03-02ChapGere.0004

03-02ChapGere.0004 - t A 5 maximum intensity of torque d 5...

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Problem 3.4-13 A prismatic bar AB of solid circular cross section (diameter d ) is loaded by a distributed torque (see figure). The intensity of the torque, that is, the torque per unit distance, is denoted t ( x ) and varies linearly from a maximum value t A at end A to zero at end B . Also, the length of the bar is L and the shear modulus of elasticity of the material is G . (a) Determine the maximum shear stress t max in the bar. (b) Determine the angle of twist f between the ends of the bar. Solution 3.4-13 Bar with linearly varying torque SECTION 3.4 Nonuniform Torsion 207 A B t ( x ) L t ( x ) 5 intensity of distributed torque
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Unformatted text preview: t A 5 maximum intensity of torque d 5 diameter G 5 shear modulus T A 5 maximum torque 5 1 2 t A L (a) M AXIMUM SHEAR STRESS (b) A NGLE OF TWIST T ( x ) 5 torque at distance x from end B f 5 # L d f 5 16 t A p GLd 4 # L x 2 dx 5 16 t A L 2 3 p Gd 4 d f 5 T ( x ) dx GI P 5 16 t A x 2 dx p GLd 4 T ( x ) 5 t ( x ) x 2 5 t A x 2 2 L I P 5 p d 4 32 t max 5 16 T max p d 3 5 16 T A p d 3 5 8 t A L p d 3 A B t ( x ) L dx x T A L t A t(x) = x A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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