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721_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

721_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 9.3 Deflections by Integration of the Bending-Moment Equation 715 M AXIMUM DEFLECTION Set and solve for x : x 1 L a 1 1 3 3 b ; ¿ 0 ¿ M 0 6 LEI (2 L 2 6 Lx + 3 x 2 ) Substitute x 1 into the equation for n : (These results agree with Case 7, Table G-2.) M 0 L 2 9 1 3 EI ; d max ( ) x x 1 Problem 9.3-10 A cantilever beam AB supporting a triangularly distributed load of maximum intensity q 0 is shown in the figure. Derive the equation of the deflection curve and then obtain formulas for the deflection d B and angle of rotation u B at the free end. ( Note : Use the second-order differential equation of the deflection curve.) B A q 0 x y L Solution 9.3-10 Cantilever beam (triangular load) B ENDING - MOMENT EQUATION (E Q . 9-12a) B . C . n (0) 0 B . C . n (0) 0 C 2 q 0 L 4 120 EI q 0 120 L ( L x ) 5 q 0 L 3 x 24 + C 2 C 1 q 0 L 3 24 EI ¿ q 0 24 L ( L x ) 4 + C 1 EI M q 0 6 L ( L x ) 3 (These results agree with Case 8, Table G-1.)
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Unformatted text preview: u B ± ²³ ¿ ( L ) ± q 0 L 3 24 EI ; d B ± ²³ ( L ) ± q 0 L 4 30 EI ; ³ ¿ ± ² q 0 x 24 LEI (4 L 3 ² 6 L 2 x + 4 Lx 2 ² x 3 ) ³ ± ² q 0 x 2 120 LEI (10 L 3 ² 10 L 2 x + 5 Lx 2 ² x 3 ) ; Problem 9.3-11 A cantilever beam AB is acted upon by a uniformly distributed moment (bending moment, not torque) of intensity m per unit distance along the axis of the beam (see figure). Derive the equation of the deflection curve and then obtain formulas for the deflection d B and angle of rotation u B at the free end. ( Note : Use the second-order differential equation of the deflection curve.) B A y x m L 09Ch09.qxd 9/27/08 1:31 PM Page 715...
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