________________________________________________________________________ PROBLEMS (10. 112 and 10.113) A cantilever beam supports a partial uniform load of intensity w as shown in Figs. P10.112 and P10.113. Determine: (a) The angle of rotation at free end B. (b) The deflection at the free end B. SOLUTION (10.112) w B A EI L/2 3EI L/2 M x −3wL2 8 x1 M EI − wL2 8EI − wL2 24 EI A1 A2 x A3 − 8wLEI 2 Parabolic Spandrel x3 x2 Tangent at A A vB B 1 wL2 L wL3 =− 2 24 EI 2 96 EI 2 1 wL L wL3 A2 = − =− 2 8EI 2 32 EI 2 1 wL L wL3 A3 = − =− 3 8EI 2 48EI A1 = − θB L L 2L + = 2 6 3 L L 5L x2 = + = 2 3 6 3 L 3L x3 = ( ) = 4 2 8 x1 = (a) θ B / A = θ B − θ A0 = A1 + A2 + A3 θB = − wL3 wL3 (1 + 3 + 2) = 96 EI 16 EI 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. (b) t B / A = vB =− wL3 2 L wL3 5L wL3 3L − − 96 EI 3 32 EI 6 48EI 8 or vB = − wL4 47 wL4 (8 + 30 + 9) = ↓ 1152 EI 1152 EI SOLUTION (10.113) w a A a C M EI x2 x1 − wa 2 2 EI A2 −3 wa 2 2 EI B a D A3 x Spandrel Parabolic A1 x3 Tangent at A vB A D B θB bh 1 wa 2 wa 3 A1 = =− a =− 3EI 3 2 EI 6 EI 3 wa 1 1 wa 3 A2 = − A3 = − a( wa 2 ) = − 2 EI 2 2 EI x1 = a + 3a 7 a = 4 4 x2 = 5a 2 x3 = 8a 3 (a) θ B / A = θ B − θ A0 = A1 + A2 + A3 θB = − wa 3 7 wa 3 (2 + 6 + 6) = 12 EI 6 EI 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. (b) t B / A = vB = A1 x1 + A2 x2 + A3 x3 vB = − wa 4 69 wa 4 23 wa 4 (7 + 30 + 32) = − = ↓ 24 EI 24 EI 8 EI 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.