What is the maximum torque that can be applied to a (1)/(d)-in. bolt without yielding? Take the

step 1 For still to be failed, the shear stress, that is F parallel upon A, must be equivalent to the l

What is the maximum torque that can be applied to a...

Key Concepts

Torsion Formula

The torsion formula relates the applied torque on a cylindrical member to the shear stress experienced by its cross-section. It is given by the equation ? = T*r/J, where ? is the shear stress, T is the applied torque, r is the radius at which the stress is being evaluated, and J is the polar moment of inertia. This fundamental relationship is used to ensure that the induced shear stresses do not exceed the material’s yield strength, thereby avoiding permanent deformation.

Polar Moment of Inertia

The polar moment of inertia is a geometric property of a cross-section that measures its resistance to twisting. It is calculated based on the shape and dimensions of the cross-section, and for circular sections it plays a crucial role in determining how the applied torque is distributed across the material. A higher polar moment of inertia indicates that the section can resist higher torques before reaching the yield stress.

Material Yield Strength

Material yield strength is the maximum stress that a material can withstand without undergoing permanent plastic deformation. In the context of torsion, this property determines the critical shear stress level; the applied torque must be such that the induced shear stress remains below this yield limit to avoid yielding. It is a fundamental property in design to ensure structural integrity under load.

Shear Stress

Shear stress is the stress component that acts parallel to the cross-sectional area of a material under loading. In torsional loading, shear stress arises due to the twisting action and varies linearly from the center of the cross-section to its outer surface. Understanding shear stress is essential to analyze the performance of components under torque and to design against failure modes governed by shear yielding.

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