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831_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 831_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 10Ch10.qxd 9/27/08 7:36 AM Page 825 825 SECTION 10.4 Method of Superposition Problem 10.4-16 A fixed-end beam AB of length L is subjected M0 to a moment M 0 acting at the position shown in the figure. A (a) Determine all reactions for this beam. (b) Draw shear-force and bending-moment diagrams for the special case in which a b L/2 . B MB MA a RA b RB L Fixed-end beam (M 0 = applied load) Solution 10.4-16 (uB) 2 RBL2 2EI (dB) 2 RBL3 3EI (uB)3 Select RB and MB as redundants. M BL EI (dB)3 M BL3 2EI COMPATIBILITY L dB a+b or 2RB L3 EQUILIBRIUM RA RB (dB)1 MA MB RB L M0 uB 3MB L2 or RBL 0 (1) 3M 0 a(a + 2b) (uB)1 + (uB) 2 2 RELEASED STRUCTURE AND FORCE-DISPL. EQS. (dB) 2 + (dB)3 (uB)3 2M BL 0 2M 0 a (2) SOLVE EQS. (1) AND (2): RB 6M 0 ab M0 a MB 3 L L2 (3b ; L) FROM EQUILIBRIUM: RA 6M 0 ab MA 3 L SPECIAL CASE a RA (uB)1 M 0a EI (dB)1 M0 a (a + 2b) 2EI RB b 3M 0 2L M0b L2 (3a ; L) L/2 MA MB M0 4 ...
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