the panel-points. The stresses due to these loads should be added to those obtained by drawing a reciprocal polygon for the horizontal forces due to wind. The inclination of NQ and MG may easily be adjusted from the diagram of wind pressure, so that the diagonal members MN are not necessary. Timber Trestle Piers.-Figs. 109 and 114 illustrate the method of constructing trestle piers or bents of timber in viaducts of moderate height. When the height of the trestle pier is under 10 feet it is not usual to provide sway bracing, and from 10 to 20 feet sway braces are arranged as shown in Fig. 114. The braces should be bolted to the cap, to each pile or post, and to the sill with bolts inch in diameter, with cast-iron washers under both the head and the nut. Where the height of the pier exceeds 20 feet, the upper panel should be made from 15 to 20 feet, and the odd lengths put in the lower panel. Figs. 346 and 347 illustrate a high timber trestle pier used on the Californian and Central Railway, United States, America. These high piers require the greatest care and attention on the part of the designer. High trestle piers of timber present great varieties in design. They should be thoroughly sway-braced, each story having one set of braces. Counter-posts are also used to stiffen the bent, and longitudinal bracing between the bents, either in every bay or in every third or fourth bay, arranged horizontally and diagonally. A good plan is to brace every third bay diagonally so as to form a tower, and to provide simply horizontal longitudinal braces between the bents in the intermediate bays at each story. CHAPTER XXI. CONTINUOUS GIRDER ROAD BRIDGE. THE calculation of the stresses in continuous girder bridges may be illustrated by the following example of a road bridge. The bridge is illustrated in Plate III., and consists of two wrought-iron continuous lattice main girders 464 feet long over all, supported upon iron cylinder piers, forming three spans of 140 feet 3 inches, 182 feet, and 140 feet 3 inches respectively, measured from the centres of the piers. The main girders are spaced 21 feet centres across the bridge, and are 10 feet deep, excepting at the ends, which are curved to an elliptical outline. The top and bottom booms or chords are trough-shaped, formed with horizontal plates and T-irons riveted together. The web consists of vertical struts over river piers and plates over land piers, with flat lattice bars for the tension members, and channel bar compression members braced together, with ladder bracing set at an angle, the tangent of which is 7. The cross-girders are attached to saddles riveted to the bottom boom immediately over the apices of the triangulation, dividing the girder into panel lengths, each 7 feet long measured from apex to apex, or centre to centre of cross-girder. Longitudinal timber beams are attached to the top flanges of the cross-girders, upon which is laid a continuous floor of planks 4 inches thick. There is a timber kerb on each side of the roadway having a clear width of 18 feet. The piers are each constructed with two cylinders filled with cement concrete and braced together. The diameter of the cylinders of the river piers is 6 feet, and of the land piers 4 feet 6 inches. The upper portion of each cylinder consists of wrought-iron plates inch thick, riveted together with single butt joints. The lower portion consists of cast iron in lengths of 6 feet and 1 inch thick, with making-up piece of a length depending on the depth of foundation. Only two lengths are shown on the plate; the bottom length is 14 inch thick, and is provided with a cutting edge to facilitate sinking. The wrought-iron cylinders are secured together with diaphragm bracing having elliptica openings, and consists of 3-inch plates and 3 × 3 × 3 inch angle bars arranged as shown. The cylinders are sunk by excavating the material from the interior and loading until a satisfactory foundation is obtained. The dimensions of the plates, bars, angles, channels, etc., as well as the principal details are shown on Plate III. Cross-Girders. The dead load on one cross-girder consists of the weight of the floor, timber stringers, and the weight of the cross-girder itself. The dimensions of the stringers and the thickness of the floor may easily be determined from the data given, as explained in Chapter XIV. The weight on the driving wheels of the traction engine in the worst position must be taken. The sizes actually adopted are shown on Plate III.,1 and the weight of timber is 827 lbs. per foot run of bridge. The dead load on one cross-girder is therefore— 7 × 827 = 5789 lbs. = 2.6 tons distributed Assumed weight of cross-girder = 10 Total dead load = 3.6 The distributed live load is 84 x 18 x 7 = 10,584 lbs. = 4.75 tons distributed Concentrated load from traction engine shown in Figs. 322 and 323, which may be in the centre of the bridge, = 9.5 tons. Hence we must design the cross-girder for the 9.5 tons in the centre plus the distributed dead load of 3.6 tons. This will be equivalent to a uniformly distributed load of 22.8 tons. The bending moment in the centre is, since the girder is 21 feet span The floor in this stringers of ironbark. with pine timbers. 22.8 × 21 59.85 foot-tons bridge consists of New South Wales tallow-wood, and the The weight is therefore greater than would be the case The effective depth may be 1.83 feet, and the working stress, considering that the maximum load occurs very seldom, and then without much impact, may be found by the following The moment of resistance of the bottom flange is fad5 × 1.83 × a = 9·15a .. 9.15a 59.85 ..a = 6·54 square inches The section provided consists of— 2 angles 3" x 3" x 3" 4·7 square inches = The diameter and pitch of the rivets, and the thickness of web plate with regard to the intensity of shearing stress, may be investigated as in the other examples given. The rivets are inch diameter and 4 inches pitch. The web is inch thick. The weight of the cross-girder may be calculated in the manner already sufficiently illustrated, and will be found to weigh 2238 lbs. The total weight of the deck, including cross-girders, per foot run is = 0.51 ton. Main Girders. The dead load on one main girder is half the weight of the deck and the main girder itself. Total weight of deck per foot run = 0·256 ton. The weight of the main girder per foot run may be approximately estimated by means of the formula where the mean span × 0·8, and C=1200 The total dead and live load distributed per】 per} = 0.793 ton the}= The dead load per foot run used in the Case I.-Span II. fully loaded. cwt., w3 10 cwt. 2m,(140182) + 182m2 = (10 x 1403 16.75 × 1823) say 1944 foot-tons = 10 cwt. w1 = 10 cwt., w2 = 16.75 x=30.67 feet from piers I. and II. Taking the nearest apex, say 28 feet. Case II.-Spans I. and II. fully loaded. cwt., w2 = 10 cwt. W1 = W2 = 16.75 .. 644m, + 182m2 = 4(16·75 × 1403 + 16·75 × 1823) and 182m, + 644m2 = 4(16·75 × 1823 + 10 × 1403) .30 feet and 145 feet from Pier II., say 28 and 49 feet, from Piers II. and III. respectively ..x=87.6 feet from abutment II., say 91 feet Case III.-Spans I. and III. fully loaded. cwt., w2 = 10 cwt. W1 = W3 = 16.75 |