Eccentricity 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%
✖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 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 given Deflection at Section of Column with Eccentric load [e]

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Eccentricity given Deflection at Section of Column with Eccentric load Solution

STEP 0: Pre-Calculation Summary

Formula Used

Eccentricity of Column = (Deflection 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
e = (δ_c/(1-cos(x*sqrt(P/(ε_column*I)))))-δ
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

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.
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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

e = (δ_c/(1-cos(x*sqrt(P/(ε_column*I)))))-δ --> (0.012/(1-cos(1*sqrt(40/(2000000*0.000168)))))-0.201112

Evaluating ... ...

e = 0.00249996123657184

STEP 3: Convert Result to Output's Unit

0.00249996123657184 Meter -->2.49996123657184 Millimeter (Check conversion here)

FINAL ANSWER

2.49996123657184 ≈ 2.499961 Millimeter <-- Eccentricity 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 » Eccentricity 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

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)

Eccentricity 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 Eccentricity given Deflection at Section of Column with Eccentric load?

Eccentricity given Deflection at Section of Column with Eccentric load calculator uses Eccentricity of Column = (Deflection 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 to calculate the Eccentricity of Column, Eccentricity given Deflection at Section of Column with Eccentric load formula is defined as a measure of how much the column is deviating from its vertical axis due to the eccentric load, which affects the structural integrity and stability of the column. Eccentricity of Column is denoted by e symbol.

How to calculate Eccentricity given Deflection at Section of Column with Eccentric load using this online calculator? To use this online calculator for Eccentricity given Deflection at Section of Column with Eccentric load, enter Deflection of Column (δ_c), 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) & Deflection of Free End (δ) and hit the calculate button. Here is how the Eccentricity given Deflection at Section of Column with Eccentric load calculation can be explained with given input values -> 189612 = (0.012/(1-cos(1*sqrt(40/(2000000*0.000168)))))-0.201112.

FAQ

What is Eccentricity given Deflection at Section of Column with Eccentric load?

Eccentricity given Deflection at Section of Column with Eccentric load formula is defined as a measure of how much the column is deviating from its vertical axis due to the eccentric load, which affects the structural integrity and stability of the column and is represented as e = (δ_c/(1-cos(x*sqrt(P/(ε_column*I)))))-δ or Eccentricity of Column = (Deflection 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. 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, 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 & 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.

How to calculate Eccentricity given Deflection at Section of Column with Eccentric load?

Eccentricity given Deflection at Section of Column with Eccentric load formula is defined as a measure of how much the column is deviating from its vertical axis due to the eccentric load, which affects the structural integrity and stability of the column is calculated using Eccentricity of Column = (Deflection 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. To calculate Eccentricity given Deflection at Section of Column with Eccentric load, you need Deflection of Column (δ_c), 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) & Deflection of Free End (δ). With our tool, you need to enter the respective value for Deflection of Column, Distance b/w Fixed End and Deflection Point, Eccentric Load on Column, Modulus of Elasticity of Column, Moment of Inertia & Deflection of Free End 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 Eccentricity of Column?

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

Eccentricity of Column = (Moment of Force/Eccentric Load on Column)-Deflection of Free End+Deflection of Column
Eccentricity of Column = ((Maximum Stress at Crack Tip-(Eccentric Load on Column/Cross-Sectional Area of Column))*Section Modulus for Column)/((Eccentric Load on Column*sec(Effective Column Length*sqrt(Eccentric Load on Column/(Modulus of Elasticity of Column*Moment of Inertia))))/2)

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