264_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

264_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: Sec_3.3.qxd 9/27/08 258 1:27 PM Page 258 CHAPTER 3 Torsion Problem 3.3-9 Three identical circular disks A, B, and C are welded P3 to the ends of three identical solid circular bars (see figure). The bars lie in a common plane and the disks lie in planes perpendicular to the axes of the bars. The bars are welded at their intersection D to form a rigid connection. Each bar has diameter d1 0.5 in. and each disk has diameter d2 3.0 in. Forces P1, P2, and P3 act on disks A, B, and C, respectively, thus subjecting the bars to torsion. If P1 28 lb, what is the maximum shear stress max in any of the three bars? 135∞ P1 P3 d1 A D P1 135∞ 90∞ d2 P2 P2 B Solution 3.3-9 Three circular bars THE THREE TORQUES MUST BE IN EQUILIBRIUM T1 12 P1d2 12 T3 is the largest torque MAXIMUM SHEAR STRESS (Eq. 3-12) 16T3 16P1d2 12 16T tmax 3 3 pd pd1 pd3 1 T3 d1 diameter of bars 0.5 in. d2 tmax diameter of disks 3.0 in. P1 28 lb T1 P1d2 T2 P2d2 T3 P3d2 C 16(28 lb)(3.0 in.) 12 p (0.5 in.)3 4840 psi ; ...
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