________________________________________________________________________ PROBLEM (*10.142) Determine the free-end deflection v A of the cantilever beam loaded as shown in Fig. P10.142. Assumption: The beam has a rectangular cross section of constant width b. *SOLUTION y b L P h0 2h0 A h x B M/EI x dx x A x h x h = h0 (1 + ) = 0 ( L + x) L L I 1 I A = bh03 I = A3 ( L + x)3 L 12 v A = t A / B = Ax = ∫ =− -PL/EIB M − PxL3 = EI EI A (1 + x)3 Px 2 L3 dx EI A (1 + x)3 PL3 x 2 dx EI A ∫ ( L + x)3 L PL3 2L L2 =− ln( L + x) + − EI A L + x 2( L + x) 0 =− PL3 5 PL3 PL3 = 0.06815 ↓ (ln 2 − ) = −0.06815 EI A EI A EI A 8 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.