Polar Moment of Inertia for Pin Ended Columns Calculator

✖The Shear Modulus of Elasticity is the measure of the rigidity of the body, given by the ratio of shear stress to shear strain.ⓘ Shear Modulus of Elasticity [G]			+10% -10%
✖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.ⓘ Torsional Constant [J]			+10% -10%
✖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.ⓘ Column Cross-Sectional Area [A]			+10% -10%
✖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.ⓘ Buckling Load [P_{Buckling Load}]			+10% -10%

✖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.ⓘ Polar Moment of Inertia for Pin Ended Columns [I_p]

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Formula

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Polar Moment of Inertia for Pin Ended Columns

Formula

`"I"_{"p"} = ("G"*"J"*"A")/"P"_{"Buckling Load"}`

Example

`"322000mm⁴"=("230MPa"*"10.0"*"700mm²")/"5N"`

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Polar Moment of Inertia for Pin Ended Columns Solution

STEP 0: Pre-Calculation Summary

Formula Used

Polar Moment of Inertia = (Shear Modulus of Elasticity*Torsional Constant*Column Cross-Sectional Area)/Buckling Load
I_p = (G*J*A)/P_{Buckling Load}
This formula uses 5 Variables

Variables Used

Polar Moment of Inertia - (Measured in Millimeter⁴) - 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.
Shear Modulus of Elasticity - (Measured in Megapascal) - The Shear Modulus of Elasticity is the measure of the rigidity of the body, given by the ratio of shear stress to shear strain.
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.
Column Cross-Sectional Area - (Measured in Square Millimeter) - 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.
Buckling Load - (Measured in Newton) - 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.

STEP 1: Convert Input(s) to Base Unit

Shear Modulus of Elasticity: 230 Megapascal --> 230 Megapascal No Conversion Required
Torsional Constant: 10 --> No Conversion Required
Column Cross-Sectional Area: 700 Square Millimeter --> 700 Square Millimeter No Conversion Required
Buckling Load: 5 Newton --> 5 Newton No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I_p = (G*J*A)/P_{Buckling Load} --> (230*10*700)/5

Evaluating ... ...

I_p = 322000

STEP 3: Convert Result to Output's Unit

3.22E-07 Meter⁴ -->322000 Millimeter⁴ (Check conversion here)

FINAL ANSWER

322000 Millimeter⁴ <-- Polar Moment of Inertia

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Columns » Elastic Flexural Buckling of Columns » Polar Moment of Inertia for Pin Ended Columns

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< 7 Elastic Flexural Buckling of Columns Calculators

Cross-Sectional Area given Axial Buckling Load for Warped Section

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

Polar Moment of Inertia for Axial Buckling Load for Warped Section

Go 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))

Axial Buckling Load for Warped Section

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

Shear Modulus of Elasticity given Torsional Buckling Load for Pin Ended Columns

Go Shear Modulus of Elasticity = (Buckling Load*Polar Moment of Inertia)/(Torsional Constant*Column Cross-Sectional Area)

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

Go Column Cross-Sectional Area = (Buckling Load*Polar Moment of Inertia)/(Shear Modulus of Elasticity*Torsional Constant)

Torsional Buckling Load for Pin Ended Columns

Go Buckling Load = (Shear Modulus of Elasticity*Torsional Constant*Column Cross-Sectional Area)/Polar Moment of Inertia

Polar Moment of Inertia for Pin Ended Columns

Go Polar Moment of Inertia = (Shear Modulus of Elasticity*Torsional Constant*Column Cross-Sectional Area)/Buckling Load

Polar Moment of Inertia for Pin Ended Columns Formula

Polar Moment of Inertia = (Shear Modulus of Elasticity*Torsional Constant*Column Cross-Sectional Area)/Buckling Load
I_p = (G*J*A)/P_{Buckling Load}

What is Buckling Load in Column?

Buckling can be defined as the sudden large deformation of the structure due to a slight increase of an existing load under which the structure exhibited little deformation, before the load was increased.

When does Lateral Torsional Buckling occur?

Lateral torsional buckling may occur in an unrestrained beam. A beam is considered to be unrestrained when its compression flange is free to displace laterally and rotate. When an applied load causes both lateral displacement and twisting of a member lateral torsional buckling has occurred.

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

Polar Moment of Inertia for Pin Ended Columns calculator uses Polar Moment of Inertia = (Shear Modulus of Elasticity*Torsional Constant*Column Cross-Sectional Area)/Buckling Load to calculate 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 calculate Polar Moment of Inertia for Pin Ended Columns using this online calculator? To use this online calculator 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. Here is how the Polar Moment of Inertia for Pin Ended Columns calculation can be explained with given input values -> 3.2E+17 = (230000000*10*0.0007)/5.

FAQ

What is Polar Moment of Inertia for Pin Ended Columns?

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 and is represented as I_p = (G*J*A)/P_{Buckling Load} or Polar Moment of Inertia = (Shear Modulus of Elasticity*Torsional Constant*Column Cross-Sectional Area)/Buckling Load. The Shear Modulus of Elasticity is the measure of the rigidity of the body, given by the ratio of shear stress to shear strain, 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, 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 & 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.

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

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 is calculated using Polar Moment of Inertia = (Shear Modulus of Elasticity*Torsional Constant*Column Cross-Sectional Area)/Buckling Load. To calculate Polar Moment of Inertia for Pin Ended Columns, you need Shear Modulus of Elasticity (G), Torsional Constant (J), Column Cross-Sectional Area (A) & Buckling Load (P_{Buckling Load}). With our tool, you need to enter the respective value for Shear Modulus of Elasticity, Torsional Constant, Column Cross-Sectional Area & Buckling Load 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 Polar Moment of Inertia?

In this formula, Polar Moment of Inertia uses Shear Modulus of Elasticity, Torsional Constant, Column Cross-Sectional Area & Buckling Load. We can use 1 other way(s) to calculate the same, which is/are as follows -

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))

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