Polar Moment of Inertia given Torsional Shear Stress Calculator

✖Torsional Moment is the torque applied to generate a torsion (twist) within the object.ⓘ Torsional Moment [T]			+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%
✖Maximum Shear Stress is the greatest extent a shear force can be concentrated in a small area.ⓘ Maximum Shear Stress [τ_max]			+10% -10%

✖The Polar Moment of Inertia is a shaft or beam's resistance to being distorted by torsion, as a function of its shape.ⓘ Polar Moment of Inertia given Torsional Shear Stress [J]

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Formula

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Polar Moment of Inertia given Torsional Shear Stress

Formula

`"J" = ("T"*"R")/("τ"_{"max"})`

Example

`"2.22619mm⁴"=("0.85kN*m"*"110mm")/("42MPa")`

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Polar Moment of Inertia given Torsional Shear Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Polar Moment of Inertia = (Torsional Moment*Radius of Shaft)/(Maximum Shear Stress)
J = (T*R)/(τ_max)
This formula uses 4 Variables

Variables Used

Polar Moment of Inertia - (Measured in Millimeter⁴) - The Polar Moment of Inertia is a shaft or beam's resistance to being distorted by torsion, as a function of its shape.
Torsional Moment - (Measured in Newton Meter) - Torsional Moment is the torque applied to generate a torsion (twist) within the object.
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.
Maximum Shear Stress - (Measured in Megapascal) - Maximum Shear Stress is the greatest extent a shear force can be concentrated in a small area.

STEP 1: Convert Input(s) to Base Unit

Torsional Moment: 0.85 Kilonewton Meter --> 850 Newton Meter (Check conversion here)
Radius of Shaft: 110 Millimeter --> 0.11 Meter (Check conversion here)
Maximum Shear Stress: 42 Megapascal --> 42 Megapascal No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

J = (T*R)/(τ_max) --> (850*0.11)/(42)

Evaluating ... ...

J = 2.22619047619048

STEP 3: Convert Result to Output's Unit

2.22619047619048E-12 Meter⁴ -->2.22619047619048 Millimeter⁴ (Check conversion here)

FINAL ANSWER

2.22619047619048 ≈ 2.22619 Millimeter⁴ <-- Polar Moment of Inertia

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Strength of Materials » Shear Stress » Longitudinal Shear Stress » I-Beam » Polar Moment of Inertia given Torsional Shear Stress

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< 12 I-Beam Calculators

Maximum Longitudinal Shear Stress in Web for I beam

Go Maximum Longitudinal Shear Stress = (((Width of Flange*Shear Force)/(8*Width of Web*Area Moment of Inertia)*(Overall Depth of I Beam^2-Depth of Web^2)))+((Shear Force*Depth of Web^2)/(8*Area Moment of Inertia))

Moment of Inertia given Maximum Longitudinal Shear Stress in Web for I beam

Go Area Moment of Inertia = (((Width of Flange*Shear Force)/(8*Width of Web))*(Overall Depth of I Beam^2-Depth of Web^2))/Maximum Shear Stress+((Shear Force*Depth of Web^2)/8)/Maximum Shear Stress

Transverse Shear force given Maximum Longitudinal Shear Stress in Web for I beam

Go Shear Force = (Maximum Longitudinal Shear Stress*Width of Web*8*Area Moment of Inertia)/((Width of Flange*(Overall Depth of I Beam^2-Depth of Web^2))+(Width of Web*(Depth of Web^2)))

Moment of Inertia given Longitudinal Shear Stress in Web for I beam

Go Area Moment of Inertia = ((Width of Flange*Shear Force)/(8*Shear Stress*Width of Web))*(Overall Depth of I Beam^2-Depth of Web^2)

Breadth of Web given Longitudinal Shear Stress in Web for I beam

Go Width of Web = ((Width of Flange*Shear Force)/(8*Shear Stress*Area Moment of Inertia))*(Overall Depth of I Beam^2-Depth of Web^2)

Longitudinal Shear Stress in Web for I beam

Go Shear Stress = ((Width of Flange*Shear Force)/(8*Width of Web*Area Moment of Inertia))*(Overall Depth of I Beam^2-Depth of Web^2)

Breadth of Flange Given Longitudinal Shear Stress in Web for I beam

Go Width of Flange = (8*Area Moment of Inertia*Shear Stress*Width of Web)/(Shear Force*(Overall Depth of I Beam^2-Depth of Web^2))

Transverse Shear for Longitudinal Shear Stress in Web for I Beam

Go Shear Force = (8*Area Moment of Inertia*Shear Stress*Width of Web)/(Width of Flange*(Overall Depth of I Beam^2-Depth of Web^2))

Moment of Inertia given Longitudinal Shear Stress at lower edge in Flange of I beam

Go Area Moment of Inertia = (Shear Force/(8*Shear Stress))*(Overall Depth of I Beam^2-Depth of Web^2)

Longitudinal Shear Stress in Flange at Lower Depth of I beam

Go Shear Stress = (Shear Force/(8*Area Moment of Inertia))*(Overall Depth of I Beam^2-Depth of Web^2)

Transverse Shear given Longitudinal Shear Stress in Flange for I beam

Go Shear Force = (8*Area Moment of Inertia*Shear Stress)/(Overall Depth of I Beam^2-Depth of Web^2)

Polar Moment of Inertia given Torsional Shear Stress

Go Polar Moment of Inertia = (Torsional Moment*Radius of Shaft)/(Maximum Shear Stress)

Polar Moment of Inertia given Torsional Shear Stress Formula

Polar Moment of Inertia = (Torsional Moment*Radius of Shaft)/(Maximum Shear Stress)
J = (T*R)/(τ_max)

What is Polar Moment of Inertia?

The Polar Moment of Inertia basically describes the cylindrical object's (including its segments) resistance to torsional deformation when torque is applied in a plane that is parallel to the cross-section area or in a plane that is perpendicular to the object's central axis.

How to Calculate Polar Moment of Inertia given Torsional Shear Stress?

Polar Moment of Inertia given Torsional Shear Stress calculator uses Polar Moment of Inertia = (Torsional Moment*Radius of Shaft)/(Maximum Shear Stress) to calculate the Polar Moment of Inertia, The Polar Moment of Inertia given Torsional Shear Stress is defined as a shaft or beam's resistance to being distorted by torsion, as a function of its shape. The greater the magnitude of the polar moment of inertia, the greater the torsional resistance of the object. Polar Moment of Inertia is denoted by J symbol.

How to calculate Polar Moment of Inertia given Torsional Shear Stress using this online calculator? To use this online calculator for Polar Moment of Inertia given Torsional Shear Stress, enter Torsional Moment (T), Radius of Shaft (R) & Maximum Shear Stress (τ_max) and hit the calculate button. Here is how the Polar Moment of Inertia given Torsional Shear Stress calculation can be explained with given input values -> 2.2E+12 = (850*0.11)/(42000000).

FAQ

What is Polar Moment of Inertia given Torsional Shear Stress?

The Polar Moment of Inertia given Torsional Shear Stress is defined as a shaft or beam's resistance to being distorted by torsion, as a function of its shape. The greater the magnitude of the polar moment of inertia, the greater the torsional resistance of the object and is represented as J = (T*R)/(τ_max) or Polar Moment of Inertia = (Torsional Moment*Radius of Shaft)/(Maximum Shear Stress). Torsional Moment is the torque applied to generate a torsion (twist) within the object, The Radius of Shaft is the line segment extending from the center of a circle or sphere to the circumference or bounding surface & Maximum Shear Stress is the greatest extent a shear force can be concentrated in a small area.

How to calculate Polar Moment of Inertia given Torsional Shear Stress?

The Polar Moment of Inertia given Torsional Shear Stress is defined as a shaft or beam's resistance to being distorted by torsion, as a function of its shape. The greater the magnitude of the polar moment of inertia, the greater the torsional resistance of the object is calculated using Polar Moment of Inertia = (Torsional Moment*Radius of Shaft)/(Maximum Shear Stress). To calculate Polar Moment of Inertia given Torsional Shear Stress, you need Torsional Moment (T), Radius of Shaft (R) & Maximum Shear Stress (τ_max). With our tool, you need to enter the respective value for Torsional Moment, Radius of Shaft & Maximum Shear Stress 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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