Twist angle 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%
✖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 [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.ⓘ Twist angle given maximum permissible shear stress [θ]

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Formula

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Twist angle given maximum permissible shear stress

Formula

`"θ" = ("τ"_{"max"}*"L"_{"shaft"})/("R"*"G"_{"Torsion"})`

Example

`"0.043718rad"=("42MPa"*"4.58m")/("110mm"*"40GPa")`

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Twist angle given maximum permissible shear stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Angle of Twist = (Maximum Shear Stress*Length of Shaft)/(Radius of Shaft*Modulus of Rigidity)
θ = (τ_max*L_shaft)/(R*G_Torsion)
This formula uses 5 Variables

Variables Used

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.
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.
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.
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.

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
Radius of Shaft: 110 Millimeter --> 0.11 Meter (Check conversion here)
Modulus of Rigidity: 40 Gigapascal --> 40000000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ = (τ_max*L_shaft)/(R*G_Torsion) --> (42000000*4.58)/(0.11*40000000000)

Evaluating ... ...

θ = 0.0437181818181818

STEP 3: Convert Result to Output's Unit

0.0437181818181818 Radian --> No Conversion Required

FINAL ANSWER

0.0437181818181818 ≈ 0.043718 Radian <-- Angle of Twist

(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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Verified by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

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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

Twist angle given maximum permissible shear stress Formula

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

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 Twist angle given maximum permissible shear stress?

Twist angle given maximum permissible shear stress calculator uses Angle of Twist = (Maximum Shear Stress*Length of Shaft)/(Radius of Shaft*Modulus of Rigidity) to calculate the Angle of Twist, The Twist angle given maximum permissible shear stress along with modulus of rigidity, and shaft length given is defined as the angle of rotation of any plane taken along the axis of the shaft. Angle of Twist is denoted by θ symbol.

How to calculate Twist angle given maximum permissible shear stress using this online calculator? To use this online calculator for Twist angle given maximum permissible shear stress, enter Maximum Shear Stress (τ_max), Length of Shaft (L_shaft), Radius of Shaft (R) & Modulus of Rigidity (G_Torsion) and hit the calculate button. Here is how the Twist angle given maximum permissible shear stress calculation can be explained with given input values -> 0.043718 = (42000000*4.58)/(0.11*40000000000).

FAQ

What is Twist angle given maximum permissible shear stress?

The Twist angle given maximum permissible shear stress along with modulus of rigidity, and shaft length given is defined as the angle of rotation of any plane taken along the axis of the shaft and is represented as θ = (τ_max*L_shaft)/(R*G_Torsion) or Angle of Twist = (Maximum Shear Stress*Length of Shaft)/(Radius of Shaft*Modulus of Rigidity). 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, The Radius of Shaft is the line segment extending from the center of a circle or sphere to the circumference or bounding surface & 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.

How to calculate Twist angle given maximum permissible shear stress?

The Twist angle given maximum permissible shear stress along with modulus of rigidity, and shaft length given is defined as the angle of rotation of any plane taken along the axis of the shaft is calculated using Angle of Twist = (Maximum Shear Stress*Length of Shaft)/(Radius of Shaft*Modulus of Rigidity). To calculate Twist angle given maximum permissible shear stress, you need Maximum Shear Stress (τ_max), Length of Shaft (L_shaft), Radius of Shaft (R) & Modulus of Rigidity (G_Torsion). With our tool, you need to enter the respective value for Maximum Shear Stress, Length of Shaft, Radius of Shaft & Modulus of Rigidity 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 Angle of Twist?

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

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

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