Modulus of rigidity Calculator

✖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.ⓘ Length of Shaft [L_shaft]			+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%

✖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]

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Formula

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Modulus of rigidity

Formula

`"G"_{"Torsion"} = ("T"*"L"_{"shaft"})/("θ"*"J")`

Example

`"0.022027GPa"=("28kN*m"*"4.58m")/("1.42rad"*"4.1e-3m⁴")`

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Modulus of rigidity Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

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.
Torque - (Measured in Newton Meter) - Torque is a measure of the force that can cause an object to rotate about an axis.
Length of Shaft - (Measured in Meter) - Length of Shaft is the distance between two ends of shaft.
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.

STEP 1: Convert Input(s) to Base Unit

Torque: 28 Kilonewton Meter --> 28000 Newton Meter (Check conversion here)
Length of Shaft: 4.58 Meter --> 4.58 Meter No Conversion Required
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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

G_Torsion = (T*L_shaft)/(θ*J) --> (28000*4.58)/(1.42*0.0041)

Evaluating ... ...

G_Torsion = 22026794.9158365

STEP 3: Convert Result to Output's Unit

22026794.9158365 Pascal -->0.0220267949158365 Gigapascal (Check conversion here)

FINAL ANSWER

0.0220267949158365 ≈ 0.022027 Gigapascal <-- Modulus of Rigidity

(Calculation completed in 00.007 seconds)

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National Institute of Technology Karnataka (NITK), Surathkal

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< 18 Torsion Calculators

Shaft length for given maximum permissible shear stress and modulus of rigidity

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

Maximum permissible shear stress for given Radius and modulus of rigidity

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

Modulus of rigidity given maximum permissible shear stress

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

Twist angle given maximum permissible shear stress

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

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

Go Length of Shaft = (Modulus of Rigidity*(Angle of Twist)*Polar Moment of Inertia)/Torque

Twist angle given Shaft length and modulus of rigidity

Go Angle of Twist = (Torque*Length of Shaft)/(Polar Moment of Inertia*Modulus of Rigidity)

Polar moment of inertia

Go Polar Moment of Inertia = (Torque*Length of Shaft)/(Angle of Twist*Modulus of Rigidity)

Modulus of rigidity

Go Modulus of Rigidity = (Torque*Length of Shaft)/(Angle of Twist*Polar Moment of Inertia)

Twisting Moment given Polar MOI and Twist Angle

Go Torque = (Modulus of Rigidity*Angle of Twist*Polar Moment of Inertia)/Length of Shaft

Polar Moment of Inertia of Hollow Shaft

Go Polar Moment of Inertia = pi/32*(Outer Diameter of Shaft^4-Inner Dia of Shaft^4)

Twisting Moment given Maximum Permissible Shear Stress

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

Polar Moment of Inertia given twisting moment along with maximum permissible shear stress

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

Radius given Twisting moment and Polar Moment of Inertia of shaft

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

Radius with known Maximum permissible shear stress

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

Maximum permissible shear stress

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

Radius given Torsional Section Modulus

Go Radius of Shaft = Polar Moment of Inertia/Polar Modulus

Radius of Shaft using Polar Modulus

Go Radius of Shaft = Polar Moment of Inertia/Polar Modulus

Torsional Section Modulus

Go Polar Modulus = Polar Moment of Inertia/Radius of Shaft

Modulus of rigidity Formula

Modulus of Rigidity = (Torque*Length of Shaft)/(Angle of Twist*Polar Moment of Inertia)
G_Torsion = (T*L_shaft)/(θ*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 metre, or in pounds per square inch while torque is expressed in newton metres or foot-pound force.

How to Calculate Modulus of rigidity?

Modulus of rigidity calculator uses Modulus of Rigidity = (Torque*Length of Shaft)/(Angle of Twist*Polar Moment of Inertia) to calculate the Modulus of Rigidity, The Modulus of rigidity when Shaft length, Polar MOI, Twisting Moment, and Twist angle is defined as the measure of the rigidity of the body, given by the ratio of shear stress to shear strain. Modulus of Rigidity is denoted by G_Torsion symbol.

How to calculate Modulus of rigidity using this online calculator? To use this online calculator for Modulus of rigidity, enter Torque (T), Length of Shaft (L_shaft), Angle of Twist (θ) & Polar Moment of Inertia (J) and hit the calculate button. Here is how the Modulus of rigidity calculation can be explained with given input values -> 2.2E-11 = (28000*4.58)/(1.42*0.0041).

FAQ

What is Modulus of rigidity?

The Modulus of rigidity when Shaft length, Polar MOI, Twisting Moment, and Twist angle is defined as the measure of the rigidity of the body, given by the ratio of shear stress to shear strain and is represented as G_Torsion = (T*L_shaft)/(θ*J) or Modulus of Rigidity = (Torque*Length of Shaft)/(Angle of Twist*Polar Moment of Inertia). Torque is a measure of the force that can cause an object to rotate about an axis, Length of Shaft is the distance between two ends of shaft, 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.

How to calculate Modulus of rigidity?

The Modulus of rigidity when Shaft length, Polar MOI, Twisting Moment, and Twist angle is defined as the measure of the rigidity of the body, given by the ratio of shear stress to shear strain is calculated using Modulus of Rigidity = (Torque*Length of Shaft)/(Angle of Twist*Polar Moment of Inertia). To calculate Modulus of rigidity, you need Torque (T), Length of Shaft (L_shaft), Angle of Twist (θ) & Polar Moment of Inertia (J). With our tool, you need to enter the respective value for Torque, Length of Shaft, Angle of Twist & 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 Modulus of Rigidity?

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

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

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