Effective Length of Column given Maximum Stress for Column with Eccentric Load Calculator

✖Maximum stress at crack tip refers to the highest stress concentration that occurs at the very tip of a crack in a material.ⓘ Maximum Stress at Crack Tip [σ_max]			+10% -10%
✖Eccentric load on column refers to a load that is applied at a point away from the centroidal axis of the column’s cross-section where loading introduces both axial stress and bending stress.ⓘ Eccentric Load on Column [P]			+10% -10%
✖Cross-sectional area of column is the area of the shape we get when we cut through the column perpendicular to its length, helps in determining the column’s ability to bear loads and resist stresses.ⓘ Cross-Sectional Area of Column [A_sectional]			+10% -10%
✖Section modulus for column is a geometric property of a cross-section that measures the ability of a section to resist bending and is crucial for determining the bending stress in structural elements.ⓘ Section Modulus for Column [S]			+10% -10%
✖Eccentricity of column refers to the distance between the line of action of the applied load and the centroidal axis of the column’s cross-section.ⓘ Eccentricity of Column [e]			+10% -10%
✖Modulus of elasticity of column is a measure of a material’s stiffness or rigidity, is defined as the ratio of longitudinal stress to longitudinal strain within the elastic limit of a material.ⓘ Modulus of Elasticity of Column [ε_column]			+10% -10%
✖Moment of inertia also known as the rotational inertia or angular mass, is a measure of an object’s resistance to changes in its rotational motion around a specific axis.ⓘ Moment of Inertia [I]			+10% -10%

✖Effective column length, often that represents the length of a column that influences its buckling behavior.ⓘ Effective Length of Column given Maximum Stress for Column with Eccentric Load [l_e]

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Effective Length of Column given Maximum Stress for Column with Eccentric Load Solution

STEP 0: Pre-Calculation Summary

Formula Used

Effective Column Length = asech(((Maximum Stress at Crack Tip-(Eccentric Load on Column/Cross-Sectional Area of Column))*Section Modulus for Column)/(Eccentric Load on Column*Eccentricity of Column))/(sqrt(Eccentric Load on Column/(Modulus of Elasticity of Column*Moment of Inertia))/2)
l_e = asech(((σ_max-(P/A_sectional))*S)/(P*e))/(sqrt(P/(ε_column*I))/2)
This formula uses 3 Functions, 8 Variables

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)
sech - The hyperbolic secant function is a hyperbolic function that is the reciprocal of the hyperbolic cosine function., sech(Number)
asech - The hyperbolic secant function is defined as sech(x) = 1/cosh(x), where cosh(x) is the hyperbolic cosine function., asech(Number)

Variables Used

Effective Column Length - (Measured in Meter) - Effective column length, often that represents the length of a column that influences its buckling behavior.
Maximum Stress at Crack Tip - (Measured in Pascal) - Maximum stress at crack tip refers to the highest stress concentration that occurs at the very tip of a crack in a material.
Eccentric Load on Column - (Measured in Newton) - Eccentric load on column refers to a load that is applied at a point away from the centroidal axis of the column’s cross-section where loading introduces both axial stress and bending stress.
Cross-Sectional Area of Column - (Measured in Square Meter) - Cross-sectional area of column is the area of the shape we get when we cut through the column perpendicular to its length, helps in determining the column’s ability to bear loads and resist stresses.
Section Modulus for Column - (Measured in Cubic Meter) - Section modulus for column is a geometric property of a cross-section that measures the ability of a section to resist bending and is crucial for determining the bending stress in structural elements.
Eccentricity of Column - (Measured in Meter) - Eccentricity of column refers to the distance between the line of action of the applied load and the centroidal axis of the column’s cross-section.
Modulus of Elasticity of Column - (Measured in Pascal) - Modulus of elasticity of column is a measure of a material’s stiffness or rigidity, is defined as the ratio of longitudinal stress to longitudinal strain within the elastic limit of a material.
Moment of Inertia - (Measured in Kilogram Square Meter) - Moment of inertia also known as the rotational inertia or angular mass, is a measure of an object’s resistance to changes in its rotational motion around a specific axis.

STEP 1: Convert Input(s) to Base Unit

Maximum Stress at Crack Tip: 6E-05 Megapascal --> 60 Pascal (Check conversion here)
Eccentric Load on Column: 40 Newton --> 40 Newton No Conversion Required
Cross-Sectional Area of Column: 0.66671 Square Meter --> 0.66671 Square Meter No Conversion Required
Section Modulus for Column: 13 Cubic Meter --> 13 Cubic Meter No Conversion Required
Eccentricity of Column: 15000 Millimeter --> 15 Meter (Check conversion here)
Modulus of Elasticity of Column: 2 Megapascal --> 2000000 Pascal (Check conversion here)
Moment of Inertia: 0.000168 Kilogram Square Meter --> 0.000168 Kilogram Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_e = asech(((σ_max-(P/A_sectional))*S)/(P*e))/(sqrt(P/(ε_column*I))/2) --> asech(((60-(40/0.66671))*13)/(40*15))/(sqrt(40/(2000000*0.000168))/2)

Evaluating ... ...

l_e = 58.3826916959103

STEP 3: Convert Result to Output's Unit

58.3826916959103 Meter -->58382.6916959103 Millimeter (Check conversion here)

FINAL ANSWER

58382.6916959103 ≈ 58382.69 Millimeter <-- Effective Column Length

(Calculation completed in 00.020 seconds)

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Home » Physics » Strength of Materials » Column And Struts » Mechanical » Columns With Eccentric Load » Effective Length of Column given Maximum Stress for Column with Eccentric Load

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< Columns With Eccentric Load Calculators

Modulus of Elasticity given Deflection at Section of Column with Eccentric Load

LaTeX Go Modulus of Elasticity of Column = (Eccentric Load on Column/(Moment of Inertia*(((acos(1-(Deflection of Column/(Deflection of Free End+Eccentricity of Load))))/Distance b/w Fixed End and Deflection Point)^2)))

Eccentric Load given Deflection at Section of Column with Eccentric Load

LaTeX Go Eccentric Load on Column = (((acos(1-(Deflection of Column/(Deflection of Free End+Eccentricity of Load))))/Distance b/w Fixed End and Deflection Point)^2)*(Modulus of Elasticity of Column*Moment of Inertia)

Eccentricity given Moment at Section of Column with Eccentric Load

LaTeX Go Eccentricity of Column = (Moment of Force/Eccentric Load on Column)-Deflection of Free End+Deflection of Column

Moment at Section of Column with Eccentric Load

LaTeX Go Moment of Force = Eccentric Load on Column*(Deflection of Free End+Eccentricity of Load-Deflection of Column)

Effective Length of Column given Maximum Stress for Column with Eccentric Load Formula

LaTeX Go

What is buckling or crippling load?

Buckling Load is the highest load at which the column will buckle. Crippling load is the max load beyond that load, it cant use further it becomes disable to use.

How to Calculate Effective Length of Column given Maximum Stress for Column with Eccentric Load?

Effective Length of Column given Maximum Stress for Column with Eccentric Load calculator uses Effective Column Length = asech(((Maximum Stress at Crack Tip-(Eccentric Load on Column/Cross-Sectional Area of Column))*Section Modulus for Column)/(Eccentric Load on Column*Eccentricity of Column))/(sqrt(Eccentric Load on Column/(Modulus of Elasticity of Column*Moment of Inertia))/2) to calculate the Effective Column Length, Effective Length of Column given Maximum Stress for Column with Eccentric Load formula is defined as the length of a column that takes into account the maximum stress it can withstand when subjected to an eccentric load, providing a critical value for structural engineers to ensure the column's stability and safety. Effective Column Length is denoted by l_e symbol.

How to calculate Effective Length of Column given Maximum Stress for Column with Eccentric Load using this online calculator? To use this online calculator for Effective Length of Column given Maximum Stress for Column with Eccentric Load, enter Maximum Stress at Crack Tip (σ_max), Eccentric Load on Column (P), Cross-Sectional Area of Column (A_sectional), Section Modulus for Column (S), Eccentricity of Column (e), Modulus of Elasticity of Column (ε_column) & Moment of Inertia (I) and hit the calculate button. Here is how the Effective Length of Column given Maximum Stress for Column with Eccentric Load calculation can be explained with given input values -> 5.4E+6 = asech(((60-(40/0.66671))*13)/(40*15))/(sqrt(40/(2000000*0.000168))/2).

FAQ

What is Effective Length of Column given Maximum Stress for Column with Eccentric Load?

Effective Length of Column given Maximum Stress for Column with Eccentric Load formula is defined as the length of a column that takes into account the maximum stress it can withstand when subjected to an eccentric load, providing a critical value for structural engineers to ensure the column's stability and safety and is represented as l_e = asech(((σ_max-(P/A_sectional))*S)/(P*e))/(sqrt(P/(ε_column*I))/2) or Effective Column Length = asech(((Maximum Stress at Crack Tip-(Eccentric Load on Column/Cross-Sectional Area of Column))*Section Modulus for Column)/(Eccentric Load on Column*Eccentricity of Column))/(sqrt(Eccentric Load on Column/(Modulus of Elasticity of Column*Moment of Inertia))/2). Maximum stress at crack tip refers to the highest stress concentration that occurs at the very tip of a crack in a material, Eccentric load on column refers to a load that is applied at a point away from the centroidal axis of the column’s cross-section where loading introduces both axial stress and bending stress, Cross-sectional area of column is the area of the shape we get when we cut through the column perpendicular to its length, helps in determining the column’s ability to bear loads and resist stresses, Section modulus for column is a geometric property of a cross-section that measures the ability of a section to resist bending and is crucial for determining the bending stress in structural elements, Eccentricity of column refers to the distance between the line of action of the applied load and the centroidal axis of the column’s cross-section, Modulus of elasticity of column is a measure of a material’s stiffness or rigidity, is defined as the ratio of longitudinal stress to longitudinal strain within the elastic limit of a material & Moment of inertia also known as the rotational inertia or angular mass, is a measure of an object’s resistance to changes in its rotational motion around a specific axis.

How to calculate Effective Length of Column given Maximum Stress for Column with Eccentric Load?

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