________________________________________________________________________ PROBLEM (*10.39) A beam AB supported at the ends as shown in Fig. P10.39 carries a concentrated load P at the mid span C. Determine the vertical deflection of the beam at the end B. *SOLUTION For segment AC EIv1 '' = Px 1 EIv1 ' = Px 2 + C1 2 1 3 EIv1 = Px + C1 x + C2 6 C A RA=P Px x L/2 P B Px PL/2 x L/2 For segment CB 1 EIv2 '' = PL 2 1 EIv1 ' = PLx + C3 2 1 EIv2 = PLx 2 + C3 x + C4 4 Boundary conditions: v1 (0) = 0 : C2 = 0 v2 (0) = 0 : C3 = 0 Then L L P L 3 L P L v1 ( ) = v2 ( ) : ( ) + C1 ( ) = PL( ) 2 + C4 2 2 6 2 2 4 4 L L P L 2 P L v1 '( ) = v2 '( ) : ( ) + C1 = − L( ) 2 2 2 2 2 2 Solving 3 11 C1 = − PL2 C4 = − PL3 8 48 At B(x=0): 11 11 3 vB = v2 (0) = − PL3 = PL ↓ 48 48 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.