Moment of Inertia given Deflection at Section of 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%
✖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%
✖Deflection of column refers to the degree to which a column bends or displaces under the influence of external forces such as weight, wind, or seismic activity.ⓘ Deflection of Column [δ_c]			+10% -10%
✖Deflection of free end of a beam refers to the displacement or movement of the beam’s free end from its original position due to applied loads or crippling load at the free end.ⓘ Deflection of Free End [δ]			+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%
✖Distance b/w fixed end and deflection point is the distance x between the point of deflection where the maximum deflection occurs at section and fixed point.ⓘ Distance b/w Fixed End and Deflection Point [x]			+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 Deflection at Section of Column with Eccentric Load [I]

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Moment of Inertia given Deflection at Section of Column with Eccentric Load Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
I = (P/(ε_column*(((acos(1-(δ_c/(δ+e_load))))/x)^2)))
This formula uses 2 Functions, 7 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
acos - The inverse cosine function, is the inverse function of the cosine function. It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio., acos(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.
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.
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.
Deflection of Column - (Measured in Meter) - Deflection of column refers to the degree to which a column bends or displaces under the influence of external forces such as weight, wind, or seismic activity.
Deflection of Free End - (Measured in Meter) - Deflection of free end of a beam refers to the displacement or movement of the beam’s free end from its original position due to applied loads or crippling load at the free end.
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.
Distance b/w Fixed End and Deflection Point - (Measured in Meter) - Distance b/w fixed end and deflection point is the distance x between the point of deflection where the maximum deflection occurs at section and fixed point.

STEP 1: Convert Input(s) to Base Unit

Eccentric Load on Column: 40 Newton --> 40 Newton No Conversion Required
Modulus of Elasticity of Column: 2 Megapascal --> 2000000 Pascal (Check conversion here)
Deflection of Column: 12 Millimeter --> 0.012 Meter (Check conversion here)
Deflection of Free End: 14 Millimeter --> 0.014 Meter (Check conversion here)
Eccentricity of Load: 2.5 Millimeter --> 0.0025 Meter (Check conversion here)
Distance b/w Fixed End and Deflection Point: 1000 Millimeter --> 1 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I = (P/(ε_column*(((acos(1-(δ_c/(δ+e_load))))/x)^2))) --> (40/(2000000*(((acos(1-(0.012/(0.014+0.0025))))/1)^2)))

Evaluating ... ...

I = 1.19338100921898E-05

STEP 3: Convert Result to Output's Unit

1.19338100921898E-05 Kilogram Square Meter --> No Conversion Required

FINAL ANSWER

1.19338100921898E-05 ≈ 1.2E-5 Kilogram Square Meter <-- Moment of Inertia

(Calculation completed in 00.020 seconds)

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Home » Physics » Strength of Materials » Column And Struts » Mechanical » Columns With Eccentric Load » Moment of Inertia given Deflection at Section of 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

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

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

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

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

Moment of Inertia given Deflection at Section of Column with Eccentric Load Formula

Which is example of eccentric loading?

Examples of eccentric loading activities include performing a calf raise off the ledge of a stair, an exercise that has been shown to decrease the risk of Achilles tendon injuries. Another example is the nordic curl exercise, which has been shown to help reduce the risk of hamstring strains.

How to Calculate Moment of Inertia given Deflection at Section of Column with Eccentric Load?

Moment of Inertia given Deflection at Section of Column with Eccentric Load calculator uses 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))) to calculate the Moment of Inertia, Moment of Inertia given Deflection at Section of Column with Eccentric Load formula is defined as a measure of the resistance of a cross-section to bending, which is essential in determining the stability of a column subjected to an eccentric load, where the load is not applied centrally to the column. Moment of Inertia is denoted by I symbol.

How to calculate Moment of Inertia given Deflection at Section of Column with Eccentric Load using this online calculator? To use this online calculator for Moment of Inertia given Deflection at Section of Column with Eccentric Load, enter Eccentric Load on Column (P), Modulus of Elasticity of Column (ε_column), Deflection of Column (δ_c), Deflection of Free End (δ), Eccentricity of Load (e_load) & Distance b/w Fixed End and Deflection Point (x) and hit the calculate button. Here is how the Moment of Inertia given Deflection at Section of Column with Eccentric Load calculation can be explained with given input values -> 1.2E-5 = (40/(2000000*(((acos(1-(0.012/(0.014+0.0025))))/1)^2))).

FAQ

What is Moment of Inertia given Deflection at Section of Column with Eccentric Load?

Moment of Inertia given Deflection at Section of Column with Eccentric Load formula is defined as a measure of the resistance of a cross-section to bending, which is essential in determining the stability of a column subjected to an eccentric load, where the load is not applied centrally to the column and is represented as I = (P/(ε_column*(((acos(1-(δ_c/(δ+e_load))))/x)^2))) or 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))). 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, 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, Deflection of column refers to the degree to which a column bends or displaces under the influence of external forces such as weight, wind, or seismic activity, Deflection of free end of a beam refers to the displacement or movement of the beam’s free end from its original position due to applied loads or crippling load at the free end, Eccentricity of load refers to the offset of a load from the centroid of a structural element, such as a beam or column & Distance b/w fixed end and deflection point is the distance x between the point of deflection where the maximum deflection occurs at section and fixed point.

How to calculate Moment of Inertia given Deflection at Section of Column with Eccentric Load?

Moment of Inertia given Deflection at Section of Column with Eccentric Load formula is defined as a measure of the resistance of a cross-section to bending, which is essential in determining the stability of a column subjected to an eccentric load, where the load is not applied centrally to the column is calculated using 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))). To calculate Moment of Inertia given Deflection at Section of Column with Eccentric Load, you need Eccentric Load on Column (P), Modulus of Elasticity of Column (ε_column), Deflection of Column (δ_c), Deflection of Free End (δ), Eccentricity of Load (e_load) & Distance b/w Fixed End and Deflection Point (x). With our tool, you need to enter the respective value for Eccentric Load on Column, Modulus of Elasticity of Column, Deflection of Column, Deflection of Free End, Eccentricity of Load & Distance b/w Fixed End and Deflection Point 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 Eccentric Load on Column, Modulus of Elasticity of Column, Deflection of Column, Deflection of Free End, Eccentricity of Load & Distance b/w Fixed End and Deflection Point. 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*(((arcsec((Deflection of Free End/Eccentricity of Load)+1))/Column Length)^2))
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))

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