________________________________________________________________________ PROBLEM (10.104) A cantilever beam AB and a simple beam CD are supported and loaded as shown in Fig. P10.104. A roller fits snugly between the two beam at point B. Determine: (a) The force F transmitted between the beams at B. (b) The reactions RC and RD for the lower beam. Assumption: The flexural rigidity EI is constant for both beams. SOLUTION (a) Refer to Table B.14. ∑M F C L/2 L/2 B v B RC RD P B A D vB = P vB ' + vB '' F (b) Substitute F = 2 P 3 into Eq. (1): C = 0 : RD = F 2 (1) PL3 ↓ 48 EI P( L 2)3 PL3 vB ' = = ↓ 3EI 24 EI F ( L 2)3 FL3 vB '' = = ↑ 3EI 24 EI Condition of compatibility at B: vB = vB '+ vB ' ↓ vB = FL3 PL3 FL3 = − 48EI 24 EI 24 EI 2 F= P or 3 1 RD = P = RC 3 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.