________________________________________________________________________ PROBLEM (*10.144) For the beam of variable cross section illustrated in Fig. P10.144. Determine the maximum deflection vC . *SOLUTION Beam is symmetric about C. P A L/2 B L/2 C P/2 P/2 PL/4 M A B C x y B A vC tA/C x C 1 1 x b0 h3 , I = bx h3 = I o ( I + ) , L 12 12 1 3 1 I C = ( b0 )h3 = b0 h3 12 2 8 I0 = tA/ C M PL =∫ xdx = 2 EI 0 EI = ∫ L2 0 M= P x 2 x2 dx ( L + x) PL 2 ⎧ 3 3 ⎫ PL [ L ⎨ln( ) − ⎬] = (0.03L2 ) 2 EI 0 ⎩ 2 8 ⎭ 2 EI 0 and vC = t AC = 0.18 PL3 0.0225 PL3 = ↓ Eb0 h3 EI C 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.