A spring, wound from stainless steel wire with a wire diameter d=1 mm, has n=20 turns of radius R=10 mm. How much will it extend when loaded with a mass M of 1 kg? Assume the shear modulus G of stainless steel to be 3/8E where E is Young’s modulus, retrieve this from Appendix A3, and use the expression for the extension of springs from Appendix B6 to find out.

Data From Appendix A3

Data From Appendix B6

A torque T applied to the ends of an isotropic bar of uniform section, and acting in the plane normal to the axis of the bar, produces an angle of twist . The twist is related to the torque by the first equation on the facing page, in which G is the shear modulus. For round bars and tubes of circular section, the factor K is equal to J, the polar moment of inertia of the section, For any other section shape, K is less than J. Values of K. If the bar ceases to deform elastically, it is said to have failed. This will happen if the maximum surface stress exceeds either the yield strength of the material or the stress at which it fractures, . For circular sections, the shear stress at any point a distance r from the axis of rotation is

 

Transcribed Image Text:

Table A.3 Young's Modulus and Yield Strength