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

I_p - Polar Moment of Inertia?A - Column Cross-Sectional Area?P_{Buckling Load} - Buckling Load?G - Shear Modulus of Elasticity?J - Torsional Constant?E - Modulus of Elasticity?C_w - Warping Constant?L - Effective Length of Column?π - Archimedes' constant?

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

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Here is how the Polar Moment of Inertia for Axial Buckling Load for Warped Section equation looks like with Values.

Here is how the Polar Moment of Inertia for Axial Buckling Load for Warped Section equation looks like with Units.

Here is how the Polar Moment of Inertia for Axial Buckling Load for Warped Section equation looks like.

322000.0768 = \frac{700}{5} \cdot (230 \cdot 10 + (\frac{{3.1416}^{2} \cdot 50 \cdot 10}{3000^{2}}))

322000.0768mm⁴ = \frac{700mm²}{5N} \cdot (230MPa \cdot 10 + (\frac{{3.1416}^{2} \cdot 50MPa \cdot 10kg·m²}{{3000mm}^{2}}))

322000.0768 = \frac{700}{5} \cdot (230 \cdot 10 + (\frac{{3.1416}^{2} \cdot 50 \cdot 10}{3000^{2}}))

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Columns » fx Polar Moment of Inertia for Axial Buckling Load for Warped Section

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

Follow our step by step solution on how to calculate Polar Moment of Inertia for Axial Buckling Load for Warped Section?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

I p = \frac{700mm²}{5N} \cdot (230MPa \cdot 10 + (\frac{π^{2} \cdot 50MPa \cdot 10kg·m²}{{3000mm}^{2}}))

Next Step Substitute values of Constants

∴

I p = \frac{700mm²}{5N} \cdot (230MPa \cdot 10 + (\frac{{3.1416}^{2} \cdot 50MPa \cdot 10kg·m²}{{3000mm}^{2}}))

Next Step Prepare to Evaluate

∴

I p = \frac{700}{5} \cdot (230 \cdot 10 + (\frac{{3.1416}^{2} \cdot 50 \cdot 10}{3000^{2}}))

Next Step Evaluate

∴

I p = 3.2200007676359E-07m⁴

Next Step Convert to Output's Unit

∴

I p = 322000.07676359mm⁴

LAST Step Rounding Answer

∴

I p = 322000.0768mm⁴

Polar Moment of Inertia for Axial Buckling Load for Warped Section Formula Elements

Variables

Constants

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

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

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

Modulus of Elasticity

The Modulus of Elasticity is the measure of the stiffness of a material. It is the slope of stress and strain diagram up to the limit of proportionality.

Symbol: E

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Modulus of Elasticity

Warping Constant

Warping Constant is often referred to as the warping moment of inertia. It is a quantity derived from a cross-section.

Symbol: C_w

Measurement: Moment of InertiaUnit: kg·m²

Note: Value should be greater than 0.

Formulas to find Warping Constant

Effective Length of Column

The Effective Length of Column can be defined as the length of an equivalent pin-ended column having the same load-carrying capacity as the member under consideration.

Symbol: L

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Effective Length of Column

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other Formulas to find Polar Moment of Inertia

Go Polar Moment of Inertia for Pin Ended Columns

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

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}

How to Evaluate Polar Moment of Inertia for Axial Buckling Load for Warped Section?

Polar Moment of Inertia for Axial Buckling Load for Warped Section evaluator uses 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)) to evaluate the Polar Moment of Inertia, The Polar Moment of Inertia for Axial Buckling Load for Warped Section formula is defined as a measurement of a capacity to oppose torsion. It is required to compute the twist of a column subjected to torque. Polar Moment of Inertia is denoted by I_p symbol.

How to evaluate Polar Moment of Inertia for Axial Buckling Load for Warped Section using this online evaluator? To use this online evaluator for Polar Moment of Inertia for Axial Buckling Load for Warped Section, enter Column Cross-Sectional Area (A), Buckling Load (P_{Buckling Load}), Shear Modulus of Elasticity (G), Torsional Constant (J), Modulus of Elasticity (E), Warping Constant (C_w) & Effective Length of Column (L) and hit the calculate button.

FAQs on Polar Moment of Inertia for Axial Buckling Load for Warped Section

What is the formula to find Polar Moment of Inertia for Axial Buckling Load for Warped Section?

The formula of Polar Moment of Inertia for Axial Buckling Load for Warped Section is expressed as 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)). Here is an example- 3.2E+17 = 0.0007/5*(230000000*10+((pi^2*50000000*10)/3^2)).

How to calculate Polar Moment of Inertia for Axial Buckling Load for Warped Section?

With Column Cross-Sectional Area (A), Buckling Load (P_{Buckling Load}), Shear Modulus of Elasticity (G), Torsional Constant (J), Modulus of Elasticity (E), Warping Constant (C_w) & Effective Length of Column (L) we can find Polar Moment of Inertia for Axial Buckling Load for Warped Section using the formula - 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)). This formula also uses Archimedes' constant .

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

Can the Polar Moment of Inertia for Axial Buckling Load for Warped Section be negative?

No, the Polar Moment of Inertia for Axial Buckling Load for Warped Section, measured in Second Moment of Area cannot be negative.

Which unit is used to measure Polar Moment of Inertia for Axial Buckling Load for Warped Section?

Polar Moment of Inertia for Axial Buckling Load for Warped Section 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 Axial Buckling Load for Warped Section can be measured.

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

​GoPolar Moment of Inertia for Pin Ended Columns Formula

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

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

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

FAQs on Polar Moment of Inertia for Axial Buckling Load for Warped Section

Variable Name

GoPolar Moment of Inertia for Pin Ended Columns Formula