The shear between the stringer connections is practically zero, and therefore the spacing will be very large. Being over 6 inches, it will be subject to (37).
The connection angles at the ends of the floor-beams will be taken as 6 by 31 by *-inch, the 6-inch legs being against the web of the floor-beam. The other legs are chosen small in order that they may fit into the channels which will very likely he required for the posts; and according to the sixth column, p. 183, Carnegie Handbook, only S} inches is available for this purpose. This 8} inches is taken from a 10-inch channel, since this is the smallest channel that can be used which will give room for connection and yet be in accordance with the Specifications. This is due to the fact that its web (36) is greater than inch. The rivets which connect the end angles to the floor-beam web are shop rivets, and those which connect the end angles to the posts are field rivets. Since the size of the post is not known, the thickness of its metal, of course, cannot he used, and therefore the number of rivets required in bearing in the post cannot be determined at this time.
The number of shop rivets required through the end angles and the floor-beam web is governed by the bearing of the rivets in the fi-inch web of the floor-beam. The value of a -Finch shop rivet in bearing in a *-inch web (19), as has just been computed, is equal to 7 880 pounds, and the number of rivets required is 137 600 = 18.
7 880 The number of field rivets required in single shear to connect the end angles with the posts is 1637013 600 = 23. An even number of rivets will, of course, have to be used, one-half going into each of the 31-inch legs. See Fig 171 for the position and the number of rivets. It must be remembered that more than these num bers may be used by the draftsman on account of rivet spa cing which may be required by conditions other than those of design.
The design of the end floor beam is somewhat different from that of the intermediate floor beams in that the load which comes upon it is considerably lighter, since this floor-beam takes the dead load of only one half the panel and the live load due to the maximum end reaction for a stringer length instead of the floor-beam reaction for the stringer length (see Cooper, p.
32).
The maximum end shear is computed as follows: End Shear for 21-foot Span .. \ 51 400 pounds.
300 Impact = of 400 X (21 + 300) 48 000 " 80X2 X21 Dead Load of Stringers = --- 2 1 680 " Dead Load of Track = 400X 21 2 X 2 ..... 2 '• Total 103 180 pounds.
The maximum moment due to the above load is 103 1S0 X 5.25 X 12 = 6 500 0(0 pound-inches. The weight of the beam may be assumed as 3 100 pounds. This is the same as was computed for the intermediate floor-beam, but will be used for this beam, since the size of the web will be the same as in the others; and, although the flange area will be less, the end connections will be somewhat heavier owing to the connection of the beam to the end-post and the roller bearing, and this additional weight will cause the total weight of the end floor-beam to be about the same as that of the intermediate ones. The total moment at the center will then be 6 500 000 -I- 80 700 = 6 580 700 pound-inches.
The depth of the end floor-beam will be somewhat greater than the depth of the intermediate floor-beams. This is due to the fact that it extends downward a greater distance, resting upon the bearing plate, which comes directly upon the top of the rollers. The exact depth cannot, of course, be determined until after the roller bearings are designed; but it may be safely assumed as four or five inches deeper than the intermediate floor-beams, and in case this is not enough, the draftsman can easily fill in the remaining distance with filler plates, as this distance will not be very great. In case this depth is too great, the flange angles may be bent upward at the end, or a re-design may be made.
The depth will be assumed as 52 inches in this case. The effective depth will be assumed as 48 inches, and this gives an approxi mate flange stress of 6 580 700 = 137 000 pounds, 48 A 6 by 6 by s-inch angle gives a gross area of 5.06 square inches, and a net area of‘5.06 — ( + ) ,?g = 4.62 square inches. A recomputation with the true effective depth requires 8.42 square inches net. Two of these angles give 9.24 square inches; and as this coincides very closely with the required area, it will be used: The size of the web plate is 52 by 1-inch.