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757_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 757_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 9.6 Moment-Area Method 751 Use absolute values of areas. D EFLECTION d C AT MIDPOINT OF BEAM At point C , the deflection curve is horizontal. with respect to B d C t B / C first moment of area between B and C A 2 PL 2 32 EI x 2 L 6 A 1 PL 2 16 EI x 1 3 L 8 M AGNITUDE OF LOAD TO CLOSE THE GAP S UBSTITUTE NUMERICAL VALUES : d 10 mm L 6 m E 200 GPa I 198 10 6 mm 4 P 64 kN ; d d 11 PL 3 384 EI P 384 EId 11 L 3 ; d gap between the beam and the support at C 11 PL 3 384 EI A 1 x 1 + A 2 x 2 PL 2 16 EI a 3 L 8 b + PL 2 32 EI a L 6 b Problem 9.6-9 A simple beam AB is subjected to a load in the form of a couple M 0 acting at end B (see figure). Determine the angles of rotation u A and u B at the supports and the deflection d at the midpoint. Solution 9.6-9 Simple beam with a couple

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757_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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