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

✖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 [I_p]			+10% -10%
✖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.ⓘ Cross-Sectional Area given Torsional Buckling Load for Pin Ended Columns [A]

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Formula

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

Formula

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

Example

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

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

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

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.
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.

STEP 1: Convert Input(s) to Base Unit

Buckling Load: 5 Newton --> 5 Newton No Conversion Required
Polar Moment of Inertia: 322000 Millimeter⁴ --> 322000 Millimeter⁴ No Conversion Required
Shear Modulus of Elasticity: 230 Megapascal --> 230 Megapascal No Conversion Required
Torsional Constant: 10 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A = (P_{Buckling Load}*I_p)/(G*J) --> (5*322000)/(230*10)

Evaluating ... ...

A = 700

STEP 3: Convert Result to Output's Unit

0.0007 Square Meter -->700 Square Millimeter (Check conversion here)

FINAL ANSWER

700 Square Millimeter <-- Column Cross-Sectional Area

(Calculation completed in 00.004 seconds)

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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

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

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

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

Cross-Sectional Area given Torsional Buckling Load for Pin Ended Columns calculator uses Column Cross-Sectional Area = (Buckling Load*Polar Moment of Inertia)/(Shear Modulus of Elasticity*Torsional Constant) to calculate the Column Cross-Sectional Area, The Cross-Sectional Area given Torsional Buckling Load for Pin Ended Columns formula is defined as an area of the two-dimensional shape obtained when a column is sliced perpendicular to it's length axis at a point. Column Cross-Sectional Area is denoted by A symbol.

How to calculate Cross-Sectional Area given Torsional Buckling Load for Pin Ended Columns using this online calculator? To use this online calculator for Cross-Sectional Area given Torsional Buckling Load for Pin Ended Columns, enter Buckling Load (P_{Buckling Load}), Polar Moment of Inertia (I_p), Shear Modulus of Elasticity (G) & Torsional Constant (J) and hit the calculate button. Here is how the Cross-Sectional Area given Torsional Buckling Load for Pin Ended Columns calculation can be explained with given input values -> 7E+7 = (5*3.22E-07)/(230000000*10).

FAQ

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

The Cross-Sectional Area given Torsional Buckling Load for Pin Ended Columns formula is defined as an area of the two-dimensional shape obtained when a column is sliced perpendicular to it's length axis at a point and is represented as A = (P_{Buckling Load}*I_p)/(G*J) or Column Cross-Sectional Area = (Buckling Load*Polar Moment of Inertia)/(Shear Modulus of Elasticity*Torsional Constant). 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, 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, 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.

How to calculate Cross-Sectional Area given Torsional Buckling Load for Pin Ended Columns?

The Cross-Sectional Area given Torsional Buckling Load for Pin Ended Columns formula is defined as an area of the two-dimensional shape obtained when a column is sliced perpendicular to it's length axis at a point is calculated using Column Cross-Sectional Area = (Buckling Load*Polar Moment of Inertia)/(Shear Modulus of Elasticity*Torsional Constant). To calculate Cross-Sectional Area given Torsional Buckling Load for Pin Ended Columns, you need Buckling Load (P_{Buckling Load}), Polar Moment of Inertia (I_p), Shear Modulus of Elasticity (G) & Torsional Constant (J). With our tool, you need to enter the respective value for Buckling Load, Polar Moment of Inertia, Shear Modulus of Elasticity & Torsional Constant 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 Column Cross-Sectional Area?

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

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))

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