________________________________________________________________________ PROBLEM (10.52 ) A simple beam AB is subjected to couple M0 at midspan acting as shown in Fig.P10.52.Determine: (a) The equation of the deflection curve. (b) The deflection at midspan. (c) The magnitude and location of the maximum deflection. (d) The slope at the free end. SOLUTION y M0 A L/2 L/2 C L M0/L B x M0/L M0 L x − M 0 < x − >0 2 L M L EIv ' = 0 x 2 − M 0 < x − > +C1 2L 2 M M L EIv = 0 x 3 − 0 < x − > 2 +C1 x + C2 6L 2 2 EIv '' = Boundary conditions: v(0) = 0 : C2 = 0 M L v( L) = 0 : C1 = − 0 24 Equations (a) and (b) become M0 L EIv ' = [12 x 2 − 24 L < x − > − L2 ] 24 EIL 2 M0 L EIv = [4 x 3 − 12 L < x − > 2 − L2 x] 24 EIL 2 (a) (b) (1) (2) These lead to the results given in solution of Prob. 10.31. Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful.