Chapter 3

| | | 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.

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

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'.