Shaft length for given maximum permissible shear stress and modulus of rigidity 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%
✖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%
✖Maximum Shear Stress is the greatest extent a shear force can be concentrated in a small area.ⓘ Maximum Shear Stress [τ_max]			+10% -10%

✖Length of Shaft is the distance between two ends of shaft.ⓘ Shaft length for given maximum permissible shear stress and modulus of rigidity [L_shaft]

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

STEP 0: Pre-Calculation Summary

Formula Used

Length of Shaft = (Modulus of Rigidity*(Angle of Twist)*Radius of Shaft)/Maximum Shear Stress
L_shaft = (G_Torsion*(θ)*R)/τ_max
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.
Radius of Shaft - (Measured in Meter) - The Radius of Shaft is the line segment extending from the center of a circle or sphere to the circumference or bounding surface.
Maximum Shear Stress - (Measured in Pascal) - Maximum Shear Stress is the greatest extent a shear force can be concentrated in a small area.

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
Radius of Shaft: 110 Millimeter --> 0.11 Meter (Check conversion here)
Maximum Shear Stress: 42 Megapascal --> 42000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L_shaft = (G_Torsion*(θ)*R)/τ_max --> (40000000000*(1.42)*0.11)/42000000

Evaluating ... ...

L_shaft = 148.761904761905

STEP 3: Convert Result to Output's Unit

148.761904761905 Meter --> No Conversion Required

FINAL ANSWER

148.761904761905 ≈ 148.7619 Meter <-- Length of Shaft

(Calculation completed in 00.020 seconds)

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Created by Rithik Agrawal

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

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

LaTeX Go

Length of Shaft = (Modulus of Rigidity*(Angle of Twist)*Radius of Shaft)/Maximum Shear Stress
L_shaft = (G_Torsion*(θ)*R)/τ_max

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 maximum permissible shear stress and modulus of rigidity?

Shaft length for given maximum permissible shear stress and modulus of rigidity calculator uses Length of Shaft = (Modulus of Rigidity*(Angle of Twist)*Radius of Shaft)/Maximum Shear Stress to calculate the Length of Shaft, The Shaft length for given maximum permissible shear stress and modulus of rigidity along with twist angle 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 maximum permissible shear stress and modulus of rigidity using this online calculator? To use this online calculator for Shaft length for given maximum permissible shear stress and modulus of rigidity, enter Modulus of Rigidity (G_Torsion), Angle of Twist (θ), Radius of Shaft (R) & Maximum Shear Stress (τ_max) and hit the calculate button. Here is how the Shaft length for given maximum permissible shear stress and modulus of rigidity calculation can be explained with given input values -> 148.7619 = (40000000000*(1.42)*0.11)/42000000.

FAQ

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

The Shaft length for given maximum permissible shear stress and modulus of rigidity along with twist angle is defined as the length of the shaft that is undergoing torsion and is represented as L_shaft = (G_Torsion*(θ)*R)/τ_max or Length of Shaft = (Modulus of Rigidity*(Angle of Twist)*Radius of Shaft)/Maximum Shear Stress. 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, The Radius of Shaft is the line segment extending from the center of a circle or sphere to the circumference or bounding surface & Maximum Shear Stress is the greatest extent a shear force can be concentrated in a small area.

How to calculate Shaft length for given maximum permissible shear stress and modulus of rigidity?

The Shaft length for given maximum permissible shear stress and modulus of rigidity along with twist angle is defined as the length of the shaft that is undergoing torsion is calculated using Length of Shaft = (Modulus of Rigidity*(Angle of Twist)*Radius of Shaft)/Maximum Shear Stress. To calculate Shaft length for given maximum permissible shear stress and modulus of rigidity, you need Modulus of Rigidity (G_Torsion), Angle of Twist (θ), Radius of Shaft (R) & Maximum Shear Stress (τ_max). With our tool, you need to enter the respective value for Modulus of Rigidity, Angle of Twist, Radius of Shaft & Maximum Shear Stress 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, Radius of Shaft & Maximum Shear Stress. 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)*Polar Moment of Inertia)/Torque

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