________________________________________________________________________ PROBLEM (*10.62) A nonprismatic cantilever beam with flexural rigidity 2EI in part AC and flexural rigidity EI in part BC carries a uniform load of intensity w (Fig. P10.62). What is the deflection at the free end ? *SOLUTION w A L/2 w A 2EI C L/2 = Actual Loading B wL 2 wL2 + C 8 Equivalent Loadings C w EI B Use Table B.14 (cases 3.1, and 2): w( L 2) 4 ( wL 2)( L 2)3 ( wL2 8)( L 2) 2 17 wL4 vC = − − − =− 768 EI 8(2 EI ) 3(2 EI ) 2(2 EI ) θC = − w( L 2)3 ( wL 2)( L 2)2 ( wL2 8)( L 2) 7 wL3 =− − − 96 EI 6(2 EI ) 2(2 EI ) 2 EI Thus, L w( L 2) 4 vB = vC + θC ( ) − 2 8( EI ) 17 wL4 7 wL4 wL4 =− − − 768 EI 192 EI 128 EI 17 wL4 = ↓ 256 EI 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.