Pins for Country Highway Bridges 89. The Portal. In order to have a clearance of 21 feet (2) above the top of rail, it is necessary that the portal be as shown in Fig. 189. The stresses are found by methods of Article 54, Part I, the wind Load being computed according to (10). It must be remembered that the column is hinged.
In case the members of the portal braces bend about one axis, their length will be equal to the distance from one end to the other. In case they bend about the other axis as indicated by the broken line in Fig. 189, their length will be one-half of what it was in the first case.
The portal struts or diagonals will be designed first. Their length is 8.5 X 1.414 = 12 feet, or 144 inches. This is the total length. Although the Specifications do not men tion it, the ratio of the length to the radius of gyration should not exceed 120. This means that the radius of gyration in this case should be greater than 1o= 1.2. The section of the strut will be composed of two angles placed back to back.
Two angles 3- by 3 by i-inch, with an area of 4.6 square inches and equal to 1.72—see Carnegie Handbook, p. 146, and (72)—will be assumed to be sufficient to take the stress, and they must now be examined to see if the assumption is correct.
The allowable unit-stress (23) is 25 per cent greater than in the case of live or dead loads. This makes the unit-stress as computed from the formula: P = 1 16 000 — 70 X 111 11 = 12 680 pounds per square inch.
The required area is 38 500 _ 3.05 square inches; and since this is 12 6S0 less than the given area, the angle will be amply sufficient. The re quired area is over one square inch less than the given area, but this angle must be used, since it is the smallest angle allowed by the Specifi cations. Note that unequal legged angles should be used, as this will make the radius of gyration about one axis larger than about the other; and this will prove economical, since, when one axis is considered, the length of the member is greater than when the other is considered.
The above angle should also be examined for tension, it being considered that one rivet-hole is taken out of the section of each angle. The net section of the two angles will now be 4.60 — 2 (b) X
= 3.55 square inches; and the area required for tension is 38 500 r 16 000X 1.2a = 1 .93 square inches, which shows that the angle is amply sufficient. It should be noted that these Specifications do not require that only one leg of the angle shall be efficient unless both legs are connected. In ease this strut had been designed according to Cooper's Specifica tions, two angles 5 by 3 by -inch would have been required, and the 5-inch leg would have been placed vertically and the angle connected by this leg alone. While it is not within the province of this work to discuss the question of connecting angles by one or by both legs, yet it might be said that tests made on angles connected with one leg only, seem to indicate that the ultimate strength in tension is about 60 per cent of that obtained from the same angle when tested with both legs connected.
While according to (20) the alternate strains in the wind bracing do not have to be considered, since they do not occur very closely together, yet in framing the connections it is required that the sum of both positive and negative stresses shall be added. In this case the stress for which the connections must be designed is 2 X 38 500 = 77 000. It must be remembered that in this case also, the unit-stresses are increased 25 per cent over those allowed for live and dead loads.
The number of rivets required in the end connections will be governed by bearing in the connection plates, and these plates are usually made i-inch thick. The number of rivets required is 77 7 880X 11= S shop rivets, or 6 60 = 10 field rivets.
The portal bracing is riveted up in the shop and brought to the bridge site, where it is connected to the trusses by field-riveted con nections at its end. Therefore the end of the portal struts which connect with the top piece will have 8 shop rivets, and the other end which connects with the end-post will have 10 field rivets. Since the angles are small, all the above rivets must go in one line, and this will cause the connection plate to be quite large. It will probably be better to connect both legs of the angle by means of clip angles and thus reduce the size of the connection plates.