Maximum permissible shear stress for given Radius 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%
✖Length of Shaft is the distance between two ends of shaft.ⓘ Length of Shaft [L_shaft]			+10% -10%

✖Maximum Shear Stress is the greatest extent a shear force can be concentrated in a small area.ⓘ Maximum permissible shear stress for given Radius and modulus of rigidity [τ_max]

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Formula

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Maximum permissible shear stress for given Radius and modulus of rigidity

Formula

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

Example

`"1364.192MPa"=("40GPa"*("1.42rad")*"110mm")/"4.58m"`

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Maximum permissible shear stress for given Radius and modulus of rigidity Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

Maximum Shear Stress - (Measured in Pascal) - Maximum Shear Stress is the greatest extent a shear force can be concentrated in a small area.
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.
Length of Shaft - (Measured in Meter) - Length of Shaft is the distance between two ends of shaft.

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)
Length of Shaft: 4.58 Meter --> 4.58 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

τ_max = (G_Torsion*(θ)*R)/L_shaft --> (40000000000*(1.42)*0.11)/4.58

Evaluating ... ...

τ_max = 1364192139.73799

STEP 3: Convert Result to Output's Unit

1364192139.73799 Pascal -->1364.19213973799 Megapascal (Check conversion here)

FINAL ANSWER

1364.19213973799 ≈ 1364.192 Megapascal <-- Maximum Shear Stress

(Calculation completed in 00.020 seconds)

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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

Maximum permissible shear stress for given Radius and modulus of rigidity Formula

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

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 Maximum permissible shear stress for given Radius and modulus of rigidity?

Maximum permissible shear stress for given Radius and modulus of rigidity calculator uses Maximum Shear Stress = (Modulus of Rigidity*(Angle of Twist)*Radius of Shaft)/Length of Shaft to calculate the Maximum Shear Stress, Maximum permissible shear stress for given Radius and modulus of rigidity, twist angle, and shaft length formula is defined as the limit up to which the material can withstand shear. Maximum Shear Stress is denoted by τ_max symbol.

How to calculate Maximum permissible shear stress for given Radius and modulus of rigidity using this online calculator? To use this online calculator for Maximum permissible shear stress for given Radius and modulus of rigidity, enter Modulus of Rigidity (G_Torsion), Angle of Twist (θ), Radius of Shaft (R) & Length of Shaft (L_shaft) and hit the calculate button. Here is how the Maximum permissible shear stress for given Radius and modulus of rigidity calculation can be explained with given input values -> 0.001364 = (40000000000*(1.42)*0.11)/4.58.

FAQ

What is Maximum permissible shear stress for given Radius and modulus of rigidity?

Maximum permissible shear stress for given Radius and modulus of rigidity, twist angle, and shaft length formula is defined as the limit up to which the material can withstand shear and is represented as τ_max = (G_Torsion*(θ)*R)/L_shaft or Maximum Shear Stress = (Modulus of Rigidity*(Angle of Twist)*Radius of Shaft)/Length of Shaft. 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 & Length of Shaft is the distance between two ends of shaft.

How to calculate Maximum permissible shear stress for given Radius and modulus of rigidity?

Maximum permissible shear stress for given Radius and modulus of rigidity, twist angle, and shaft length formula is defined as the limit up to which the material can withstand shear is calculated using Maximum Shear Stress = (Modulus of Rigidity*(Angle of Twist)*Radius of Shaft)/Length of Shaft. To calculate Maximum permissible shear stress for given Radius and modulus of rigidity, you need Modulus of Rigidity (G_Torsion), Angle of Twist (θ), Radius of Shaft (R) & Length of Shaft (L_shaft). With our tool, you need to enter the respective value for Modulus of Rigidity, Angle of Twist, Radius of Shaft & Length 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 Maximum Shear Stress?

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

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

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