Mechanics of the girder; a treatise on bridges and roofs, in which the necessary and sufficient weight of the structure is calculated, not assumed

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. 1886 Excerpt: ... End, but simply supported at the Left.--The point of contrary flexure must be at the distance xa = l--a') from the unfixed end, in order that the greatest positive moment may be equal to the greatest negative moment. Equations (43) and (93) apply, giving, since Mt = o, Mx = Wl-=a' + JfJ = BM (352) if the cross-section be rectangular, and x 7 d. For x = /, M2 = BAh2. For = (/ + /), M2 =-Wa'V-& when b = o. I Jc a For x = a', = Wa'-f. I + a 1-ih(l + '-» 3" Which shows that the width at D, Fig. 101, is the same as the width at C for h constant. When x a', use (40) and (93), giving To find the lowest point, E, in the curve, Fig. 101, we equate the deflection, D„ between the lowest point and left end of the beam, to the total deflection, D2 + A between the same point and the right end of the beam, and solve the equation A = A + Dv For the length AE = z, (307) gives Example.--Given W = 4,000 pounds at the distance a' = l from the unfixed end, A, Fig. 101; / = 180 inches; h = 15 inches = uniform height of beam; B, = rfoB--1,060 pounds = working inch strain for oak; E = 2,150,000. Crosssection rectangular. Then width of beam is, At left end, (354), x--o, b = o. At the weight, (353), x = l, b = 4 X 180 _ inches. 1060 x 151 J y (353). x = §/, 3 = o. At fixed end, (353), x = l, b=-4000 x 180 =-3.0x9 inches; 1060 x is» the negative sign simply showing that the lines cd, cldl, have crossed somewhere between x = l and x--I. Moment at fixed end, M2 =--4000 x =--izoooo. 1 + i Moment at the weight, Ma? = 120000 inch-pounds. The deflection at the lowest point, E, is given by (355), 105. Continuous Uniform Load, wl, on a Beam of Uniform Strength, fixed at the Right End, and simply supported at the Left, Fig. xoi.--The figure shows the curvature a...