The equivalent flange area is assumed to act at the center of gravity of the flange; and the bending moments equivalent to the above areas dead load; 0.59 X 20 000 X 72.554 = 856 000 pound-inches; and for live load: 2.88 X 10 000 X 72.551 = 2 090 000 pound-inches.
These bending moments must be taken up by the horizontal plates The stresses in these plates (see Fig. 160) are, for dead load: While the allowable unit-stresses are a maximum at the center of gravity of the flange and are those given by the Specifications, they decrease rapidly towards the center of the girder, being zero at the neutral axis of the entire section. The unit allowable stress at the center of the horizontal plates will not be so great as the maximum allowable, but will be proportional to the distance from center (see Fig. 160). The horizontal be taken 8 inches in width. The unit-stresses are easily determined by means of the similar triangles oab and nab'. The dead-load stress is determined front the proportion: .54.2., 4' 2 20 000' and is 14 950 pounds. For live load, the unit-stress will be of this amount, or 7 475 pounds.
The area required for this plate is, for dead load, 15. 1110 — 1 .05 38 square inches, and for live load '1 5.16 square inches, making a total of 6.21 square inches for both plates. Assuming two rivet holes out of the section, the net width is S — 2 e) = 6 inches; and the required thickness for one plate is X = 0.52, say inch. _ The joint will be weakest in bearing in the y-inch web. The number of rivets required is: 15 670 + aR 500 = 11 shop rivets. 4J20 The design of the shear plate is as follows: The shear is 28 COO 28 600 pounds, and the required area = 3.1S square inches. As the length of the plate is 461 inches, the required thickness is 2 X = 0.034 inch, but on account of the Specifications it cannot be less than inch thick. It will, however, be made ,9a inch thick, since it will then fill out even with the horizontal tension plates and no filler will be required. Bearing in the web plate decides the number of rivets, which is: 28 600 — 6 shop rivets.
4 920 The width of this shear plate should be, as before, 10' inches. The same conditions limiting the spacing of the rivets apply here as in the ease where the splice was designed for shear only. The length of the
horizontal plates should be sufficient to get in all the rivets, and this is a detail which is left to the judgment of the draftsman.
1. A plate girder is 87 ft. 9 in. center to center of end bearings. The dead-load moment is 0 125 000 pound inehes, and the live load moment is 3S 265 000 pound inches, the total shear at the sec tion being 202 700 pounds. The web is 00 by and the flange angles are 6 by 6 by l-inch. Design the web splice when no part of fhe web is considered as taking bending moment.
2. For the girder of Problem 1, above, design the splice when of the gross area of the web is considered as effective flange, area.
77. The Bearings. Articles 113 to 119 of the Specifications should be carefully studied before proceeding; also Article 87. Article 70 should be referred to, and the retnarks there made about bearings should be read. In case the length of bearing is such as to allow a simple ;-inch plate, care must be taken that the bearing plate does not extend past the flange angles more than 2 inches, or that the masonry plate does not extend past the bearing plate over 2 inches. Reference to "Steel Construction," Part II, p. 96, to Fig. 161, and to the discussion which follows, will explain the reason of this.
M= Si = 250 X 1 X 2' IaP _ 12 12 d 1 I 1 X 9 2 • c 16X 12'and as s = 10 000, 250 P 2 16X 12from which, d = 1.94, say 2 inches.
In case it is desirable to have a simple masonry plate instead of a cast-steel pedestal, and to have the plate extend over the sides of the angles a distance greater than 2 in ches, then some arrangementmust be made for sup porting the pro jecting portion. Fig.162 shows one of the methods most commonly used. Notwith standing the brac ing of the gusset plates, the mason ry plate is not ade quatelysupported, the greater pro portion of the stress coming upon the ends.
The disadvan tage of having the masonry plate too long is plainly shown by Fig. 163. Here the girder is shown deflected under a live load, the rear end of the plate being tilted up and the greater part of the pressure coming upon the forward end. The use of this style of plate is not to be recommended for spans over 40 feet.