Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load Calculator

✖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%
✖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%
✖Eccentricity of load refers to the offset of a load from the centroid of a structural element, such as a beam or column.ⓘ Eccentricity of Load [e_load]			+10% -10%
✖Effective column length, often that represents the length of a column that influences its buckling behavior.ⓘ Effective Column Length [l_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%
✖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%

✖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 given Maximum Stress for Column with Eccentric Load [A_sectional]

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Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Functions Used

sec - Secant is a trigonometric function that is defined ratio of the hypotenuse to the shorter side adjacent to an acute angle (in a right-angled triangle); the reciprocal of a cosine., sec(Angle)
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

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.
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.
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.
Eccentricity of Load - (Measured in Meter) - Eccentricity of load refers to the offset of a load from the centroid of a structural element, such as a beam or column.
Effective Column Length - (Measured in Meter) - Effective column length, often that represents the length of a column that influences its buckling behavior.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Eccentric Load on Column: 40 Newton --> 40 Newton No Conversion Required
Maximum Stress at Crack Tip: 6E-05 Megapascal --> 60 Pascal (Check conversion here)
Eccentricity of Load: 2.5 Millimeter --> 0.0025 Meter (Check conversion here)
Effective Column Length: 200 Millimeter --> 0.2 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
Section Modulus for Column: 13 Cubic Meter --> 13 Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A_sectional = (P)/(σ_max-(((P*e_load*sec(l_e*sqrt(P/(ε_column*I))))/2)/S)) --> (40)/(60-(((40*0.0025*sec(0.2*sqrt(40/(2000000*0.000168))))/2)/13))

Evaluating ... ...

A_sectional = 0.666709506414469

STEP 3: Convert Result to Output's Unit

0.666709506414469 Square Meter --> No Conversion Required

FINAL ANSWER

0.666709506414469 ≈ 0.66671 Square Meter <-- Cross-Sectional Area of Column

(Calculation completed in 00.020 seconds)

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Home » Physics » Strength of Materials » Column And Struts » Mechanical » Columns With Eccentric Load » Cross Sectional Area 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)

Cross Sectional Area 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 Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load?

Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load calculator uses Cross-Sectional Area of Column = (Eccentric Load on Column)/(Maximum Stress at Crack Tip-(((Eccentric Load on Column*Eccentricity of Load*sec(Effective Column Length*sqrt(Eccentric Load on Column/(Modulus of Elasticity of Column*Moment of Inertia))))/2)/Section Modulus for Column)) to calculate the Cross-Sectional Area of Column, Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load formula is defined as a measure of the area of a column's cross-section when subjected to an eccentric load, taking into account the maximum stress, load eccentricity, and column properties, providing a critical design parameter for structural integrity. Cross-Sectional Area of Column is denoted by A_sectional symbol.

How to calculate Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load using this online calculator? To use this online calculator for Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load, enter Eccentric Load on Column (P), Maximum Stress at Crack Tip (σ_max), Eccentricity of Load (e_load), Effective Column Length (l_e), Modulus of Elasticity of Column (ε_column), Moment of Inertia (I) & Section Modulus for Column (S) and hit the calculate button. Here is how the Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load calculation can be explained with given input values -> 0.66671 = (40)/(60-(((40*0.0025*sec(0.2*sqrt(40/(2000000*0.000168))))/2)/13)).

FAQ

What is Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load?

Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load formula is defined as a measure of the area of a column's cross-section when subjected to an eccentric load, taking into account the maximum stress, load eccentricity, and column properties, providing a critical design parameter for structural integrity and is represented as A_sectional = (P)/(σ_max-(((P*e_load*sec(l_e*sqrt(P/(ε_column*I))))/2)/S)) or Cross-Sectional Area of Column = (Eccentric Load on Column)/(Maximum Stress at Crack Tip-(((Eccentric Load on Column*Eccentricity of Load*sec(Effective Column Length*sqrt(Eccentric Load on Column/(Modulus of Elasticity of Column*Moment of Inertia))))/2)/Section Modulus for Column)). 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, Maximum stress at crack tip refers to the highest stress concentration that occurs at the very tip of a crack in a material, Eccentricity of load refers to the offset of a load from the centroid of a structural element, such as a beam or column, Effective column length, often that represents the length of a column that influences its buckling behavior, 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 & 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.

How to calculate Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load?

Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load formula is defined as a measure of the area of a column's cross-section when subjected to an eccentric load, taking into account the maximum stress, load eccentricity, and column properties, providing a critical design parameter for structural integrity is calculated using Cross-Sectional Area of Column = (Eccentric Load on Column)/(Maximum Stress at Crack Tip-(((Eccentric Load on Column*Eccentricity of Load*sec(Effective Column Length*sqrt(Eccentric Load on Column/(Modulus of Elasticity of Column*Moment of Inertia))))/2)/Section Modulus for Column)). To calculate Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load, you need Eccentric Load on Column (P), Maximum Stress at Crack Tip (σ_max), Eccentricity of Load (e_load), Effective Column Length (l_e), Modulus of Elasticity of Column (ε_column), Moment of Inertia (I) & Section Modulus for Column (S). With our tool, you need to enter the respective value for Eccentric Load on Column, Maximum Stress at Crack Tip, Eccentricity of Load, Effective Column Length, Modulus of Elasticity of Column, Moment of Inertia & Section Modulus for Column 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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