________________________________________________________________________ PROBLEMS (10.155 and 10.156) A beam AB is supported and loaded as shown in Figs. P10.155 and P10.156. Determine the reactions at supports A and B. SOLUTION (10.155) Consider RA as redundant. P tangent at A A L/2 B L/2 C MB RA vA = t A / B = 0 θB = 0 RB M RAL 2L/3 A1 A C L/2 EIt A / B = 0 = A1 ( B A2 L/3 x 1 1 A1 = ( RA L) L = RA L2 2 2 1 PL L 1 A2 = − ( ) = − PL2 2 2 2 8 -PL/2 2L 5L ) + A2 ( ) 3 6 or RA = 5 P↑ 16 RB = 11 P↑ 16 Statics: MB = 3 PL 16 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. SOLUTION (10.156) Consider RA and M A as redundants. w0 Tangent at B MA A L RA M MB B RB 2L/3 RAL L/2 A1 x A2 -MA Cubic 4L/5 A3 -w0L2/6 1 1 RA L( L) = RA L2 2 2 A2 = − M A L A1 = A3 = − w L2 1 w0 L2 ( L) = − 0 4 6 EI 24 EI θ A / B = θ B 0 − θ A0 = 0 = A1 + A2 + A3 or 1 1 RA L = w0 L2 2 24 2L L 4L = 0 = A1 ( ) + A2 ( ) + A3 ( ) 3 2 5 −M A + EIt AB (1) or 2 1 − M A + RA L = w0 L2 3 15 From Eqs.(1) and (2): 1 3 MA = w0 L2 RA = w0 L ↑ 30 20 Statics: 7 1 RB = w0 L ↑ MB = w0 L2 20 20 (2) 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.