________________________________________________________________________ PROBLEM (12.57) For the truss loaded as shown in Fig. P12.56, determine the horizontal deflection at point C. Use Castigliano's theorem. SOLUTION P+Q A Joint C B RA FBC 2L 2L L D L RE E Q 1 FCD C C P P FBC = 2 P FCD = − P Joint B B FAB 1 FBD FBC FDE FAE 1 P 1 P D Q P+Q A 2P FAB FAD Joint D FAD = 2 P + 2Q FDE = −2 P − Q Joint A 1 FBC = P 2 1 =− FBC = − P 2 FAB = P FAE = P + Q − 1 FAD 2 FAD Continued on next slide 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. We have ∂FAD ∂FDE ∂FAE = 2, = −1, = 0, Q=0 ∂Q ∂Q ∂Q and other derivatives are zero. Thus, ∂F 1 Fi Li i δD = ∑ AE ∂Q 1 PL [ 2 P( 2 L) 2 + (−2 P) L(−1)] = (2 2 + 2) = AE AE PL = 4.828 ↓ AE 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.