759_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

759_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 753 SECTION 9.6 Moment-Area Method Problem 9.6-11 A simple beam AB is subjected to couples M0 and 2M0 as M0 shown in the figure. Determine the angles of rotation uA and uB at the beam and the deflection d at point D where the load M0 is applied. 753 2M0 A B D L — 3 E L — 3 L — 3 Solution 9.6-11 Simple beam with two couples DEFLECTION CURVE AND M EI ANGLE OF ROTATION uB AT END B DIAGRAM tA/B AA1 A1 a uB first moment of area between A and B with respect to A 2L L 2L L 2L b + A2 a + b + A3 a +b 9 3 9 3 9 AA1 L 0 0 ; DEFLECTION d AT POINT D M0 L2 18EI Distance DD1 1 (BB1) 3 tD2/A first moment of area between A and D with respect to D D2D1 L A1 a b 9 M0L2 54EI A1 A2 1 M0 L a ba b 2 EI 3 M0 L 6EI A3 M0 L 6EI ANGLE OF ROTATION uA AT END A tB/A BB1 A1 a first moment of area between A and B with respect to B L L 2L L + b + A2 a + b 3 9 3 9 A3 a M0 L2 6EI uA BB1 L M0 L 6EI (clockwise) ; 2L b 9 D2D1 M0 L2 27EI (downward) d ; DD1 NOTE: This deflection is also the maximum deflection. ...
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