_______________________________________________________________________ PROBLEM (12.77) A propped cantilever beam AB is supported at one end by a spring of constant stiffness k and carries a uniform load of intensity w as shown in Fig. P12.77. Apply the unit-load method to determine the reaction at A. x A R = kδ A w x B A B 1 Refer to the above figures, we write: 1 M = Rx − wx 2 m = −1x 2 Hence, deflection spring at A: Mm R dx = δA = ∫ EI k L 1 1 R ( Rx − wx 2 )(− x)dx = = ∫ 0 2 EI k Solving 3wL 8 1 + (3EI kL3 ) Reactions at B may then be found from statics. R= 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.