83. The Floor-Beams. All floor-beams should be of sufficient depth to allow the use of small-legged connection angles at the ends where they join the end-posts. The thickness of the web should also be greater than that which is theoretically computed, in order that sufficient bearing may be given so that the rivets for the stringer connections will not require the stringers to be of too great a depth. The depth of the floor-beam will, of course, vary somewhat with the length of the panel and with the loading, but should not be less than 36 inches in any case. A considerable variation in the depth will not affect the weight of the floor-beam or the bridge to an appreciable extent. A rood plan is not to exceed a depth of 5 feet, with panel lengths of 25 feet and E 50 loading. In this bridge the depth of all intermediate floor-beams will be taken as 4S inches. It is good practice not to consider the web area when designing flanges of floor-beams and stringers, and the design here given does not consider the web as taking any bending moment.
The design of an intermediate floor-beam will now be made. The loads for which it is designed are the floor-beam reaction due to the live load (see Cooper, p. 32), the floor-beam reaction due to impact, the dead weight of the stringers and track, and the weight of the beam itself. The latter weight is distributed uniformly over the entire length of the beam, and the other loads act as concentrated loads spaced 6 feet 6 inches apart at equal distances from the center. The computation of the concentrated loads is as follows: The moment at points under the loads (see Fig. 168) is 136 020 X 5.25 X 12 = 8 575 000 pound-inches. This is due . to the con centrated loads only. The weight of one floor-beam may be approxi mately determined by the same formula as used to determine the weight of plate-girder spans; only, in place of the length of the span, the length of the_ panel must be substituted. The total weight of the above floor-beam, then, is: = S 655 700 pound-inches. Note that the dead-load moment at the center of the beam is added to the concentrated-load moment at the point where the concentrated load is applied. This will give the total moment at the center of the beam as shown by Fig. 169, since the concentrated-load moment, is constant between the points of application. The end shear . is readily computed to be 136 020 + 1 5S0 = 137 600 pounds. The curves of moments and shears are shown in Fig. 169.
The total depth of the floor beam, back to back of angles, is 481 inches ;and the effective depth will, for approximate computa tion of the flange area, be taken as somewhat less, say 441 inches, since the flange angles will probably be 6 by 6-inch and the center of gravity of most of these angles lies about 11 inches from the hack. The approximate flange stress is S 655 194 500
44.5 194 500 pounds, and the required net area (17) will be 16 000 = 12.2 square inches. In assuming the size of the angle, it is to be remembered that when, as in this case, no cover-plates are used, no rivet-holes will be taken out of the top flange, and only one rivet hole will be taken out of the vertical flange.
Two fi by 6 by -inch angles give a gross area of 7.11 square inches each, and a net section of 7.11 — 0.625 = 6.485 square inches each, or 12.07 square inches net for both. As this is near the required area, these angles will be taken; and a recomputation will now be made with the actual effective depth, in order to see if sufficient variation in the areas occurs to require another angle to be taken. The actual effective depth is now 48+ — 2 X 1 .84 — 44.57 inches; and making computations with this, it will be found that a net area of 12.10 square inches is required. As this is practically the same as was determined at first, no change will be made in the size of the angle.
The web is to be designed for a total shear of 137 600 pounds. The required area (18) is 137 600 = 13.76 square inches, 10 000 acid the required thickness is 13.76 = 0.286 inch; but on ac 48 count of the Specifications (36), Fl inch must be used. The web will accordingly be 48 by *-inch. The determination of the number of rivets which go through the connection angle of the stringer and the web of the floor-beam can now be made. The value of field rivet in bearing in a *-inch plate (19) is s X c X 20 000 = 6 560 pounds, and the total number required in one connection angle will be 136 020 = 11 field rivets 2X6 560 (see Fig. 170).
The pitch of the rivets in the flange can in this case be determined by the use of the formula: the Since the flange is of the same cross-section throughout, the value of the effective depth will not change, and it can therefore be used in the above equation instead of considering the value of the distance between rivet lines. The shear being practically constant from the connection of the stringers to the end of the floor-beams, the rivet spacing will be constant in this distance. It will be: the value of a T,-inch shop rivet in bearing in the *-inch web being X * X 24 000 = 7 8S0 pounds. This is seen to be less than 2* inches; but, as the angles have 6-inch legs, this spacing can be used in a horizontal direction; and the distance from center to center of rivets, which will be placed in rows on two gauge lines, will still be greater than 2* inches.