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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Unformatted text preview: 09Ch09.qxd 9/27/08 1:33 PM Page 751 751 SECTION 9.6 Moment-Area Method A1 PL2 16EI x1 3L 8 A2 PL2 32EI x2 L 6 PL2 3L PL2 L a b+ ab 16EI 8 32EI 6 A1x1 + A2x2 11PL3 384EI Use absolute values of areas. d DEFLECTION dC AT MIDPOINT OF BEAM MAGNITUDE OF LOAD TO CLOSE THE GAP At point C, the deflection curve is horizontal. dC tB/C first moment of area between B and C with respect to B d gap between the beam and the support at C 11PL3 384EI d 384EId P ; 11L3 SUBSTITUTE NUMERICAL VALUES: d I 10 mm 198 Problem 9.6-9 A simple beam AB is subjected to a load in the form of a couple M0 acting at end B (see figure). Determine the angles of rotation uA and uB at the supports and the deflection d at the midpoint. L 6 10 mm 6m 4 E P 200 GPa ; 64 kN M0 A B L Solution 9.6-9 Simple beam with a couple M0 DEFLECTION CURVE AND M EI DIAGRAM ANGLE OF ROTATION uA tB/A BB1 first moment of area between A and B with respect to B 1 M0 L a b (L) a b 2 EI 3 uA BB1 L M0 L 6EI M0 L2 6EI (clockwise) ; ANGLE OF ROTATION uB tA/B AA1 first moment of area between A and B with respect to A 2L 1 M0 a b (L) a b 2 EI 3 d deflection at the midpoint C d distance CC2 Use absolute values of areas. uB AA1 L M0 L 3EI M0 L2 3EI (Counterclockwise) ; ...
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This note was uploaded on 12/22/2011 for the course MEEG 310 taught by Professor Staff during the Fall '11 term at University of Delaware.

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