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

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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. Check FAQs

P = ({(\frac{a \cos (1 - (\frac{δ c}{δ + e load}))}{x})}^{2}) \cdot (ε column \cdot I)

P - Eccentric Load on Column?δ_c - Deflection of Column?δ - Deflection of Free End?e_load - Eccentricity of Load?x - Distance b/w Fixed End and Deflection Point?ε_column - Modulus of Elasticity of Column?I - Moment of Inertia?

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

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Here is how the Eccentric Load given Deflection at Section of Column with Eccentric Load equation looks like with Values.

Here is how the Eccentric Load given Deflection at Section of Column with Eccentric Load equation looks like with Units.

Here is how the Eccentric Load given Deflection at Section of Column with Eccentric Load equation looks like.

40 = ({(\frac{a \cos (1 - (\frac{12}{201.112 + 2.5}))}{1000})}^{2}) \cdot (2 \cdot 0.0002)

40N = ({(\frac{a \cos (1 - (\frac{12mm}{201.112mm + 2.5mm}))}{1000mm})}^{2}) \cdot (2MPa \cdot 0.0002kg·m²)

40 = ({(\frac{a \cos (1 - (\frac{12}{201.112 + 2.5}))}{1000})}^{2}) \cdot (2 \cdot 0.0002)

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

Follow our step by step solution on how to calculate Eccentric Load given Deflection at Section of Column with Eccentric Load?

FIRST Step Consider the formula

P = ({(\frac{a \cos (1 - (\frac{δ c}{δ + e load}))}{x})}^{2}) \cdot (ε column \cdot I)

Next Step Substitute values of Variables

∴

P = ({(\frac{a \cos (1 - (\frac{12mm}{201.112mm + 2.5mm}))}{1000mm})}^{2}) \cdot (2MPa \cdot 0.0002kg·m²)

Next Step Convert Units

∴

P = ({(\frac{a \cos (1 - (\frac{0.012m}{0.2011m + 0.0025m}))}{1m})}^{2}) \cdot (2E+6Pa \cdot 0.0002kg·m²)

Next Step Prepare to Evaluate

∴

P = ({(\frac{a \cos (1 - (\frac{0.012}{0.2011 + 0.0025}))}{1})}^{2}) \cdot (2E+6 \cdot 0.0002)

Next Step Evaluate

∴

P = 39.9999923083865N

LAST Step Rounding Answer

∴

P = 40N

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

Variables

Functions

Eccentric Load on Column

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.

Symbol: P

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Eccentric Load on Column

Deflection of Column

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.

Symbol: δ_c

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Deflection of Column

Deflection of Free End

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.

Symbol: δ

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Deflection of Free End

Eccentricity of Load

Eccentricity of load refers to the offset of a load from the centroid of a structural element, such as a beam or column.

Symbol: e_load

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Eccentricity of Load

Distance b/w Fixed End and Deflection Point

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.

Symbol: x

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Distance b/w Fixed End and Deflection Point

Modulus of Elasticity of Column

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.

Symbol: ε_column

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Modulus of Elasticity of Column

Moment of Inertia

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.

Symbol: I

Measurement: Moment of InertiaUnit: kg·m²

Note: Value should be greater than 0.

Formulas to find Moment of Inertia

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: 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.

Syntax: acos(Number)

Other formulas in Columns With Eccentric Load category

Go Moment at Section of Column with Eccentric Load

M = P \cdot (δ + e load - δ c)

Go Eccentricity given Moment at Section of Column with Eccentric Load

e = (\frac{M}{P}) - δ + δ c

How to Evaluate Eccentric Load given Deflection at Section of Column with Eccentric Load?

Eccentric Load given Deflection at Section of Column with Eccentric Load evaluator 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 evaluate 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 evaluate Eccentric Load given Deflection at Section of Column with Eccentric Load using this online evaluator? To use this online evaluator 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.

FAQs on Eccentric Load given Deflection at Section of Column with Eccentric Load

What is the formula to find Eccentric Load given Deflection at Section of Column with Eccentric Load?

The formula of Eccentric Load given Deflection at Section of Column with Eccentric Load is expressed as 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). Here is an example- 563.106 = (((acos(1-(0.012/(0.201112+0.0025))))/1)^2)*(2000000*0.000168).

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

With 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) we can find Eccentric Load given Deflection at Section of Column with Eccentric Load using the formula - 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). This formula also uses Cosine (cos), Inverse Cosine (acos) function(s).

Can the Eccentric Load given Deflection at Section of Column with Eccentric Load be negative?

No, the Eccentric Load given Deflection at Section of Column with Eccentric Load, measured in Force cannot be negative.

Which unit is used to measure Eccentric Load given Deflection at Section of Column with Eccentric Load?

Eccentric Load given Deflection at Section of Column with Eccentric Load is usually measured using the Newton[N] for Force. Exanewton[N], Meganewton[N], Kilonewton[N] are the few other units in which Eccentric Load given Deflection at Section of Column with Eccentric Load can be measured.

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

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

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

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

Other formulas in Columns With Eccentric Load category

How to Evaluate Eccentric Load given Deflection at Section of Column with Eccentric Load?

FAQs on Eccentric Load given Deflection at Section of Column with Eccentric Load

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