Essentials in the theory of framed structures . 1 , h — h hence <^ = = ? = 50 5° , , area KRWLalso EI = 155,000 a = ft. The centroid of the area KRWL is approximately P, and the area-moment of KRWL about P is 155,000 X = 3,774,000 A _ , _ 3,774,000 _ 29,976,000^- ~^ EI EI . 29,976,000 -. o- . Amax. = = ft. = m. 420,400,000 Although the loads are eccentric, it is clear that there is practi-cally no difference between the deflection at the center and themaximum deflection. The deflection at the center may be found from Eq.
Essentials in the theory of framed structures . 1 , h — h hence <^ = = ? = 50 5° , , area KRWLalso EI = 155,000 a = ft. The centroid of the area KRWL is approximately P, and the area-moment of KRWL about P is 155,000 X = 3,774,000 A _ , _ 3,774,000 _ 29,976,000^- ~^ EI EI . 29,976,000 -. o- . Amax. = = ft. = m. 420,400,000 Although the loads are eccentric, it is clear that there is practi-cally no difference between the deflection at the center and themaximum deflection. The deflection at the center may be found from Eq. 5, page218. The coefficients F are given in Table I. c = ; ife = 228 , THEORY OF FRAMED STRUCTURES Chap. V for the load A; , for the load at B; and for theload at C; hence 10,000 X 50 5,000 X so X = 14,792,000 X = 13,021,000 1,000 X 50 ^. 2,062,000 ^__^x ;p^;^ 29,871; ,000 r. Q, ;„ ^ _ yt /J, — ft. = in. 420,400,000 H- /5--. 5000* Fig. 139. The deflection at the center, due to the weight of the beam, may be found from equation 7, page 223. The coefficient of / when c = is TT = 50 X 80 = 4,000. 4,000 X 150 . .. A = —— X = ft. = m. 24 X 420,400,000 Sec. II DEFLECTION OF BEAMS 229 The total deflection at the center is + = in.,which in this case may be assumed without appreciable erroras the maximum deflection. A deflection of 3^60 of the spanis considered not excessive. 147. Deflection for Uniform and Concentrated Loads.—In Fig. 139, the tangent is drawn through C at the center of thespan. Assume that EI is expressed in foot^-pounds. TheM-diagram under the uniform load cannot be accuratelydivided into triangles, and an integration is necessary if anaccurate solution is desired. A sufficiently accurate solutionfor all practical purposes may be obtained by the geometricprocess by dividing the area QBDFJ by vertical ordinates intostrips, so narrow that their
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Keywords: ., bookcentury1900, bookdecade1920, booksubjectstructu, bookyear1922
