Shear Stress induced at Radius 'r' from Center of Shaft using Modulus of Rigidity Calculator

✖The Radius from Center to Distance r of the shaft is a radial line from the focus to any point of a curve.ⓘ Radius from Center to Distance r [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 for Circular Shafts is the angular deformation along the length of a circular shaft subjected to torsion, measured in radians.ⓘ Angle of Twist for Circular Shafts [θ_{Circularshafts}]			+10% -10%
✖Shear Stress in Shaft is when a shaft is subjected to torque or twisting shearing stress is produced in the shaft.ⓘ Shear Stress in Shaft [τ]			+10% -10%

✖Shear Stress at Radius r from shaft is a force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.ⓘ Shear Stress induced at Radius 'r' from Center of Shaft using Modulus of Rigidity [T_r]

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Shear Stress induced at Radius 'r' from Center of Shaft using Modulus of Rigidity Solution

STEP 0: Pre-Calculation Summary

Formula Used

Shear Stress at Radius r = (Radius from Center to Distance r*Modulus of Rigidity*Angle of Twist for Circular Shafts)/Shear Stress in Shaft
T_r = (r*G_Torsion*θ_{Circularshafts})/τ
This formula uses 5 Variables

Variables Used

Shear Stress at Radius r - (Measured in Pascal) - Shear Stress at Radius r from shaft is a force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.
Radius from Center to Distance r - (Measured in Meter) - The Radius from Center to Distance r of the shaft is a radial line from the focus to any point of a curve.
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 for Circular Shafts - (Measured in Radian) - Angle of Twist for Circular Shafts is the angular deformation along the length of a circular shaft subjected to torsion, measured in radians.
Shear Stress in Shaft - (Measured in Pascal) - Shear Stress in Shaft is when a shaft is subjected to torque or twisting shearing stress is produced in the shaft.

STEP 1: Convert Input(s) to Base Unit

Radius from Center to Distance r: 0.122 Meter --> 0.122 Meter No Conversion Required
Modulus of Rigidity: 40 Gigapascal --> 40000000000 Pascal (Check conversion here)
Angle of Twist for Circular Shafts: 72 Radian --> 72 Radian No Conversion Required
Shear Stress in Shaft: 180 Megapascal --> 180000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T_r = (r*G_Torsion*θ_{Circularshafts})/τ --> (0.122*40000000000*72)/180000000

Evaluating ... ...

T_r = 1952

STEP 3: Convert Result to Output's Unit

1952 Pascal -->0.001952 Megapascal (Check conversion here)

FINAL ANSWER

0.001952 Megapascal <-- Shear Stress at Radius r

(Calculation completed in 00.004 seconds)

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< Deviation of Shear Stress produced in a Circular Shaft subjected to Torsion Calculators

Length of Shaft with known Shear Strain at Outer Surface of Shaft

LaTeX Go Length of Shaft = (Radius of Shaft*Angle of Twist for Circular Shafts)/Shear Strain

Angle of Twist with known Shear Strain at Outer Surface of Shaft

LaTeX Go Angle of Twist for Circular Shafts = (Shear Strain*Length of Shaft)/Radius of Shaft

Radius of Shaft using Shear Strain at Outer Surface of Shaft

LaTeX Go Radius of Shaft = (Shear Strain*Length of Shaft)/Angle of Twist for Circular Shafts

Shear Strain at Outer Surface of Circular Shaft

LaTeX Go Shear Strain = (Radius of Shaft*Angle of Twist for Circular Shafts)/Length of Shaft

< Torsion Equation of Circular Shafts Calculators

Angle of Twist with known Shear Stress induced at Radius r from Center of Shaft

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

Angle of Twist with known Shear Stress in Shaft

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

Length of Shaft with known Shear Strain at Outer Surface of Shaft

LaTeX Go Length of Shaft = (Radius of Shaft*Angle of Twist for Circular Shafts)/Shear Strain

Angle of Twist with known Shear Strain at Outer Surface of Shaft

LaTeX Go Angle of Twist for Circular Shafts = (Shear Strain*Length of Shaft)/Radius of Shaft

Shear Stress induced at Radius 'r' from Center of Shaft using Modulus of Rigidity Formula

LaTeX Go

Shear Stress at Radius r = (Radius from Center to Distance r*Modulus of Rigidity*Angle of Twist for Circular Shafts)/Shear Stress in Shaft
T_r = (r*G_Torsion*θ_{Circularshafts})/τ

What is Torsional Force?

A Torsion Force is a load that is applied to material through torque. The torque that is applied creates shear stress. If a torsion force is large enough, it can cause a material to undergo a twisting motion during elastic and plastic deformation.

What is Modulus of Rigidity?

The Modulus of Rigidity is the elastic coefficient when a shear force is applied resulting in lateral deformation. It gives us a measure of how rigid a body is. The table given below briefs everything you need to know about rigidity modulus. Shear modulus is the ratio of shear stress to shear strain in a body.

How to Calculate Shear Stress induced at Radius 'r' from Center of Shaft using Modulus of Rigidity?

Shear Stress induced at Radius 'r' from Center of Shaft using Modulus of Rigidity calculator uses Shear Stress at Radius r = (Radius from Center to Distance r*Modulus of Rigidity*Angle of Twist for Circular Shafts)/Shear Stress in Shaft to calculate the Shear Stress at Radius r, The Shear Stress induced at Radius 'r' from Center of Shaft using Modulus of Rigidity formula is defined as a force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress. Shear Stress at Radius r is denoted by T_r symbol.

How to calculate Shear Stress induced at Radius 'r' from Center of Shaft using Modulus of Rigidity using this online calculator? To use this online calculator for Shear Stress induced at Radius 'r' from Center of Shaft using Modulus of Rigidity, enter Radius from Center to Distance r (r), Modulus of Rigidity (G_Torsion), Angle of Twist for Circular Shafts (θ_{Circularshafts}) & Shear Stress in Shaft (τ) and hit the calculate button. Here is how the Shear Stress induced at Radius 'r' from Center of Shaft using Modulus of Rigidity calculation can be explained with given input values -> 2.4E-10 = (0.122*40000000000*72)/180000000.

FAQ

What is Shear Stress induced at Radius 'r' from Center of Shaft using Modulus of Rigidity?

The Shear Stress induced at Radius 'r' from Center of Shaft using Modulus of Rigidity formula is defined as a force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress and is represented as T_r = (r*G_Torsion*θ_{Circularshafts})/τ or Shear Stress at Radius r = (Radius from Center to Distance r*Modulus of Rigidity*Angle of Twist for Circular Shafts)/Shear Stress in Shaft. The Radius from Center to Distance r of the shaft is a radial line from the focus to any point of a curve, 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 for Circular Shafts is the angular deformation along the length of a circular shaft subjected to torsion, measured in radians & Shear Stress in Shaft is when a shaft is subjected to torque or twisting shearing stress is produced in the shaft.

How to calculate Shear Stress induced at Radius 'r' from Center of Shaft using Modulus of Rigidity?

The Shear Stress induced at Radius 'r' from Center of Shaft using Modulus of Rigidity formula is defined as a force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress is calculated using Shear Stress at Radius r = (Radius from Center to Distance r*Modulus of Rigidity*Angle of Twist for Circular Shafts)/Shear Stress in Shaft. To calculate Shear Stress induced at Radius 'r' from Center of Shaft using Modulus of Rigidity, you need Radius from Center to Distance r (r), Modulus of Rigidity (G_Torsion), Angle of Twist for Circular Shafts (θ_{Circularshafts}) & Shear Stress in Shaft (τ). With our tool, you need to enter the respective value for Radius from Center to Distance r, Modulus of Rigidity, Angle of Twist for Circular Shafts & Shear Stress in 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 Shear Stress at Radius r?

In this formula, Shear Stress at Radius r uses Radius from Center to Distance r, Modulus of Rigidity, Angle of Twist for Circular Shafts & Shear Stress in Shaft. We can use 2 other way(s) to calculate the same, which is/are as follows -

Shear Stress at Radius r = (Shear Stress in Shaft*Radius from Center to Distance r)/Radius of Shaft
Shear Stress at Radius r = (Shear Stress in Shaft*Radius from Center to Distance r)/Radius of Shaft

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