________________________________________________________________________ PROBLEM (12.48) A pin-ended truss in which all members have the same axial rigidity AE is loaded as shown in Fig. P12.48. Using Castigliano’s theorem, determine the vertical displacement of point D. SOLUTION B L L A L D LAB = LCD = 2 L W LBC = LAC = LBD = L C The method of joints(or sections) is applied: FAB = 2W FBC = −W FCD = − 2W FBD = W FAC = −W Thus, ∂F 1 δV = Fi i Li ∑ AE ∂W WL WL = [ 2( 2) 2 + 1 + 1 + 1 + 2( 2) 2] = 8.657 ↓ AE 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.