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753_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

753_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 9.6 Moment-Area Method 747 ( u B is positive when counterclockwise) D EFLECTION Q first moment of areas A 1 and A 2 with respect to point B Q A 1 x 1 + A 2 x 2 M 0 L 2 2 EI PL 3 3 EI u B A 0 M 0 L EI PL 2 2 EI u B / A u B u A A 0 u A 0 A 0 A 1 + A 2 M 0 L EI PL 2 2 EI ( d B is positive when upward) F INAL RESULTS To match the sign conventions for u B and d B used in Appendix G, change the signs as follows. (These results agree with Cases 4 and 6, Table G-1.) d B PL 3 3 EI M 0 L 2 2 EI (positive downward) ; u B PL 2 2 EI M 0 L EI (positive clockwise) ; t B / A Q d B d B M 0 L 2 2 EI PL 3 3 EI Problem 9.6-4 Determine the angle of rotation u B and the deflection d B at the free end of a cantilever beam AB with a uniform load of intensity q acting over the middle third of the length (see figure). Solution 9.6-4 Cantilever beam with partial uniform load DIAGRAM M EI D EFLECTION
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