Modulus of rigidity given maximum permissible shear stress Calculator

✖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.ⓘ 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%
✖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%

✖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 given maximum permissible shear stress [G_Torsion]

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Modulus of rigidity given maximum permissible shear stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Modulus of Rigidity = (Maximum Shear Stress*Length of Shaft)/(Angle of Twist*Radius of Shaft)
G_Torsion = (τ_max*L_shaft)/(θ*R)
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.
Maximum Shear Stress - (Measured in Pascal) - Maximum Shear Stress is the greatest extent a shear force can be concentrated in a small area.
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.
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.

STEP 1: Convert Input(s) to Base Unit

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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

G_Torsion = (τ_max*L_shaft)/(θ*R) --> (42000000*4.58)/(1.42*0.11)

Evaluating ... ...

G_Torsion = 1231498079.3854

STEP 3: Convert Result to Output's Unit

1231498079.3854 Pascal -->1.2314980793854 Gigapascal (Check conversion here)

FINAL ANSWER

1.2314980793854 ≈ 1.231498 Gigapascal <-- Modulus of Rigidity

(Calculation completed in 00.005 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

Modulus of rigidity given maximum permissible shear stress Formula

LaTeX Go

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

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 given maximum permissible shear stress?

Modulus of rigidity given maximum permissible shear stress calculator uses Modulus of Rigidity = (Maximum Shear Stress*Length of Shaft)/(Angle of Twist*Radius of Shaft) to calculate the Modulus of Rigidity, The Modulus of rigidity given maximum permissible shear stress, twist angle, and shaft length 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 given maximum permissible shear stress using this online calculator? To use this online calculator for Modulus of rigidity given maximum permissible shear stress, enter Maximum Shear Stress (τ_max), Length of Shaft (L_shaft), Angle of Twist (θ) & Radius of Shaft (R) and hit the calculate button. Here is how the Modulus of rigidity given maximum permissible shear stress calculation can be explained with given input values -> 1.2E-9 = (42000000*4.58)/(1.42*0.11).

FAQ

What is Modulus of rigidity given maximum permissible shear stress?

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

How to calculate Modulus of rigidity given maximum permissible shear stress?

The Modulus of rigidity given maximum permissible shear stress, twist angle, and shaft length 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 = (Maximum Shear Stress*Length of Shaft)/(Angle of Twist*Radius of Shaft). To calculate Modulus of rigidity given maximum permissible shear stress, you need Maximum Shear Stress (τ_max), Length of Shaft (L_shaft), Angle of Twist (θ) & Radius of Shaft (R). With our tool, you need to enter the respective value for Maximum Shear Stress, Length of Shaft, Angle of Twist & Radius of Shaft 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 Maximum Shear Stress, Length of Shaft, Angle of Twist & Radius of Shaft. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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