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03-01ChapGere.0011

03-01ChapGere.0011 - r 2 5 3.0 in d 1 5 4.5 in r 1 5 2.25...

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Problem 3.3-11 A hollow steel shaft used in a construction auger has outer diameter d 2 6.0 in. and inner diameter d 1 4.5 in. (see figure). The steel has shear modulus of elasticity G 11.0 10 6 psi. For an applied torque of 150 k-in., determine the following quantities: (a) shear stress 2 at the outer surface of the shaft, (b) shear stress 1 at the inner surface, and (c) rate of twist (degrees per unit of length). Also, draw a diagram showing how the shear stresses vary in mag- nitude along a radial line in the cross section. Solution 3.3-11 Construction auger SECTION 3.3 Circular Bars and Tubes
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Unformatted text preview: r 2 5 3.0 in. d 1 5 4.5 in. r 1 5 2.25 in. G 5 11 3 10 6 psi T 5 150 k-in. (a) S HEAR STRESS AT OUTER SURFACE 5 5170 psi Ê t 2 5 Tr 2 I P 5 (150 k-in.)(3.0 in.) 86.98 in. 4 I P 5 p 32 ( d 2 4 2 d 1 4 ) 5 86.98 in. 4 (b) S HEAR STRESS AT INNER SURFACE (c) R ATE OF TWIST (d) S HEAR STRESS DIAGRAM u 5 157 3 10 2 6 rad / in. 5 0.00898 8 / in. Ê u 5 T GI P 5 (150 k-in.) (11 3 10 6 psi)(86.98 in. 4 ) t 1 5 Tr 1 I P 5 r 1 r 2 t 2 5 3880 psi Ê d 1 d 2 C C 0.75 1.50 2.25 3.00 3880 psi 5170 psi A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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