09-01ChapGere.0011

# 09-01ChapGere.0011 - A-PDF Split DEMO PurchaseSECTION 9.3...

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SECTION 9.3 Deflection by Integration of the Bending-Moment Equation 557 Problem 9.3-14 Derive the equations of the deflection curve for a cantilever beam AB carrying a uniform load of intensity q over part of the span (see figure). Also, determine the deflection B at the end of the beam. ( Note: Use the second-order differential equation of the deflection curve.) Solution 9.3-14 Cantilever beam (partial uniform load) A B q y x L a b B ENDING - MOMENT EQUATION (E Q . 9-12a) (0 x a ) (0 x a ) B . C . 1 (0) 0 C 1 0 M 0 ( a x L ) C 2 ( a x L ) B . C . 2 ( ) Left ( ) Right at x a (0 x a ) EIv q 2 ¢ a 2 x 2 2 ax 3 3 x 4 12 C 3 C 2 qa 3 6 v ¿ v ¿ EIv ¿ EIv v ¿ EIv ¿ q 2 ¢ a 2 x ax 2 x 3 3 C 1 EIv M q 2 ( a x ) 2 q 2 ( a 2 2 ax x 2 ) B . C . 3 v (0) 0 C 3 0 (a x L ) B . C . 4 ( v ) Left ( v ) Right at x a (0 x a ) (a x L ) (These results agree with Case 2, Table G-1.) B v ( L ) qa 3 24 EI (4 L a ) v qa 3 24 EI (4 x a ) v qx 2 24 EI (6 a 2 4 ax x 2 ) C 4 qa 4 24 EIv C 2 x C 4 qa 3 x 6 C 4 Problem 9.3-15 Derive the equations of the deflection curve for a cantilever beam AB supporting a uniform load of intensity
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