09-01ChapGere.0012

09-01ChapGere.0012 - x 48 1 C 4 B . C . 2 ( ) Left 5 ( )...

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558 CHAPTER 9 Deflections of Beams Problem 9.3-16 Derive the equations of the deflection curve for a simple beam AB with a uniform load of intensity q acting over the left-hand half of the span (see figure). Also, determine the deflection d C at the midpoint of the beam. ( Note: Use the second-order differential equation of the deflection curve.) Solution 9.3-16 Simple beam (partial uniform load) A B C q x y L 2 L 2 B ENDING - MOMENT EQUATION (E Q . 9-12a) B . C . 1 ( ) Left 5 () Right at ¢ 0 ± x ± L 2 EIv 5 qLx 3 16 2 qx 4 24 1 C 1 x 1 C 3 C 2 5 C 1 2 qL 2 48 x 5 L 2 v ¿ v ¿ ¢ L 2 ± x ± L EIv ¿ 5 qL 2 x 8 2 qLx 2 16 1 C 2 ¢ L 2 ± x ± L EIv 5 M 5 qL 2 8 2 qLx 8 ¢ 0 ± x ± L 2 EIv ¿ 5 3 qLx 2 16 2 qx 3 6 1 C 1 ¢ 0 ± x ± L 2 EIv 5 M 5 3 qLx 8 2 qx 2 2 B . C . 2 v (0) 5 0 [ C 3 5 0 B . C . 3 v ( L ) 5 0 B . C . 4 ( v ) Left 5 ( v ) Right at (These results agree with Case 2, Table G-2.) d C 52 v ¢ L 2 5 5 qL 4 768 EI ¢ L 2 ± x ± L v 52 qL 384 EI (8 x 3 2 24 Lx 2 1 17 L 2 x 2 L 3 ) ¢ 0 ± x ± L 2 v 52 qx 384 EI (9 L 3 2 24 Lx 2 1 16 x 3 ) C 1 52 3 qL 3 128 x 5 L 2 C 4 52 C 1 L 2 qL 4 48 ¢ L 2 ± x ± L EIv 5 qL 2 x 2 16 2 qLx 3 48 1 C 1 x 2 qL 3
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Unformatted text preview: x 48 1 C 4 B . C . 2 ( ) Left 5 ( ) Right at B . C . 3 v (0) 5 [ C 3 5 ¢ L 2 ± x ± L ≤ EIv 5 2 q 2 ¢ L 2 x 2 2 2 Lx 3 3 1 x 4 12 ≤ 1 qL 3 48 x 1 C 4 ¢ ± x ± L 2 ≤ EIv 5 2 qL 8 ¢ 3 Lx 2 2 2 2 x 3 3 ≤ 1 C 3 ∴ C 2 5 qL 3 48 x 5 L 2 v ¿ v ¿ B . C . 4 ( v ) Left 5 ( v ) Right at d B 5 2 v ( L ) 5 41 qL 4 384 EI ¢ L 2 ± x ± L ≤ v 5 2 q 384 EI (16 x 4 2 64 Lx 3 1 96 L 2 x 2 2 8 L 3 x 1 L 4 ) d C 5 2 v ¢ L 2 ≤ 5 7 qL 4 192 EI ¢ ± x ± L 2 ≤ v 5 2 qLx 2 48 EI (9 L 2 4 x ) ∴ C 4 5 2 qL 4 384 x 5 L 2 A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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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 Tech.

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