Shaft length for given Polar MOI, Twisting Moment, Modulus of rigidity, and Twist angle Calculator

✖Modulus of Rigidity is the measure of the rigidity of the body, given by the ratio of shear stress to shear strain. It is often denoted by G.ⓘ Modulus of Rigidity [G_Torsion]			+10% -10%
✖Angle of twist is the angle through which the fixed end of a shaft rotates with respect to the free end.ⓘ Angle of Twist [θ]			+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%
✖Torque is a measure of the force that can cause an object to rotate about an axis.ⓘ Torque [T]			+10% -10%

✖Length of Shaft is the distance between two ends of shaft.ⓘ Shaft length for given Polar MOI, Twisting Moment, Modulus of rigidity, and Twist angle [L_shaft]

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Shaft length for given Polar MOI, Twisting Moment, Modulus of rigidity, and Twist angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Length of Shaft = (Modulus of Rigidity*(Angle of Twist)*Polar Moment of Inertia)/Torque
L_shaft = (G_Torsion*(θ)*J)/T
This formula uses 5 Variables

Variables Used

Length of Shaft - (Measured in Meter) - Length of Shaft is the distance between two ends of shaft.
Modulus of Rigidity - (Measured in Pascal) - Modulus of Rigidity is the measure of the rigidity of the body, given by the ratio of shear stress to shear strain. It is often denoted by G.
Angle of Twist - (Measured in Radian) - Angle of twist is the angle through which the fixed end of a shaft rotates with respect to the free end.
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.
Torque - (Measured in Newton Meter) - Torque is a measure of the force that can cause an object to rotate about an axis.

STEP 1: Convert Input(s) to Base Unit

Modulus of Rigidity: 40 Gigapascal --> 40000000000 Pascal (Check conversion here)
Angle of Twist: 1.42 Radian --> 1.42 Radian No Conversion Required
Polar Moment of Inertia: 0.0041 Meter⁴ --> 0.0041 Meter⁴ No Conversion Required
Torque: 28 Kilonewton Meter --> 28000 Newton Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L_shaft = (G_Torsion*(θ)*J)/T --> (40000000000*(1.42)*0.0041)/28000

Evaluating ... ...

L_shaft = 8317.14285714286

STEP 3: Convert Result to Output's Unit

8317.14285714286 Meter --> No Conversion Required

FINAL ANSWER

8317.14285714286 ≈ 8317.143 Meter <-- Length of Shaft

(Calculation completed in 00.020 seconds)

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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

Shaft length for given Polar MOI, Twisting Moment, Modulus of rigidity, and Twist angle Formula

LaTeX Go

Length of Shaft = (Modulus of Rigidity*(Angle of Twist)*Polar Moment of Inertia)/Torque
L_shaft = (G_Torsion*(θ)*J)/T

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 metre, or in pounds per square inch while torque is expressed in newton metres or foot-pound force.

How to Calculate Shaft length for given Polar MOI, Twisting Moment, Modulus of rigidity, and Twist angle?

Shaft length for given Polar MOI, Twisting Moment, Modulus of rigidity, and Twist angle calculator uses Length of Shaft = (Modulus of Rigidity*(Angle of Twist)*Polar Moment of Inertia)/Torque to calculate the Length of Shaft, The Shaft length for given Polar MOI, Twisting Moment, Modulus of rigidity, and Twist angle formula is defined as the length of the shaft that is undergoing torsion. Length of Shaft is denoted by L_shaft symbol.

How to calculate Shaft length for given Polar MOI, Twisting Moment, Modulus of rigidity, and Twist angle using this online calculator? To use this online calculator for Shaft length for given Polar MOI, Twisting Moment, Modulus of rigidity, and Twist angle, enter Modulus of Rigidity (G_Torsion), Angle of Twist (θ), Polar Moment of Inertia (J) & Torque (T) and hit the calculate button. Here is how the Shaft length for given Polar MOI, Twisting Moment, Modulus of rigidity, and Twist angle calculation can be explained with given input values -> 8317.143 = (40000000000*(1.42)*0.0041)/28000.

FAQ

What is Shaft length for given Polar MOI, Twisting Moment, Modulus of rigidity, and Twist angle?

The Shaft length for given Polar MOI, Twisting Moment, Modulus of rigidity, and Twist angle formula is defined as the length of the shaft that is undergoing torsion and is represented as L_shaft = (G_Torsion*(θ)*J)/T or Length of Shaft = (Modulus of Rigidity*(Angle of Twist)*Polar Moment of Inertia)/Torque. Modulus of Rigidity is the measure of the rigidity of the body, given by the ratio of shear stress to shear strain. It is often denoted by G, Angle of twist is the angle through which the fixed end of a shaft rotates with respect to the free end, 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 & Torque is a measure of the force that can cause an object to rotate about an axis.

How to calculate Shaft length for given Polar MOI, Twisting Moment, Modulus of rigidity, and Twist angle?

The Shaft length for given Polar MOI, Twisting Moment, Modulus of rigidity, and Twist angle formula is defined as the length of the shaft that is undergoing torsion is calculated using Length of Shaft = (Modulus of Rigidity*(Angle of Twist)*Polar Moment of Inertia)/Torque. To calculate Shaft length for given Polar MOI, Twisting Moment, Modulus of rigidity, and Twist angle, you need Modulus of Rigidity (G_Torsion), Angle of Twist (θ), Polar Moment of Inertia (J) & Torque (T). With our tool, you need to enter the respective value for Modulus of Rigidity, Angle of Twist, Polar Moment of Inertia & Torque 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 Length of Shaft?

In this formula, Length of Shaft uses Modulus of Rigidity, Angle of Twist, Polar Moment of Inertia & Torque. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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