Deflection at Free End 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%
✖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%

✖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 given Deflection at Section of Column with Eccentric load [δ]

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Deflection at Free End given Deflection at Section of Column with Eccentric load Solution

STEP 0: Pre-Calculation Summary

Formula Used

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
δ = (δ_c/(1-cos(x*sqrt(P/(ε_column*I)))))-e_load
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 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.
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.
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.

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
Eccentricity of Load: 2.5 Millimeter --> 0.0025 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

δ = (δ_c/(1-cos(x*sqrt(P/(ε_column*I)))))-e_load --> (0.012/(1-cos(1*sqrt(40/(2000000*0.000168)))))-0.0025

Evaluating ... ...

δ = 0.201111961236572

STEP 3: Convert Result to Output's Unit

0.201111961236572 Meter -->201.111961236572 Millimeter (Check conversion here)

FINAL ANSWER

201.111961236572 ≈ 201.112 Millimeter <-- Deflection of Free End

(Calculation completed in 00.021 seconds)

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Home » Physics » Strength of Materials » Column And Struts » Mechanical » Columns With Eccentric Load » Deflection at Free End 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)

Deflection at Free End 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 Deflection at Free End given Deflection at Section of Column with Eccentric load?

Deflection at Free End given Deflection at Section of Column with Eccentric load calculator uses 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 to calculate the Deflection of Free End, Deflection at Free End given Deflection at Section of Column with Eccentric load formula is defined as a measure of the maximum displacement of the free end of a column subjected to an eccentric load, taking into account the deflection at a specific section of the column and the load's eccentricity. Deflection of Free End is denoted by δ symbol.

How to calculate Deflection at Free End given Deflection at Section of Column with Eccentric load using this online calculator? To use this online calculator for Deflection at Free End 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) & Eccentricity of Load (e_load) and hit the calculate button. Here is how the Deflection at Free End given Deflection at Section of Column with Eccentric load calculation can be explained with given input values -> 201112 = (0.012/(1-cos(1*sqrt(40/(2000000*0.000168)))))-0.0025.

FAQ

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

Deflection at Free End given Deflection at Section of Column with Eccentric load formula is defined as a measure of the maximum displacement of the free end of a column subjected to an eccentric load, taking into account the deflection at a specific section of the column and the load's eccentricity and is represented as δ = (δ_c/(1-cos(x*sqrt(P/(ε_column*I)))))-e_load or 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. 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 & Eccentricity of load refers to the offset of a load from the centroid of a structural element, such as a beam or column.

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

Deflection at Free End given Deflection at Section of Column with Eccentric load formula is defined as a measure of the maximum displacement of the free end of a column subjected to an eccentric load, taking into account the deflection at a specific section of the column and the load's eccentricity is calculated using 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. To calculate Deflection at Free End 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) & Eccentricity of Load (e_load). 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 & Eccentricity of Load 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 Deflection of Column, Distance b/w Fixed End and Deflection Point, Eccentric Load on Column, Modulus of Elasticity of Column, Moment of Inertia & Eccentricity of Load. We can use 1 other way(s) to calculate the same, which is/are as follows -

Deflection of Free End = Eccentricity of Load*(sec(Column Length*sqrt(Eccentric Load on Column/(Modulus of Elasticity of Column*Moment of Inertia)))-1)

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