Moment of Inertia 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%
✖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 given Maximum Stress for Column with Eccentric Load [I]

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Moment of Inertia given Maximum Stress for Column with Eccentric Load Solution

STEP 0: Pre-Calculation Summary

Formula Used

Moment of Inertia = ((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))/(Effective Column Length))^2)/(Eccentric Load on Column/(Modulus of Elasticity of Column))
I = ((asech(((σ_max-(P/A_sectional))*S)/(P*e))/(l_e))^2)/(P/(ε_column))
This formula uses 2 Functions, 8 Variables

Functions Used

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

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.
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.
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.

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)
Effective Column Length: 200 Millimeter --> 0.2 Meter (Check conversion here)
Modulus of Elasticity of Column: 2 Megapascal --> 2000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I = ((asech(((σ_max-(P/A_sectional))*S)/(P*e))/(l_e))^2)/(P/(ε_column)) --> ((asech(((60-(40/0.66671))*13)/(40*15))/(0.2))^2)/(40/(2000000))

Evaluating ... ...

I = 126805754.82365

STEP 3: Convert Result to Output's Unit

126805754.82365 Kilogram Square Meter --> No Conversion Required

FINAL ANSWER

126805754.82365 ≈ 1.3E+8 Kilogram Square Meter <-- Moment of Inertia

(Calculation completed in 00.004 seconds)

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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)

Moment of Inertia 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 Moment of Inertia given Maximum Stress for Column with Eccentric Load?

Moment of Inertia given Maximum Stress for Column with Eccentric Load calculator uses Moment of Inertia = ((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))/(Effective Column Length))^2)/(Eccentric Load on Column/(Modulus of Elasticity of Column)) to calculate the Moment of Inertia, Moment of Inertia given Maximum Stress for Column with Eccentric Load formula is defined as a measure of the resistance of a column to bending under an eccentric load, taking into account the maximum stress, sectional area, and eccentricity of the load, providing a critical parameter in structural analysis and design. Moment of Inertia is denoted by I symbol.

How to calculate Moment of Inertia given Maximum Stress for Column with Eccentric Load using this online calculator? To use this online calculator for Moment of Inertia 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), Effective Column Length (l_e) & Modulus of Elasticity of Column (ε_column) and hit the calculate button. Here is how the Moment of Inertia given Maximum Stress for Column with Eccentric Load calculation can be explained with given input values -> 1.1E+6 = ((asech(((60-(40/0.66671))*13)/(40*15))/(0.2))^2)/(40/(2000000)).

FAQ

What is Moment of Inertia given Maximum Stress for Column with Eccentric Load?

Moment of Inertia given Maximum Stress for Column with Eccentric Load formula is defined as a measure of the resistance of a column to bending under an eccentric load, taking into account the maximum stress, sectional area, and eccentricity of the load, providing a critical parameter in structural analysis and design and is represented as I = ((asech(((σ_max-(P/A_sectional))*S)/(P*e))/(l_e))^2)/(P/(ε_column)) or Moment of Inertia = ((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))/(Effective Column Length))^2)/(Eccentric Load on Column/(Modulus of Elasticity of Column)). 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, 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.

How to calculate Moment of Inertia given Maximum Stress for Column with Eccentric Load?

Moment of Inertia given Maximum Stress for Column with Eccentric Load formula is defined as a measure of the resistance of a column to bending under an eccentric load, taking into account the maximum stress, sectional area, and eccentricity of the load, providing a critical parameter in structural analysis and design is calculated using Moment of Inertia = ((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))/(Effective Column Length))^2)/(Eccentric Load on Column/(Modulus of Elasticity of Column)). To calculate Moment of Inertia given Maximum Stress for Column with Eccentric Load, you need 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), Effective Column Length (l_e) & Modulus of Elasticity of Column (ε_column). With our tool, you need to enter the respective value for Maximum Stress at Crack Tip, Eccentric Load on Column, Cross-Sectional Area of Column, Section Modulus for Column, Eccentricity of Column, Effective Column Length & Modulus of Elasticity 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 Moment of Inertia?

In this formula, Moment of Inertia uses Maximum Stress at Crack Tip, Eccentric Load on Column, Cross-Sectional Area of Column, Section Modulus for Column, Eccentricity of Column, Effective Column Length & Modulus of Elasticity of Column. We can use 2 other way(s) to calculate the same, which is/are as follows -

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

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