54. Portals and Sway Bracing. One half of the wind on the top chord is trans ferred to the hips U,'U, and From there it is carried to the abutments by means of the portal bracing and the end posts. Various styles of portal bracing are in use, but few are so easily analyzed and constructed as that of Fig. 101. This form of portal is at present being used almost universally on all spans up to 250 feet.
Let it be required to analyze a portal of this form, all the dis tances being as indicated in Fig. 101; and let: w = Wind panel load of upper chord; m' = Number of panels in upper chord; It must be remembered that h, is not the height of the truss, but is the length of the end-post from to U,.
For the truss of Article 47, w = 1.5; m' = 4; and P = 4.5. The value h, = + = 32.0 feet. The distance a must be so chosen that BD will not interfere with engines or other traffic which passes through the bridge. It will be assumed as 5 feet in this case. Then V = (4.5 + 1.5 + 1.5) 12 = 14.08; and H, = 7.5 = = 3.75; whence, 2 Sec = — (6.0 + 3.75 X 57) _ — 26.25 When the wind blows from the other side, the stresses in the diagonals are reversed, and those in the top are transposed. The members shown by broken lines take no stress. When the wind blows, the end-posts tend to bend as shown in Fig.. 102. This is with stood by the cross-section of the post at the points E and D. The bending moment caused at these points by the wind is X 1 and x 1. For the truss under consideration, If the posts are fixed at the lower end, then they will tend to bend as shown in Fig. 103, the post resisting the bending at two points D and d. The section at each point withstands in this case only half of the moment just computed, or 1 215 000 _ 2 = 607 500 lb.-ins. A further discussion of this will be given in Part II, on
"Bridge Design." Various -forms of sway bracing are used to connect the inter mediate posts and thus stiffen the cross-section of the bridge at those points. The form of portal just given is often used, as is also the form shown in Fig. 104. Here h is the height of the truss. The braces BD are called knee-braces. Here w is the wind panel load of the top chord, and The stress in B'B is the direct compression due to wind right or left, and differs in accordance with the position of the top strut.
There is also a bending moment at B' and B, which is: The bending moment at D and D' is equal to or 141 _ 2, according to whether or not the lower ends of the posts are fixed.
The determination of the stresses for the truss of Article 47 is left to the student.
When the wind is from the other side of the truss, the signs of the stresses in the knee-braces and the members C'B' and CB are reversed.
55. Final Stresses. The class of stresses which go to make up the maximum or minimum for which the member is designed, is .determined by the specifications used. The dead-load and live-load stresses are always included, and then those due to impact and wind should be added if required. In computing the maximum stresses, the algebraic sum should always be used. In a large majority of cases, all stresses which go to make up the maximum have the same sign, but some exceptions have been noted, as in the middle vertical of a Pratt or Howe truss. The minimum stresses are, with rare exceptions, obtained by combining stresses with signs of opposite character.