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Polar Moment of Inertia for Pin Ended Columns Formula

GoPolar Moment of Inertia for Axial Buckling Load for Warped Section Formula

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The Polar Moment of Inertia is a measure of an object’s capacity to oppose or resist torsion when some amount of torque is applied to it on a specified axis. Check FAQs

I p = \frac{G \cdot J \cdot A}{P Buckling Load}

I_p - Polar Moment of Inertia?G - Shear Modulus of Elasticity?J - Torsional Constant?A - Column Cross-Sectional Area?P_{Buckling Load} - Buckling Load?

Polar Moment of Inertia for Pin Ended Columns Example

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Here is how the Polar Moment of Inertia for Pin Ended Columns equation looks like with Values.

Here is how the Polar Moment of Inertia for Pin Ended Columns equation looks like with Units.

Here is how the Polar Moment of Inertia for Pin Ended Columns equation looks like.

322000 = \frac{230 \cdot 10 \cdot 700}{5}

322000mm⁴ = \frac{230MPa \cdot 10 \cdot 700mm²}{5N}

322000 = \frac{230 \cdot 10 \cdot 700}{5}

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Polar Moment of Inertia for Pin Ended Columns Solution

Follow our step by step solution on how to calculate Polar Moment of Inertia for Pin Ended Columns?

FIRST Step Consider the formula

I p = \frac{G \cdot J \cdot A}{P Buckling Load}

Next Step Substitute values of Variables

∴

I p = \frac{230MPa \cdot 10 \cdot 700mm²}{5N}

Next Step Prepare to Evaluate

∴

I p = \frac{230 \cdot 10 \cdot 700}{5}

Next Step Evaluate

∴

I p = 3.22E-07m⁴

LAST Step Convert to Output's Unit

∴

I p = 322000mm⁴

Polar Moment of Inertia for Pin Ended Columns Formula Elements

Variables

Polar Moment of Inertia

The Polar Moment of Inertia is a measure of an object’s capacity to oppose or resist torsion when some amount of torque is applied to it on a specified axis.

Symbol: I_p

Measurement: Second Moment of AreaUnit: mm⁴

Note: Value should be greater than 0.

Formulas to find Polar Moment of Inertia

Shear Modulus of Elasticity

The Shear Modulus of Elasticity is the measure of the rigidity of the body, given by the ratio of shear stress to shear strain.

Symbol: G

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Shear Modulus of Elasticity

Torsional Constant

Torsional Constant is a geometrical property of a bar's cross-section which is involved in the relationship between the angle of twist and applied torque along the axis of the bar.

Symbol: J

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Torsional Constant

Column Cross-Sectional Area

Column Cross-Sectional Area is the area of a two-dimensional shape that is obtained when a three-dimensional object is sliced perpendicular to some specified axis at a point.

Symbol: A

Measurement: AreaUnit: mm²

Note: Value should be greater than 0.

Formulas to find Column Cross-Sectional Area

Buckling Load

The Buckling Load is the load at which the column starts buckling. The buckling load of a given material depends on the Slenderness ratio, Area of a cross-section, and Modulus of Elasticity.

Symbol: P_{Buckling Load}

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Buckling Load

Other Formulas to find Polar Moment of Inertia

Go Polar Moment of Inertia for Axial Buckling Load for Warped Section

I p = \frac{A}{P Buckling Load} \cdot (G \cdot J + (\frac{π^{2} \cdot E \cdot C w}{L^{2}}))

Other formulas in Elastic Flexural Buckling of Columns category

Go Torsional Buckling Load for Pin Ended Columns

P Buckling Load = \frac{G \cdot J \cdot A}{I p}

Go Cross-Sectional Area given Torsional Buckling Load for Pin Ended Columns

A = \frac{P Buckling Load \cdot I p}{G \cdot J}

Go Axial Buckling Load for Warped Section

P Buckling Load = (\frac{A}{I p}) \cdot (G \cdot J + \frac{π^{2} \cdot E \cdot C w}{L^{2}})

Go Cross-Sectional Area given Axial Buckling Load for Warped Section

A = \frac{P Buckling Load \cdot I p}{G \cdot J + (\frac{π^{2} \cdot E \cdot C w}{L^{2}})}

How to Evaluate Polar Moment of Inertia for Pin Ended Columns?

Polar Moment of Inertia for Pin Ended Columns evaluator uses Polar Moment of Inertia = (Shear Modulus of Elasticity*Torsional Constant*Column Cross-Sectional Area)/Buckling Load to evaluate the Polar Moment of Inertia, The Polar Moment of Inertia for Pin Ended Columns formula is defined as a measurement of a round bar's capacity to oppose torsion. It is required to compute the twist of a column subjected to a torque. Polar Moment of Inertia is denoted by I_p symbol.

How to evaluate Polar Moment of Inertia for Pin Ended Columns using this online evaluator? To use this online evaluator for Polar Moment of Inertia for Pin Ended Columns, enter Shear Modulus of Elasticity (G), Torsional Constant (J), Column Cross-Sectional Area (A) & Buckling Load (P_{Buckling Load}) and hit the calculate button.

FAQs on Polar Moment of Inertia for Pin Ended Columns

What is the formula to find Polar Moment of Inertia for Pin Ended Columns?

The formula of Polar Moment of Inertia for Pin Ended Columns is expressed as Polar Moment of Inertia = (Shear Modulus of Elasticity*Torsional Constant*Column Cross-Sectional Area)/Buckling Load. Here is an example- 3.2E+17 = (230000000*10*0.0007)/5.

How to calculate Polar Moment of Inertia for Pin Ended Columns?

With Shear Modulus of Elasticity (G), Torsional Constant (J), Column Cross-Sectional Area (A) & Buckling Load (P_{Buckling Load}) we can find Polar Moment of Inertia for Pin Ended Columns using the formula - Polar Moment of Inertia = (Shear Modulus of Elasticity*Torsional Constant*Column Cross-Sectional Area)/Buckling Load.

What are the other ways to Calculate Polar Moment of Inertia?

Here are the different ways to Calculate Polar Moment of Inertia-

Polar Moment of Inertia=Column Cross-Sectional Area/Buckling Load*(Shear Modulus of Elasticity*Torsional Constant+((pi^2*Modulus of Elasticity*Warping Constant)/Effective Length of Column^2))

Can the Polar Moment of Inertia for Pin Ended Columns be negative?

No, the Polar Moment of Inertia for Pin Ended Columns, measured in Second Moment of Area cannot be negative.

Which unit is used to measure Polar Moment of Inertia for Pin Ended Columns?

Polar Moment of Inertia for Pin Ended Columns is usually measured using the Millimeter⁴[mm⁴] for Second Moment of Area. Meter⁴[mm⁴], Centimeter⁴[mm⁴] are the few other units in which Polar Moment of Inertia for Pin Ended Columns can be measured.

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Polar Moment of Inertia for Pin Ended Columns Formula

​GoPolar Moment of Inertia for Axial Buckling Load for Warped Section Formula

Polar Moment of Inertia for Pin Ended Columns Example

Polar Moment of Inertia for Pin Ended Columns Solution

Polar Moment of Inertia for Pin Ended Columns Formula Elements

Other Formulas to find Polar Moment of Inertia

Other formulas in Elastic Flexural Buckling of Columns category

How to Evaluate Polar Moment of Inertia for Pin Ended Columns?

FAQs on Polar Moment of Inertia for Pin Ended Columns

Variable Name

GoPolar Moment of Inertia for Axial Buckling Load for Warped Section Formula