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09-01ChapGere.0009

# 09-01ChapGere.0009 - A-PDF Split DEMO Purchase from9.3...

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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.) Solution 9.3-10 Cantilever beam (triangular load) SECTION 9.3 Deflections by Integration of the Bending-Moment Equation 555 B A q 0 x y L B ENDING - MOMENT EQUATION (E Q . 9-12a) B . C . EIv 52 q 0 120 L ( L 2 x ) 5 2 q 0 L 3 x 24 1 C 2 v ¿ (0) 5 0 Ê c 2 52 q 0 L 3 24 EIv ¿ 5 q 0 24 L ( L 2 x ) 4 1 C 1 EIv 5 M 52 q 0 6 L ( L 2 x ) 3 B . C . (These results agree with Case 8, Table G-1.) u B 52 v ¿ ( L ) 5 q 0 L 3 24 EI d B 52 v ( L ) 5 q 0 L 4 30 EI v ¿ 52 q 0 x 24 LEI (4 L 3 2 6 L 2 x 1 4 Lx 2 2 x 3 ) v 52 q 0 x 2 120 LEI (10 L 3 2 10 L 2 x 1 5 Lx 2 2 x 3 ) v (0) 5 0 Ê c 2 5 q 0 L 4 120 Problem 9.3-11 A cantilever beam AB is acted upon by a uniformly distributed moment (bending moment, not torque) of intensity
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