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 d 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) 5 0 [ C 1 5 0 5 M 5 0( a ± x ± L ) 5 C 2 ( a ± x ± L ) B . C . 2 ( ) Left 5 () Right at x 5 a (0 ± x ± a ) EIv 52 q 2 ¢ a 2 x 2 2 2 ax 3 3 1 x 4 12 1 C 3 C 2 qa 3 6 v ¿ v ¿ EIv ¿ EIv v ¿ EIv ¿ q 2 ¢ a 2 x 2 ax 2 1 x 3 3 1 C 1 EIv 5 M q 2 ( a 2 x ) 2 q 2 ( a 2 2 2 ax 1 x 2 ) B . C . 3 v (0) 5 0 [ C 3 5 0 (a ± x ± L ) B . C . 4 ( v ) Left 5 ( v ) Right at x 5 a (0 ± x ± a ) (a ± x ± L ) (These results agree with Case 2, Table G-1.) d B v ( L ) 5 qa 3 24 EI (4 L 2 a ) v qa 3 24 EI x 2 a ) v qx 2 24 EI (6 a 2 2 4 ax 1 x 2 ) C 4 5 qa 4 24 EIv 5 C 2 x 1 C 4 qa 3 x 6 1 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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This note was uploaded on 09/20/2009 for the course COE 3001 taught by Professor Armanios during the Spring '08 term at Georgia Institute of Technology.

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