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325_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 325_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: Sec_3.9-3.11.qxd 9/27/08 1:14 PM Page 319 SECTION 3.9 Strain Energy in Torsion 319 Strain Energy in Torsion 11.4 106 psi) with length L 30 in. and diameter d 1.75 in. is subjected to pure torsion by torques T acting at the ends (see figure). Problem 3.9-1 A solid circular bar of steel (G d T T (a) Calculate the amount of strain energy U stored in the bar when the maximum shear stress is 4500 psi. (b) From the strain energy, calculate the angle of twist (in degrees). Solution 3.9-1 L Steel bar pd2Lt2 max 16G (Eq. 2) Substitute numerical values: U 106 psi G 11.4 L 30 in. d 1.75 in. max tmax IP ; 32.0 in.-lb (b) ANGLE OF TWIST U Tf 2 f 2U T 4500 psi 16 T pd3 Substitute for T and U from Eqs. (1) and (2): pd3tmax 16 T pd 4 32 f (Eq. 1) 2Ltmax Gd (Eq. 3) Substitute numerical values: 0.013534 rad 0.775° ; (a) STRAIN ENERGY U T2L 2GIP a pd3tmax 2 L 32 ba b a 4b 16 2G pd Problem 3.9-2 A solid circular bar of copper (G 45 GPa) with length L to pure torsion by torques T acting at the ends (see figure). 0.75 m and diameter d 40 mm is subjected (a) Calculate the amount of strain energy U stored in the bar when the maximum shear stress is 32 MPa. (b) From the strain energy, calculate the angle of twist (in degrees) ...
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