Cross-Sectional Area given Axial Buckling Load for Warped Section 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%
✖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.ⓘ Modulus of Elasticity [E]			+10% -10%
✖Warping Constant is often referred to as the warping moment of inertia. It is a quantity derived from a cross-section.ⓘ Warping Constant [C_w]			+10% -10%
✖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.ⓘ Effective Length of Column [L]			+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 Axial Buckling Load for Warped Section [A]

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Cross-Sectional Area given Axial Buckling Load for Warped Section

Formula

`"A" = ("P"_{"Buckling Load"}*"I"_{"p"})/("G"*"J"+((pi^2*"E"*"C"_{"w"})/"L"^2))`

Example

`"699.9998mm²"=("5N"*"322000mm⁴")/("230MPa"*"10.0"+((pi^2*"50MPa"*"10kg·m²")/("3000mm")^2))`

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Download Elastic Flexural Buckling of Columns Formulas PDF

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

STEP 0: Pre-Calculation Summary

Formula Used

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))
A = (P_{Buckling Load}*I_p)/(G*J+((pi^2*E*C_w)/L^2))
This formula uses 1 Constants, 8 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

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.
Modulus of Elasticity - (Measured in Megapascal) - 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.
Warping Constant - (Measured in Kilogram Square Meter) - Warping Constant is often referred to as the warping moment of inertia. It is a quantity derived from a cross-section.
Effective Length of Column - (Measured in Millimeter) - 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.

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
Modulus of Elasticity: 50 Megapascal --> 50 Megapascal No Conversion Required
Warping Constant: 10 Kilogram Square Meter --> 10 Kilogram Square Meter No Conversion Required
Effective Length of Column: 3000 Millimeter --> 3000 Millimeter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A = (P_{Buckling Load}*I_p)/(G*J+((pi^2*E*C_w)/L^2)) --> (5*322000)/(230*10+((pi^2*50*10)/3000^2))

Evaluating ... ...

A = 699.999833122671

STEP 3: Convert Result to Output's Unit

0.000699999833122671 Square Meter -->699.999833122671 Square Millimeter (Check conversion here)

FINAL ANSWER

699.999833122671 ≈ 699.9998 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 Axial Buckling Load for Warped Section Formula

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 Axial Buckling Load for Warped Section?

Cross-Sectional Area given Axial Buckling Load for Warped Section calculator uses 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)) to calculate the Column Cross-Sectional Area, The Cross-Sectional Area given Axial Buckling Load for Warped Section formula is defined as the area of a two-dimensional shape obtained when a Column is sliced perpendicular to its length axis at a point. Column Cross-Sectional Area is denoted by A symbol.

How to calculate Cross-Sectional Area given Axial Buckling Load for Warped Section using this online calculator? To use this online calculator for Cross-Sectional Area given Axial Buckling Load for Warped Section, enter Buckling Load (P_{Buckling Load}), Polar Moment of Inertia (I_p), 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. Here is how the Cross-Sectional Area given Axial Buckling Load for Warped Section calculation can be explained with given input values -> 7E+7 = (5*3.22E-07)/(230000000*10+((pi^2*50000000*10)/3^2)).

FAQ

What is Cross-Sectional Area given Axial Buckling Load for Warped Section?

The Cross-Sectional Area given Axial Buckling Load for Warped Section formula is defined as the area of a two-dimensional shape obtained when a Column is sliced perpendicular to its length axis at a point and is represented as A = (P_{Buckling Load}*I_p)/(G*J+((pi^2*E*C_w)/L^2)) or 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)). 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, 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, Warping Constant is often referred to as the warping moment of inertia. It is a quantity derived from a cross-section & 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.

How to calculate Cross-Sectional Area given Axial Buckling Load for Warped Section?

The Cross-Sectional Area given Axial Buckling Load for Warped Section formula is defined as the area of a two-dimensional shape obtained when a Column is sliced perpendicular to its length axis at a point is calculated using 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)). To calculate Cross-Sectional Area given Axial Buckling Load for Warped Section, you need Buckling Load (P_{Buckling Load}), Polar Moment of Inertia (I_p), Shear Modulus of Elasticity (G), Torsional Constant (J), Modulus of Elasticity (E), Warping Constant (C_w) & Effective Length of Column (L). With our tool, you need to enter the respective value for Buckling Load, Polar Moment of Inertia, Shear Modulus of Elasticity, Torsional Constant, Modulus of Elasticity, Warping Constant & Effective Length of Column 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, Modulus of Elasticity, Warping Constant & Effective Length of Column. 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)

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