Deflection at Free End of Column with Eccentric load Calculator

✖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%
✖Column length refers to the distance between its two ends, typically measured from the base to the top, crucial as it influences the column’s stability and load-bearing capacity.ⓘ Column Length [L]			+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 at Free End of Column with Eccentric load [δ]

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Deflection at Free End of Column with Eccentric load Solution

STEP 0: Pre-Calculation Summary

Formula Used

Deflection of Free End = Eccentricity of Load*(sec(Column Length*sqrt(Eccentric Load on Column/(Modulus of Elasticity of Column*Moment of Inertia)))-1)
δ = e_load*(sec(L*sqrt(P/(ε_column*I)))-1)
This formula uses 2 Functions, 6 Variables

Functions Used

sec - Secant is a trigonometric function that is defined ratio of the hypotenuse to the shorter side adjacent to an acute angle (in a right-angled triangle); the reciprocal of a cosine., sec(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 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.
Column Length - (Measured in Meter) - Column length refers to the distance between its two ends, typically measured from the base to the top, crucial as it influences the column’s stability and load-bearing capacity.
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

Eccentricity of Load: 2.5 Millimeter --> 0.0025 Meter (Check conversion here)
Column Length: 5000 Millimeter --> 5 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 = e_load*(sec(L*sqrt(P/(ε_column*I)))-1) --> 0.0025*(sec(5*sqrt(40/(2000000*0.000168)))-1)

Evaluating ... ...

δ = -0.018759610370341

STEP 3: Convert Result to Output's Unit

-0.018759610370341 Meter -->-18.759610370341 Millimeter (Check conversion here)

FINAL ANSWER

-18.759610370341 ≈ -18.75961 Millimeter <-- Deflection of Free End

(Calculation completed in 00.022 seconds)

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National Institute Of Technology (NIT), Hamirpur

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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 Free End of Column with Eccentric load Formula

LaTeX Go

Deflection of Free End = Eccentricity of Load*(sec(Column Length*sqrt(Eccentric Load on Column/(Modulus of Elasticity of Column*Moment of Inertia)))-1)
δ = e_load*(sec(L*sqrt(P/(ε_column*I)))-1)

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 Free End of Column with Eccentric load?

Deflection at Free End of Column with Eccentric load calculator uses Deflection of Free End = Eccentricity of Load*(sec(Column Length*sqrt(Eccentric Load on Column/(Modulus of Elasticity of Column*Moment of Inertia)))-1) to calculate the Deflection of Free End, Deflection at Free End of Column with Eccentric load formula is defined as the maximum displacement of the column's free end due to the eccentric load, which affects the column's stability and structural integrity, and is a critical parameter in designing columns to withstand external loads. Deflection of Free End is denoted by δ symbol.

How to calculate Deflection at Free End of Column with Eccentric load using this online calculator? To use this online calculator for Deflection at Free End of Column with Eccentric load, enter Eccentricity of Load (e_load), Column Length (L), 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 Free End of Column with Eccentric load calculation can be explained with given input values -> -18759.61037 = 0.0025*(sec(5*sqrt(40/(2000000*0.000168)))-1).

FAQ

What is Deflection at Free End of Column with Eccentric load?

Deflection at Free End of Column with Eccentric load formula is defined as the maximum displacement of the column's free end due to the eccentric load, which affects the column's stability and structural integrity, and is a critical parameter in designing columns to withstand external loads and is represented as δ = e_load*(sec(L*sqrt(P/(ε_column*I)))-1) or Deflection of Free End = Eccentricity of Load*(sec(Column Length*sqrt(Eccentric Load on Column/(Modulus of Elasticity of Column*Moment of Inertia)))-1). Eccentricity of load refers to the offset of a load from the centroid of a structural element, such as a beam or column, Column length refers to the distance between its two ends, typically measured from the base to the top, crucial as it influences the column’s stability and load-bearing capacity, 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 Free End of Column with Eccentric load?

Deflection at Free End of Column with Eccentric load formula is defined as the maximum displacement of the column's free end due to the eccentric load, which affects the column's stability and structural integrity, and is a critical parameter in designing columns to withstand external loads is calculated using Deflection of Free End = Eccentricity of Load*(sec(Column Length*sqrt(Eccentric Load on Column/(Modulus of Elasticity of Column*Moment of Inertia)))-1). To calculate Deflection at Free End of Column with Eccentric load, you need Eccentricity of Load (e_load), Column Length (L), 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 Eccentricity of Load, Column Length, 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 Free End?

In this formula, Deflection of Free End uses Eccentricity of Load, Column Length, Eccentric Load on Column, Modulus of Elasticity of Column & Moment of Inertia. We can use 1 other way(s) to calculate the same, which is/are as follows -

Deflection of Free End = (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)))))-Eccentricity of Load

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