________________________________________________________________________ PROBLEM (*10.161) Before the load is applied to the beam shown in Fig. P10.161, a small gap δC exists between beam AB and the support at C. Following the application of load, the gab closes and reactions develop at each support. Determine the reactions for the beam. *SOLUTION Consider RC as redundant. A RA M B 2a 2a RC RB 4a/3 4RBa 2RBa A1 x A2 - P δc Pa a M 1 A1 = (4 RB a)4a = 8 RB a 2 2 1 9 A2 = − (3Pa )3a = − Pa 2 2 2 1 A3 = (2 RC a )2a = 2 RC a 2 2 2RCa A A3 x C 2a/3 y δc x A 2a tA/B=2( tC/B+ δc) B tC/B tangent at B 4a 2a 32 9 4 ) + A2 (a ) + A3 ( ) = RB a 3 − Pa 3 + RC a 3 3 3 3 2 3 1 1 a 4 1 = [ (2 RB a)2a] − [ ( Pa)a] = RB a 3 − Pa 3 2 2 3 3 6 EIt A / B = A1 ( EItC / B We have 2(tCB + δ C ) = t AB : 2δ EI 4 25 = 8RB + RC − P = C3 3 6 a 1 3 ∑ M A = 0 : RB + 2 RC = 4 P 3 3 δ C EI 9 3 δ EI From Eqs.(1) and (2): RC = P − RB = P + C 3 3 8 4 a 16 8 a Then, ∑ Fy = 0 : RA = (1) (2) 1 3 δ EI P+ C3 16 8 a 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.