Mechanics of Materials; A Treatise on the Elasticity and Strength of Beams, Columns, Arches, Etc., for Students of Engineering

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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1887 edition. Excerpt: ...at the middle, each half will be bent in the same manner as the cantilever in Fig. 302; l/2P" corresponding to P sin a, and P' to Pcos . (14). The equation of the curve, then, substituting (14) in 298. Inclined Beam with Hinge at One End.--Fig. 304. Let e = e, . Required the equation for safe loading; also the maximum shear, there being but one load, P, and that in the middle. The vertical wall being smooth, its reaction, B, at 0 is horizontal, while that of the hinge-pin being unknown, both in amount and direction, is best replaced by its horizontal and vertical components H0 and V0, unknown in amount only. Supposing the flexure slight, we find these external forces in the same manner as in Prob. 1 37, by considering the whole beam free, and obtain ff=f cota; H0 also = C. cota; F0 = P... (1) For any section n between 0 and B, we have, from the free body nO, Fig. 305, uniform thrust = = H cos a.. (2) and from-(moms, ) = 0, PlI=Hx sin a (3) e and the shear = J = H sin a = y2 P cos a (4) The max. (Pi]p2) to be found on OB is.-. close above B, where x = I, and is As showing graphically all the results found, moment, thrust, and shear diagrams are drawn in Fig. 307, and also a diagram whose ordinates represent the variation of (Pi+Pt) along the beam. Each ordinate is placed vertically under the gravity axis of the section to which it refers. 299. Numerical Example of the Foregoing.--Fig. 308. Let the beam be of wrought iron, the load P = 1,800 lbs., hanging from the middle. Cross section rectangular 2 in. by 1 in., the 2 in. being parallel to the force-plane. Required the max. normal stress in any outer fibre; also the max. total shear. This max. stress-intensity will be in the outer fibres in the section just below B and on...show more

Product details

• Paperback | 76 pages
• 189 x 246 x 4mm | 154g
• United States
• English
• black & white illustrations
• 1236784693
• 9781236784698