Maximum shear stress in shaft given polar moment of inertia Calculator

✖Torque Exerted on Wheel is described as the turning effect of force on the axis of rotation. In brief, it is a moment of force. It is characterized by τ.ⓘ Torque Exerted on Wheel [τ]			+10% -10%
✖Radius of shaft is the distance between the center and the circumference of the shaft.ⓘ Radius of Shaft [R_shaft]			+10% -10%
✖Polar Moment of Inertia of shaft is the measure of object resistance to torsion.ⓘ Polar Moment of Inertia of shaft [J_shaft]			+10% -10%

✖Maximum Shear Stress on Shaft that acts coplanar with a cross-section of material arises due to shear forces.ⓘ Maximum shear stress in shaft given polar moment of inertia [𝜏_max]

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Formula

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Maximum shear stress in shaft given polar moment of inertia

Formula

`"𝜏"_{"max"} = ("τ"*"R"_{"shaft"})/"J"_{"shaft"}`

Example

`"6.8E^-6MPa"=("50N*m"*"1350mm")/"10m⁴"`

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Maximum shear stress in shaft given polar moment of inertia Solution

STEP 0: Pre-Calculation Summary

Formula Used

Maximum Shear Stress on Shaft = (Torque Exerted on Wheel*Radius of Shaft)/Polar Moment of Inertia of shaft
𝜏_max = (τ*R_shaft)/J_shaft
This formula uses 4 Variables

Variables Used

Maximum Shear Stress on Shaft - (Measured in Pascal) - Maximum Shear Stress on Shaft that acts coplanar with a cross-section of material arises due to shear forces.
Torque Exerted on Wheel - (Measured in Newton Meter) - Torque Exerted on Wheel is described as the turning effect of force on the axis of rotation. In brief, it is a moment of force. It is characterized by τ.
Radius of Shaft - (Measured in Meter) - Radius of shaft is the distance between the center and the circumference of the shaft.
Polar Moment of Inertia of shaft - (Measured in Meter⁴) - Polar Moment of Inertia of shaft is the measure of object resistance to torsion.

STEP 1: Convert Input(s) to Base Unit

Torque Exerted on Wheel: 50 Newton Meter --> 50 Newton Meter No Conversion Required
Radius of Shaft: 1350 Millimeter --> 1.35 Meter (Check conversion here)
Polar Moment of Inertia of shaft: 10 Meter⁴ --> 10 Meter⁴ No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

𝜏_max = (τ*R_shaft)/J_shaft --> (50*1.35)/10

Evaluating ... ...

𝜏_max = 6.75

STEP 3: Convert Result to Output's Unit

6.75 Pascal -->6.75E-06 Megapascal (Check conversion here)

FINAL ANSWER

6.75E-06 ≈ 6.8E-6 Megapascal <-- Maximum Shear Stress on Shaft

(Calculation completed in 00.020 seconds)

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Home » Physics » Strength of Materials » Torsion of Shafts And Springs » Expression for Torque in terms of Polar Moment of Inertia » Maximum shear stress in shaft given polar moment of inertia

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< 11 Expression for Torque in terms of Polar Moment of Inertia Calculators

Modulus of Rigidity of Shaft given Torque Transmitted and Polar Moment of Inertia

Go Modulus of Rigidity = (Torque Exerted on Wheel*Length of Shaft)/(Angle of twist*Polar Moment of Inertia of shaft)

Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity

Go Polar Moment of Inertia of shaft = (Torque Exerted on Wheel*Length of Shaft)/(Modulus of Rigidity*Angle of twist)

Angle of Twist for Shaft given Polar Moment of Inertia and Modulus of Rigidity

Go Angle of twist = (Torque Exerted on Wheel*Length of Shaft)/(Modulus of Rigidity*Polar Moment of Inertia of shaft)

Torque Transmitted by Shaft given Polar Moment of Inertia and Modulus of Rigidity

Go Torque Exerted on Wheel = (Modulus of Rigidity*Angle of twist*Polar Moment of Inertia of shaft)/Length of Shaft

Length of Shaft given Polar Moment of Inertia and Modulus of Rigidity

Go Length of Shaft = (Modulus of Rigidity*Angle of twist*Polar Moment of Inertia of shaft)/Torque Exerted on Wheel

Polar moment of inertia of shaft given torque transmitted by shaft

Go Polar Moment of Inertia of shaft = (Torque Exerted on Wheel*Radius of Shaft)/Maximum Shear Stress on Shaft

Maximum shear stress in shaft given polar moment of inertia

Go Maximum Shear Stress on Shaft = (Torque Exerted on Wheel*Radius of Shaft)/Polar Moment of Inertia of shaft

Torque transmitted by shaft given polar moment of inertia

Go Torque Exerted on Wheel = (Maximum Shear Stress on Shaft*Polar Moment of Inertia of shaft)/Radius of Shaft

Radius of shaft given polar moment of inertia

Go Radius of Shaft = (Maximum Shear Stress on Shaft*Polar Moment of Inertia of shaft)/Torque Exerted on Wheel

Diameter of shaft given polar moment of inertia of shaft

Go Diameter of Shaft = ((32*Polar Moment of Inertia of shaft)/pi)^(1/4)

Polar moment of inertia of shaft

Go Polar Moment of Inertia of shaft = (pi*Diameter of Shaft^4)/32

Maximum shear stress in shaft given polar moment of inertia Formula

Maximum Shear Stress on Shaft = (Torque Exerted on Wheel*Radius of Shaft)/Polar Moment of Inertia of shaft
𝜏_max = (τ*R_shaft)/J_shaft

What is difference between moment of inertia and polar moment of inertia?

The main difference between the moment of inertia and the polar moment of inertia is that the moment of inertia measures how an object resists angular acceleration, whereas the polar moment of inertia measures how an object resists torsion.

How to Calculate Maximum shear stress in shaft given polar moment of inertia?

Maximum shear stress in shaft given polar moment of inertia calculator uses Maximum Shear Stress on Shaft = (Torque Exerted on Wheel*Radius of Shaft)/Polar Moment of Inertia of shaft to calculate the Maximum Shear Stress on Shaft, Maximum shear stress in shaft given polar moment of inertia is defined as a force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress. Maximum Shear Stress on Shaft is denoted by 𝜏_max symbol.

How to calculate Maximum shear stress in shaft given polar moment of inertia using this online calculator? To use this online calculator for Maximum shear stress in shaft given polar moment of inertia, enter Torque Exerted on Wheel (τ), Radius of Shaft (R_shaft) & Polar Moment of Inertia of shaft (J_shaft) and hit the calculate button. Here is how the Maximum shear stress in shaft given polar moment of inertia calculation can be explained with given input values -> 6.8E-12 = (50*1.35)/10.

FAQ

What is Maximum shear stress in shaft given polar moment of inertia?

Maximum shear stress in shaft given polar moment of inertia 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 𝜏_max = (τ*R_shaft)/J_shaft or Maximum Shear Stress on Shaft = (Torque Exerted on Wheel*Radius of Shaft)/Polar Moment of Inertia of shaft. Torque Exerted on Wheel is described as the turning effect of force on the axis of rotation. In brief, it is a moment of force. It is characterized by τ, Radius of shaft is the distance between the center and the circumference of the shaft & Polar Moment of Inertia of shaft is the measure of object resistance to torsion.

How to calculate Maximum shear stress in shaft given polar moment of inertia?

Maximum shear stress in shaft given polar moment of inertia 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 Maximum Shear Stress on Shaft = (Torque Exerted on Wheel*Radius of Shaft)/Polar Moment of Inertia of shaft. To calculate Maximum shear stress in shaft given polar moment of inertia, you need Torque Exerted on Wheel (τ), Radius of Shaft (R_shaft) & Polar Moment of Inertia of shaft (J_shaft). With our tool, you need to enter the respective value for Torque Exerted on Wheel, Radius of Shaft & Polar Moment of Inertia of shaft and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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