Slenderness Ratio given Elastic Critical Buckling Load 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 Elastic Critical Buckling Load [λ]

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Slenderness Ratio given Elastic Critical Buckling Load 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 00.006 seconds)

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< Slender Columns Calculators

Radius of Gyration of Column given Elastic Critical Buckling Load

LaTeX 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 Elastic Critical Buckling Load

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

Elastic Critical Buckling Load

LaTeX 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 Elastic Critical Buckling Load

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

Slenderness Ratio given Elastic Critical Buckling Load Formula

LaTeX Go

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

Column End Conditions for effective length of column

The coefficient n accounts for end conditions.
When the column is pivoted at both ends, n = 1;
when one end is fixed and the other end is rounded, n = 0.7;
when both ends are fixed, n = 0.5; and
when one end is fixed and the other is free, n = 2.

Define Buckling.

In structural engineering, buckling is the sudden change in shape (deformation) of a structural component under load, such as the bowing of a column under compression or the wrinkling of a plate under shear.

How to Calculate Slenderness Ratio given Elastic Critical Buckling Load?

Slenderness Ratio given Elastic Critical Buckling Load 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 Elastic Critical Buckling Load formula is defined as the ratio used to describe the distribution of cross-sectional area in a column around its centroidal axis. Slenderness Ratio is denoted by λ symbol.

How to calculate Slenderness Ratio given Elastic Critical Buckling Load using this online calculator? To use this online calculator for Slenderness Ratio given Elastic Critical Buckling Load, 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 Elastic Critical Buckling Load calculation can be explained with given input values -> 262844.5 = sqrt((pi^2*50000000*0.0007)/5).

FAQ

What is Slenderness Ratio given Elastic Critical Buckling Load?

The Slenderness Ratio given Elastic Critical Buckling Load formula is defined as the ratio used to describe the distribution of cross-sectional area in a column around its centroidal axis 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 Elastic Critical Buckling Load?

The Slenderness Ratio given Elastic Critical Buckling Load formula is defined as the ratio used to describe the distribution of cross-sectional area in a column around its centroidal axis is calculated using Slenderness Ratio = sqrt((pi^2*Modulus of Elasticity*Column Cross-Sectional Area)/Buckling Load). To calculate Slenderness Ratio given Elastic Critical Buckling Load, 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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