03-03ChapGere.0006

03-03ChapGere.0006 - S TRAIN ENERGY OF ELEMENT dx S TRAIN...

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Solution 3.9-8 Cantilever bar with distributed torque SECTION 3.9 Strain Energy in Torsion 241 x 5 distance from right-hand end of the bar E LEMENT d j Consider a differential element d j at distance j from the right-hand end. dT 5 external torque acting on this element dT 5 t ( j ) d j 5 E LEMENT dx AT DISTANCE x T ( x ) 5 internal torque acting on this element T ( x ) 5 total torque from x 5 0 to x 5 x 5 t 0 x 2 2 L T ( x ) 5 # x 0 dT 5 # x 0 t 0 ¢ j L d j t 0 ¢ j L d j L t(x) = t 0 t 0 x L dx x d j j dT d j dx T(x) T(x)
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Unformatted text preview: S TRAIN ENERGY OF ELEMENT dx S TRAIN ENERGY OF ENTIRE BAR U 5 t 2 L 3 40 GI P 5 t 2 8 L 2 GI P L 5 5 U 5 # L dU 5 t 2 8 L 2 GI P # L x 4 dx 5 t 2 8 L 2 GI P x 4 dx dU 5 [ T ( x ) ] 2 dx 2 GI P 5 1 2 GI P t 2 L 2 x 4 dx A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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