________________________________________________________________________ PROBLEM (10.145) In the fixed beam AB shown in Fig. P10.145, the left-hand support has settled a distance δ0 below the right-hand support. Determine the support reactions. SOLUTION Consider RA and M A as redudants. MA δ0 A L RA MA RB A x B RA M/EI MB B L/2 MA/EI A1 x A2 -RAL/EI 2L/3 A1 = θB/ A M AL 1 RA L2 A2 = − 2 EI EI 0 0 = θ B − θ A = A1 + A2 Thus, 2 M A = RA L (1) 2 3 M L R L 2 L t A / B = −δ 0 = A1 ( ) + A2 ( L) = A − A 2 3 2 EI 3EI or 6 EI δ 0 −2 RA L + 3M A = − L2 From Eqs. (1) and (2): 12 EI δ 0 ↓ RA = − L3 MA = − (2) 6 EI δ 0 L2 Continued on next slide 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. Symmetry dictates that RB = − RA ↑ MB = MA 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.