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## Homework Statement

## Homework Equations

maximum torsional shear stress = (Torque*radius)/polar moment of inertia

## The Attempt at a Solution

I am lost on equation(4-14), I looked through the textbook but didn't find a derivation.

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In summary, the conversation discusses the derivation of the maximum torsional shear stress equation (4-14) for a circular rod under torsion. It involves calculating the shear strain and stress between adjacent cross sections, integrating the differential torque on each cross section, and utilizing the polar moment of inertia to determine the maximum shear stress at a given location.

- #1

- 128

- 3

maximum torsional shear stress = (Torque*radius)/polar moment of inertia

I am lost on equation(4-14), I looked through the textbook but didn't find a derivation.

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Torsional shear stress in the x-y plane refers to the force that is applied to an object in a twisting or rotational motion, causing it to experience shear stress in the x-y direction. This type of stress is commonly seen in structural engineering, as it can affect the stability and strength of a structure.

Torsional shear stress is calculated by taking the torque applied to an object and dividing it by the polar moment of inertia, which is a measure of an object's resistance to torsion. The resulting value is the shear stress in the x-y plane.

There are several factors that can contribute to torsional shear stress in the x-y plane, including the shape and material properties of an object, the magnitude and direction of the applied torque, and the boundary conditions of the object.

Torsional shear stress is different from other types of stress, such as tensile or compressive stress, because it is caused by a twisting or rotational force rather than a pulling or pushing force. It also acts in a different direction, causing shear forces along a plane rather than normal forces along an axis.

Torsional shear stress in the x-y plane can be reduced by using materials with higher shear strength, increasing the size or shape of an object to increase its resistance to torsion, or by adding reinforcement such as bracing or cross-sections to distribute the stress more evenly.

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