A circular shaft has a diameter D = 40 mm and a length L = 1.5 m and is made of structural steel with elastic perfectly plastic behavior (G = 95.98 GPa and Ty = 180 MPa). The shaft fixed at one end and subjected to a torque T at the other end. The angle of twist is measured between the ends as op = 0.2 rad. a) Calculate the yield shear strain yy. b) Calculate the maximum shear strain ymax. c) Determine the radius py to the elastic- plastic boundary. d) Determine the torque T. If the member has yielded and then unloaded. e) Determine the residual shear stress at p=5 mm. 0.001667 rad 0.0016774 rad 0.002 rad 0.0015 rad 0.00225 rad 0.002667 rad 0.001333 rad 0.004 rad 0.002 rad 0.002667 rad 12.5026 mm 12.5806 mm 12.5026 mm 8.3351 mm 16.6701 mm 15 mm 11.25 mm 16.875 mm 2.5171 kN.m 2.0426 kN.m 0.17138 kN.m 2.6323 KN.m 2.2927 kN.m 2.3981 kN.m 1.9212 kN.m 2.563 KN.m 106.6667 MPa 86.6667 MPa 53.33 MPa 80 MPa 120 MPa

A circular shaft has a diameter D = 40 mm and a length L = 1.5 m and is made of structural steel with elastic perfectly plastic behavior (G = 95.98 GPa and Ty = 180 MPa). The shaft fixed at one end and subjected to a torque T at the other end. The angle of twist is measured between the ends as op = 0.2 rad. a) Calculate the yield shear strain yy. b) Calculate the maximum shear strain ymax. c) Determine the radius py to the elastic- plastic boundary. d) Determine the torque T. If the member has yielded and then unloaded. e) Determine the residual shear stress at p=5 mm. 0.001667 rad 0.0016774 rad 0.002 rad 0.0015 rad 0.00225 rad 0.002667 rad 0.001333 rad 0.004 rad 0.002 rad 0.002667 rad 12.5026 mm 12.5806 mm 12.5026 mm 8.3351 mm 16.6701 mm 15 mm 11.25 mm 16.875 mm 2.5171 kN.m 2.0426 kN.m 0.17138 kN.m 2.6323 KN.m 2.2927 kN.m 2.3981 kN.m 1.9212 kN.m 2.563 KN.m 106.6667 MPa 86.6667 MPa 53.33 MPa 80 MPa 120 MPa

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter3: Torsion

Section: Chapter Questions

Problem 3.2.5P: Solve the preceding problem if the length L = 56 in., the inner radius r1— 1.25 in., the angle of...

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Solve the preceding problem if the length L = 56 in., the inner radius r1— 1.25 in., the angle of twist is 0.5°, and the allowable shear strain is 0.0004 rad.
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