Framed structures and girders, theory and practice

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1911 Excerpt: ...t in like units, and h and i in feet. Again, in Figs, (a), (6), and (c), t=-n, (11) from which v may be found in terms of panel lengths by expressing t and n in panel lengths. For two diagonals in the same panel, the lever arms of the diagonals are in the inverse ratio of the lengths of the members. Thus, in Fig. (d), z = th/i and zi = tihi/i. But lh = tih; therefore %/%=i/i. The general case in which both chords are inclined at unequal tingles with the horizontal is shown in Fig. 5. Eq. (10) is applicable also to this case, t denoting the horizontal distance from G to the diagonal. It is more convenient, however, under these conditions to express the value of z in another form. With the notation shown in the figure, k denoting the normal distance from d to CD, the following relations may be derived from similar triangles: Fig. 5. As will be seen later, this equation may be conveniently applied to bridge trusses in which both chords are inclined, (Art. 145, Example) and to the trussed supports (' bents') of viaducts (Chapter XV). If the heights h and hi in any of the above figures are varied in a constant ratio, it is seen that the position of the moment center G remains unaffected. Since the horizontal lever arms v, t, ti, etc., remain unchanged, the stresses in the verticals are unaltered, as will be seen in the next article. The principle that the stresses in the vertical members of a truss are not affected if all its vertical dimensions are varied in a constant ratio is a perfectly general one. The lengths of the inclined lever arms, z and Zi, and therefore the stresses in the diagonals, are obviously affected by variations in h and h. But since under the conditions stated, t in Eq. (3), Art. 130, is constant, the stress in any diagonal varies in propor...