On account of the cheapness of I-beams, they will be used for stringers in this bridge; and sufficiently heavy shelf angles will be used to take up any distorting influences due to the eccentric connections which are unavoidable in this case. In case an I-beam had not been decided upon, the stringers would have been small plate-girders with a span of 21 feet and depth according to formul<•e given. They would have been computed in exactly the same manner as a plate-girder span of 21 feet' center to center of bearings.
Since the dead-load moment cannot be determined until the size of the stringer is known, an approximate design must first be made by using the live-load bending moment alone; and then, with the size determined in this manner, the extra section modulus required for the dead-load moment due to the weight of the beam and the track must be computed. If this extra section modulus, added to the one previously determined, is greater than that given by the beam in question, a larger size beam must be used and a recomputation made.
The section modulus (17) required for live load only is 5 247 000 16 000 = 327.9. As this is too large for one beam, two beams will be used, thus giving a required section modulus of 164 for one beam. Two 24-inch 80-pound I-beams will be used, giving a total section modulus of 2 X 174 = 348.
Assuming the rails and ties to weigh 400 pounds per linear foot, the. dead load per linear foot per stringer is SO + 400 = 180 pounds.
180X 21X 21X 12 The dead-load moment is therefore = 119 000 pound-inches. This requires an additional section modulus of 110 000 = 7.45. This, added to the 164 as determined above, makes 16 000 a total required section modulus of 171.25, which, being less than 174 (which is that for one I-beam), indicates that the above chosen beam is sufficient in strength, and it will therefore be used.
The number of rivets in the end connections will now be deter mined. The total end reaction for one I-beam is equal to the weight of one-half the beam, one-eighth the track in the panel, and one-half the maximum live-load reaction for one rail. These quantities are: Live-Load Reaction = 5.42400 =25 700 pounds.
Impact = 25 700 X 0.935 =24 030 " Weight of Track = X = 530 " Weight of Stringer = 21 X SO = 840 " The coefficient of impact is that for a loaded length of 21 feet.
From p. 177, Carnegie Handbook, sixth column, it is seen that the longest connection angle which can be used with a 24-inch I-beam is say 20 inches. In this case the thickness of the connection angles must be 51 100 10 000X 0.23 inch; but according td (36), inch will be used. The angles chosen will be 6 by 3I by 5-inch. The 6-inch leg will be placed against the web of the floor-beam in order to allow for sufficient room for rivets to be driven.
The rivets will tend to shear off at places between the webs of the stringer and floor-beam and the connection angles. They will also tend to tear out of the web of the stringer and out of the web of the floor-beam. As the thickness of this latter is not known, the determination of the rivets for this condition will be made under the next article. The bearing value of a --inch rivet in a 2-inch plate (19) is s X X 24 000 = 10 500 pounds, and 100 10 5(l0 = 5 shop rivets are required in bearing in the web of the stringer. The value of a K-inch shop rivet in single shear (18) is 0.6013 X 12 000 = 7 220 pounds, and the number of rivets required to prevent shearing between the connection angles and the webs is 51 1°° = 7 shop rivets. The value of a ;-inch field rivet in single shear (18) is 0.6013 X 10 000 = 6 013 pounds, and therefore 51 100 = 9 field rivets are required to 6 013 connect the connection angle to the web of the floor-beam. As men tioned above, the number of rivets in bearing in the web of the floor beam will be determined in the next article; and if the number required for bearing is greater than 9, then that number must be used instead of 9. Fig. 167 shows the connection of the stringer to the floor-beam web, and also the number of rivets as determined above, in their proper positions. The distance between the webs of the stringers must be such as to prevent their flanges from touching at the top.
The stringers should be connected at the bottom by a system of lateral bracing of the Warren type. The size of these angles cannot be determined by theoretical considerations, but is usually chosen to be 31 by 31 by s-in. See Plate II (p. 172) for the general arrangement of this bracing.