Deflection at Section of Column with Eccentric Load Calculator

✖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 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%
✖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%
✖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%
✖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%

✖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 at Section of Column with Eccentric Load [δ_c]

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Deflection at Section of Column with Eccentric Load Solution

STEP 0: Pre-Calculation Summary

Formula Used

Deflection of Column = (Deflection of Free End+Eccentricity of Column)*(1-cos(Distance b/w Fixed End and Deflection Point*sqrt(Eccentric Load on Column/(Modulus of Elasticity of Column*Moment of Inertia))))
δ_c = (δ+e)*(1-cos(x*sqrt(P/(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)
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

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 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.
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.
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.
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 Free End: 201.112 Millimeter --> 0.201112 Meter (Check conversion here)
Eccentricity of Column: 15000 Millimeter --> 15 Meter (Check conversion here)
Distance b/w Fixed End and Deflection Point: 1000 Millimeter --> 1 Meter (Check conversion here)
Eccentric Load on Column: 40 Newton --> 40 Newton No Conversion Required
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

δ_c = (δ+e)*(1-cos(x*sqrt(P/(ε_column*I)))) --> (0.201112+15)*(1-cos(1*sqrt(40/(2000000*0.000168))))

Evaluating ... ...

δ_c = 0.895887171324175

STEP 3: Convert Result to Output's Unit

0.895887171324175 Meter -->895.887171324175 Millimeter (Check conversion here)

FINAL ANSWER

895.887171324175 ≈ 895.8872 Millimeter <-- Deflection of 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)

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 Deflection at Section of Column with Eccentric Load?

Deflection at Section of Column with Eccentric Load calculator uses Deflection of Column = (Deflection of Free End+Eccentricity of Column)*(1-cos(Distance b/w Fixed End and Deflection Point*sqrt(Eccentric Load on Column/(Modulus of Elasticity of Column*Moment of Inertia)))) to calculate the Deflection of Column, Deflection at Section of Column with Eccentric Load formula is defined as a measure of the lateral displacement of a column under an eccentric load, which affects the column's stability and structural integrity, and is critical in designing columns to withstand external loads. Deflection of Column is denoted by δ_c symbol.

How to calculate Deflection at Section of Column with Eccentric Load using this online calculator? To use this online calculator for Deflection at Section of Column with Eccentric Load, enter Deflection of Free End (δ), Eccentricity of Column (e), Distance b/w Fixed End and Deflection Point (x), Eccentric Load on Column (P), Modulus of Elasticity of Column (ε_column) & Moment of Inertia (I) and hit the calculate button. Here is how the Deflection at Section of Column with Eccentric Load calculation can be explained with given input values -> 884859.6 = (0.201112+15)*(1-cos(1*sqrt(40/(2000000*0.000168)))).

FAQ

What is Deflection at Section of Column with Eccentric Load?

Deflection at Section of Column with Eccentric Load formula is defined as a measure of the lateral displacement of a column under an eccentric load, which affects the column's stability and structural integrity, and is critical in designing columns to withstand external loads and is represented as δ_c = (δ+e)*(1-cos(x*sqrt(P/(ε_column*I)))) or Deflection of Column = (Deflection of Free End+Eccentricity of Column)*(1-cos(Distance b/w Fixed End and Deflection Point*sqrt(Eccentric Load on Column/(Modulus of Elasticity of Column*Moment of Inertia)))). 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 column refers to the distance between the line of action of the applied load and the centroidal axis of the column’s cross-section, 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, 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 & 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 Deflection at Section of Column with Eccentric Load?

Deflection at Section of Column with Eccentric Load formula is defined as a measure of the lateral displacement of a column under an eccentric load, which affects the column's stability and structural integrity, and is critical in designing columns to withstand external loads is calculated using Deflection of Column = (Deflection of Free End+Eccentricity of Column)*(1-cos(Distance b/w Fixed End and Deflection Point*sqrt(Eccentric Load on Column/(Modulus of Elasticity of Column*Moment of Inertia)))). To calculate Deflection at Section of Column with Eccentric Load, you need Deflection of Free End (δ), Eccentricity of Column (e), Distance b/w Fixed End and Deflection Point (x), Eccentric Load on Column (P), Modulus of Elasticity of Column (ε_column) & Moment of Inertia (I). With our tool, you need to enter the respective value for Deflection of Free End, Eccentricity of Column, Distance b/w Fixed End and Deflection Point, Eccentric Load on Column, 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.

How many ways are there to calculate Deflection of Column?

In this formula, Deflection of Column uses Deflection of Free End, Eccentricity of Column, Distance b/w Fixed End and Deflection Point, Eccentric Load on Column, Modulus of Elasticity of Column & Moment of Inertia. We can use 2 other way(s) to calculate the same, which is/are as follows -

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

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