03-01ChapGere.0020

03-01ChapGere.0020 - 200 A-PDF Torsion CHAPTER 3 Split DEMO...

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Problem 3.4-4 A solid circular bar ABC consists of two segments, as shown in the figure. One segment has diameter d 1 5 50 mm and length L 1 5 1.25 m; the other segment has diameter d 2 5 40 mm and length L 2 5 1.0 m. What is the allowable torque T allow if the shear stress is not to exceed 30 MPa and the angle of twist between the ends of the bar is not to exceed 1.5°? (Assume G 5 80 GPa.) Solution 3.4-4 Bar consisting of two segments 200 CHAPTER 3 Torsion L 1 L 2 T AB C d 1 d 2 T t allow 5 30 MPa f allow 5 1.5 85 0.02618 rad G 5 80 GPa A LLOWABLE TORQUE BASED UPON SHEAR STRESS Segment BC has the smaller diameter and hence the larger stress. t max 5 16 T p d 3 T allow 5 p d 2 3 t allow 16 5 3.77 N # m A LLOWABLE TORQUE BASED UPON ANGLE OF TWIST A NGLE OF TWIST GOVERNS T allow 5 348 N ? m Ê T allow 5 p f allow G 32 ¢ L 1 d 1 4 1 L 2 d 2 4 5 348 N ? m f 5 32 T p G ¢ L 1 d 1 4 1 L 2 d 2 4 f 5 a T i L i GI Pi 5 TL 1 GI P 1 1 TL 2 GI P 2 5 T G ¢ L 1 I P 1 1 L 2 I P 2 L 1 = 1.25 m L 2 = 1.0 m
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