Slenderness Ratio given Critical Buckling Load for Pin Ended Columns by Euler's Formula Calculator

✖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%
✖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%

✖Slenderness Ratio is the ratio of the length of a column and the least radius of gyration of its cross section.ⓘ Slenderness Ratio given Critical Buckling Load for Pin Ended Columns by Euler's Formula [λ]

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Slenderness Ratio given Critical Buckling Load for Pin Ended Columns by Euler's Formula

Formula

`"λ" = sqrt((pi^2*"E"*"A")/"P"_{"Buckling Load"})`

Example

`"262.8445"=sqrt((pi^2*"50MPa"*"700mm²")/"5N")`

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Slenderness Ratio given Critical Buckling Load for Pin Ended Columns by Euler's Formula Solution

STEP 0: Pre-Calculation Summary

Formula Used

Slenderness Ratio = sqrt((pi^2*Modulus of Elasticity*Column Cross-Sectional Area)/Buckling Load)
λ = sqrt((pi^2*E*A)/P_{Buckling Load})
This formula uses 1 Constants, 1 Functions, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Slenderness Ratio - Slenderness Ratio is the ratio of the length of a column and the least radius of gyration of its cross section.
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.
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

Modulus of Elasticity: 50 Megapascal --> 50 Megapascal 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

λ = sqrt((pi^2*E*A)/P_{Buckling Load}) --> sqrt((pi^2*50*700)/5)

Evaluating ... ...

λ = 262.844499291169

STEP 3: Convert Result to Output's Unit

262.844499291169 --> No Conversion Required

FINAL ANSWER

262.844499291169 ≈ 262.8445 <-- Slenderness Ratio

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Columns » Elastic Flexural Buckling of Columns » Pin-Ended Columns » Slenderness Ratio given Critical Buckling Load for Pin Ended Columns by Euler's Formula

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< 4 Pin-Ended Columns Calculators

Radius of Gyration given Critical Buckling Load for Pin Ended Columns by Euler's Formula

Go Radius of Gyration of Column = sqrt((Buckling Load*Effective Length of Column^2)/(pi^2*Modulus of Elasticity*Column Cross-Sectional Area))

Cross-Sectional Area given Critical Buckling Load for Pin Ended Columns by Euler's Formula

Go Column Cross-Sectional Area = (Buckling Load*(Effective Length of Column/Radius of Gyration of Column)^2)/(pi^2*Modulus of Elasticity)

Critical Buckling Load for Pin Ended Columns by Euler's Formula

Go Buckling Load = (pi^2*Modulus of Elasticity*Column Cross-Sectional Area)/((Effective Length of Column/Radius of Gyration of Column)^2)

Slenderness Ratio given Critical Buckling Load for Pin Ended Columns by Euler's Formula

Go Slenderness Ratio = sqrt((pi^2*Modulus of Elasticity*Column Cross-Sectional Area)/Buckling Load)

Slenderness Ratio given Critical Buckling Load for Pin Ended Columns by Euler's Formula Formula

Slenderness Ratio = sqrt((pi^2*Modulus of Elasticity*Column Cross-Sectional Area)/Buckling Load)
λ = sqrt((pi^2*E*A)/P_{Buckling Load})

What is Slenderness Ratio?

The slenderness ratio is defined as the ratio of length l to the radius of gyration k, represented as l/k. When the slenderness ratio exceeds a value of 100 for a strong slim column, failure by buckling can be expected. Columns of stiffer and more brittle materials will buckle at lower slenderness ratios.

What is Critical Buckling Load?

Buckling is a sudden lateral failure of an axially loaded member in compression, under a load value less than the compressive load-carrying capacity of that member. The axial compression load corresponding to this mode of failure is referred to as critical buckling load.

How to Calculate Slenderness Ratio given Critical Buckling Load for Pin Ended Columns by Euler's Formula?

Slenderness Ratio given Critical Buckling Load for Pin Ended Columns by Euler's Formula calculator uses Slenderness Ratio = sqrt((pi^2*Modulus of Elasticity*Column Cross-Sectional Area)/Buckling Load) to calculate the Slenderness Ratio, The Slenderness Ratio given Critical Buckling Load for Pin Ended Columns by Euler's formula is defined as a function of elastic modulus, critical buckling load, and cross-sectional area of the column. Slenderness Ratio is denoted by λ symbol.

How to calculate Slenderness Ratio given Critical Buckling Load for Pin Ended Columns by Euler's Formula using this online calculator? To use this online calculator for Slenderness Ratio given Critical Buckling Load for Pin Ended Columns by Euler's Formula, enter Modulus of Elasticity (E), Column Cross-Sectional Area (A) & Buckling Load (P_{Buckling Load}) and hit the calculate button. Here is how the Slenderness Ratio given Critical Buckling Load for Pin Ended Columns by Euler's Formula calculation can be explained with given input values -> 262844.5 = sqrt((pi^2*50000000*0.0007)/5).

FAQ

What is Slenderness Ratio given Critical Buckling Load for Pin Ended Columns by Euler's Formula?

The Slenderness Ratio given Critical Buckling Load for Pin Ended Columns by Euler's formula is defined as a function of elastic modulus, critical buckling load, and cross-sectional area of the column and is represented as λ = sqrt((pi^2*E*A)/P_{Buckling Load}) or Slenderness Ratio = sqrt((pi^2*Modulus of Elasticity*Column Cross-Sectional Area)/Buckling Load). 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, 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 Slenderness Ratio given Critical Buckling Load for Pin Ended Columns by Euler's Formula?

The Slenderness Ratio given Critical Buckling Load for Pin Ended Columns by Euler's formula is defined as a function of elastic modulus, critical buckling load, and cross-sectional area of the column is calculated using Slenderness Ratio = sqrt((pi^2*Modulus of Elasticity*Column Cross-Sectional Area)/Buckling Load). To calculate Slenderness Ratio given Critical Buckling Load for Pin Ended Columns by Euler's Formula, you need Modulus of Elasticity (E), Column Cross-Sectional Area (A) & Buckling Load (P_{Buckling Load}). With our tool, you need to enter the respective value for Modulus of Elasticity, 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.

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