815_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

815_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 10Ch10.qxd 9/27/08 7:32 AM Page 809 809 SECTION 10.4 Method of Superposition Method of Superposition P The problems for Section 10.4 are to be solved by the method of superposition. All beams have constant flexural rigidity EI unless otherwise stated. When drawing shear-force and bending-moment diagrams, be sure to label all critical ordinates, including maximum and minimum values. B A MA RA Problem 10.4-1 A proposed cantilever beam AB of length L carries a a concentrated load P acting at the position shown in the figure. Determine the reactions RA, RB , and MA for this beam. Also, draw the shear-force and bending-moment diagrams, labeling all critical ordinates. b L Solution 10.4-1 Propped cantilever beam Select RB as redundant. OTHER REACTIONS (FROM EQUILIBRIUM) EQUILIBRIUM RA RA P RB MA Pa RBL MA RELEASED STRUCTURE AND FORCE-DISPLACEMENT RELATIONS Pb 2L3 (3L2 Pab 2L2 b2) (L + b) ; SHEAR-FORCE AND BENDING-MOMENT DIAGRAMS COMPATIBILITY dB (dB)1 (dB)2 dB RB Pa (3L 6EI Pa2 2L3 (3L 0 a) RBL3 3EI a) ; 2 0 RB ...
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