Maximum permissible shear stress Calculator

✖Torque is a measure of the force that can cause an object to rotate about an axis.ⓘ Torque [T]			+10% -10%
✖The Radius of Shaft is the line segment extending from the center of a circle or sphere to the circumference or bounding surface.ⓘ Radius of Shaft [R]			+10% -10%
✖Polar Moment of Inertia is the moment of inertia of a cross-section with respect to its polar axis, which is an axis at right angles to the plane of the cross-section.ⓘ Polar Moment of Inertia [J]			+10% -10%

✖Maximum Shear Stress is the greatest extent a shear force can be concentrated in a small area.ⓘ Maximum permissible shear stress [τ_max]

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Maximum permissible shear stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Maximum Shear Stress = Torque*Radius of Shaft/Polar Moment of Inertia
τ_max = T*R/J
This formula uses 4 Variables

Variables Used

Maximum Shear Stress - (Measured in Pascal) - Maximum Shear Stress is the greatest extent a shear force can be concentrated in a small area.
Torque - (Measured in Newton Meter) - Torque is a measure of the force that can cause an object to rotate about an axis.
Radius of Shaft - (Measured in Millimeter) - The Radius of Shaft is the line segment extending from the center of a circle or sphere to the circumference or bounding surface.
Polar Moment of Inertia - (Measured in Meter⁴) - Polar Moment of Inertia is the moment of inertia of a cross-section with respect to its polar axis, which is an axis at right angles to the plane of the cross-section.

STEP 1: Convert Input(s) to Base Unit

Torque: 28 Kilonewton Meter --> 28000 Newton Meter (Check conversion here)
Radius of Shaft: 110 Millimeter --> 110 Millimeter No Conversion Required
Polar Moment of Inertia: 0.0041 Meter⁴ --> 0.0041 Meter⁴ No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

τ_max = T*R/J --> 28000*110/0.0041

Evaluating ... ...

τ_max = 751219512.195122

STEP 3: Convert Result to Output's Unit

751219512.195122 Pascal -->751.219512195122 Megapascal (Check conversion here)

FINAL ANSWER

751.219512195122 ≈ 751.2195 Megapascal <-- Maximum Shear Stress

(Calculation completed in 00.020 seconds)

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National Institute of Technology Karnataka (NITK), Surathkal

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< Torsion Calculators

Maximum permissible shear stress for given Radius and modulus of rigidity

LaTeX Go Maximum Shear Stress = (Modulus of Rigidity*(Angle of Twist)*Radius of Shaft)/Length of Shaft

Twisting Moment given Maximum Permissible Shear Stress

LaTeX Go Torque = (Polar Moment of Inertia*Maximum Shear Stress)/Radius of Shaft

Radius with known Maximum permissible shear stress

LaTeX Go Radius of Shaft = Maximum Shear Stress*Polar Moment of Inertia/Torque

Maximum permissible shear stress

LaTeX Go Maximum Shear Stress = Torque*Radius of Shaft/Polar Moment of Inertia

Maximum permissible shear stress Formula

LaTeX Go

Maximum Shear Stress = Torque*Radius of Shaft/Polar Moment of Inertia
τ_max = T*R/J

What is Torsion?

n the field of solid mechanics, torsion is the twisting of an object due to an applied torque. Torsion is expressed in either the Pascal, an SI unit for newtons per square meter, or in pounds per square inch while torque is expressed in newton meters or foot-pound force.

How to Calculate Maximum permissible shear stress?

Maximum permissible shear stress calculator uses Maximum Shear Stress = Torque*Radius of Shaft/Polar Moment of Inertia to calculate the Maximum Shear Stress, The Maximum permissible shear stress is defined as the limit up-to which the material can withstand shear. Maximum Shear Stress is denoted by τ_max symbol.

How to calculate Maximum permissible shear stress using this online calculator? To use this online calculator for Maximum permissible shear stress, enter Torque (T), Radius of Shaft (R) & Polar Moment of Inertia (J) and hit the calculate button. Here is how the Maximum permissible shear stress calculation can be explained with given input values -> 7.5E-7 = 28000*0.11/0.0041.

FAQ

What is Maximum permissible shear stress?

The Maximum permissible shear stress is defined as the limit up-to which the material can withstand shear and is represented as τ_max = T*R/J or Maximum Shear Stress = Torque*Radius of Shaft/Polar Moment of Inertia. Torque is a measure of the force that can cause an object to rotate about an axis, The Radius of Shaft is the line segment extending from the center of a circle or sphere to the circumference or bounding surface & Polar Moment of Inertia is the moment of inertia of a cross-section with respect to its polar axis, which is an axis at right angles to the plane of the cross-section.

How to calculate Maximum permissible shear stress?

The Maximum permissible shear stress is defined as the limit up-to which the material can withstand shear is calculated using Maximum Shear Stress = Torque*Radius of Shaft/Polar Moment of Inertia. To calculate Maximum permissible shear stress, you need Torque (T), Radius of Shaft (R) & Polar Moment of Inertia (J). With our tool, you need to enter the respective value for Torque, Radius of Shaft & Polar Moment of Inertia and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Maximum Shear Stress?

In this formula, Maximum Shear Stress uses Torque, Radius of Shaft & Polar Moment of Inertia. We can use 1 other way(s) to calculate the same, which is/are as follows -

Maximum Shear Stress = (Modulus of Rigidity*(Angle of Twist)*Radius of Shaft)/Length of Shaft

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