Eccentric Load given Deflection at Section of Column with Eccentric Load Calculator

✖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%
✖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%

✖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 given Deflection at Section of Column with Eccentric Load [P]

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

STEP 0: Pre-Calculation Summary

Formula Used

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)
P = (((acos(1-(δ_c/(δ+e_load))))/x)^2)*(ε_column*I)
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

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.
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.
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

Deflection of Column: 12 Millimeter --> 0.012 Meter (Check conversion here)
Deflection of Free End: 201.112 Millimeter --> 0.201112 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)
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

P = (((acos(1-(δ_c/(δ+e_load))))/x)^2)*(ε_column*I) --> (((acos(1-(0.012/(0.201112+0.0025))))/1)^2)*(2000000*0.000168)

Evaluating ... ...

P = 39.9999923083865

STEP 3: Convert Result to Output's Unit

39.9999923083865 Newton --> No Conversion Required

FINAL ANSWER

39.9999923083865 ≈ 39.99999 Newton <-- Eccentric Load on Column

(Calculation completed in 00.020 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)

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

LaTeX Go

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 Eccentric Load given Deflection at Section of Column with Eccentric Load?

Eccentric Load given Deflection at Section of Column with Eccentric Load calculator uses 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) to calculate the Eccentric Load on Column, Eccentric Load given Deflection at Section of Column with Eccentric Load formula is defined as a measure of the load applied at a distance from the central axis of a column, causing bending and deflection, which is critical in determining the column's stability and structural integrity. Eccentric Load on Column is denoted by P symbol.

How to calculate Eccentric Load given Deflection at Section of Column with Eccentric Load using this online calculator? To use this online calculator for Eccentric Load given Deflection at Section of Column with Eccentric Load, enter Deflection of Column (δ_c), Deflection of Free End (δ), Eccentricity of Load (e_load), Distance b/w Fixed End and Deflection Point (x), Modulus of Elasticity of Column (ε_column) & Moment of Inertia (I) and hit the calculate button. Here is how the Eccentric Load given Deflection at Section of Column with Eccentric Load calculation can be explained with given input values -> 563.106 = (((acos(1-(0.012/(0.201112+0.0025))))/1)^2)*(2000000*0.000168).

FAQ

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

Eccentric Load given Deflection at Section of Column with Eccentric Load formula is defined as a measure of the load applied at a distance from the central axis of a column, causing bending and deflection, which is critical in determining the column's stability and structural integrity and is represented as P = (((acos(1-(δ_c/(δ+e_load))))/x)^2)*(ε_column*I) or 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). 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, 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 Eccentric Load given Deflection at Section of Column with Eccentric Load?

Eccentric Load given Deflection at Section of Column with Eccentric Load formula is defined as a measure of the load applied at a distance from the central axis of a column, causing bending and deflection, which is critical in determining the column's stability and structural integrity is calculated using 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). To calculate Eccentric Load given Deflection at Section of Column with Eccentric Load, you need Deflection of Column (δ_c), Deflection of Free End (δ), Eccentricity of Load (e_load), Distance b/w Fixed End and Deflection Point (x), Modulus of Elasticity of Column (ε_column) & Moment of Inertia (I). With our tool, you need to enter the respective value for Deflection of Column, Deflection of Free End, Eccentricity of Load, Distance b/w Fixed End and Deflection Point, Modulus of Elasticity of Column & Moment of Inertia 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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