To calculate the stress in 4-Y, take center of moments at joint P2, and pass a section cutting members 5-X, 4-5 and 4-Y, and assume the stress in 4-Y as an external force acting from the outside toward the cut section. Then 4-YX 15.6′ — 3,000 X 15' - 3,000 X 23′ = 0. Then 4-Y+7,300 lb.

Graphic Resolution. The load P。 is assumed as transferred to the bent by means of the auxiliary members. The loads Po, P1, P2, P3, P4 are laid off as shown, and with the load Pa the stress triangle Y-X-2 is drawn. The remainder of the solution is easily followed.

(c) Results.-The stress in the auxiliary member 2-Y acts as a load at the top of post 4-Y. Load Po is the wind load on the train and is transferred to the rails by the car. For the reason that the wind may blow from the opposite direction, both sets of stresses must be considered in combination with the dead and live load stresses in designing the columns.

PROBLEM 26A. WIND LOAD STRESSES IN A TRESTLE BENT.

(a) Problem.—Given a trestle bent, height 54′ 0′′, panels 18′ o", width at the base 30′ 0′′, width at the top 8′ o", wind loads Po, P1, P2, P3, P4 as shown in Problem 26. Calculate the stresses in the members of the bent due to wind loads by algebraic moments, and check by calculating the stresses by graphic resolution. Assume that the diagonal members are tension members, and that the dotted members are not acting for the wind blowing as shown. Scale of truss, I' o". Scale of loads, I' = 2,000 lb.

= 10'

PROBLEM 27. WIND LOAD STRESSES IN A Transverse BeNT BY GRAPHIc Resolution. (a) Problem.-Given a transverse bent, span 40′ o", pitch of roof, height of posts 20′ 0′′, posts pin-connected at the base, wind load 20 lb. per square foot of vertical projection. Calculate the wind load stresses in the bent by graphic resolution. Scale of bent, I' IO' o". Scale of loads, I' = 3,000 lb.

=

=

To construct the stress diagram lay off the load line P1 + P2 + P3 + P1 + Pь, and 1-Y = V = 3,375. lb. Beginning at the foot of the windward post, V acts downward, H X-I acts to the left, P, acts to the right. The polygon is closed by drawing lines parallel to 1-X and 1-Y, the final stress polygon being Y-1-X-X-1'. Then pass to the load P, in the transverse bent, and in the stress diagram P, acts to the right, I-X acts upwards to the left, 1-2 acts to the right, and 2-X acts downwards to the left, closing the polygon. The remainder of the stress diagram is drawn in a similar manner, passing to the foot of the knee brace, then to the top of the post, etc., finally checking up at the foot of the leeward post. The maximum shear is in the leeward post, below the knee brace the shear is H 4,500 lb., above the knee brace the shear is the horizontal component of the stress in 10-X = 10'-X = 9,000 lb. The maximum bending moment in the post is at the foot of the leeward knee brace and is M = 4,500 X 13 60,000 ft.-lb. For further explanation see the author's "The Design of Steel Mill Buildings."

=

=

(c) Results.-The stresses in the members do not follow the usual rules for trusses loaded with vertical loads; the top chord is partly in tension and partly in compression, while the bottom chord is in compression. The bent should be designed for the wind load stresses combined with the dead load and the minimum snow load stresses, for the snow load and the dead load stresses, or for the wind load and the dead load stresses, whichever combination produces maximum stresses or reversals of stresses.

The stresses in the posts are calculated by dropping the points 1, 2, 10 and II to the points I', 2', 10 and 11', respectively, on the load line, or on load line produced. The stresses in the windward post are 1'-Y and 2'-3, while the stresses in the leeward post are 11'-Y and 9-10'. The maximum shear in the leeward post is above the knee brace and is 10'-X

=

9,000 lb.

PROBLEM 27A. WIND LOAD STRESSES IN A TRANSVERSE BENT BY GRAPHIC RESOLUTION.

(a) Problem.-Given a transverse bent, span 40′ o", pitch of roof, height of posts 20' 0", posts pin-connected at the base, wind load 20 lb. per square foot normal to the sides and the normal component of a horizontal wind load of 30 lb. per square foot on the roof. (The normal load on the roof for a horizontal wind load of 30 lb., is 22 lb. per sq. ft., see "Steel Mill Buildings.") Calculate the wind load stresses in the transverse bent by graphic resolution. Scale of bent, I' 10' 0". Scale of loads, 1": = 3,000 lb.

=

PART II.

DESIGN OF STEEL AND TIMBER BRIDGES.

CHAPTER VIII.

TYPES OF BRIDGES.

Introduction. A truss is a framework composed of individual members so fastened together that loads applied at the joints produce only direct tension or compression. The triangle is the only geometrical figure in which the form is changed only by changing the lengths of the sides. In its simplest form every truss is a triangle or a combination of triangles. The members of the truss are either fastened together with pins, pin-connected, or with plates and rivets, riveted.

FIG. 1.

DIAGRAMMATIC SKETCH OF A THROUGH PRATT TRUSS HIGHWAY BRIDGE.

The bridge in Fig. I consists of two vertical trusses which carry the floor and the load; two horizontal trusses in the planes of the top and bottom chords, respectively, which carry the horizontal wind load along the bridge; and cross-bracing in the plane of the end-posts, called

portals, and in the plane of the intermediate posts, called sway bracing. The floor is carried on joists placed parallel to the length of the bridge, and which are supported in turn by the floor beams. The names of the different parts of the bridge are shown in Fig. 1. The main ties, hip verticals, counters and intermediate posts are together called webs. The bridge shown in Fig. I is a through pin-connected bridge of the Pratt type, the traffic passing through the bridge. The bridge shown

in Fig. I has square abutments; the abutments are not at right angles to the center line of the bridge in a "skew" bridge. Short span highway and railway bridges have low trusses and no top lateral system nor portals. In a railway bridge the track and ties are supported on stringers, which replace the joists in Fig. 1.

A low truss highway bridge of the Warren type is shown in Fig. 2, and a view of a similar bridge is shown in Fig. 3. The trusses are built up of angles riveted together by means of connection plates. Bridges of this type are built with spans of from 30 to 75 feet. Low truss bridges are also made with pin-connected joints. A pin-connected low Pratt truss bridge is shown in Fig. 4.