12&quot;, to form the chord
+(the greater dimension being the depth,) we shall have
+3 x 8&quot; x 12&quot; = 288 square inches area of section, and</p>
+
+<table align="center" cellspacing="0" cellpadding="4" border="0" summary="table layout">
+<tr>
+	<td>allowing</td>
+	<td>for </td>
+	<td>splicing</td>
+	<td>72</td>
+	<td>square</td>
+	<td>inches,</td>
+</tr>
+<tr>
+	<td align="center">&quot;</td>
+	<td align="center">&quot;</td>
+	<td>foot blocks,</td>
+	<td align="right">24</td>
+	<td align="center">&quot;</td>
+	<td align="center">&quot;</td>
+</tr>
+<tr>
+	<td align="center">&quot;</td>
+	<td align="center">&quot;</td>
+	<td>bolts,</td>
+	<td align="right">24</td>
+	<td align="center">&quot;</td>
+	<td align="center">&quot;</td>
+</tr>
+<tr>
+	<td align="center">&quot;</td>
+	<td align="center">&quot;</td>
+	<td>washers,</td>
+	<td align="right">8</td>
+	<td align="center">&quot;</td>
+	<td align="center">&quot;</td>
+</tr>
+</table>
+
+
+<p>we shall have
+after deducting allowances (288-128) 160 square inches area,
+giving an excess over 134.4, the area demanded, sufficient to
+cover allowances for any accidental strain.<br />&nbsp;</p>
+
+
+<p><span class="boldhead">Upper Chords.</span> The upper chords are compressed
+as forcibly as the lower ones suffer tension&mdash;owing to
+the action and reaction of the diagonals. In this case the compression
+is 268800 lbs., and as 1 square inch of section will safely
+bear 1000 lbs., we have for the area required, 268800 &divide; 1000 = 268.8
+square inches,&mdash;three pieces 8&quot; x 11&quot; will give 264 square inches
+and this area will require no reduction, as the whole chord
+presses together when properly framed and is not weakened by
+splicing. So far, the calculations made would apply to either of
+the three Bridges mentioned, as well as to a Warren Truss.
+But now, to obtain the dimensions of the web members, so called,
+of the Truss, it is necessary to decide upon the specific variety.
+The form of Bridge in more general use in the United
+States is called the Howe Truss, from its inventor, and in spans
+of 150 feet, and under, is very reliable; for spans exceeding 150
+ft. it should be strengthened either by Arch Braces or by the
+addition of Arches, as the heavy strains from the weight of
+bridge and load bearing on the feet of the braces near the abutments,
+tend to cripple and distort the truss by sagging, although
+the Baltimore Bridge Co. have built a Wooden Howe Bridge
+of two Trusses of 300 ft. span, 30 ft. rise, and 26 ft. wide, without
+any arch, but it has a wrought iron lower chord, and is only
+proportioned for a moving load of 1000 lbs. per ft. run. [Vide
+Vose on R.R. construction.]</p>
+
+<p>In order to ensure uniformity in strength in the chords&mdash;but
+one joint should be allowed in a panel&mdash;and that should
+come at the centre of the panel length&mdash;but in long spans this
+cannot always be done.<br />&nbsp;</p>
+
+<p><span class="boldhead">Web Members.</span> We will now proceed to calculate
+the web members of a Howe Truss of the foregoing dimensions,
+when subjected to the strains above mentioned.<br />&nbsp;</p>
+
+<p><span class="boldhead">Braces.</span> The end braces must evidently support the
+whole weight of the bridge and load, which for one end of one
+truss will be 134400 lbs., and as these braces are in pairs,&mdash;67200 lbs.
+will be the strain vertically on the stick&mdash;but as this
+stick is a diagonal&mdash;whose vertical is 15 ft., and horizontal 10 ft.,
+we shall have for its length 18 ft. in round numbers, whence the
+strain along the diagonal will be found from the proportion
+15 : 18 :: 67200 : 80640 lbs., whence we have an area of 80
+inches required for compression, or a stick of 8&quot; x 10&quot;. Now, to
+ascertain if this is stiff enough for flexure, we will substitute
+these values in the equation
+<img src="images/p18_eq1.gif" width="109" height="46" align="middle"
+alt="Equation: W = 2240 bd^3 / L^2" title="Equation: W = 2240 bd^3 / L^2" />
+, and we have
+<img src="images/p24_eq1.gif" width="156" height="46" align="middle"
+alt="Equation: W = 2240 x 8 x 1000 / 324" title="Equation: W = 2240 x 8 x 1000 / 324" />
+, or reducing, W = 55308 lbs. Now, these proportions will give ample strength for both
+flexure and compression, for if we block the two sticks composing the end brace
+together, and firmly connect them by bolts, we shall have a built
+beam of 24&quot; x 10&quot;&mdash;whence
+<img src="images/p24_eq2.gif" width="164" height="43" align="middle"
+alt="Equation: W = 2240 x 24 x 1000 / 324" title="Equation: W = 2240 x 24 x 1000 / 324" />
+= 165925 lbs., and as 134400 lbs. was all that the conditions demand,
+we really have an excess of strength. The next set of braces supports
+the weight of the rectangle included between the upper
+ends of the braces and the two chords, and the dimensions of
+the sticks are calculated in the same manner. We find, as we
+approach the centre of the bridge, that the strains on the braces
+become less, and consequently their scantling should be reduced,
+but in ordinary practice this is seldom done.<br />&nbsp;</p>
+
+<p><span class="boldhead">Rods.</span> The next thing is to ascertain the
+dimensions of the various tie rods. It is evident that the same weight
+comes upon the first set of rods, as on the first set of braces&mdash;which
+will give for the rods at one end of one truss, 134400 lbs.;
+and as there are two of these rods, each will sustain a strain of
+67200 lbs.&mdash;and, at 15,000 lbs. per square inch, will have an
+area of 4.48 sq. inches, and, by Vose's Tables, must have a diameter
+of 2&frac12; inches. The sizes of the rods in each set will decrease
+towards the centre of the bridge as the weight becomes less.</p>
+
+<p>&nbsp;</p>
+
+<div class="figcenter">
+<img src="images/plate-ii.gif" width="612" height="839" alt="Plate II" title="Plate II" />
+</div>
+
+<p>&nbsp;</p>
+
+<p><span class="boldhead">Counterbraces.</span> Now, as to the necessity of
+Counterbracing, there are various opinions. The object of it is
+to stiffen the truss and check vibrations. If a load be placed
+over any panel point, it causes that portion of the truss to sink,
+and produces an elevation of the corresponding panel point at
+the other end of the truss&mdash;thus producing a distortion, which
+change of form is resisted by proper counterbraces. The strain
+to which this timber is subjected is caused by the moving load
+on one panel only&mdash;and requires only scantling of the size of
+the middle braces. These counterbraces should not be pinned
+or bolted to the braces where the cross&mdash;as their action is thereby
+entirely altered&mdash;but it is well to so confine them as to prevent
+vertical or lateral motion.<br />&nbsp;</p>
+
+<p><span class="boldhead">Shoes.</span> Formerly it was the custom to foot the braces
+and counters on hard wood blocks on one side of the chord,
+the vertical rods passing through and screwing against a block
+on the other side&mdash;thus the whole strain tended to crush the
+chord across its fibres. This is now remedied by the use of
+cast iron blocks, bearing on one side of the chord, but having
+tubes extending through to the other side, where the washer
+plate for the bolts fits firmly on their ends, forming a complete
+protection, as all the crushing strain is received on the block itself.<br />&nbsp;</p>
+
+<p><span class="boldhead">Width.</span> It now becomes necessary to determine upon
+the width between the two trusses. For a single track bridge
+for a railroad, 14 ft. is the usual width adopted, and for a highway
+bridge, from 12 to 16 ft. When a double track is required,
+three trusses are usually employed, with a width for each roadway
+of 14 ft. for railroads.<br />&nbsp;</p>
+
+<p><span class="boldhead">Bolsters.</span> Large timbers 12 x 12, or thereabouts,
+are laid on the bridge seats of the abutments to support the
+ends of the trusses, one of these should be directly under each
+of the extreme panel points. A panel point is the intersection
+of the centre line of a brace produced, with the centre line of
+a chord. The rise of a truss is the vertical distance between
+the centre lines of the upper and lower chords.<br />&nbsp;</p>
+
+<p><span class="boldhead">Camber.</span> Were a bridge to be framed with
+its chords perfectly horizontal, it would be found to fall below the
+horizontal line on being placed in its proper position, owing to
+the closing up of the joints in the upper parts of the structure,
+and opening of joints in the lower parts, as well as to the
+compression of the parts. To obviate this defect, it is usual to
+curve the chords slightly in a vertical direction, by elongating
+the upper chord, so that the bays or panels are no longer
+rectangular but of a trapezoidal form&mdash;and, as a consequence, the
+inclined web members are slightly lengthened, and the verticals
+become radii of the curve. The amount of deviation from a
+horizontal line is called the Camber.</p>
+
+<p>A table of Cambers for different spans will be found further
+on, as also a table of multipliers, by which to multiply the
+camber in order to find the elongation of the upper chord. Part
+of the Camber table is taken from Trautwine's Engineer's Pocket-Book,
+(which should be the inseparable companion of every
+engineer,) and part was calculated for this pamphlet, according
+to Trautwine's rules. The table of multipliers is Trautwine's.<br />&nbsp;</p>
+
+<p><span class="boldhead">Diagonal Bracing.</span> In order to stiffen a
+bridge, it should have the two Trusses braced together at the
+Lower Chords always, at the Upper Chords when practicable&mdash;and
+in case of a deck bridge, where the roadway is supported on
+the upper chords, it is as well to have rods for vertical diagonal
+braces, their planes being perpendicular to the axis of the bridge.
+The more usual form is similar to the web members of the Howe
+Truss&mdash;the rods from &frac34;&quot; to 1&quot; in diameter, and the braces of
+6&quot; x 7&quot; scantling, footed on wooden blocks, usually. It is more
+usual to have the tie rods of the horizontal diagonal bracing,
+and the braces themselves, meet in a point about midway of a
+Truss panel on the centre line, nearly, of the chord. This will
+generally give a half panel of diagonal bracing near each end of
+the truss&mdash;and it is very usual to have the diagonals foot at
+their intersection there against a cross timber interposed between
+the trusses, while the tie rod prevents any spreading.<br />&nbsp;</p>
+
+<p><span class="boldhead">Floor Timbers.</span> The general dimensions of
+the transverse floor beams, when about 3 feet apart, from centre
+to centre, are 8&quot; x 14&quot;, the largest dimension being the depth.
+The stringers should be notched to the floor beams about 1&quot; or 2&quot;,
+and should be about 10&quot; or 12&quot; x 14&quot;. The cross ties should
+be 18&quot; to 24&quot; apart, from centre to centre, and be 3&frac12;&quot; x 6&quot;.</p>
+
+<p>Large, heavy bridges require no fastening to connect them
+with their seats, but light bridges should be fastened, as the
+spring on the sudden removal of a load, (as when the last car of
+a train has passed,) may move it from its proper position.<br />&nbsp;</p>
+
+<p><span class="boldhead">Splices.</span> As the upper and lower chords have to be
+made in several lengths, securely fastened to each other, and,
+in order to weaken the built beam as little as possible, it is
+necessary to adopt some form of splicing whereby the greatest
+amount of tensional strength may be retained in the chord with
+the least amount of cutting, and yet have a secure joint. Such
+a splice is shown in Pl. II, Fig. 4, and below is a table from
+Vose's Hand-book, giving reliable dimensions.</p>
+
+<table cellspacing="0" cellpadding="4" border="0"
+summary="Splice table from Vose's Hand-Book">
+<tr>
+	<th align="center">Span. <br />Feet.</th> 	<th align="center">AC <br />Feet.</th>
+	<th align="center">BB <br />Inches.</th> 	<th align="center">CD <br />Feet.</th>
+</tr>
+<tr>
+	<td align="center">50</td> 	<td align="center">1.00</td>
+	<td align="center">1&frac12;</td> 	<td align="center">1.50</td>
+</tr>
+<tr>
+	<td align="center">100</td> 	<td align="center">1.25</td>
+	<td align="center">2</td> 	<td align="center">2.00</td>
+</tr>
+<tr>
+	<td align="center">150</td> 	<td align="center">1.75</td>
+	<td align="center">2&frac12;</td> 	<td align="center">2.25</td>
+</tr>
+<tr>
+	<td align="center">200</td> 	<td align="center">2.00</td>
+	<td align="center">3</td> 	<td align="center">2.75</td>
+</tr>
+</table>
+
+<p>This manner of splicing requires the back of the splice block to
+be let into the chord stick, against which it lies, about &frac34; of an
+inch. To show how the various Engineers differ, as to their estimates
+of the sizes of the several parts of bridges, I subjoin two
+Tables&mdash;one by Prof. G.L. Vose, a well known Engineer, and
+one by Jno. C. Trautwine, an Engineer of note also&mdash;and I
+would premise that a bridge built according to either would be
+amply strong.</p>
+
+<p class="heading">TABLE FOR DIMENSIONING A HOWE TRUSS BRIDGE.<br />
+G.L. VOSE.</p>
+
+<table cellspacing="0" cellpadding="4" border="0"
+summary="Table for dimensioning a Howe Truss Bridge, G.L. Vose">
+<tr>
+	<th align="center">Span.</th> 	<th>Rise.</th> 	<th align="center">Panel.</th> 	<th>Chords.</th>
+	<th align="center">End <br />Braces.</th> 	<th align="center">Centre <br />Braces.</th>
+	<th align="center">End <br />Rods.</th> 	<th align="center">Centre <br />Rods.</th>
+</tr>
+<tr>
+	<td align="center">50</td> 	<td align="center">10</td>
+	<td align="center">7</td> 	<td align="center">2&mdash;8 x 10</td>
+	<td align="center">7 x 7</td> 	<td align="center">5 x 5</td>
+	<td align="center">1&mdash;1&#8539;</td> 	<td align="center">2&mdash;1</td>
+</tr>
+<tr>
+	<td align="center">75</td> 	<td align="center">12</td>
+	<td align="center">9</td> 	<td align="center">2&mdash;8 x 10</td>
+	<td align="center">8 x 8</td> 	<td align="center">5 x 5</td>
+	<td align="center">2&mdash;1&frac12;</td> 	<td align="center">2&mdash;1</td>
+</tr>
+<tr>
+	<td align="center">100</td> 	<td align="center">15</td>
+	<td align="center">11</td> 	<td align="center">2&mdash;8 x 10</td>
+	<td align="center">8 x 9</td> 	<td align="center"> 6 x 6</td>
+	<td align="center">2&mdash;1&frac34;</td> 	<td align="center">2&mdash;1</td>
+</tr>
+<tr>
+	<td align="center">150</td> 	<td align="center">20</td>
+	<td align="center">13</td> 	<td align="center">4&mdash;8 x 12</td>
+	<td align="center">10 x 10</td> 	<td align="center">6 x 7</td>
+	<td align="center">3&mdash;2</td> 	<td align="center">3&mdash;1</td>
+</tr>
+<tr>
+	<td align="center">200</td> 	<td align="center">25</td>
+	<td align="center">15</td> 	<td align="center">4&mdash;8 x 16</td>
+	<td align="center">12 x 12</td> 	<td align="center">7 x 7</td>
+	<td align="center">5&mdash;2</td> 	<td align="center">5&mdash;1</td>
+</tr>
+</table>
+
+
+<p class="heading">&nbsp;<br />
+TABLE FOR DIMENSIONING A HOWE TRUSS BRIDGE.<br />
+JNO. C. TRAUTWINE, C.E.</p>
+
+<table cellspacing="0" cellpadding="4" border="1"
+summary="Table for dimensioning a Howe Truss Bridge, Jno. C. Trautwine">
+<tr>
+	<td colspan="3">&nbsp;</td>
+	<td align="center" colspan="2"><span class="smtxt">An Upper Chord.</span></td>
+	<td align="center" colspan="2"><span class="smtxt">A Lower Chord.</span></td>
+	<td align="center" colspan="2"><span class="smtxt">An End Brace.</span></td>
+	<td align="center" colspan="2"><span class="smtxt">A Centre Brace.</span></td>
+	<td align="center" colspan="2"><span class="smtxt">Counter.</span></td>
+	<td align="center" colspan="2"><span class="smtxt">End Rod.</span></td>
+	<td align="center" colspan="2"><span class="smtxt">Centre Rod.</span></td>
+</tr>
+
+<tr>
+	<td align="center"><span class="smtxt">Clear Span in feet.</span></td> 	<td align="center"><span class="smtxt">Rise in feet.</span></td>
+	<td align="center"><span class="smtxt">No. of panels.</span></td>
+	<td align="center"><span class="smtxt">No. pieces.</span></td> 	<td align="center"><span class="smtxt">Size.</span></td>
+	<td align="center"><span class="smtxt">No. pieces.</span></td> 	<td align="center"><span class="smtxt">Size.</span></td>
+	<td align="center"><span class="smtxt">No. pieces.</span></td> 	<td align="center"><span class="smtxt">Size.</span></td>
+	<td align="center"><span class="smtxt">No. pieces.</span></td> 	<td align="center"><span class="smtxt">Size.</span></td>
+	<td align="center"><span class="smtxt">No. pieces.</span></td> 	<td align="center"><span class="smtxt">Size.</span></td>
+	<td align="center"><span class="smtxt">No. rods.</span></td> 	<td align="center"><span class="smtxt">Size.</span></td>
+	<td align="center"><span class="smtxt">No. rods.</span></td> 	<td align="center"><span class="smtxt">Size.</span></td>
+</tr>
+<tr>
+	<td align="center"><span class="smtxt">25</span></td>
+	<td align="center"><span class="smtxt">6</span></td> 	<td align="center"><span class="smtxt">8</span></td>
+	<td align="center"><span class="smtxt">3</span></td> 	<td align="center"><span class="smtxt">4 x 5</span></td>
+	<td align="center"><span class="smtxt">3</span></td> 	<td align="center"><span class="smtxt">4 x 10</span></td>
+	<td align="center"><span class="smtxt">2</span></td> 	<td align="center"><span class="smtxt">4 x 6</span></td>
+	<td align="center"><span class="smtxt">2</span></td> 	<td align="center"><span class="smtxt">5 x 5</span></td>
+	<td align="center"><span class="smtxt">1</span></td> 	<td align="center"><span class="smtxt">4 x 5</span></td>
+	<td align="center"><span class="smtxt">2</span></td> 	<td align="center"><span class="smtxt">1-5/16</span></td>
+	<td align="center"><span class="smtxt">2</span></td> 	<td align="center"><span class="smtxt">&#8542;</span></td>
+</tr>
+<tr>
+	<td align="center"><span class="smtxt">50</span></td>
+	<td align="center"><span class="smtxt">9</span></td> 	<td align="center"><span class="smtxt">9</span></td>
+	<td align="center"><span class="smtxt">3</span></td> 	<td align="center"><span class="smtxt">6 x 7</span></td>
+	<td align="center"><span class="smtxt">3</span></td> 	<td align="center"><span class="smtxt">6 x 10</span></td>
+	<td align="center"><span class="smtxt">2</span></td> 	<td align="center"><span class="smtxt">6 x 7</span></td>
+	<td align="center"><span class="smtxt">2</span></td> 	<td align="center"><span class="smtxt">5 x 6</span></td>
+	<td align="center"><span class="smtxt">1</span></td> 	<td align="center"><span class="smtxt">5 x 6</span></td>
+	<td align="center"><span class="smtxt">2</span></td> 	<td align="center"><span class="smtxt">1&#8541; </span></td>
+	<td align="center"><span class="smtxt">2</span></td> 	<td align="center"><span class="smtxt">1-1/16</span></td>
+</tr>
+<tr>
+	<td align="center"><span class="smtxt">75</span></td>
+	<td align="center"><span class="smtxt">12</span></td> 	<td align="center"><span class="smtxt">10</span></td>
+	<td align="center"><span class="smtxt">3</span></td> 	<td align="center"><span class="smtxt">6 x 9</span></td>
+	<td align="center"><span class="smtxt">3</span></td> 	<td align="center"><span class="smtxt">6 x 11</span></td>
+	<td align="center"><span class="smtxt">2</span></td> 	<td align="center"><span class="smtxt">6 x 8</span></td>
+	<td align="center"><span class="smtxt">2</span></td> 	<td align="center"><span class="smtxt">6 x 6</span></td>
+	<td align="center"><span class="smtxt">1</span></td> 	<td align="center"><span class="smtxt">6 x 6</span></td>
+	<td align="center"><span class="smtxt">2</span></td> 	<td align="center"><span class="smtxt">1&#8542;</span></td>
+	<td align="center"><span class="smtxt">2</span></td> 	<td align="center"><span class="smtxt">1-3/16</span></td>
+</tr>
+<tr>
+	<td align="center"><span class="smtxt">100</span></td>
+	<td align="center"><span class="smtxt">15</span></td> 	<td align="center"><span class="smtxt">11</span></td>
+	<td align="center"><span class="smtxt">3</span></td> 	<td align="center"><span class="smtxt">6 x 10</span></td>
+	<td align="center"><span class="smtxt">3</span></td> 	<td align="center"><span class="smtxt">6 x 12</span></td>
+	<td align="center"><span class="smtxt">2</span></td> 	<td align="center"><span class="smtxt">8 x 9</span></td>
+	<td align="center"><span class="smtxt">2</span></td> 	<td align="center"><span class="smtxt">6 x 8</span></td>
+	<td align="center"><span class="smtxt">1</span></td> 	<td align="center"><span class="smtxt">6 x 8</span></td>
+	<td align="center"><span class="smtxt">2</span></td> 	<td align="center"><span class="smtxt">2-3/16</span></td>
+	<td align="center"><span class="smtxt">2</span></td> 	<td align="center"><span class="smtxt">1-5/16</span></td>
+</tr>
+<tr>
+	<td align="center"><span class="smtxt">125</span></td>
+	<td align="center"><span class="smtxt">18</span></td> 	<td align="center"><span class="smtxt">12</span></td>
+	<td align="center"><span class="smtxt">4</span></td> 	<td align="center"><span class="smtxt">6 x 10</span></td>
+	<td align="center"><span class="smtxt">4</span></td> 	<td align="center"><span class="smtxt">6 x 13</span></td>
+	<td align="center"><span class="smtxt">2</span></td> 	<td align="center"><span class="smtxt">8 x 10</span></td>
+	<td align="center"><span class="smtxt">2</span></td> 	<td align="center"><span class="smtxt">6 x 9</span></td>
+	<td align="center"><span class="smtxt">1</span></td> 	<td align="center"><span class="smtxt">6 x 9</span></td>
+	<td align="center"><span class="smtxt">2</span></td> 	<td align="center"><span class="smtxt">2&#8541;</span></td>
+	<td align="center"><span class="smtxt">2</span></td> 	<td align="center"><span class="smtxt">1&#8540;</span></td>
+</tr>
+<tr>
+	<td align="center"><span class="smtxt">150</span></td>
+	<td align="center"><span class="smtxt">21</span></td> 	<td align="center"><span class="smtxt">13</span></td>
+	<td align="center"><span class="smtxt">4</span></td> 	<td align="center"><span class="smtxt">8 x 10</span></td>
+	<td align="center"><span class="smtxt">4</span></td> 	<td align="center"><span class="smtxt">8 x 14</span></td>
+	<td align="center"><span class="smtxt">3</span></td> 	<td align="center"><span class="smtxt">9 x 10</span></td>
+	<td align="center"><span class="smtxt">3</span></td> 	<td align="center"><span class="smtxt">6 x 9</span></td>
+	<td align="center"><span class="smtxt">2</span></td> 	<td align="center"><span class="smtxt">6 x 9</span></td>
+	<td align="center"><span class="smtxt">3</span></td> 	<td align="center"><span class="smtxt">2&#8540;</span></td>
+	<td align="center"><span class="smtxt">3</span></td> 	<td align="center"><span class="smtxt">1-3/16</span></td>
+</tr>
+<tr>
+	<td align="center"><span class="smtxt">175</span></td>
+	<td align="center"><span class="smtxt">24</span></td> 	<td align="center"><span class="smtxt">14</span></td>
+	<td align="center"><span class="smtxt">4</span></td> 	<td align="center"><span class="smtxt">10 x 12</span></td>
+	<td align="center"><span class="smtxt">4</span></td> 	<td align="center"><span class="smtxt">10 x 15</span></td>
+	<td align="center"><span class="smtxt">3</span></td> 	<td align="center"><span class="smtxt">9 x 11</span></td>
+	<td align="center"><span class="smtxt">3</span></td> 	<td align="center"><span class="smtxt">8 x 8</span></td>
+	<td align="center"><span class="smtxt">2</span></td> 	<td align="center"><span class="smtxt">8 x 8</span></td>
+	<td align="center"><span class="smtxt">3</span></td> 	<td align="center"><span class="smtxt">2&#8541;</span></td>
+	<td align="center"><span class="smtxt">3</span></td> 	<td align="center"><span class="smtxt">1&frac14;</span></td>
+</tr>
+
+<tr>
+	<td align="center"><span class="smtxt">200</span></td>
+	<td align="center"><span class="smtxt">27</span></td> 	<td align="center"><span class="smtxt">15</span></td>
+	<td align="center"><span class="smtxt">4</span></td> 	<td align="center"><span class="smtxt">12 x 12</span></td>
+	<td align="center"><span class="smtxt">4</span></td> 	<td align="center"><span class="smtxt">12 x 16</span></td>
+	<td align="center"><span class="smtxt">3</span></td> 	<td align="center"><span class="smtxt">9 x 12</span></td>
+	<td align="center"><span class="smtxt">3</span></td> 	<td align="center"><span class="smtxt">8 x 10</span></td>
+	<td align="center"><span class="smtxt">2</span></td> 	<td align="center"><span class="smtxt">8 x 10</span></td>
+	<td align="center"><span class="smtxt">3</span></td> 	<td align="center"><span class="smtxt">2&#8542;</span></td>
+	<td align="center"><span class="smtxt">3</span></td> 	<td align="center"><span class="smtxt">1&#8540;</span></td>
+</tr>
+</table>
+
+<p>&nbsp;<br />Both of these tables were calculated for a single Railroad
+track, and would answer equally well for a double Highway
+Bridge. In the bridge according to Trautwine's Table, each
+lower chord is supposed to have a piece of plank, half as thick
+as one of the chord pieces, and as long as three panels, firmly
+bolted on each of its sides, in the middle of its length.</p>
+
+
+<hr style="width: 20%;" />
+
+
+<p class="heading">PRATT'S BRIDGE.</p>
+
+<p>This is opposite in arrangement of parts to a Howe Bridge,
+as the diagonals are rods, and sustain tension, and the verticals
+are posts, and suffer compression:</p>
+
+
+<table class="left" cellspacing="0" cellpadding="4" border="0" summary="Example">
+<tr>
+	<td><i>Example.</i>&mdash;</td>
+	<td>Span</td>
+	<td>= 100 feet.</td>
+</tr>
+<tr>
+	<td>&nbsp;</td>
+	<td>Rise</td>
+	<td>= 12 &nbsp; &quot;</td>
+</tr>
+<tr>
+	<td>&nbsp;</td>
+	<td>Panel </td>
+	<td>= 10 &nbsp; &quot;</td>
+</tr>
+<tr>
+	<td>&nbsp;</td>
+	<td>Weight per lineal ft.</td>
+	<td>= 3000 lbs.</td>
+</tr>
+</table>
+
+<p>The tension on the lower, or compression on the upper chord,
+will be 300000 X 100 / 96 = 333333 lbs. The dimensions of the
+chord and splicing would be found in the same manner as for
+a Howe Truss.<br />&nbsp;</p>
+
+<p><span class="boldhead">Suspension Rods.</span> Fig. 1, Pl. III., represents
+an elevation of a Pratt Bridge. Now, it is evident that the first
+sets of rods must support the weight of the whole bridge and
+its load, which we have found to be 300000 lbs. Each truss
+will have to sustain 150,000 lbs., and each end set of rods 75,000
+lbs. Now, if there are two rods in each set,&mdash;each rod will
+have to bear a strain of 37500 lbs., and this will have an increase
+due to its inclination, so that the strain on it must be
+found by the following proportion:</p>
+
+<p class="center">
+Height : diagonal :: W : W' or<br />
+12 : 15.8 :: 37500 : 49375 lbs.
+</p>
+
+<p>Referring to the Table for bolts, we find that 2&#8539; gives a strength
+a little in excess, and will be the proper size. The next set of
+rods bear the weight of the whole load, less that due to the two
+end panels, and so on. Fig. 2, Pl. III, shows the manner of applying
+the rods. The bevel block should be so fitted to the
+chord that it will not have a crushing action.<br />&nbsp;</p>
+
+<p><span class="boldhead">Counters.</span> Top and bottom chords are always
+used in this bridge, and consequently the counter rods have only
+to sustain the movable load on one panel. The weight of the
+moving load cannot be more than 2000 lbs. per lineal foot
+which, for a panel of 10 ft., gives 20000 lbs., or 10,000 lbs. for
+each set, and if we have two rods in a set, the strain on each
+rod will be 5000 lbs., increasing this for inclination, we shall
+have,</p>
+
+<p class="center">
+12 : 15.8 :: 5000 : 6585 lbs.,<br />
+</p>
+
+<p>requiring a rod of &frac34; of an inch diameter. The posts in this
+bridge correspond to the braces of the Howe Truss, but being
+vertical, are not so large.</p>
+
+<p>Subjoined are two Tables, one by Prof. G.L. Vose, and one
+by Mr. Trautwine, giving principal dimensions for bridges of
+different spans of the Pratt type of Truss.</p>
+
+<p class="heading">TABLE OF DIMENSIONS OF A PRATT TRUSS.<br />
+PROF. G. L. VOSE.</p>
+
+<table cellspacing="0" cellpadding="4" border="0"
+summary="Table for dimensioning a Pratt Truss, G.L. Vose">
+<tr>
+	<th align="center">Span.</th> 	<th align="center">Rise.</th>
+	<th align="center">Chords.</th> 	<th align="center">End <br />Post.</th>
+	<th align="center">Centre <br />Post.</th><th align="center">End <br />Rod.</th>
+	<th align="center">Centre <br />Rod.</th> 	<th align="center">Counter <br />Rod.</th>
+</tr>
+<tr>
+	<td align="center">50</td> 	<td align="center">10</td>
+	<td align="center">2&mdash;8 x 10</td> 	<td align="center">5 x 5</td>
+	<td align="center">4 x 4</td> 	<td align="center">2&mdash;1&#8540;</td>
+	<td align="center">2&mdash;1</td> 	<td align="center">1&mdash;1&frac12;</td>
+</tr>
+<tr>
+	<td align="center">75</td> 	<td align="center">12</td>
+	<td align="center">2&mdash;8 x 10</td> 	<td align="center">6 x 6</td>
+	<td align="center">5 x 5</td> 	<td align="center">2&mdash;1&#8541;</td>
+	<td align="center">2&mdash;1</td> 	<td align="center">1&mdash;1&frac12;</td>
+</tr>
+<tr>
+	<td align="center">100</td> 	<td align="center">15</td>
+	<td align="center">3&mdash;8 x 10</td> 	<td align="center">7 x 7</td>
+	<td align="center">6 x 6</td> 	<td align="center">2&mdash;1&frac34;</td>
+	<td align="center">2&mdash;1</td> 	<td align="center">2&mdash;1&#8539;</td>
+</tr>
+<tr>
+	<td align="center">125</td> 	<td align="center">18</td>
+	<td align="center">3&mdash;8 x 10</td> 	<td align="center">8 x 8</td>
+	<td align="center">6 x 6</td> 	<td align="center"> 3&mdash;1&#8542;</td>
+	<td align="center">3&mdash;1</td> 	<td align="center">2&mdash;1&#8540;</td>
+</tr>
+<tr>
+	<td align="center">150</td> 	<td align="center">21</td>
+	<td align="center">4&mdash;8 x 12</td> 	<td align="center">9 x 9</td>
+	<td align="center">6 x 6</td> 	<td align="center">3&mdash;2&#8539;</td>
+	<td align="center">3&mdash;1</td> 	<td align="center">3&mdash;1&#8539;</td>
+</tr>
+<tr>
+	<td align="center">200</td> 	<td align="center">24</td>
+	<td align="center">4&mdash;8 x 16</td> 	<td align="center">10 x 10</td>
+	<td align="center">6 x 6</td> 	<td align="center">5&mdash;1&#8542;</td>
+	<td align="center">5&mdash;1</td> 	<td align="center">3&mdash;1&#8539;</td>
+</tr>
+</table>
+
+<p class="heading">&nbsp;<br />TABLE OF DIMENSIONS OF A PRATT'S TRUSS.</p>
+
+<table border="1" cellspacing="0" cellpadding="4"
+summary="Table of dimensions of a Pratt's truss">
+
+<tr><td align="center">Clear Span in feet.</td><td align="center">25</td><td align="center">50</td>
+<td align="center">75</td><td align="center">100</td><td align="center">125</td>
+<td align="center">150</td><td align="center">175</td><td align="center">200</td></tr>
+
+<tr><td align="left">Rise in feet</td><td align="center">6</td><td align="center">9</td>
+<td align="center">12</td><td align="center">15</td><td align="center">18</td>
+<td align="center">21</td><td align="center">24</td><td align="center">27</td></tr>
+
+<tr><td align="left">No. of Panels.</td><td align="center">8</td><td align="center">9</td>
+<td align="center">10</td><td align="center">11</td><td align="center">12</td>
+<td align="center">13</td><td align="center">14</td><td align="center">15</td></tr>
+
+<tr><td align="left">Upper Chord.</td></tr>
+
+<tr><td align="left">&nbsp; No. Pieces.</td><td align="center">3</td><td align="center">3</td>
+<td align="center">3</td><td align="center">3</td><td align="center">4</td><td align="center">4</td>
+<td align="center">4</td><td align="center">4</td></tr>
+
+<tr><td align="left">&nbsp; Size.</td><td align="center">4 x 5</td><td align="center">6 x 7</td>
+<td align="center">6 x 9</td><td align="center">6 x 10</td><td align="center">6 x 10</td>
+<td align="center">8 x 10</td><td align="center">10 x 12</td><td align="center">12 x 12</td></tr>
+
+<tr><td align="left">Lower Chord.</td></tr>
+
+<tr><td align="left">&nbsp; No. of Pieces.</td><td align="center">3</td><td align="center">3</td>
+<td align="center">3</td><td align="center">3</td><td align="center">4</td><td align="center">4</td>
+<td align="center">4</td><td align="center">4</td></tr>
+
+<tr><td align="left">&nbsp; Size.</td><td align="center">4 x 10</td><td align="center">6 x 10</td>
+<td align="center">6 x 11</td><td align="center">6 x 12</td><td align="center">6 x 13</td>
+<td align="center">8 x 14</td><td align="center">10 x 15</td><td align="center">12 x 16</td></tr>
+
+<tr><td align="left">Main Brace Rods.</td><td align="center"></td></tr>
+
+<tr><td align="left">&nbsp; No. Ctr.</td><td align="center">2</td>
+<td align="center">2</td><td align="center">2</td><td align="center">2</td>
+<td align="center">2</td><td align="center">3</td><td align="center">3</td><td align="center">3</td></tr>
+
+<tr><td align="left">&nbsp; Size. Ctr.</td><td align="center">1</td><td align="center">1-3/16</td>
+<td align="center">1-5/16</td><td align="center">1-7/16</td><td align="center">1&frac12;</td>
+<td align="center">1-5/16</td><td align="center">1&#8540;</td><td align="center">1&frac12;</td></tr>
+
+<tr><td align="left">&nbsp; No. End.</td><td align="center">2</td>
+<td align="center">2</td><td align="center">2</td><td align="center">2</td><td align="center">2</td>
+<td align="center">3</td><td align="center">3</td><td align="center">3</td></tr>
+
+<tr><td align="left">&nbsp; Size. End.</td><td align="center">1&#8540;</td><td align="center">1&#8542;</td>
+<td align="center">2&#8539;</td><td align="center">2&frac12;</td><td align="center">2&#8542;</td>
+<td align="center">2&frac12;</td><td align="center">2&frac34;</td><td align="center">3&#8539;</td></tr>
+
+<tr><td align="left">Counter Rods.</td></tr>
+
+<tr><td align="left">&nbsp; Number.</td><td align="center">1</td><td align="center">1</td>
+<td align="center">1</td><td align="center">1</td><td align="center">1</td><td align="center">2</td>
+<td align="center">2</td><td align="center">2</td></tr>
+
+<tr><td align="left">&nbsp; Size.</td><td align="center">1-7/16</td><td align="center">1&#8541;</td>
+<td align="center">1&#8542;</td><td align="center">2</td><td align="center">2&#8539;</td>
+<td align="center">1&#8541;</td><td align="center">1-11/16</td><td align="center">1-13/16</td></tr>
+
+<tr><td align="left">Posts.</td></tr>
+
+<tr><td align="left">&nbsp; No. End.</td><td align="center">3</td><td align="center">3</td>
+<td align="center">3</td><td align="center">3</td><td align="center">4</td><td align="center">4</td>
+<td align="center">4</td><td align="center">4</td></tr>
+
+<tr><td align="left">&nbsp; Size. End.</td><td align="center">4 x 5</td><td align="center">6 x 6</td>
+<td align="center">6 x 7</td><td align="center">6 x 9</td><td align="center">6 x 9</td>
+<td align="center">8 x 8</td><td align="center">10 x 10</td><td align="center">12 x 10</td></tr>
+
+<tr><td align="left">&nbsp; No. Ctr.</td><td align="center">3</td><td align="center">3</td>
+<td align="center">3</td><td align="center">3</td><td align="center">4</td><td align="center">4</td>
+<td align="center">4</td><td align="center">4</td></tr>
+
+<tr><td align="left">&nbsp; Size. Ctr.</td><td align="center">4 x 4</td><td align="center">6 x 5</td>
+<td align="center">6 x 5</td><td align="center">6 x 7</td><td align="center">6 x 7</td>
+<td align="center">8 x 7</td><td align="center">10 x 8</td><td align="center">10 x 8</td></tr>
+</table>
+
+<p><br />This table is partly given in Trautwine's Engineer's Pocket
+Book, and partly made up from directions therein given.</p>
+<p>&nbsp;</p>
+
+<p class="heading">TABLE OF DIMENSIONS FOR SMALL SINGLE TRACK PRATT TRUSSES.</p>
+
+<table border="1" cellspacing="0" cellpadding="4"
+summary="Table of dimensions for small single track Pratt trusses">
+<tr><td align="center">Clear<br />Span,<br />Ft.</td><td align="center">Chords each,<br />Ins.</td>
+<td align="center">Centre<br />Post,<br />Ins.</td><td align="center">End Posts,<br />Ins.</td>
+<td align="center">At centre<br />of truss, <br />Diam. of<br />Rods.</td>
+<td align="center">At end<br />of truss,<br />Diam. of<br />Rods.</td>
+<td align="center">Centre<br />Counter,<br />Diameter,<br />Ins.</td>
+<td align="center">End Counter,<br />Diameter,<br />Ins.</td></tr>
+<tr><td align="center">30</td><td align="center">9 x 11</td><td align="center">4 x 9</td>
+<td align="center">7 x 9</td><td align="center">1</td><td align="center">1&#8541;</td>
+<td align="center">1&#8540;</td><td align="center">1</td></tr>
+<tr><td align="center">40</td><td align="center">10 x 12</td><td align="center">4 x 10</td>
+<td align="center">8 x 10</td><td align="center">1&#8539;</td><td align="center">1&#8542;</td>
+<td align="center">1&#8541;</td><td align="center">1</td></tr>
+<tr><td align="center">50</td><td align="center">10 x 14</td><td align="center">5 x 10</td>
+<td align="center">9 x 10</td><td align="center">1&frac14;</td><td align="center">2&#8539;</td>
+<td align="center">1&frac34;</td><td align="center">1</td></tr>
+<tr><td align="center">60</td><td align="center">12 x 15</td><td align="center">5 x 12</td>
+<td align="center">9 x 12</td><td align="center">1&#8540;</td><td align="center">2&#8540;</td>
+<td align="center">2</td><td align="center">1</td></tr>
+<tr><td align="center">70</td><td align="center">12 x 17</td><td align="center">6 x 12</td>
+<td align="center">11 x 12</td><td align="center">1&frac12;</td><td align="center">2&frac12;</td>
+<td align="center">2&#8539;</td><td align="center">1</td></tr>
+</table>
+
+<p><br />This bridge possesses an advantage over the Howe Truss,
+for the panel diagonals can be tightened up by screws, so that
+every part of the truss can be forced to perform its work. In
+Howe's bridge the adjustments must be made by wedging the
+braces and counters.</p>
+
+<p>Below are given the dimensions of a Howe bridge on the
+Vermont Central R.R., at South Royalton, (single track, deck.)</p>
+
+<table cellspacing="0" cellpadding="4" border="0"
+summary="Dimensions of bridge on Vermont Central R.R.">
+<tr>
+	<td>Span.</td><td>150</td>
+</tr>
+<tr>
+	<td>Rise. </td><td>20</td>
+</tr>
+<tr>
+	<td>No. of Panels. </td><td>12</td>
+</tr>
+<tr>
+	<td>Upper Chord. </td><td>4&mdash;6&frac12; x 13</td>
+</tr>
+<tr>
+	<td>Lower Chord. </td><td>4&mdash;6&frac12; x 13</td>
+</tr>
+<tr>
+	<td>Braces.</td><td>2&mdash;8  x 9</td>
+</tr>
+<tr>
+	<td>Counters. </td><td>1&mdash;8  x 9</td>
+</tr>
+<tr>
+	<td>Rods. </td><td>3&mdash;1&frac14;&quot;</td>
+</tr>
+<tr>
+	<td>Transverse Bracing.</td><td>&nbsp;</td>
+</tr>
+<tr>
+	<td> &nbsp; &nbsp;Braces.</td><td>6 x 8</td>
+</tr>
+<tr>
+	<td> &nbsp; &nbsp;Rods.</td><td>&#8542;</td>
+</tr>
+</table>
+
+<p>&nbsp;<br />The bridge over the White River, on the Passumpsic R.R., is
+a Howe Truss, strengthened by an arch. The verticals are of
+wood, and the diagonals foot on steps formed by enlarging the
+ends of the verticals. The counters are in two lengths, and are
+adjusted by wedges at the points where they intersect the braces.
+The bridge is in two spans, and has a double track, and
+consequently three trusses. There are two timber arches to
+each truss, and the truss is supported on them by connecting
+them to the verticals by short cross pieces notched into the
+posts, and resting on the upper surface of the arches. It is a
+very stiff bridge, and similar to the one at Bellows Falls, both
+having their axis oblique to the channel of the stream they cross.
+The timbers could hardly be procured now, except at great expense.</p>
+
+<table border="1" cellspacing="0" cellpadding="4"
+summary="Dimensions of bridge over White River">
+<tr><td align="center">Span.</td><td align="center">No. of <br />Panels.</td><td align="center">Rods.</td>
+<td align="center">Upper Chord.</td><td align="center">Lower Chord.</td><td align="center">Braces.</td>
+<td align="center">Counters.</td><td align="center">Uprights.</td><td align="center">Arches.</td></tr>
+<tr><td align="center">182</td><td align="center">14</td><td align="center">21</td>
+<td align="center">2&mdash;8 x 16,<br />1&mdash;5 x 16</td><td align="center"> 2&mdash;8 x 17,<br />2&mdash;4 x 17,<br />1&mdash;5 x 17</td>
+<td align="center">1&mdash;21 x 8</td><td align="center">1&mdash;8 x 10</td><td align="center">21 x 11</td>
+<td align="center">2&mdash;8 x 9</td></tr>
+</table>
+
+<p><br />
+Diagonals 6 x 8, Rods &#8542;. Floor timbers suspended both from
+arches and truss, 9 x 13; stringers 10 x 14.
+</p>
+
+<p>In the Cheshire Bridge, the braces are only 20 x 8, and the
+span is only 175 feet, the number of Panels being 14, as in the
+W.R. Bridge&mdash;the other dimensions are the same. Below are
+given the dimensions of a Howe Truss of 108 ft. span, weight
+to be borne on upper chord.</p>
+
+<table border="1" cellspacing="0" cellpadding="4"
+summary="Dimensions of a Howe Truss of 108 ft. span">
+<tr><td align="center">Rise <br />Ft.</td><td align="center">Camber <br />Ins.</td>
+<td align="center">No. of <br />Panels.</td><td align="center">Upper Chord <br />Ins.</td><td align="center">Lower Chord <br />Ins.</td>
+<td align="center">Braces <br />Ins.</td><td align="center">Counters <br />Ins.</td>
+<td align="center">E Rods <br />Ins.</td><td align="center">Floor Timbers <br />Ins.</td></tr>
+<tr><td align="center">13&frac12;</td><td align="center">3</td><td align="center">12</td>
+<td align="center">8&mdash;3 x 12</td><td align="center">8&mdash;3x12</td><td align="center">2&mdash;8 x 10</td>
+<td align="center"> 1&mdash;7 x 10</td><td align="center">2&mdash;2&#8539;</td><td align="center">9 x 16</td></tr>
+</table>
+
+<p>&nbsp;</p>
+
+<p>As plank is used for the chords, the pieces must be bolted thoroughly
+with &#8541; bolts.</p>
+
+<p>&nbsp;</p>
+
+<div class="figcenter">
+<img src="images/plate-iii.gif" width="595" height="835"  alt="Plate III" title="Plate III" />
+</div>
+
+<p>&nbsp;</p>
+
+<p>A form of bridge that has been used to some extent on the
+Baltimore and Ohio Railroad, by Mr. Latrobe, is the Arch Brace
+Truss. In this form of Truss the braces lead directly from the
+abutments to the head of each vertical; thus the load is transferred
+at once to the abutments, without passing through a series
+of web members. The counterbracing is effected by means
+of a light lattice,&mdash;and is applied to both sides of the chords,
+and the intersections of the diagonals are fastened while the
+bridge is strained by a load&mdash;thus preventing recoil&mdash;so that the
+effect of a moving load is to lighten the strain on the lattice&mdash;without
+otherwise affecting the Truss. There are two models
+of this style of bridge, to my knowledge; one built by Prof.
+G.L. Vose, on a scale of &frac12; an inch to the foot, and representing a
+span of 150 feet, which supported 2,500 lbs. at the centre, and a
+movable load of 150 lbs., proving itself to be strong and rigid
+enough for any thing. The other, on a scale of 1 inch to the
+foot, and representing a span of 76 feet, was built by the Class
+of '73, of the Thayer Engineering School, under the writer's direction,
+and though bearing very heavy weights, has never been
+thoroughly tested&mdash;it has, however, been subjected to the sudden
+shock of 1040 lbs. falling 20 inches, without injury, several
+times. Subjoined are the dimensions of the models mentioned.</p>
+
+<p class="heading">
+DIMENSIONS OF A MODEL OF AN ARCH BRACE TRUSS.<br />
+G.L. VOSE.</p>
+
+<table cellspacing="0" cellpadding="4" border="0"
+summary="Dimensions of model arch brace truss">
+<tr>
+	<td>Length, &nbsp; &nbsp; </td>
+	<td>7 feet.</td>
+</tr>
+<tr>
+	<td>Height,</td>
+	<td>1 foot.</td>
+</tr>
+<tr>
+	<td>Width,</td>
+	<td>1 foot.</td>
+</tr>
+<tr>
+	<td>Chords,</td>
+	<td>4&mdash;&frac14; x &frac12;  inch.</td>
+</tr>
+<tr>
+	<td>Braces  </td>
+	<td>4&mdash;&frac14; x 1/3&nbsp; &quot;</td>
+</tr>
+<tr>
+	<td>Lattice, </td>
+	<td>&frac14; x 1/16 &nbsp; &nbsp; &quot;</td>
+</tr>
+</table>
+
+<p>This represented a span of 150 ft, a rise of 20 feet, and a panel
+of 15 ft. Weight, per running foot of bridge and load, was taken
+at 3000 lbs.</p>
+
+<p>The method of calculating the dimensions of this truss, from
+the foregoing data, is as follows. The half number of panels is
+5, and the lengths of the corresponding diagonals (neglecting
+fractions) are</p>
+
+<p class="center"><img src="images/p37_eq1.gif" width="87" height="25" align="middle"
+alt="Formula = {sqrt)(15^2 + 30^2)" title="Formula = {sqrt)(15^2 + 30^2)" />
+ = 25 feet.</p>
+
+<p class="center"><img src="images/p37_eq2.gif" width="87" height="25" align="middle"
+alt="Formula = {sqrt)(15^2 + 45^2)" title="Formula = {sqrt)(15^2 + 45^2)" />
+= 37 &nbsp;  &quot; &nbsp;</p>
+
+<p class="center"><img src="images/p37_eq3.gif" width="87" height="24" align="middle"
+alt="Formula = {sqrt)(15^2 + 60^2)" title="Formula = {sqrt)(15^2 + 60^2)" />
+= 49 &nbsp;   &quot; &nbsp;</p>
+
+<p class="center"><img src="images/p37_eq4.gif" width="87" height="24" align="middle"
+alt="Formula = {sqrt)(15^2 + 60^2)" title="Formula = {sqrt)(15^2 + 60^2)" />
+= 64  &nbsp; &quot; &nbsp;</p>
+
+<p class="center"><img src="images/p37_eq5.gif" width="87" height="25" align="middle"
+alt="Formula = {sqrt)(15^2 + 60^2)" title="Formula = {sqrt)(15^2 + 60^2)" />
+= 78  &nbsp; &quot; &nbsp;</p>
+
+<p>The weight upon each set of braces is that due to one panel, or
+3000 x 15 = 45000 lbs., half of this, or 22500 lbs., is the weight for
+one truss only&mdash;and, as there is a brace under each of the 4
+chord sticks, we divide by 4, and have 5625 lbs. per stick of the
+brace;&mdash;now, correcting for inclination, we shall have</p>
+
+<p class="center">
+20 : 25 :: 5625 : &nbsp; 7031 lbs.<br />
+20 : 37 :: 5625 : 10406 lbs.<br />
+20 : 49 :: 5625 : 13781 lbs.<br />
+20 : 64 :: 5625 : 18000 lbs.<br />
+20 : 78 :: 5625 : 21937 lbs.<br />
+</p>
+
+<p>The weights fouud show the compressional strains on the several
+braces;&mdash;and, were the pieces to be proportioned for compression
+only, their scantling would be quite small&mdash;but on account
+of their elasticity, they require larger dimensions.</p>
+
+<p>These braces should not be fastened to the verticals,&mdash;but
+should be confined both laterally and vertically, where they pass
+them. The length of beam, for which we have to guard agains
+flexure, is the length between verticals in any panel.</p>
+
+<p class="center">
+In panel No. 1, it will be 25 feet,<br />
+&nbsp; &nbsp; &nbsp; &quot;&nbsp; &nbsp; &quot; &nbsp; &nbsp; 2,&nbsp; &nbsp; &quot; &nbsp;  &quot; &nbsp;&nbsp;18 &nbsp; &quot;<br />
+&nbsp; &nbsp; &nbsp; &quot;&nbsp; &nbsp; &quot; &nbsp; &nbsp; 3,&nbsp; &nbsp; &quot; &nbsp;  &quot; &nbsp;&nbsp;17 &nbsp; &quot;<br />
+&nbsp; &nbsp; &nbsp; &quot;&nbsp; &nbsp; &quot; &nbsp; &nbsp; 4,&nbsp; &nbsp; &quot; &nbsp;  &quot; &nbsp;&nbsp;16 &nbsp; &quot;<br />
+&nbsp; &nbsp; &nbsp; &quot;&nbsp; &nbsp; &quot; &nbsp; &nbsp; 5,&nbsp; &nbsp; &quot; &nbsp;  &quot; &nbsp;&nbsp;16 &nbsp; &quot;
+</p>
+
+<p>Now, using the formula</p>
+
+<p class="center"><img src="images/p38_eq1.gif" width="111" height="45" align="middle"
+alt="Equation: 2240 bd^3 / L^2 = W" title="Equation: 2240 bd^3 / L^2 = W" />
+</p>
+
+<p>we shall have, in round numbers, the following dimensions:</p>
+
+<p class="center">For the 1st panel, 25 feet long, 8 x 10<br />
+&nbsp; &nbsp; &nbsp; &quot; &nbsp; &nbsp; 2d &nbsp;  &nbsp; &quot; &nbsp;  37 &nbsp;  &quot; &nbsp; &nbsp; &quot; &nbsp; &nbsp;  8 x 10<br />
+&nbsp; &nbsp; &nbsp; &quot; &nbsp; &nbsp; 3d &nbsp;  &nbsp; &quot; &nbsp;  49 &nbsp;  &quot; &nbsp; &nbsp; &quot; &nbsp; &nbsp;  8 x 10<br />
+&nbsp; &nbsp; &nbsp; &quot; &nbsp; &nbsp; 4th &nbsp;&nbsp; &quot; &nbsp;  64 &nbsp;  &quot; &nbsp; &nbsp; &quot; &nbsp; &nbsp;  8 x 10<br />
+&nbsp; &nbsp; &nbsp; &quot; &nbsp; &nbsp; 5th &nbsp;&nbsp; &quot; &nbsp;  78 &nbsp;  &quot; &nbsp; &nbsp; &quot;  &nbsp; &nbsp;  8 x 10
+</p>
+
+<p>For the lattice work, a double course on each side of each truss,
+in long spans; and a single course, in shorter spans, of 3 x 6, or
+2 x 9 plank, bolted at intersections, is sufficient.</p>
+
+<p class="heading">GENERAL TABLE OF DIMENSIONS FOR ARCH <br />BRACE TRUSS. G.L. VOSE.</p>
+
+<table border="0" cellspacing="0" cellpadding="6"
+summary="General table of dimensions for arch brace truss">
+<tr><td align="center">Span.</td><td align="center">Rise.</td><td align="center">Chords.</td><td align="center">Ties.</td><td align="center">Braces.</td><td align="center">Lattice.</td></tr>
+<tr><td align="center">50</td><td align="center">10</td><td align="center">2&mdash;8 x 10</td><td align="center">1&mdash;8 x 10</td><td align="center">2&mdash;6 x 6</td><td>&nbsp;</td></tr>
+<tr><td align="center">75</td><td align="center">12</td><td align="center">2&mdash;8 x 10</td><td align="center">1&mdash;8 x 10</td><td align="center">2&mdash;6 x 6</td><td align="center">2 x 9</td></tr>
+<tr><td align="center"> 100</td><td align="center">15</td><td align="center">3&mdash;8 x 10</td><td align="center">2&mdash;8 x 10</td><td align="center">3&mdash;6 x 6</td><td align="center">or</td></tr>
+<tr><td align="center"> 150</td><td align="center">20</td><td align="center">4&mdash;8 x l2</td><td align="center">3&mdash;8 x 10</td><td align="center">4&mdash;6 x 8</td><td align="center">3 x 6</td></tr>
+<tr><td align="center"> 200</td><td align="center">25</td><td align="center">4&mdash;8 x 16</td><td align="center">3&mdash;8 x 10</td><td align="center">4&mdash;6 x 9</td><td>&nbsp;</td></tr>
+</table>
+
+<p>&nbsp;</p>
+
+<p>The arch braces must all foot on an iron thrust block, of
+which a view is given in Fig. 4, Pl. III; and the centre of
+pressure of the braces must be directly over a bolster, to prevent
+crippling.</p>
+
+<p>The several sticks forming a brace must be blocked together
+at intervals, and when they are spliced,&mdash;a butt joint should
+be used&mdash;and it should come in the centre of a panel. Below
+are given the dimensions of the Thayer Engineering School
+model.</p>
+
+<table border="0" cellspacing="0" cellpadding="4"
+summary="Dimensions of the Thayer Engineering School model.">
+<tr><td align="left">Height Ins.&nbsp; </td><td align="left">12</td></tr>
+<tr><td align="left">No. Panels</td><td align="left">8</td></tr>
+<tr><td align="left">Chords Ins.&nbsp; </td><td align="left">2&mdash;1 x &frac12;</td></tr>
+<tr><td align="left">Posts Ins.</td><td align="left">1&mdash;2/3 x 5/6</td></tr>
+<tr><td align="left">Braces Ins.&nbsp; </td><td align="left">2&mdash;&frac12; x &frac12;</td></tr>
+<tr><td align="left">Lattice Ins.&nbsp; </td><td align="left">&frac14; x &frac12;</td></tr>
+<tr><td align="left">Width Ins.</td><td align="left">13</td></tr>
+</table>
+
+<p>&nbsp;</p>
+
+<p>There are several other forms of Bridge, the most notable
+among which are the Whipple, McCallum's, Post's, Towne's,
+Haupt's, and Burr's. But enough has been said to give the student
+an idea of the general arrangement of the different parts of
+a Truss, arid to enable him to determine the strains to which
+the various members are subjected. Nothing will be said in
+regard to Wooden Arches, as our space is too limited.<br />&nbsp;</p>
+
+<p><span class="boldhead">Pile Bridging.</span> A bridge of this description is
+useful in crossing marshes, or in shallow water. Fig. 5, Pl. III,
+gives a good example of this kind of bridge, under 20 feet in
+height. If on a curve, there must be extra bracing on the convex side.<br />&nbsp;</p>
+
+<p><span class="boldhead">Trestle Work.</span> This is a combination of posts,
+caps, and braces; and is used for both temporary and permanent
+works. Plate IV, Figs. 1, 2, 3 and 4, give some of the
+best varieties in use. Figs. 1 and 2, may be used up to 15 feet
+in height; Fig. 4, up to 20 feet; and Fig. 3, to 30 ft. The distance
+apart of the various bents should not exceed 10 or 12 ft.,
+unless bracing is introduced between them, and the bents should
+always be raised above the ground a few feet on a solid masonry
+foundation. Want of space forbids any mention of abutments
+and piers, which really come more properly under the
+head of masonry.</p>
+
+<p>Iron Bridging is gradually working its way into favor, and
+will probably eventually supersede wooden trusses;&mdash;but in
+many cases wood is the only material at hand&mdash;and therefore
+some knowledge of Wooden Bridging is desirable. It is intended
+to follow this pamphlet with a portfolio of sheets containing
+working drawings of several kinds of Wooden Bridges, taken
+from actual measurements of some of the best specimens of the
+different styles of Truss in use.</p>
+
+<hr style="width: 45%;" />
+
+<p class="heading">PRACTICAL NOTES.</p>
+
+
+<p>When putting a truss together in its proper position, on
+the abutments, 'false works' must first be erected to support the
+parts until they are so joined together as to forma complete
+self-sustaining truss. The bottom chords are first laid as level
+as possible on the false works, then the top chords are raised on
+temporary supports, sustained by those of the lower chord, and
+are placed a few inches higher at first than their proper position,
+in order that the web members may be slipped into place.
+When this is done the top chords are gradually lowered into
+place. The screws are then gradually tightened, (beginning at
+the centre and working towards both ends,) to bring the surfaces
+of the joints into proper contact, and by this method, the
+camber forms itself, and lifts the lower chords clear of the false
+works, leaving the truss resting only upon its proper supports.
+The subjoined Table will be found useful in estimating the
+strains on a truss when proportioning a bridge for any moving
+load.</p>
+
+<h4>Table of weights per running foot of a bridge, (either of
+wood or iron,) including weights of floor, lateral bracing, &amp;c.,
+complete, for a single track.</h4>
+
+<table border="1" cellspacing="0" cellpadding="4"
+summary="Table of weights per running foot of a bridge, complete, for a single track.">
+<tr><td align="center">Clear <br />Span.</td><td align="center" colspan="2">Weight of Bridge.</td>
+<td align="center">Clear <br />Span.</td><td align="center" colspan="2">Weight of Bridge.</td>
+<td align="center">Clear <br />Span.</td><td align="center" colspan="2">Weight of Bridge.</td>
+<td align="center">Clear <br />Span.</td><td align="center" colspan="2">Weight of Bridge.</td></tr>
+
+<tr><td></td><td align="center">Tons.</td><td align="center">lbs.</td>
+<td></td><td align="center">Tons.</td><td align="center">lbs.</td>
+<td></td><td align="center">Tons.</td><td align="center">lbs.</td>
+<td></td><td align="center">Tons.</td><td align="center">lbs.</td></tr>
+
+<tr><td align="center"> 25</td><td align="center">.266</td><td align="center">596</td>
+<td align="center"> 70</td><td align="center">.404</td><td align="center">905</td>
+<td align="center">140</td><td align="center">.614</td><td align="center">1375</td>
+<td align="center">200</td><td align="center">.792</td><td align="center">1774</td></tr>
+
+<tr><td align="center"> 30</td><td align="center">.281</td><td align="center">629</td>
+<td align="center"> 80</td><td align="center">.434</td><td align="center">972</td>
+<td align="center">150</td><td align="center">.643</td><td align="center">1440</td>
+<td align="center">225</td><td align="center">.867</td><td align="center">1942</td></tr>
+
+<tr><td align="center"> 40</td><td align="center">.313</td><td align="center">701</td>
+<td align="center"> 90</td><td align="center">.464</td><td align="center">1039</td>
+<td align="center">160</td><td align="center">.673</td><td align="center">1507</td>
+<td align="center">250</td><td align="center">.940</td><td align="center">2105</td></tr>
+
+<tr><td align="center"> 50</td><td align="center">.343</td><td align="center">768</td>
+<td align="center">100</td><td align="center">.494</td><td align="center">1106</td>
+<td align="center">170</td><td align="center">.703</td><td align="center">1575</td>
+<td align="center">275</td><td align="center">1.013</td><td align="center">2269</td></tr>
+
+<tr><td align="center"> 60</td><td align="center">.374</td><td align="center">838</td>
+<td align="center">120</td><td align="center">.554</td><td align="center">1241</td>
+<td align="center">180</td><td align="center">.733</td><td align="center">1642</td>
+<td align="center">300</td><td align="center">1.087</td><td align="center">2435</td></tr>
+</table>
+
+<p>&nbsp;</p>
+
+
+<p>The weight of a single track railway bridge may be taken
+as equal to that of a double track highway bridge,&mdash;and the
+trusses that will be large enough for one will be large enough
+for the other.</p>
+
+<p>The greatest load that a highway bridge can be subjected
+to is 120 lbs. to the square foot of surface.</p>
+
+<p class="heading">TABLE OF CAMBERS FOR BRIDGE TRUSSES.</p>
+
+<table border="1" cellspacing="0" cellpadding="4"
+summary="Table of cambers for bridge trusses.">
+<tr><td align="center">Span. <br />feet.</td><td align="center">Camber. <br />Inches.</td>
+<td align="center">Span. <br />Feet.</td><td align="center">Camber. <br />Inches.</td>
+<td align="center">Span. <br />Feet.</td><td align="center">Camber. <br />Inches.</td>
+<td align="center">Span. <br />Feet.</td><td align="center">Camber. <br />Inches.</td></tr>
+<tr><td align="center"> 25</td><td align="center">0.8</td><td align="center">75</td>
+<td align="center">2.5</td><td align="center">175</td><td align="center">5.8</td>
+<td align="center">275</td><td align="center">9.2</td></tr>
+<tr><td align="center"> 30</td><td align="center">1.0</td><td align="center">100</td>
+<td align="center">3.3</td><td align="center">200</td><td align="center">6.7</td>
+<td align="center">300</td><td align="center">10.0</td></tr>
+<tr><td align="center"> 50</td><td align="center">1.7</td><td align="center">120</td>
+<td align="center">4.0</td><td align="center">225</td><td align="center">7.5</td>
+<td align="center">325</td><td align="center">10.8</td></tr>
+<tr><td align="center"> 60</td><td align="center">2.0</td><td align="center">150</td>
+<td align="center">5.0</td><td align="center">250</td><td align="center">8.3</td>
+<td align="center">350</td><td align="center">11.7</td></tr>
+</table>
+
+<p class="heading">&nbsp;<br />TRAUTWINE'S TABLE FOR FINDING INCREASE IN LENGTH OF UPPER CHORD BEYOND THE
+LOWER CHORD ON ACCOUNT OF THE CAMBER.</p>
+
+<table border="1" cellspacing="0" cellpadding="4"
+summary="Trautwine's table for finding increase in length of upper chord beyond the lower chord on account of the camber.">
+
+<tr><td align="center">Depth of Truss.</td><td align="center">Multiply Camber by</td>
+<td align="center">Depth of Truss.</td><td align="center">Multiply Camber by</td></tr>
+<tr><td align="center">1-4 span</td><td align="center">2.00</td><td align="center">1-12 span</td>
+<td align="center">.666</td></tr>
+<tr><td align="center">1-5 &nbsp; "</td><td align="center">1.60</td><td align="center">1-13 &nbsp; "</td><td align="center">.614</td></tr>
+<tr><td align="center">1-6 &nbsp; "</td><td align="center">1.33</td><td align="center">1-14 &nbsp; "</td><td align="center">.571</td></tr>
+<tr><td align="center">1-7 &nbsp; "</td><td align="center">1.15</td><td align="center">1-15 &nbsp; "</td><td align="center">.533</td></tr>
+<tr><td align="center">1-8 &nbsp; "</td><td align="center">1.00</td><td align="center">1-16 &nbsp; "</td><td align="center">.500</td></tr>
+<tr><td align="center">1-9 &nbsp; "</td><td align="center">.888</td><td align="center">1-17 &nbsp; "</td><td align="center">.470</td></tr>
+<tr><td align="center">1-10 &nbsp; "</td><td align="center">.800</td><td align="center">1-18 &nbsp; "</td><td align="center">.444</td></tr>
+<tr><td align="center">1-11 &nbsp; "</td><td align="center">.727</td><td align="center">1-20 &nbsp; "</td><td align="center">.400</td></tr>
+</table>
+
+<p class="heading">&nbsp;<br />TABLE OF AMERICAN WOODS.</p>
+
+<table border="1" cellspacing="0" cellpadding="4"
+summary="Table Of American Woods">
+<tr><td align="center">Kind.</td><td align="center">Weight per <br />cubic foot </td>
+<td align="center" colspan="2">Resistance in lbs. <br />per square inch.</td><td align="center">Value of s.</td></tr>
+<tr><td>&nbsp;</td><td align="center">in pounds.</td><td align="center">Extension</td>
+<td align="center">Compression.</td><td>&nbsp;</td></tr>
+<tr><td align="center">White Pine.</td><td align="center">26</td><td align="center">12,000</td>
+<td align="center">6000</td><td align="center">1229</td></tr>
+<tr><td align="center">Yellow Pine.</td><td align="center">31</td><td align="center">12,000</td>
+<td align="center">6000</td><td align="center">1185</td></tr>
+<tr><td align="center">Pitch Pine.</td><td align="center">46</td><td align="center">12,000</td>
+<td align="center">6000</td><td align="center">1727</td></tr>
+<tr><td align="center">Red Pine.</td><td align="center">35</td><td align="center">12,000</td>
+<td align="center">6000</td><td align="center">1527</td></tr>
+<tr><td align="center">Virginia Pine.</td><td align="center">37</td><td align="center">12,000</td>
+<td align="center">6000</td><td align="center">1456</td></tr>
+<tr><td align="center">Spruce.</td><td align="center">48</td><td align="center">12,000</td>
+<td align="center">6000</td><td align="center">1036</td></tr>
+<tr><td align="center">Tamarack.</td><td align="center">26</td><td align="center">12,000</td>
+<td align="center">6000</td><td align="center">907</td></tr>
+<tr><td align="center">Canada Balsam.</td><td align="center">34</td><td align="center">12,000</td>
+<td align="center">6000</td><td align="center">1123</td></tr>
+<tr><td align="center">White Oak.</td><td align="center">48</td><td align="center">15,000</td>
+<td align="center">7500</td><td align="center">1743</td></tr>
+<tr><td align="center">Red Oak.</td><td align="center">41</td><td align="center">15,000</td
+><td align="center">7600</td><td align="center">1687</td></tr>
+<tr><td align="center">Birch.</td><td align="center">44</td><td align="center">15,000</td>
+<td align="center">7000</td><td align="center">1928</td></tr>
+<tr><td align="center">Ash.</td><td align="center">38</td><td align="center">16,000</td>
+<td align="center">8100</td><td align="center">1795</td></tr>
+<tr><td align="center">Hickory.</td><td align="center">51</td><td align="center">15,000</td>
+<td align="center">7200</td><td align="center">2129</td></tr>
+<tr><td align="center">Elm.</td><td align="center">45</td><td align="center">16,000</td>
+<td align="center">8011</td><td align="center">1970</td></tr>
+</table>
+
+<p>&nbsp;<br />The above table is compiled from a much fuller one in Vose's
+Treatise on R.R. Construction.</p>
+
+<p class="heading">&nbsp;<br />TABLE OF BOLTS AND NUTS CALCULATED FOR A
+WORKING STRAIN OF 15,000 LBS. PER
+SQUARE INCH OF SECTION.</p>
+
+<table border="1" cellspacing="0" cellpadding="4"
+summary="Table of bolts and nuts calculated for a working strain of 15,000 lbs. per square inch of section">
+<tr><td align="center">Diameter. <br />Inches.</td><td align="center">Area.  Sq. <br />inches.</td>
+<td align="center">Strength in <br />Pounds</td><td align="center">Weight <br />per Foot.</td>
+<td align="center">Square <br />nut.</td><td align="center">Thick's <br />of nut.</td>
+<td align="center">No. thr's. <br />per inch.</td></tr>
+<tr><td align="center">&frac12;</td><td align="center">.19635</td><td align="center">2940</td><td align="center">0.66</td>
+<td align="center">1&frac14; in</td><td align="center">&frac34; in</td><td align="center">12 </td></tr>
+<tr><td align="center">&#8541;</td><td align="center">.30680</td><td align="center">4602</td><td align="center">1.03</td>
+<td align="center">1&#8540;</td><td align="center">&frac34;</td><td align="center">10 </td></tr>
+<tr><td align="center">&frac34;</td><td align="center">.44179</td><td align="center">6630</td><td align="center">1.49</td>
+<td align="center">1&frac12;</td><td align="center">&#8542;</td><td align="center">10 </td></tr>
+<tr><td align="center">&#8542;</td><td align="center">.60132</td><td align="center">9019</td><td align="center">2.03</td>
+<td align="center">1&frac34;</td><td align="center">1</td><td align="center">9 </td></tr>
+<tr><td align="center">1</td><td align="center">.78540</td><td align="center">11775</td><td align="center">2.65</td>
+<td align="center">2</td><td align="center">1</td><td align="center">8 </td></tr>
+<tr><td align="center">1&#8539;</td><td align="center">.99402</td><td align="center">14910</td><td align="center">3.36</td>
+<td align="center">2</td><td align="center">1&#8539;</td><td align="center">7</td></tr>
+<tr><td align="center">1&frac14;</td><td align="center">1.2272</td><td align="center">18405</td><td align="center">4.17</td>
+<td align="center">2&frac14;</td><td align="center">1&frac14;</td><td align="center">7</td></tr>
+<tr><td align="center">1&#8540;</td><td align="center">1.4849</td><td align="center">22260</td><td align="center">5.02</td>
+<td align="center">2&frac12;</td><td align="center">1&#8540;</td><td align="center">6</td></tr>
+<tr><td align="center">1&frac12;</td><td align="center">1.7671</td><td align="center">25505</td><td align="center">5.97</td>
+<td align="center">2&frac34;</td><td align="center">1&frac12;</td><td align="center">6 </td></tr>
+<tr><td align="center">1&#8541;</td><td align="center">2.0739</td><td align="center">31095</td><td align="center">7.01</td>
+<td align="center">2&#8542;</td><td align="center">1&#8541;</td><td align="center">5 </td></tr>
+<tr><td align="center">1&frac34;</td><td align="center">2.4053</td><td align="center">36075</td><td align="center">8.13</td>
+<td align="center">3</td><td align="center">1&frac34;</td><td align="center">5</td></tr>
+<tr><td align="center">1&#8542;</td><td align="center">2.7612</td><td align="center">41415</td><td align="center">9.33</td>
+<td align="center">3&frac14;</td><td align="center">1&#8542;</td><td align="center">4&frac12;</td></tr>
+<tr><td align="center">2</td><td align="center">3.1416</td><td align="center">47130</td><td align="center">10.62</td>
+<td align="center">3&frac12;</td><td align="center">2</td><td align="center">4&frac12;</td></tr>
+<tr><td align="center">2&#8539;</td><td align="center">3.5166</td><td align="center">53190</td><td align="center">12.00</td>
+<td align="center">3&frac34;</td><td align="center">2&#8539;</td><td align="center">4 </td></tr>
+<tr><td align="center">2&frac14;</td><td align="center">3.9761</td><td align="center">59640</td><td align="center">13.40</td>
+<td align="center">4</td><td align="center">2&frac14;</td><td align="center">4 </td></tr>
+<tr><td align="center">2&#8540;</td><td align="center">4.4301</td><td align="center">66450</td><td align="center">15.00</td>
+<td align="center">4&#8539;</td><td align="center">2&#8540;</td><td align="center">4 </td></tr>
+<tr><td align="center">2&frac12;</td><td align="center">4.9087</td><td align="center">73620</td><td align="center">16.70</td>
+<td align="center">4&frac14;</td><td align="center">2&frac12;</td><td align="center">3&frac12;</td></tr>
+<tr><td align="center">2&#8541;</td><td align="center">5.4119</td><td align="center">81178</td><td align="center">18.20</td>
+<td align="center">4&frac12;</td><td align="center">2&#8541;</td><td align="center">3&frac12;</td></tr>
+<tr><td align="center">2&frac34;</td><td align="center">5.9396</td><td align="center">89094</td><td align="center">20.00</td>
+<td align="center">4&frac34;</td><td align="center">2&frac34;</td><td align="center">3&frac12;</td></tr>
+<tr><td align="center">2&#8542;</td><td align="center">6.4918</td><td align="center">97377</td><td align="center">21.90</td>
+<td align="center">5</td><td align="center">2&#8542;</td><td align="center">3</td></tr>
+<tr><td align="center">3</td><td align="center">7.0686</td><td align="center">106029</td><td align="center">23.80</td>
+<td align="center">5&frac14;</td><td align="center">3</td><td align="center">3 </td></tr>
+<tr><td align="center">3&frac14;</td><td align="center">8.2958</td><td align="center">124437</td><td align="center">27.90</td>
+<td align="center">5&frac34;</td><td align="center">3&frac14;</td><td align="center">3 </td></tr>
+<tr><td align="center">3&frac12;</td><td align="center">9.6211</td><td align="center">144316</td><td align="center">32.40</td>
+<td align="center">6</td><td align="center">3&frac12;</td><td align="center">2&frac12; </td></tr>
+</table>
+
+<p class="heading">&nbsp;<br />TABLE OF SAFE WORKING LOAD IN LBS., FOR
+HOLLOW CAST-IRON COLUMNS.</p>
+<span class="ind65">[<i>G.L. Vose.</i>]</span>
+<p>&nbsp;</p>
+
+
+<table border="1" cellspacing="0" cellpadding="4"
+summary="Table of safe working load in lbs., for hollow cast-iron columns">
+<tr><td align="center"> Outside  Diameter</td><td align="center" colspan="7">Length or height in Feet</td><td align="center">Metal Thickness</td></tr>
+
+<tr><td align="center">in inches.</td><td align="center">6</td><td align="center">8</td><td align="center">10</td><td align="center">12</td><td align="center">15</td><td align="center">18</td><td align="center">20</td><td align="center">in inches.</td></tr>
+
+<tr><td align="center">3</td><td align="center">16000</td><td align="center">14000</td>
+<td align="center">13000</td><td align="center">11000</td><td align="center">9000</td><td align="center">7000</td>
+<td align="center">6000</td><td align="center">&#8540;</td></tr>
+
+<tr><td align="center">4</td><td align="center">30000</td><td align="center">29000</td>
+<td align="center">26000</td><td align="center">24000</td><td align="center">22000</td><td align="center">18000</td>
+<td align="center">16000</td><td align="center">&frac12; </td></tr>
+
+<tr><td align="center">5</td><td align="center">50000</td><td align="center">37000</td>
+<td align="center">45000</td><td align="center">42000</td><td align="center">39000</td><td align="center">37000</td>
+<td align="center">31000</td><td align="center">&#8541; </td></tr>
+
+<tr><td align="center">6</td><td align="center">59000</td><td align="center">57000</td>
+<td align="center">55000</td><td align="center">52000</td><td align="center">49000</td><td align="center">44000</td>
+<td align="center">41000</td><td align="center">&frac34; </td></tr>
+
+<tr><td align="center">7</td><td align="center">101000</td><td align="center">99000</td>
+<td align="center">96000</td><td align="center">92000</td><td align="center">88000</td><td align="center">81000</td>
+<td align="center">76000</td><td align="center">13/16</td></tr>
+
+<tr><td align="center">8</td><td align="center">131000 </td><td align="center">129000 </td>
+<td align="center">126000 </td><td align="center">122000 </td><td align="center">118000 </td><td align="center">109000 </td>
+<td align="center">105000</td><td align="center">&#8542;</td></tr>
+
+<tr><td align="center">9</td><td align="center">169000 </td><td align="center">167000 </td>
+<td align="center">164000 </td><td align="center">160000 </td><td align="center">156000 </td><td align="center">146000 </td>
+<td align="center">141000</td><td align="center">1</td></tr>
+
+<tr><td align="center">10</td><td align="center">210000 </td><td align="center">200000 </td>
+<td align="center">200000 </td><td align="center">200000 </td><td align="center">190000 </td><td align="center">180000 </td>
+<td align="center">180000</td><td align="center">1&#8539;</td></tr>
+
+<tr><td align="center">11</td><td align="center">250000 </td><td align="center">250000 </td>
+<td align="center">240000 </td><td align="center">240000 </td><td align="center">240000 </td><td align="center">230000 </td>
+<td align="center">220000</td><td align="center">1&frac14;</td></tr>
+
+<tr><td align="center">12</td><td align="center">300000 </td><td align="center">300000 </td>
+<td align="center">290000 </td><td align="center">290000 </td><td align="center">290000 </td><td align="center">270000 </td>
+<td align="center">270000</td><td align="center">1&frac12;</td></tr>
+
+<tr><td align="center">14</td><td align="center">450000 </td><td align="center">430000 </td>
+<td align="center">410000 </td><td align="center">380000 </td><td align="center">370000 </td><td align="center">350000 </td>
+<td align="center">330000</td><td align="center">1&frac34;</td></tr>
+
+<tr><td align="center">16</td><td align="center">520000 </td><td align="center">500000 </td>
+<td align="center">480000 </td><td align="center">460000 </td><td align="center">440000 </td><td align="center">420000 </td>
+<td align="center">400000</td><td align="center">2</td></tr>
+
+<tr><td align="center">18</td><td align="center">650000 </td><td align="center">630000 </td>
+<td align="center">610000 </td><td align="center">590000 </td><td align="center">560000 </td><td align="center">520000 </td>
+<td align="center">470000</td><td align="center">2&frac12;</td></tr>
+
+<tr><td align="center">20</td><td align="center">800000 </td><td align="center">760000 </td>
+<td align="center">740000 </td><td align="center">690009 </td><td align="center">650000 </td><td align="center">590000 </td>
+<td align="center">540000</td><td align="center">3</td></tr>
+</table>
+
+<p>&nbsp;</p>
+
+<div class="figcenter">
+<img src="images/plate-iv.gif" width="526" height="762"  alt="Plate IV" title="Plate IV" />
+</div>
+
+<p>&nbsp;</p>
+
+<pre>
+TRANSCRIBER'S NOTES:
+
+DISCLAIMER: This document should NOT be used to engineer any bridge projects!
+It is possible that there are further errors in the information that were not caught.
+
+The page numbers listed below are project page numbers.
+(The original book used Roman numerals to number the pages.)
+
+Note that the book uses the "long" ton equal to 2,240 pounds.
+
+CORRECTIONS MADE:
+ 1. Page 8 - the formula for "d" must use a cube root, which is how it is shown here,
+     but the '3' to indicate a cube root is not found in the original document.
+ 2. Page 8 - typo in word 'sectien' - changed to 'section'.
+ 3. Page 10 - Value for working comp. strength of cast iron in the table had a typo (25,v00).
+     Since other values use round numbers, it is assumed the value should be 25,000.
+ 4. Page 10 - Two other typos. Changed 'the the' to 'the', and in table heading, original
+     word was 'detrution', changed to correct spelling of 'detrusion'.
+ 5. Page 12 - changed 'woooden' to 'wooden'.
+ 6. Page 13 - Example II - In the calculations, the intermediate value in the book was
+     printed as the square root of 67.2. The left part is correct, but reduces to the square root
+     of 268.8, and that is ~16.395. So I have corrected the intermediate value.
+ 7. Page 13 - Because the original page scan cut off the text on the right edge, I have
+     made assumptions on what text was missing. Because the scans came from an
+     outside source, I could not get the missing information, which was the words at the
+     end of Example II, and words in the last paragraph of the page.
+ 8. Page 14 - Three typos found: 'dimensiens' for 'dimensions', 'betng' for 'being',
+     and 'ars' for 'are'.
+ 9. Page 17 - a value in a formula was printed as 6000, but in the context of the other
+     information, particularly the example immediately following, the value was believed
+     to be incorrect, and was changed to 5000.
+10. Page 23 - The value of 388 sq. inches at the top of the page in the book is incorrect;
+     3 x 8 x 12 = 288, so has been corrected.
+11. Page 24 - Rods section, numerical value appeared to be 15.000 in book, but from
+     context, must be 15,000 instead.
+12. Page 28 - Typos: changed 'Trautwine's Edgineer's Pocket-Bood' to Trautwine's
+     Engineer's Pocket-Book'; corrected  'af' to 'as', 'bracas' to 'braces'.
+13. Page 30 - Apparent typo in the table at the bottom of page.  Value for Center Brace
+     size for 200' span was shown as '8 x 1', believed from context of table to be '8 x 10'.
+14. Page 33 - table of dimensions of a Pratt Truss, last column, row starting with 150,
+     the original says 8--1-1/8, this is believed to be, and has been changed to, 3--1-1/8.
+15. Page 37 - The five formulas with square roots were incorrectly printed in the book,
+     multiplying the terms inside the square root instead of adding them, which is obviously
+     incorrect per the Pythagorean theorem of right triangles.
+16. Page 38: The fifth ratio in the group of five near the top of the page must start with 20,
+     not 10 as in the book
+17. Page 38 - The equation for W as printed on this page is not consistent with that
+     found on pages 18 to 24, so has been corrected from 'bd^2' to 'bd^3'.
+18. Page 39 - arch brace truss table heading typo - changed 'FOE' to 'FOR'.
+</pre>
+
+
+
+
+
+
+
+
+<pre>
+
+
+
+
+
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@@ -0,0 +1,2112 @@
+The Project Gutenberg EBook of Instructions on Modern American Bridge
+Building, by G. B. N. Tower
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: Instructions on Modern American Bridge Building
+
+Author: G. B. N. Tower
+
+Release Date: February 2, 2005 [EBook #14873]
+
+Language: English
+
+Character set encoding: ASCII
+
+*** START OF THIS PROJECT GUTENBERG EBOOK AMERICAN BRIDGE BUILDING ***
+
+
+
+
+Produced by Curtis Weyant, Ronald Holder and the PG Online Distributed
+Proofreading Team.
+
+
+
+
+
+
+INSTRUCTIONS
+
+ON
+
+MODERN AMERICAN
+
+BRIDGE BUILDING.
+
+WITH
+
+PRACTICAL APPLICATIONS AND EXAMPLES,
+
+ESTIMATES OF QUANTITIES, AND
+VALUABLE TABLES.
+
+Illustrated by four Plates and Thirty Figures.
+
+BY G.B.N. TOWER,
+
+CIVIL AND MECHANICAL ENGINEER,
+
+_Formerly Chief Engineer U.S. Navy, and late Chandler Instructor in Civil_
+_Engineering at Dartmouth College._
+
+BOSTON:
+
+A. WILLIAMS & COMPANY,
+
+135 WASHINGTON STREET.
+
+1874.
+
+  Entered according to act of Congress, in the year 1874, by
+  A. WILLIAMS & CO.,
+ in the office of the Librarian of Congress, at Washington, D.C.
+
+
+
+
+PREFACE.
+
+
+This little treatise was written for the purpose of supplying a want
+felt by the author while giving instruction upon the subject. It was
+intended for an aid to the young Engineer, and is not to be considered
+as a complete substitute for the more elaborate works on the subject.
+
+The first portion of this work mentions the various strains to which
+beams are subjected, and gives the formulae used in determining the
+amount of those strains, together with a few examples to illustrate
+their application, and also the method of calculating a simple truss.
+
+The second portion names and explains the various members of a Bridge
+Truss, and, by means of examples, shows the method of calculating the
+strains upon the various timbers, bolts, etc., as well as their proper
+dimensions; and gives, in addition, several useful tables.
+
+The explanatory plates, which are referred to freely throughout the
+work, are believed to be amply sufficient for the purpose intended.
+
+So much has been written on this subject that it is next to impossible
+to be wholly original, and no claim of that nature is preferred. It is
+simply an arrangement of ideas, gleaned from the various works of
+standard authorities, and modified by the author's practice, embodied
+in book form. To give a correct list of all the books consulted would
+be simply impossible;--but it is well to state that the Hand-book of
+Railroad Construction, by Prof. G.L. Vose, under whom the author
+served as an Engineer, has been used as authority in many cases where
+there has been a difference of opinions among other authors. Some
+parts have been quoted entirely; but due credit has been given, it is
+believed, wherever such is the case.
+
+It is not claimed that this little work covers the whole ground, but
+it is intended to describe, and explain thoroughly, three or four of
+the more prominent styles of Truss, leaving the other forms of Wooden
+Bridges to a subsequent volume.
+
+Abutments and Piers, as well as Box and Arch Culverts, belonging more
+properly to masonry, will be treated of hereafter under that head.
+
+Iron Bridges form a distinct class, and may be mentioned separately at
+some future period.
+
+If this small volume should lead the student of Engineering to examine
+carefully the best Bridges of modern practice, and study the larger
+scientific works on this art, the author will feel satisfied that his
+efforts have not been entirely in vain.
+
+_Cambridge, February 23, 1874._
+
+
+
+
+TOWER'S
+
+Modern American Bridge Building.
+
+
+
+
+BRIDGE BUILDING
+
+
+The simplest bridge that can be built, is a single beam, or stick of
+timber, spanning the opening between the abutments--but this is only
+of very limited application--(only for spans of 20 feet and less)
+owing to the rapid increase in sectional dimensions which is required
+as the span becomes greater.
+
+Next comes the single beam supported by an inclined piece from each
+abutment meeting each other at the middle point of the under side of
+the beam--or, another arrangement, of two braces footing securely on
+the beam and meeting at a point above the middle point of the beam,
+which is suspended from the apex of the triangle formed by them, by
+means of an iron rod--These arrangements may be used up to 50 feet.
+For any span beyond 50 feet, modifications of this arrangement are
+used which will be described hereafter. Now let us investigate shortly
+the different strains that the various parts of a bridge have to
+bear--and the strength of the materials used. The theory of strains in
+bridge trusses is merely that of the Composition and Resolution of
+Forces. The various strains, to which the materials of a bridge are
+subjected--are compression, extension and detrusion.
+
+Wood and Iron are the materials more generally employed in bridge
+construction--and in this pamphlet we shall take the following as the
+working strength of the materials--per square inch of section.
+
+             Tension.  Compression.  Detrusion.
+
+Wood,          2000       1000          150
+
+Wro't Iron,   15000      11000
+
+Cast Iron,     4500      25000
+
+
+=Tension.= If a weight of 2000 lbs. were hung to the lowest end of a
+vertical beam, so that the line of action of the weight and axis of
+the beam formed one and the same straight line--the tension on the
+beam would be 2000 lbs. But, if the beam were inclined, and the force
+acted in a vertical direction, then the strain would be increased in
+the ratio of the increase of the diagonal of inclination over the
+vertical;--suppose the beam is 20 ft. long and inclined at an angle of
+45 deg.--and let 2000 lbs., as before, be suspended from its lower end.
+Now the diagonal being 20 deg.,--the vertical will be 14.014 ft.--and the
+strain will be found as follows,--
+
+  14.014 : 20 :: 2000 : 2854--lbs.
+
+The greater the angle of inclination from the horizontal, the less the
+strain from a given load--and when the beam is vertical the weight
+causes the least strain.
+
+
+=Compression.= If we load a vertical post with a weight of 2000 lbs.,
+the strain of compression exerted upon the post will be 2000 lbs. Now,
+if we incline the post--the strain will be increased, as we have shown
+above under the head of tension, and in like manner, dependent upon
+the inclination.
+
+But when wood, iron, or any other material is used for a pillar or
+strut, it has not only to resist a crushing force, but also a force
+tending to bend or bulge it laterally.
+
+A post of circular section with a length of 7 or 8 diameters will not
+bulge with any force applied longitudinally, but will split. But if
+the length exceeds this limit--it will be destroyed by an action
+similar to that of a transverse strain.
+
+A cast iron column of thirty diameters in length, is fractured by
+bending; when the length is less than this ratio--by bending and
+splitting off of wedge shaped pieces. But by casting the column
+hollow, and swelling it in the middle, its strength is greatly
+increased.
+
+Barlow's formula for finding the weight that can be sustained by any
+beam, acting as a pillar or strut, before bending, is:--
+
+  WL squared                    bd cubed x 80 E
+  ---- = bd cubed, whence W = -----------
+  80 E                       L squared
+
+[TeX: $\frac{WL^2}{80 E} = {bd^3}$, whence $W = \frac{{bd^3} x 80 E}{L^2}$]
+
+now, having the weight given, and assuming the dimensions of
+the cross-section--we shall have
+
+          -----
+         / WL squared              WL squared
+  d =   cubed/ -----,  and b = ------
+      \/  80 Eb           80 Ed cubed
+
+[TeX: $d = \sqrt[3]{\frac{WL^2}{80 EB}}$, and $b = \frac{WL^2}{80 ED^3}$]
+
+in the above formulae,
+
+  W = weight in pounds.
+  L = length in feet.
+  E = a constant.
+  b = breadth in inches.
+  d = depth in inches.
+
+
+=Transverse Strains.= The strain caused by any weight, applied
+transversely, to a beam supported at both ends, is directly as the
+breadth, and square of the depth, and inversely as the length. It
+causes the beam to be depressed towards the middle of its length,
+forming a curve, concave to the horizontal and below it. In assuming
+this form--the fibres of the upper part of the beam are compressed,
+and those of the lower part are extended--consequently there must be
+some line situated between the upper and lower surfaces of the beam
+where the fibers are subjected to neither of these two forces, this
+line is called the _neutral axis_.
+
+These two strains of compression and extension must be equal in
+amount--and upon the relative strength of the material to resist these
+strains, as well as its form and position, the situation of this axis
+depends. If wood resists a compression of 1000 lbs. per square inch of
+section, and a tension of 2000 lbs. the axis will be twice as far from
+the top as from the bottom in a rectangular beam.
+
+The following table by Mr. G.L. Vose gives, with sufficient accuracy
+for practice, the relative resisting powers of wood, wrought, and cast
+iron, with the corresponding positions of the axis.
+
+                                                 Dist. of axis
+               Resistance  Resistance            from top in
+                   to          to                frac's of
+  Material.    Extension.  Compression.  Ratio.  the depth.
+
+  Wrought Iron,    90          66        90/66   90/156, or 0.58.
+
+  Cast Iron,       20         111       20/111   20/131, or 0.15.
+
+  Wood,             2           1          2/1    2/3, or 0.66.
+
+
+Thus we see that the resistance of a beam to a cross strain, as well
+as to tension and compression, is affected by the incompressibility
+and inextensibility of the material.
+
+The formula for the dimensions of any beam to support a strain
+transversely is
+
+      4 bd squared
+  S = ----
+       l
+
+[TeX: $S = \frac{4 bd^2}{l}$]
+
+  S = the ultimate strength in lbs.
+  b = the breadth in inches.
+  d = the depth in inches.
+  l = the length in inches.
+
+
+=Detrusion.= Detrusion is the crushing against some fixed point, such
+as obtains where a brace abuts against a chord, or where a bridge
+rests on a bolster; and the shearing of pins, bolts and rivets, also
+comes under this head.
+
+
+=General Abstract.= The resistance to the above mentioned strains
+varies as the area of the cross section; so that by doubling the area
+we double the strength. Any material will bear a much greater strain
+for a short time than for a long one. The working strength of materials,
+or the weight which does not injure them enough, to render them unsafe,
+is a mooted point, and varies, according to the authority, from 1-3
+to 1-10 of the ultimate strength. The ratio of the ultimate strength
+to the working strength is called the _factor of safety_.
+
+The following is a table of ultimate and working strengths of
+materials, and factors of safety:
+
+  Weight                Ult.    Ult.   Working Strengths Factor  Safety.
+  in lbs.  Materials.   Ext.    Comp.  Exten.    Comp.   Tension  Comp.
+
+    30    Wood.        14,000   7,000   2,000    1,000      7      7
+   480    Wrou't Iron. 60,000  64,000  15,000   12,000      4      5.33
+   450    Cast Iron.   18,000 100,000   4,500   25,000      4      4
+
+
+=Lateral Adhesion.= Lateral adhesion is the resistance offered by the
+fibres to sliding past each other in the direction of the grain, as
+when a brace is notched into a chord, or tie beam, at its foot, it is
+prevented by the lateral adhesion of the fibres from crowding off the
+piece, to the depth of the notch, against which it toes. Barlow's
+experiments give the lateral adhesion of fir as 600 lbs. per square
+inch, and the factor of safety employed varies in practice from 4 to
+6, giving a working strength of from 150 to 100 lbs. per square inch.
+
+
+=TABLE OF COMPRESSIVE RESISTANCE OF TIMBER.=
+
+  Length      Safety       Length    Safety     Length    Safety
+  given in    Weig't in   given in   Wt. in    given in   Wt. in
+  Diameters.  Pounds.    Diameters.  Pounds.  Diameters.  Pounds.
+
+     6         1000         24         440       42         203
+     8          960         26         394       44         185
+    10          910         28         358       46         169
+    12          860         30         328       48         155
+    14          810         32         299       50         143
+    16          760         34         276       52         132
+    18          710         36         258       54         122
+    20          660         38         239       56         114
+    22          570         40         224       58         106
+                                                 60          99
+
+In tensional strains, the length of the beam does not affect the
+strength; but in the beams submitted to compression, the length is a
+most important element, and in the table given above, the safety
+strains to which beams may be subjected, without crushing or bending,
+has been given for lengths, varying from 6 to 60 diameters.
+
+
+PRACTICAL RULES.
+
+=Tensional Strain.=
+
+  Let T = whole tensional strain.
+  "   S = strength per square inch.
+  "   a = sectional area in inches.
+  Then we have T = Sa.
+
+Now to find the necessary sectional area for resisting any strain, we
+have the following general formula:
+
+       T
+  a = ---
+       S
+
+[TeX: $a = \frac{T}{S}$]
+
+or, by substituting the working strengths for the various materials in
+the formula, we have for wood,
+
+                  a = T/2000
+
+  Wrought Iron,   a = T/1500
+
+  Cast Iron,      a = T/4500
+
+But, in practice, cast iron is seldom used except to resist
+compression.
+
+=Strains of Compression.= Allowing the same letters to denote the
+same things as above, we have for
+
+  Wood, a = T/1000
+
+  Wrought Iron, a = T/12000
+
+  Cast Iron, a = T/25000
+
+As this pamphlet has to do with wooden bridges only, nothing will be
+said of the proper relative dimensions of cast-iron columns to sustain
+the strains to which they may be subjected, but a table of the
+strength of columns will be found further on.
+
+=Transverse Strains.=
+
+  Let W = breaking weight in lbs.
+   "  s = constant in table.
+   "  b = breadth in inches.
+   "  d = depth in inches.
+   "  L = length in inches.
+
+Then, for the power of a beam to resist a transverse strain, we shall
+have,
+
+      4 sbd squared
+  W = ------
+        L
+
+[TeX: $W = \frac{4 sbd^2}{L}$]
+
+This formula has been derived from experiments made by the most
+reliable authorities.
+
+The constant, 1250, adopted for wood in the following formula, is an
+average constant, derived from the table, of those woods more commonly
+used.
+
+Now to reduce the formula to the most convenient shape for use, we
+substitute the value of s, and we have
+
+      4 x 1250 bd squared
+  W = ------------,
+           L
+
+[TeX: $W = \frac{4 \times 1250 bd^2}{L}$]
+
+or
+
+      5000 bd squared
+  W = --------.
+          L
+
+
+[TeX: $W = \frac{5000 bd^2}{L}$]
+
+But, to reduce the load to the proper working strain, we must divide
+this equivalent by 4, the factor of safety, and we shall have
+
+      5000 bd squared
+  W = --------.
+         4L
+
+[TeX: $W = \frac{5000 bd^2}{4 L}$]
+
+Let us apply the formula--
+
+  Case I. Given a span of 14 feet,
+                a breadth of 8 inches,
+                a depth of 14 inches.
+
+Required the safe load.
+
+                  5000 bd squared
+  The formula W = --------
+                     4L
+
+[TeX: $W = \frac{5000 bd^2}{4 L}$]
+
+becomes, by substitution,
+
+      5000 x 8 x 196
+  W = -------------- = 11.666 lbs.
+          4 x 8
+
+[TeX: $W = \frac{5000 \times 8 \times 196}{4 \times 168} = 11,666$ lbs.]
+
+  Case II. Given the safety load 18000 lbs.
+                 the breadth 9 inches,
+                 the length 14 feet.
+
+Required the depth.
+From the above formula we have
+
+         -------
+        / W X 4L
+  d =  /  ------
+     \/   5000 b
+
+
+[TeX: $d = \sqrt{\frac{w \times 4L}{5000 b}}$]
+
+substituting
+
+         ----------------
+        / 18000 x 168 x 4      ------
+  d =  /  --------------- =   / 268.8 = 16, inches nearly.
+     \/      5000 x 9       \/
+
+
+[TeX: $d = \sqrt{\frac{1800 \times 168 \times 4}{5000 \times 9}}
+ = \sqrt{268.8} = 16$]
+
+  Case III. Given the safety load 22,400 lbs.
+  the depth 18 inches.
+  the length 14 feet.
+
+Required the breadth.
+Deriving b from the foregoing, we have,
+
+        W x 4L
+  b = ----------
+      5000 x d squared
+
+[TeX: $b = \frac{W \times 4L}{5000 \times d^2}$]
+
+substituting
+
+      22400 x 4 x 168
+  b = --------------- = 9.3 inches nearly.
+        5000 x 324
+
+[TeX: $b = \frac{22400 \times 4 \times 168}{5000 \times 324} = 9.3$]
+
+For a cast iron beam or girder--Mr. Hodgkinson found from numerous
+carefully conducted experiments that, by arranging the material in the
+form of an inverted T--thus creating a small top flange as well as the
+larger bottom one, the resistance was increased, per unit of section,
+over that of a rectangular beam, in the ratio of 40 to 23.
+
+In this beam the areas of the top and bottom flanges are inversely
+proportional to the power of the iron to resist compression and
+extension. Mr. Hodgkinson's formula for the dimensions of his girder,
+is
+
+       26 ad
+  W = ------
+         L
+
+[TeX: $W = \frac{26 ad}{L}$]
+
+The factor of safety being 6 for cast iron beams--the formula for the
+working load will be,
+
+       26 ad
+  W = ------
+        6 L
+
+[TeX: $W = \frac{26 ad}{6 L}$]
+
+and, to find area of lower flange, we shall have
+
+      6 WL
+  a = ----
+      26 d
+
+[TeX: $a = \frac{6 WL}{26 d}$]
+
+The general proportions of his girders are as follows:
+
+  Length,             16
+  Height,              1
+  Area Top Flange,     1.0
+  Area Bottom Flange,  6.1
+
+In the above formula for cast iron beams,
+
+  W = weight in tons.
+  a = area in square inches of bottom flange.
+  d = depth in inches.
+  h = length in inches.
+
+The web uniting the two flanges must be made solid--as any opening, by
+causing irregularity in cooling, would seriously affect the strength
+of the beam.
+
+_Example._--Required the dimensions of a Hodgkinson girder--for a span
+of 60 feet--with a load of 10 tons in the centre.
+
+      6 x 10 x 60 x 12
+  a = ---------------- = 37 inches nearly.
+            60 x 12
+       26 x -------
+              16
+
+[TeX: $a = \frac{6 \times 10 \times 60 \times 12}{26 \times \frac{60
+\times 12}{16}} = 37$]
+
+and the area of the top flange will be,
+
+  37
+  -- = 6.16 inches--
+  6
+
+[TeX: $\frac{37}{6} = 6.16$]
+
+so that our dimensions will be as follows:
+
+  Length,              30 feet.
+  Depth,               45 inches.
+  Area Top Flange,      6.16 inches.
+  Area Bottom Flange,  37 inches.
+
+[Illustration: Pl. 1.]
+
+The thickness of web is usually a little greater at the bottom than
+at the top, and varies from 1/14 to 1/24 of the depth of the girder.
+The bottom rib is usually made from six to eight times as wide as it
+is thick, and the top rib from three to six times as wide as thick, so
+that, in the example above given, we could have as dimensions for the
+parts
+
+  Top Flange,     4 1/4 x 1 1/2 inches nearly.
+  Bottom Flange,  6 x 2 1/2 inches nearly.
+  Web,            1 1/2 inches thick.
+
+The simplest bridge, consisting of a single stick, to span openings of
+20 feet and under, is calculated according to the formula
+
+          ------
+         /  4WL
+  d =   / ------ --
+      \/  5000 b
+
+
+[TeX: $d = \sqrt{\frac{4 WL}{5000 b}}$]
+
+_Example._--The depth of a beam, of 12 feet span and 12
+feet wide, to support a load of 22400 lbs. will be
+
+          ------       --------------------
+         / 4WL        / 4 X 22400 x 12 x 12      -------
+  d =   / ------ =   /  ------------------- =   / 215.04 = 15 in. nearly
+      \/  5000 b   \/        5000 x 12        \/
+
+
+[TeX: $d = \sqrt\frac{4 WL}{5000 b}} = \sqrt\frac{4 \times 22400
+\times 12 \times 12}{5000 \times 12} = \sqrt{215.04} = 15$]
+
+The following Table was calculated by the above rule--and the
+dimensions altered according to the actual practice of the writer.
+
+  Span.  Breadth.  Depth.
+
+    4       10       12
+    6       10       12
+    8       12       12
+   10       12       13
+   12       12       15
+   16       12       18
+   18       12       20
+   20       12       22
+
+These dimensions will give ample strength and stiffness. Fig. 1, Plate
+I. gives an illustration of this kind of bridge--in which a, a, are
+the bolsters or wall plates, shown in section, to which the bridge
+beams are notched and bolted. Fig. 1, A, Plate I, shows the method of
+diagonally bracing these beams by planks, dimensions of which in
+general use are 6 to 8 by 2 to 3 inches. The track should rest on
+ties, about 6 inches by 8 or 10 inches--the same bolt confining the
+ends of the ties and diagonal braces when practicable. These ties
+should be notched on the string pieces 2 or 3 inches--without cutting
+the stringers. Below is a table giving general dimensions, in inches,
+of the several parts of a bridge of this description.
+
+  Span.  Bolsters.  Stringers.   Ties.   Braces.   Diameter of Bolts.
+
+    4     12 x 12    10 x 12     6 x 8    2 x 8         1 inch.
+   10     12 x 12    12 x 13     6 x 8    2 x 8         1  "
+   16     14 x 14    12 x 18     6 x 8    2 x 8         1  "
+   20     14 x 14    12 x 22     6 x 8    2 x 8         1  "
+
+
+Each bolt must have a washer under the head, and also under the nut.
+For a span of from 15 to 30 feet, we can use the combination shown in
+Plate II, Fig. 3. The piece A F must have the same dimensions as a
+simple string piece of a length A B--so that it may not yield between
+B and either of the points A or D. The two braces D F and E F must be
+stiff enough to support the load coming upon them. Suppose the weight
+on a pair of drivers of a Locomotive to be 10 tons, then each side
+must bear 5 tons, and each brace 2-1/2 tons = 2-1/2 x 2240 = 5600 lbs.
+Now, to allow for sudden or extra strains, call 8000 lbs. the strain
+to be supported by each brace, and, accordingly, 8 square inches of
+sectional area would be sufficient for compression only; but, as the
+brace is inclined, the strain is increased. Let the vertical distance
+from A to D be 10 ft., and, calling the span 30 ft.--A B will be 15
+ft.--from whence D F must be 18 ft., then we shall have the proportion
+
+  10 : 18 :: 8000 : 14400 lbs.
+
+which would require an area of about 15 square inches of section to
+resist compression, or a piece 3x5 inches. Now, as this stick is more
+than 6 or 8 diameters in length, it will yield by bending--and
+consequently its area must be increased. The load, which a piece of
+wood acting as a post or strut will safely sustain, is found by the
+formula already given.
+
+      2240 bd cubed
+  W = --------
+         L squared
+
+[TeX: $W = \frac{2240 bd^3}{L^2}$]
+
+Now substituting 3 for b, and 5 for d, we have
+
+      2240 x 3 x 125   840000
+  W = -------------- = ------ = 2592 lbs.
+           324           324
+
+[TeX: $W=\frac{2240 \times 3 \times 125}{324}=\frac{840000}{324}=2592$]
+
+which is not enough. Using 6 for b and 8 for d, we have
+
+      2240 x 6 x 512
+  W = -------------- = 21238 lbs.
+            324
+
+[TeX: $W = \frac{2240 \times 6 \times 512}{324} = 21238$]
+
+which is something larger than is actually required, but it is no
+harm to have an excess of strength. Now in many cases this arrangement
+would be objectionable, as not affording sufficient head room on
+account of the braces--and we can as well use the form of structure
+given in Pl. I. Fig. 3, since it is evidently immaterial whether the
+point B be supported on F or suspended from it, provided we can
+prevent motion in the feet of the braces, which is done by notching
+them into the stringer at that point. This of course creates a
+tensional strain along the stringer, which is found as
+follows:--Representing the applied weight by F B, Pl. II, Fig. 2, draw
+B D parallel to F C, also D H parallel to A C--D H is the tension.
+This is the graphical construction, and is near enough for practice.
+Geometrically we have the two similar triangles A F B and D F H,
+whence
+
+  A F : D F :: A B : D H
+
+            D F x A B
+  and D H = ---------
+               A F
+
+[TeX: $DH = \frac{DF \times AB}{AF}$]
+
+This style of structure may be used up to 50 feet, but it is not
+employed for spans exceeding 30 feet in length. It is very customary
+to make the braces in pairs so as to use smaller scantling, and gain
+in lateral stiffness--the two pieces forming one brace by being
+properly blocked and bolted together. Below is given a table of
+dimensions for the various parts of this style of structure:
+
+  Span.    Rise.    Bolster.    Stringer.     Braces.     Rod.
+                                                         No. Size.
+
+   15        6      12 x 12     12 x 12       2--5 x 6    1-1/8
+   20        7      14 x 14     12 x 13       2--5 x 8    1-3/8
+   25        8      14 x 14     12 x 15       2--6 x 8    1-1/2
+   30       10      14 x 14     12 x 18       2--6 x 9    1-5/8
+
+Single Beams under each rail firmly braced laterally, and trussed by
+an iron rod, (or preferably by two iron rods,) and a post on the under
+side of the beam. The deflection of the rod is usually taken at 1\8 of
+the span. Pl. II., Fig. 1, represents this style of trussing a
+beam--which is generally used for spans of from 15 to 30 ft. Below is
+a table of dimensions for this truss with single and double rods; if
+double rods are used only half the given section will be necessary for
+each one of the pair.
+
+  Span.     Rise.      Stringer.    Post.      Rod.           Rods.
+  Feet.    In Feet.                          (single.)      (double.)
+
+   15       1-7/8      12 x 12      6 x 8    2-1/8 diam. or 1-1/2 diam.
+   20       2-1/2      12 x 14      7 x 8    2-1/2   "      1-3/4   "
+   25       3-1/8      12 x 16      8 x 8    2-3/4   "      2       "
+   30       3-3/4      13 x 18      9 x 9    3       "      2-1/8   "
+
+It is as well to tenon the post into the beam, and also strap it
+firmly with iron plates--and the end should be shod with iron to form
+a saddle for the rods to bear upon.
+
+Now if we should make a bridge, on the plan of Fig. 3, Pl. I., 75 or
+100 feet, or perhaps more, in length, the braces A F and F C, would
+not only be very long but very large and heavy, and one chief
+requisite in a good bridge is, to have all the beams so proportioned
+that they will resist all the strains acting upon them, without being
+unnecessarily large. It now becomes necessary to have a different
+arrangement of the parts of the truss in order to obtain increased
+length of span.
+
+Suppose we have a span, of 40 feet, as represented in Fig 2, Pl. I.
+Now instead of running the braces from A C until they meet in a point,
+as before we stop them at a, and c, and place the straining beam, a c,
+between them to prevent those points from approaching, suspend the
+points B and D from them, and start the braces B b and D b--and, if
+the truss were longer, would continue on in the same manner as far as
+needful. To prevent the. truss from altering its form, as shown by the
+dotted lines A' b C', and A E C, by any passing load, we insert the
+counter braces marked R.
+
+The braces A a and C c, must support all of the weight of the bridge
+and its load within the parallelogram B a c D--and the next set of
+braces, B b and D b, sustain that part of the load which comes over
+the centre of the bridge. Consequently the braces must increase in
+size from the centre towards the abutments. The rods resist the same
+pressure in amount as their braces--but being vertical, do not need
+the increase, given to the braces on account of their inclination--but
+increase simply with the strain upon them, from the centre to the ends
+of the truss.
+
+There are many forms of small bridges differing from those enumerated,
+in various minor details, but sufficient has been said to give the
+reader a fair idea of the strains upon the different parts, and how to
+arrange and proportion the materials to resist them.
+
+
+
+
+PRACTICAL RULES AND EXAMPLES IN WOODEN BRIDGE BUILDING.
+
+
+In any case that may arise, we must determine approximately the gross
+weight of the bridge and its load--as a basis, and then we can proceed
+as follows--in case of a Howe, Pratt, or Arch Brace Truss.
+
+
+=To find the dimensions of the Lower Chord.=
+
+The tension at the centre of the Lower Chord is found by _dividing the_
+_product of the weight of the whole bridge and load by the span_, by
+sight times the height--or letting T=tension in lbs., W=weight of
+bridge and load in lbs., S=span in feet, and h=rise or height--we have
+
+      W x S
+  T = ----- --.
+       8 h
+
+[TeX: $T = \frac{W \times S}{8 h}$]
+
+In this case we have taken the rise at 1/8 of the span, which is
+evidently the best ratio between those dimensions, as it equalizes
+the vertical and horizontal forces. As to the proportions of the
+_bays_ or _panels_, (or that portion of the truss bounded by two
+adjacent verticals, as struts or ties, and the chords,) the ratio of
+the rise (or the vertical distance between the centre lines of the two
+chords,) and the length on the chord should be such, that the diagonal
+truss members may make an angle of about 50 deg. with the chords; as the
+size of the timbers is increased by decreasing the angle, and, if the
+angle is increased, there are more timbers required.
+
+Mr. G.L. Vose, in his admirable work on R.R. Construction, observes
+very truly that "The braces, at the end of a long span, may be nearer
+the vertical than those near the centre, as they have more work to do.
+If the end panel be made twice as high as long, and the centre panel
+square, the intermediates varying as their distance from the end, a
+good architectural effect is produced."
+
+Now it is necessary for us to have some data from which to determine
+the approximate weight of the bridge, and also its load. These can be
+found by comparing weights of bridges in common use, as obtained from
+reports. In a small bridge of short span, the weight of the structure
+itself may be entirely neglected, because of. the very small
+proportion the strains caused by it bear to those due to the
+load;--but, in long spans, the weight becomes a very important element
+in the calculations for strength and safety--inasmuch as it may exceed
+the weight of the load.
+
+In all Bridges of 120 ft. span, about 1/3 of a ton, per foot run, will
+be the weight of each truss for a single track, including floor
+timbers--transverse bracing, &c. If the bridge were loaded with
+Locomotives only, the greatest load would be, on the whole bridge--160
+tons = 1.33 tons per ft. run of the bridge or .666 tons per ft. run of
+each truss. Now if we make the rise of the bridge 15 ft., and divide
+the span into 12 panels of 10 ft. each, we shall have for total weight
+of bridge and load 240 tons, or for a single truss 10 tons to each
+panel.
+
+
+=Lower Chords.= Now to find the tension on the Lower Chords,
+
+      W x S
+  T = ----- and supplying values, we have
+       8 h
+
+[TeX: $T = \frac{W \times S}{8 h}$]
+
+      240 x 120
+  T = --------- = 240 tons, or 537600 lbs.,
+        8 x 15
+
+[TeX: $T = \frac{240 \times 120}{8 \times 15 = 240$}
+
+for the two Lower Chords, and 1/2 of this, or 268800 lbs. for one
+chord. The Tensional Strength of timber for safety may be taken at
+2000 lbs. per square inch of section, and hence the area of timber
+required to sustain the above strain will be
+
+  268800
+  ------ = 134.4 sq. inches.
+   2000
+
+[TeX: $\frac{268800}{2000} = 134.4$]
+
+But this chord has also to sustain the transverse strains arising from
+the weights passing over it, and, as in the case of a Locomotive, the
+weight of 20 tons on 2 pair of drivers, (or 10 tons for one truss,)
+may be concentrated on the middle point of a panel--the chord must be
+so proportioned as to safely bear, as a horizontal beam, this weight.
+Suppose we take three sticks of 8" x 12", to form the chord (the
+greater dimension being the depth,) we shall have 3 x 8" x l2" = 288
+square inches area of section, and
+
+   allowing for splicing     72 square inches,
+     "      "  foot blocks, 24   "       "
+     "      "  bolts,       24   "       "
+     "      "  washers,      8   "       "
+
+we shall have after deducting allowances (288-128) 160 square inches
+area, giving an excess over 134.4, the area demanded, sufficient to
+cover allowances for any accidental strain.
+
+
+=Upper Chords.= The upper chords are compressed as forcibly as the
+lower ones suffer tension--owing to the action and reaction of the
+diagonals. In this case the compression is 268800 lbs., and as 1
+square inch of section will safely bear 1000 lbs., we have for the
+
+                 268800
+  area required, ------ = 268.8
+                  1000
+
+[TeX: $\frac{268800}{1000} = 268.8$]
+
+square inches,--three pieces 8" x 11" will give 264 square inches and
+this area will require no reduction, as the whole chord presses
+together when properly framed and is not weakened by splicing. So far,
+the calculations made would apply to either of the three Bridges
+mentioned, as well as to a Warren Truss. But now, to obtain the
+dimensions of the web members, so called, of the Truss, it is
+necessary to decide upon the specific variety. The form of Bridge in
+more general use in the United States is called the Howe Truss, from
+its inventor, and in spans of 150 feet, and under, is very reliable;
+for spans exceeding 150 ft. it should be strengthened either by Arch
+Braces or by the addition of Arches, as the heavy strains from the
+weight of bridge and load bearing on the feet of the braces near the
+abutments, tend to cripple and distort the truss by sagging, although
+the Baltimore Bridge Co. have built a Wooden Howe Bridge of two
+Trusses of 300 ft. span, 30 ft. rise, and 26 ft. wide, without any
+arch, but it has a wrought iron lower chord, and is only proportioned
+for a moving load of 1000 lbs. per ft. run. [Vide Vose on R.R.
+construction.]
+
+In order to ensure uniformity in strength in the chords--but one joint
+should be allowed in a panel--and that should come at the centre of
+the panel length--but in long spans this cannot always be done.
+
+
+=Web Members.= We will now proceed to calculate the web members of a
+Howe Truss of the foregoing dimensions, when subjected to the strains
+above mentioned.
+
+=Braces.= The end braces must evidently support the whole weight of
+the bridge and load, which for one end of one truss will be 134400
+lbs., and as these braces are in pairs,--67200 lbs. will be the strain
+vertically on the stick--but as this stick is a diagonal--whose
+vertical is 15 ft., and horizontal 10 ft., we shall have for its
+length 18 ft. in round numbers, whence the strain along the diagonal
+will be found from the proportion 15 : 18 :: 67200 : 80640 lbs.,
+whence we have an area of 80 inches required for compression, or a
+stick of 8" x 10". Now, to ascertain if this is stiff enough for
+flexure, we will substitute these values in the equation
+
+      2240 bd cubed
+  W = --------, and we have
+         L squared
+
+[TeX: $W = \frac{2240 \times bd^3}{L^2}$]
+
+      2240 x 8 x 1000
+  W = ---------------, or reducing, W=55308 lbs.
+            324
+
+[TeX: $W = \frac{2240 \times 8 \times 1000}{324} = 55308$]
+
+Now, these proportions will give ample strength for both flexure and
+compression, for if we block the two sticks composing the end brace
+together, and firmly connect them by bolts, we shall have a built beam
+
+                           2240 x 24 x 1000
+  of 24" x 10"--whence W = ---------------- = 165925 lbs.,
+                                 324
+
+[TeX: $W = \frac{2240 \times 24 \times 1000}{324} = 165925$]
+
+and as 134400 lbs. was all that the conditions demand, we really have
+an excess of strength. The next set of braces supports the weight of
+the rectangle included between the upper ends of the braces and the
+two chords, and the dimensions of the sticks are calculated in the
+same manner. We find, as we approach the centre of the bridge, that
+the strains on the braces become less, and consequently their
+scantling should be reduced, but in ordinary practice this is seldom
+done.
+
+=Rods.= The next thing is to ascertain the dimensions of the various
+tie rods. It is evident that the same weight comes upon the first set
+of rods, as on the first set of braces--which will give for the rods
+at one end of one truss, 134400 lbs.; and as there are two of these
+rods, each will sustain a strain of 67200 lbs.--and, at 15,000 lbs.
+per square inch, will have an area of 4.48 sq. inches, and, by Vose's
+Tables, must have a diameter of 2-1/2 inches. The sizes of the rods in
+each set will decrease towards the centre of the bridge as the weight
+becomes less.
+
+[Illustration: Pl. II. with Fig. 1., Fig. 2., Fig. 3., Fig. 4.]
+
+
+=Counterbraces.= Now, as to the necessity of Counterbracing, there are
+various opinions. The object of it is to stiffen the truss and check
+vibrations. If a load be placed over any panel point, it causes that
+portion of the truss to sink, and produces an elevation of the
+corresponding panel point at the other end of the truss--thus
+producing a distortion, which change of form is resisted by proper
+counterbraces. The strain to which this timber is subjected is caused
+by the moving load on one panel only--and requires only scantling of
+the size of the middle braces. These counterbraces should not be
+pinned or bolted to the braces where the cross--as their action is
+thereby entirely altered--but it is well to so confine them as to
+prevent vertical or lateral motion.
+
+
+=Shoes.= Formerly it was the custom to foot the braces and counters on
+hard wood blocks on one side of the chord, the vertical rods passing
+through and screwing against a block on the other side--thus the whole
+strain tended to crush the chord across its fibres. This is now
+remedied by the use of cast iron blocks, bearing on one side of the
+chord, but having tubes extending through to the other side, where the
+washer plate for the bolts fits firmly on their ends, forming a
+complete protection, as all the crushing strain is received on the
+block itself.
+
+
+=Width.= It now becomes necessary to determine upon the width between
+the two trusses. For a single track bridge for a railroad, 14 ft. is
+the usual width adopted, and for a highway bridge, from 12 to 16 ft.
+When a double track is required, three trusses are usually employed,
+with a width for each roadway of 14 ft. for railroads.
+
+
+=Bolsters.= Large timbers 12 x 12, or thereabouts, are laid on the
+bridge seats of the abutments to support the ends of the trusses, one
+of these should be directly under each of the extreme panel points. A
+panel point is the intersection of the centre line of a brace
+produced, with the centre line of a chord. The rise of a truss is the
+vertical distance between the centre lines of the upper and lower
+chords.
+
+=Camber.= Were a bridge to be framed with its chords perfectly
+horizontal, it would be found to fall below the horizontal line on
+being placed in its proper position, owing to the closing up of the
+joints in the upper parts of the structure, and opening of joints in
+the lower parts, as well as to the compression of the parts. To
+obviate this defect, it is usual to curve the chords slightly in a
+vertical direction, by elongating the upper chord, so that the bays or
+panels are no longer rectangular but of a trapezoidal form--and, as a
+consequence, the inclined web members are slightly lengthened, and the
+verticals become radii of the curve. The amount of deviation from a
+horizontal line is called the Camber.
+
+A table of Cambers for different spans will be found further on, as
+also a table of multipliers, by which to multiply the camber in order
+to find the elongation of the upper chord. Part of the Camber table is
+taken from Trautwine's Engineer's Pocket-Book, (which should be the
+inseparable companion of every engineer,) and part was calculated for
+this pamphlet, according to Trautwine's rules. The table of
+multipliers is Trautwine's.
+
+=Diagonal Bracing.= In order to stiffen a bridge, it should have the
+two Trusses braced together at the Lower Chords always, at the Upper
+Chords when practicable--and in case of a deck bridge, where the
+roadway is supported on the upper chords, it is as well to have rods
+for vertical diagonal braces, their planes being perpendicular to the
+axis of the bridge. The more usual form is similar to the web members
+of the Howe Truss--the rods from 3/4" to 1" in diameter, and the
+braces of 6" x 7" scantling, footed on wooden blocks, usually. It is
+more usual to have the tie rods of the horizontal diagonal bracing,
+and the braces themselves, meet in a point about midway of a Truss
+panel on the centre line, nearly, of the chord. This will generally
+give a half panel of diagonal bracing near each end of the truss--and
+it is very usual to have the diagonals foot at their intersection
+there against a cross timber interposed between the trusses, while the
+tie rod prevents any spreading.
+
+
+=Floor Timbers.= The general dimensions of the transverse floor beams,
+when about 3 feet apart, from centre te centre, are 8" x 14", the
+largest dimension being the depth. The stringers should be notched to
+the floor beams about 1" or 2", and should be about 10" or 12" x 14".
+The cross ties should be 18" to 24" apart, from centre to centre, and
+be 3-1/2" x 6".
+
+Large, heavy bridges require no fastening to connect them with their
+seats, but light bridges should be fastened, as the spring on the
+sudden removal of a load, (as when the last car of a train has
+passed,) may move it from its proper position.
+
+
+=Splices.= As the upper and lower chords have to be made in several
+lengths, securely fastened to each other, and, in order to weaken the
+built beam as little as possible, it is necessary to adopt some form
+of splicing whereby the greatest amount of tensional strength may be
+retained in the chord with the least amount of cutting, and yet have a
+secure joint. Such a splice is shown in Pl. II, Fig. 4, and below is a
+table from Vose's Hand-book, giving reliable dimensions.
+
+        Span.    A C     B B      C D
+        Feet.   Feet.  Inches.   Feet.
+          50    1.00    1-1/2    1.50
+         100    1.25      2      2.00
+         150    1.75    2-1/2    2.25
+         200    2.00      3      2.75
+
+This manner of splicing requires the back of the splice block to be
+let into the chord stick, against which it lies, about 3/4 of an inch.
+To show how the various Engineers differ, as to their estimates of the
+sizes of the several parts of bridges, I subjoin two Tables--one by
+Prof. G.L. Vose, a well known Engineer, and one by Jno. C. Trautwine,
+an Engineer of note also--and I would premise that a bridge built
+according to either would be amply strong.
+
+
+TABLE FOR DIMENSIONING A HOWE TRUSS BRIDGE.
+G.L. VOSE.
+
+                                      End    Centre           Centre
+      Span. Rise. Panel.  Chords.    Braces. Braces. End Rods. Rods.
+       50    10     7    2--8 x 10   7 x  7   5 x 5  1--1-1/8  2--1
+       75    12     9    2--8 x 10   8 x  8   5 x 5  2--1-1/2  2--1
+      100    15    11    2--8 x 10   8 x  9   6 x 6  2--1-3/4  2--1
+      150    20    13    4--8 x 12  10 x 10   6 x 7    3--2    3--1
+      200    25    15    4--8 x 16  12 x 12   7 x 7    5--2    5--1
+
+
+TABLE FOR DIMENSIONING A HOWE TRUSS BRIDGE.
+JNO. C. TRAUTWINE, C.E.
+
+       |    |    |An Upper | A Lower |  An End |A Centre|        |   End     |  Centre
+  Clear|    | No.| Chord.  |  Chord. |  Brace. |  Brace.|Counter.|   Rod.    |   Rod.
+  Span |Rise| of |---------|---------|---------|--------|--------|-----------|-----------
+   in  | in |Pan-| No|     | No|     | No.|    | No|    | No|    | No.|      | No.|
+  feet.|feet|els.|Pcs|Size.|Pcs|Size.|Pcs.|Size|Pcs|Size|Pcs|Size|Rods|Size. |Rods|Size.
+  -----|----|----|---|-----|---|-----|----|----|---|----|---|----|----|------|----|-----
+    25 |  6 |  8 | 3 | 4x5 | 3 | 4x10|  2 |4x6 | 2 |5x5 | 1 |4x5 |  2 |1-5/16|  2 |  7/8
+    50 |  9 |  9 | 3 | 6x7 | 3 | 6x10|  2 |6x7 | 2 |5x6 | 1 |5x6 |  2 |1-5/8 |  2 |1-1/16
+    75 | 12 | 10 | 3 | 6x9 | 3 | 6x11|  2 |6x8 | 2 |6x6 | 1 |6x6 |  2 |1-7/8 |  2 |1-3/16
+   100 | 15 | 11 | 3 | 6x10| 3 | 6x12|  2 |8x9 | 2 |6x8 | 1 |6x8 |  2 |2-3/16|  2 |1-5/16
+   125 | 18 | 12 | 4 | 6x10| 4 | 6x13|  2 |8x10| 2 |6x9 | 1 |6x9 |  2 |2-5/8 |  2 |1-3/8
+   150 | 21 | 13 | 4 | 8x10| 4 | 8x14|  3 |9x10| 3 |6x9 | 2 |6x9 |  3 |2-3/8 |  3 |1-3/16
+   175 | 24 | 14 | 4 |10x12| 4 |10x15|  3 |9x11| 3 |8x8 | 2 |8x8 |  3 |2-5/8 |  3 |1-1/4
+   200 | 27 | 15 | 4 |12x12| 4 |12x16|  3 |9x12| 3 |8x10| 2 |8x10|  3 |2-7/8 |  3 |1-3/8
+
+Both of these tables were calculated for a single Railroad track, and
+would answer equally well for a double Highway Bridge. In the bridge
+according to Trautwine's Table, each lower chord is supposed to have a
+piece of plank, half as thick as one of the chord pieces, and as long
+as three panels, firmly bolted on each of its sides, in the middle of
+its length.
+
+       *       *       *       *       *
+
+
+=PRATT'S BRIDGE.=
+
+This is opposite in arrangement of parts to a Howe Bridge, as the
+diagonals are rods, and sustain tension, and the verticals are posts,
+and suffer compression:
+
+  _Example._--Span                  = 100 feet.
+              Rise                  =  12   "
+              Panel                 =  10   "
+              Weight per lineal ft. = 3000 lbs.
+
+The tension on the lower, or compression on the upper chord, will be
+
+  300000 x 100
+  ------------ = 3333333 lbs.
+       96
+
+[TeX: $\frac{300000 \times 100}{96} = 3333333$]
+
+The dimensions of the chord and splicing would be found in the same
+manner as for a Howe Truss.
+
+
+=Suspension Rods.= Fig. 1, Pl. III., represents an elevation of a
+Pratt Bridge. Now, it is evident that the first sets of rods must
+support the weight of the whole bridge and its load, which we have
+found to be 300000 lbs. Each truss will have to sustain 150,000 lbs.,
+and each end set of rods 75,000 lbs. Now, if there are two rods in
+each set,--each rod will have to bear a strain of 37500 lbs., and this
+will have an increase due to its inclination, so that the strain on it
+must be found by the following proportion:
+
+    Height : diagonal :: W : W' or
+
+    12 : 15.8 :: 37500 : 49375 lbs.
+
+Referring to the Table for bolts, we find that 2-1/8 gives a strength
+a little in excess, and will be the proper size. The next set of rods
+bear the weight of the whole load, less that due to the two end
+panels, and so on. Fig. 2, Pl. III, shows the manner of applying the
+rods. The bevel block should be so fitted to the chord that it will
+not have a crushing action.
+
+
+=Counters.= Top and bottom chords are always used in this bridge, and
+consequently the counter rods have only to sustain the movable load on
+one panel. The weight of the moving load cannot be more than 2000 lbs.
+per lineal foot which, for a panel of 10 ft., gives 20000 lbs., or
+10,000 lbs. for each set, and if we have two rods in a set, the strain
+on each rod will be 5000 lbs., increasing this for inclination, we
+shall have,
+
+  12 : 15.8 :: 5000 : 6585 lbs.,
+
+requiring a rod of 3/4 of an inch diameter. The posts in this bridge
+correspond to the braces of the Howe Truss, but being vertical, are
+not so large.
+
+Subjoined are two Tables, one by Prof. G.L. Vose, and one by Mr.
+Trautwine, giving principal dimensions for bridges of different spans
+of the Pratt type of Truss.
+
+
+TABLE OF DIMENSIONS OF A PRATT TRUSS.
+
+PROF. G. L. VOSE.
+
+                          End   Centre    End     Centre  Counter
+  Span. Rise. Chords.    Post.   Post.    Rod.     Rod.     Rod.
+
+    50   10   2--8x10   5 x  5   4 x 4  2--1-3/8   2--1   1--1-1/2
+    75   12   2--8x10   6 x  6   5 x 5  2--1-5/8   2--1   1--1-1/2
+   100   15   3--8x10   7 x  7   6 x 6  2--1-3/4   2--1   2--1-1/8
+   125   18   3--8x10   8 x  8   6 x 6  3--1-7/8   3--1   2--1-1/3
+   150   21   4--8x12   9 x  9   6 x 6  3--2-1/8   3--1   8--1-1/8
+   200   24   4--8x16  10 x 10   6 x 6  5--1-7/8   5--1   3--1-1/8
+
+
+TABLE OF DIMENSIONS OF A PRATT'S TRUSS.
+
+       |    |    | Upper   |  Lower  |  Main Brace Rods.  |  Counter  |   |     |          |
+  Clear|    | No.| Chord.  |  Chord. |                    |   Rods.   |   |     |  Posts.  |
+  Span |Rise| of |---------|---------|--------------------|-----------|   |     |----------|
+   in  | in |Pan-|No.|     |No.|     |No.| Size |No.|Size.|Num|       |No.| Size|No.|Size. |
+  feet.|feet|els.|Pcs|Size.|Pcs|Size.|Ctr|Centre|End| End.|ber| Size. |End| End.|Ctr|Centre|
+  -----|----|----|---|-----|---|-----|---|------|---|-----|---|-------|---|-----|---|------|
+    25 |  6 |  8 | 3 | 4x5 | 3 | 4x10| 2 |1     | 2 |1-3/8| 1 |1-7/16 | 3 | 4x5 | 3 |  4x4 |
+    50 |  9 |  9 | 3 | 6x7 | 3 | 6x10| 2 |1-3/16| 2 |1-1/8| 1 |1-5/8  | 3 | 6x6 | 3 |  6x5 |
+    75 | 12 | 10 | 3 | 6x9 | 3 | 6x11| 2 |1-5/16| 2 |2-1/2| 1 |1-7/8  | 3 | 6x7 | 3 |  6x5 |
+   100 | 15 | 11 | 3 | 6x10| 3 | 6x12| 2 |1-7/16| 2 |2-7/8| 1 |2      | 3 | 6x9 | 3 |  6x7 |
+   125 | 18 | 12 | 4 | 6x10| 4 | 6x13| 2 |1-1/2 | 2 |2-3/8| 1 |2-1/8  | 4 | 6x9 | 4 |  6x7 |
+   150 | 21 | 13 | 4 | 8x10| 4 | 8x14| 3 |1-5/16| 3 |2-1/2| 2 |1-5/8  | 4 | 8x8 | 4 |  8x7 |
+   175 | 24 | 14 | 4 |10x12| 4 |10x15| 3 |1-5/8 | 3 |2-3/4| 2 |1-11/16| 4 |10x10| 4 | 10x8 |
+   200 | 27 | 15 | 4 |12x12| 4 |12x16| 3 |1-1/2 | 3 |3-1/8| 2 |1-13/16| 4 |12x10| 4 | 10x8 |
+
+This table is partly given in Trautwine's Engineer's Pocket Book, and
+partly made up from directions therein given.
+
+
+TABLE OF DIMENSIONS FOR SMALL SINGLE TRACK PRATT TRUSSES.
+
+                                 At centre   At end    Centre      End
+  Clear Chords  Centre    End    of truss,  of truss,  Counter,  Counter,
+  Span, each,    Post,   Posts,  Diam. of   Diam. of   Diameter, Diameter,
+  Ft.   Ins.     Ins.     Ins.     Rods.     Rods.      Ins.      Ins.
+
+   30    9 x 11  4 x 9    7 x 9    1         1-5/8      1-3/8      1
+   40   10 x 12  4 x 10   8 x 10   1-1/8     1-7/8      1-5/8      1
+   50   10 x 14  5 x 10   9 x 10   1-1/4     2-1/8      1-3/4      1
+   60   12 x 15  5 x 12   9 x 12   1-3/8     2-3/8      2          1
+   70   12 x 17  6 x 12  11 x 12   1-1/2     2-1/2      2-1/8      1
+
+This bridge possesses an advantage over the Howe Truss, for the panel
+diagonals can be tightened up by screws, so that every part of the
+truss can be forced to perform its work. In Howe's bridge the
+adjustments must be made by wedging the braces and counters.
+
+Below are given the dimensions of a Howe bridge on the Vermont Central
+R.R., at South Royalton, (single track, deck.)
+
+              No. of     Upper        Lower
+  Span. Rise. Panels.    Chord.       Chord.      Braces.   Counters.
+  150    20    12     4--6-1/2 x 13 4--6-1/2 x 13 2--8 x 9  1--8 x 9
+
+    Rods.    Transverse Bracing.
+              Braces.    Rods.
+  3--1-1/4"   6 x 8      7/8
+
+The bridge over the White River, on the Passumpsic R.R., is a Howe
+Truss, strengthened by an arch. The verticals are of wood, and the
+diagonals foot on steps formed by enlarging the ends of the verticals.
+The counters are in two lengths, and are adjusted by wedges at the
+points where they intersect the braces. The bridge is in two spans,
+and has a double track, and consequently three trusses. There are two
+timber arches to each truss, and the truss is supported on them by
+connecting them to the verticals by short cross pieces notched into
+the posts, and resting on the upper surface of the arches. It is a
+very stiff bridge, and similar to the one at Bellows Falls, both
+having their axis oblique to the channel of the stream they cross. The
+timbers could hardly be procured now, except at great expense.
+
+       No.
+       of        Upper     Lower
+  Span Pan- Rods Chord     Chord     Braces   Counters  Uprights Arches
+       els
+  182   14   21  2--8 x16  2--8 x17, 1--21 x8 1--8 x10  21 x11   2--8 x9
+                 1--5 x16  2--4 x17,
+                           1--5 x17,
+
+Diagonals 6 x 8, Rods 7/8. Floor timbers suspended both from
+arches and truss, 9 x 13; stringers 10 x 14.
+
+In the Cheshire Bridge, the braces are only 20x8, and the span is only
+175 feet, the number of Panels being 14, as in the W.R. Bridge--the
+other dimensions are the same. Below are given the dimensions of a
+Howe Truss of 108 ft. span, weight to be borne on upper chord.
+
+               No.
+               of    Upper    Lower                        E.        Floor
+  Rise  Camber Pan-  Chord    Chord    Braces    Counters  Rods     Timbers
+   Ft.   Ins.  els    Ins.     Ins.     Ins.       Ins.    Ins.      Ins.
+
+  13-1/2  3     12   8--3 x12 8--3 x12 2--8 x10  1--7 x10  2--2-1/8  9 x16
+
+As plank is used for the chords, the pieces must be bolted thoroughly
+with 5/8 bolts.
+
+
+A form of bridge that has been used to some extent on the Baltimore
+and Ohio Railroad, by Mr. Latrobe, is the Arch Brace Truss. In this
+form of Truss the braces lead directly from the abutments to the head
+of each vertical; thus the load is transferred at once to the
+abutments, without passing through a series of web members. The
+counterbracing is effected by means of a light lattice,--and is
+applied to both sides of the chords, and the intersections of the
+diagonals are fastened while the bridge is strained by a load--thus
+preventing recoil--so that the effect of a moving load is to lighten
+the strain on the lattice--without otherwise affecting the Truss.
+
+[Illustration: Pl. III. with Fig. 1., Fig. 2., Fig. 3., Fig. 4., Fig. 5.]
+
+There are two models of this style of bridge, to my knowledge; one
+built by Prof. G.L. Vose, on a scale of 1/2 an inch to the foot,
+and representing a span of 150 feet, which supported 2,500 lbs. at
+the centre, and a movable load of 150 lbs., proving itself to be
+strong and rigid enough for any thing. The other, on a scale of 1
+inch to the foot, and representing a span of 76 feet, was built by
+the Class of '73, of the Thayer Engineering School, under the
+writer's direction, and though bearing very heavy weights, has never
+been thoroughly tested--it has, however, been subjected to the
+sudden shock of 1040 lbs. falling 20 inches, without injury, several
+times. Subjoined are the dimensions of the models mentioned.
+
+DIMENSIONS OF A MODEL OF AN ARCH BRACE TRUSS.
+
+                  G.L. VOSE.
+
+        Length,  7 feet.
+        Height,  1 foot.
+        Width,   1 foot.
+        Chords,  4--1/4 x 1/2  inch.
+        Braces   4--1/4 x 1/8   "
+        Lattice,    1/4 x 1/16  "
+
+This represented a span of 150 ft, a rise of 20 feet, and a panel
+of 15 ft. Weight, per running foot of bridge and load, was taken
+at 3000 lbs.
+
+The method of calculating the dimensions of this truss, from the
+foregoing data, is as follows. The half number of panels is 5, and the
+lengths of the corresponding diagonals (neglecting fractions) are
+
+     ---------
+    /20 squared + 15 squared = 25 feet. [TeX: $\root{20^2 + 15^2} = 25$]
+  \/
+
+     ---------
+    /20 squared + 30 squared = 37  "    [TeX: $\root{20^2 + 30^2} = 37$]
+  \/
+
+     ---------
+    /20 squared + 45 squared = 49  "    [TeX: $\root{20^2 + 45^2} = 49$]
+  \/
+
+     ---------
+    /20 squared + 60 squared = 64  "    [TeX: $\root{20^2 + 60^2} = 64$]
+  \/
+
+     ---------
+    /20 squared + 75 squared = 78  "    [TeX: $\root{20^2 + 75^2} = 78$]
+  \/
+
+The weight upon each set of braces is that due to one panel, or 3000
+x 15 = 45000 lbs., half of this, or 22500 lbs., is the weight for one
+truss only--and, as there is a brace under each of the 4 chord sticks,
+we divide by 4, and have 5625 lbs. per stick of the brace;--now,
+correcting for inclination, we shall have
+
+  20 : 25 :: 5625 :  7031 lbs.
+  20 : 37 :: 5625 : 10406 lbs.
+  20 : 49 :: 5625 : 13781 lbs.
+  20 : 64 :: 5625 : 18000 lbs.
+  20 : 78 :: 5625 : 21937 lbs.
+
+The weights fouud show the compressional strains on the several
+braces;--and, were the pieces to be proportioned for compression
+only, their Scantling would be quite small--but on account
+of their elasticity, they require larger dimensions.
+
+These braces should not be fastened to the verticals,--but
+should be confined both laterally and vertically, where they pass
+them. The length of beam, for which we have to guard agains
+flexure, is the length between verticals in any panel.
+
+  In panel No. 1, it will be 25 feet,
+       "    "  2,    "   "   18  "
+       "    "  3,    "   "   17  "
+       "    "  4,    "   "   16  "
+       "    "  5,    "   "   16  "
+
+Now, using the formula
+
+  2240 b d cubed
+  --------- = W,
+      L squared
+
+[TeX: $\frac{2240 bd^3}{L^2} = W$]
+
+we shall have, in round numbers, the following dimensions:
+
+  For the 1st panel, 25 feet long, 8 x 10
+     "    2d   "     37   "    "   8 x 10
+     "    3d   "     49   "    "   8 x 10
+     "    4th  "     64   "    "   8 x 10
+     "    5th  "     78   "    "   8 x 10
+
+For the lattice work, a double course on each side of each truss, in
+long spans; and a single course, in shorter spans, of 3 x 6, or 2 x 9
+plank, bolted at intersections, is sufficient.
+
+
+GENERAL TABLE OF DIMENSIONS FOR ARCH BRACE TRUSS.
+
+                    G.L. VOSE.
+
+  Span.  Rise.   Chords.     Ties.      Braces.     Lattice.
+    50    10    2--8 x 10   1--8 x 10   2--6 x 6
+    75    12    2--8 x 10   1--8 x 10   2--6 x 6     2 x 9
+   100    15    3--8 x 10   2--8 x 10   3--6 x 6      or
+   150    20    4--8 x l2   3--8 x 10   4--6 x 8     3 x 6
+   200    25    4--8 x 16   3--8 x 10   4--6 x 9
+
+The arch braces must all foot on an iron thrust block, of which a view
+is given in Fig. 4, Pl. III; and the centre of pressure of the braces
+must be directly over a bolster, to prevent crippling.
+
+The several sticks forming a brace must be blocked together at
+intervals, and When they are spliced,--a butt joint Should be
+used--and it should come in the centre of a panel. Below are given the
+dimensions of the Thayer Engineering School model.
+
+  Height Ins.    12
+  No. Panels      8
+  Chords Ins.    2--1 x 1/2
+  Posts Ins.     1--2/3 x 5/6
+  Braces Ins.    2--1/2 x 1/2
+  Lattice Ins.   1/4 x 1/2
+  Width Ins.     13
+
+There are several other forms of Bridge, the most notable among which
+are the Whipple, McCallum's, Post's, Towne's, Haupt's, and Burr's. But
+enough has been said to give the student an idea of the general
+arrangement of the different parts of a Truss, and to enable him to
+determine the strains to which the various members are subjected.
+Nothing will be said in regard to Wooden Arches, as our space is too
+limited.
+
+
+=Pile Bridging.= A bridge of this description is useful in crossing
+marshes, or in shallow water. Fig. 5, Pl. III, gives a good example of
+this kind of bridge, under 20 feet in height. If on a curve, there
+must be extra bracing on the convex side.
+
+
+=Trestle Work.= This is a combination of posts, caps, and braces; and
+is used for both temporary and permanent works. Plate IV, Figs. 1, 2,
+3 and 4, give some of the best varieties in use. Figs. 1 and 2, may be
+used up to 15 feet in height; Fig. 4, up to 20 feet; and Fig. 3, to 30
+ft. The distance apart of the various bents should not exceed 10 or 12
+ft., unless bracing is introduced between them, and the bents should
+always be raised above the ground a few feet on a solid masonry
+foundation. Want of space forbids any mention of abutments and piers,
+which really come more properly under the head of masonry.
+
+Iron Bridging is gradually working its way into favor, and Will
+probably eventually supersede wooden trusses;--but in many cases wood
+is the only material at hand--and therefore some knowledge of Wooden
+Bridging is desirable. It is intended to follow this pamphlet with a
+portfolio of sheets containing working drawings of several kinds of
+Wooden Bridges, taken from actual measurements of some of the best
+specimens of the different styles of Truss in use.
+
+       *       *       *       *       *
+
+
+=PRACTICAL NOTES.=
+
+
+When putting a truss together in its proper position, on the
+abutments, 'false works' must first be erected to support the parts
+until they are so joined together as to form a complete
+self-sustaining truss. The bottom chords are first laid as level as
+possible on the false works, then the top chords are raised on
+temporary supports, sustained by those of the lower chord, and are
+placed a few inches higher at first than their proper position, in
+order that the web members may be slipped into place. When this is
+done the top chords are gradually lowered into place. The screws are
+then gradually tightened, (beginning at the centre and working towards
+both ends,) to bring the surfaces of the joints into proper contact,
+and by this method, the camber forms itself, and lifts the lower
+chords clear of the false works, leaving the truss resting only upon
+its proper supports. The subjoined Table will be found useful in
+estimating the strains on a truss when proportioning a bridge for any
+moving load.
+
+Table of weights per running foot of a bridge, (either of wood or
+iron,) including weights of floor, lateral bracing, &c., complete, for
+a single track.
+
+  Clear      Weight of
+  Span.       Bridge.
+            Tons.  lbs.
+
+   25       .266    596
+   30       .281    629
+   40       .313    701
+   50       .343    768
+   60       .374    838
+   70       .404    905
+   80       .434    972
+   90       .464   1039
+  100       .494   1106
+  120       .554   1241
+  140       .614   1375
+  150       .643   1440
+  160       .673   1507
+  170       .703   1575
+  180       .733   1642
+  200       .792   1774
+  225       .867   1942
+  250       .940   2105
+  275      1.013   2269
+  300      1.087   2435
+
+
+The weight of a single track railway bridge may be taken as equal to
+that of a double track highway bridge,--and the trusses that will be
+large enough for one will be large enough for the other.
+
+The greatest load that a highway bridge can be subjected to is 120
+lbs. to the square foot of surface.
+
+
+TABLE OF CAMBERS FOR BRIDGE TRUSSES.
+
+  Span.   Camber.   Span.   Camber.   Span.   Camber.   Span.   Camber.
+  feet.   Inches.   Feet.   Inches.   Feet.   Inches.   Feet.   Inches.
+
+   25       0.8      75      2.5      175       5.8     275      9.2
+   30       1.0     100      3.3      200       6.7     300      10.0
+   50       1.7     120      4.0      225       7.5     325      10.8
+   60       2.0     150      5.0      250       8.3     350      11.7
+
+
+TRAUTWINE'S TABLE FOR FINDING INCREASE IN
+LENGTH OF UPPER CHORD BEYOND THE
+LOWER CHORD ON ACCOUNT OF THE CAMBER.
+
+             Multiply               Multiply
+  Depth of   Camber      Depth of   Camber
+   Truss.      by         Truss.      by
+
+  1-4 span    2.00      1-12 span    .666
+  1-5  "      1.60      1-13  "      .614
+  1-6  "      1.33      1-14  "      .571
+  1-7  "      1.15      1-15  "      .533
+  1-8  "      1.00      1-16  "      .500
+  1-9  "      .888      1-17  "      .470
+  1-10 "      .800      1-18  "      .444
+  1-11 "      .727      1-20  "      .400
+
+
+
+TABLE OF AMERICAN WOODS.
+
+                   Weight per   Resistance in lbs. per
+     Kind.         cubic foot        square inch.         Value of s.
+                   in pounds.   Extension  Compression.
+
+  White Pine.          26         12,000       6000          1229
+  Yellow Pine.         31         12,000       6000          1185
+  Pitch Pine.          46         12,000       6000          1727
+  Red Pine.            35         12,000       6000          1527
+  Virginia Pine.       37         12,000       6000          1456
+  Spruce.              48         12,000       6000          1036
+  Tamarack.            26         12,000       6000           907
+  Canada Balsam.       34         12,000       6000          1123
+  White Oak.           48         15,000       7500          1743
+  Red Oak.             41         15,000       7600          1687
+  Birch.               44         15,000       7000          1928
+  Ash.                 38         16,000       8100          1795
+  Hickory.             51         15,000       7200          2129
+  Elm.                 45         16,000       8011          1970
+
+
+The above table is compiled from a much fuller one in Vose's Treatise
+on R.R. Construction.
+
+
+TABLE OF BOLTS AND NUTS CALCULATED FOR A
+WORKING STRAIN OF 15,000 LBS. PER
+SQUARE INCH OF SECTION.
+
+  Diameter.  Area.    Strength in Weight per           Thick's  No. thr's
+  Inches.  Sq. inches.  Pounds      Foot.  Square nut.  of nut. per inch.
+
+    1/2      .19635        2940     0.66     1-1/4 in    3/4 in    12
+    5/8      .30680        4602     1.03     1-3/8       3/4       10
+    3/4      .44179        6630     1.49     1-1/2       7/8       10
+    7/8      .60132        9019     2.03     1-3/4     1            9
+  1          .78540       11775     2.65     2         1            8
+  1-1/8      .99402       14910     3.36     2         1-1/8        7
+  1-1/4     1.2272        18405     4.17     2-1/4     1-1/4        7
+  1-3/8     1.4849        22260     5.02     2-1/2     1-3/8        6
+  1-1/2     1.7671        25505     5.97     2-3/4     1-1/2        6
+  1-5/8     2.0739        31095     7.01     2-7/8     1-5/8        5
+  1-3/4     2.4053        36075     8.13     3         1-3/4        5
+  1-7/8     2.7612        41415     9.33     3-1/4     1-7/8        4-1/2
+  2         3.1416        47130    10.62     3-1/2     2            4-1/2
+  2-1/8     3.5166        53190    12.00     3-3/4     2-1/8        4
+  2-1/4     3.9761        59640    13.40     4         2-1/4        4
+  2-3/8     4.4301        66450    15.00     4-1/8     2-3/8        4
+  2-1/2     4.9087        73620    16.70     4-1/4     2-1/2        3-1/2
+  2-5/8     5.4119        81178    18.20     4-1/2     2-5/8        3-1/2
+  2-3/4     5.9396        89094    20.00     4-3/4     2-3/4        3-1/2
+  2-7/8     6.4918        97377    21.90     5         2-7/8        3
+  3         7.0686       106029    23.80     5-1/4     3            3
+  3-1/4     8.2958       124437    27.90     5-3/4     3-1/4        3
+  3-1/2     9.6211       144316    32.40     6         3-1/2        2-1/2
+
+
+TABLE OF SAFE WORKING LOAD IN LBS., FOR HOLLOW CAST-IRON COLUMNS.
+
+[_G.L. Vose._]
+
+   Outside             Length or height in Feet              Metal
+   Diameter                                                 Thickness
+  in inches.  6      8      10     12     15     18     20  in inches.
+
+       3    16000  14000  13000  11000   9000   7000   6000    3/8
+       4    30000  29000  26000  24000  22000  18000  16000    1/2
+       5    50000  37000  45000  42000  39000  37000  31000    5/8
+       6    59000  57000  55000  52000  49000  44000  41000    3/4
+       7   101000  99000  96000  92000  88000  81000  76000   13/16
+       8   131000 129000 126000 122000 118000 109000 105000    7/8
+       9   169000 167000 164000 160000 156000 146000 141000   1
+      10   210000 200000 200000 200000 190000 180000 180000   1-1/8
+      11   250000 250000 240000 240000 240000 230000 220000   1-1/4
+      12   300000 300000 290000 290000 290000 270000 270000   1-1/2
+      14   450000 430000 410000 380000 370000 350000 330000   1-3/4
+      16   520000 500000 480000 460000 440000 420000 400000   2
+      18   650000 630000 610000 590000 560000 520000 470000   2-1/2
+      20   800000 760000 740000 690009 650000 590000 540000   3
+
+
+[Illustration: Pl. IV. with Fig. 1., Fig. 2., Fig. 3., Fig. 4.]
+
+
+
+
+Transcriber's Notes:
+
+DISCLAIMER: This document should NOT be used to engineer any bridge
+projects! Many typesetting errors were found, and it is possible that
+there are further errors in the information that were not caught.
+
+Formulas have been provided both as ASCII and TeX following in brackets.
+Bold headings are handled with equal signs before and after the bold text.
+Italicised text uses the standard underlines before and after the text.
+Fractions are expressed in the format: 2-1/4 means two and one quarter.
+
+The page numbers listed below are project page numbers.
+(The original book used Roman numerals to number the pages.)
+
+Note that the book uses the "long" ton equal to 2,240 pounds.
+
+CORRECTIONS MADE:
+
+   1. Page 8--the formula for "d" must use a cube root, which is how it
+      is shown here, but the '3' to indicate a cube root is not found in
+      the original document.
+   2. Page 8--typo in word 'sectien'--changed to 'section'.
+   3. Page 10--Value for working comp. strength of cast iron in the
+      table had a typo (25,v00). Since other values use round numbers,
+      it is assumed the value should be 25,000.
+   4. Page 10--Two other typos. Changed 'the the' to 'the', and in
+      table heading, original word was 'detrution', changed to correct
+      spelling of 'detrusion'.
+   5. Page 12--changed 'woooden' to 'wooden'.
+   6. Page 13--Example II--In the calculations, the intermediate value
+      in the book was printed as the square root of 67.2. The left part
+      is correct, but reduces to the square root of 268.8, and that is
+      ~16.395. So I have corrected the intermediate value.
+   7. Page 13--Because the original page scan cut off the text on the
+      right edge, I have made assumptions on what text was missing.
+      Because the scans came from an outside source, I could not get
+      the missing information, which was the words at the end of Example
+      II, and words in the last paragraph of the page.
+   8. Page 14--Three typos found: 'dimensiens' for 'dimensions', 'betng'
+      for 'being', and 'ars' for 'are'.
+   9. Page 17--a value in a formula was printed as 6000, but in the
+      context of the other information, particularly the example
+      immediately following, the value was believed to be incorrect, and
+      was changed to 5000.
+  10. Page 23--The value of 388 sq. inches at the top of the page in the
+      book is incorrect; 3 x 8 x 12 = 288, so has been corrected.
+  11. Page 24--Rods section, numerical value appeared to be 15.000 in
+      the book, but from context, must be 15,000 instead.
+  12. Page 28--Typos: changed 'Trautwine's Edgineer's Pocket-Bood' to
+      Trautwine's Engineer's Pocket-Book'; corrected  'af' to 'as',
+      'bracas' to 'braces'.
+  13. Page 30--Apparent typo in the table at the bottom of page.  Value
+      for Center Brace size for 200' span was shown as '8 x 1', believed
+      from context of table to be '8 x 10'.
+  14. Page 33--table of dimensions of a Pratt Truss, last column, row
+      starting with 150, the original says 8--1-1/8, this is believed to
+      be, and has been changed to, 3--1-1/8.
+  15. Page 37--The five formulas with square roots were incorrectly
+      printed in the book, multiplying the terms inside the square root
+      instead of adding them, which is obviously incorrect per the
+      Pythagorean theorem of right triangles.
+  16. Page 38: The fifth ratio in the group of five near the top of the
+      page must start with 20, not 10 as in the book
+  17. Page 38--The equation for W as printed on this page is not
+      consistent with that found on pages 18 to 24, so has been corrected
+      from 'bd^2' to 'bd^3'.
+  18. Page 39--arch brace truss table heading typo-changed 'FOE' to 'FOR'.
+
+
+
+
+
+
+End of the Project Gutenberg EBook of Instructions on Modern American Bridge
+Building, by G. B. N. Tower
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