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Eccentricity given Deflection at Section of Column with Eccentric load Formula

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GoEccentricity given Maximum Stress for Column with Eccentric Load Formula

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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. Check FAQs

e = (\frac{δ c}{1 - \cos (x \cdot \sqrt{\frac{P}{ε column \cdot I}})}) - δ

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

Eccentricity given Deflection at Section of Column with Eccentric load Example

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

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

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

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

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

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

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Eccentricity given Deflection at Section of Column with Eccentric load Solution

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

FIRST Step Consider the formula

e = (\frac{δ c}{1 - \cos (x \cdot \sqrt{\frac{P}{ε column \cdot I}})}) - δ

Next Step Substitute values of Variables

∴

e = (\frac{12mm}{1 - \cos (1000mm \cdot \sqrt{\frac{40N}{2MPa \cdot 0.0002kg·m²}})}) - 201.112mm

Next Step Convert Units

∴

e = (\frac{0.012m}{1 - \cos (1m \cdot \sqrt{\frac{40N}{2E+6Pa \cdot 0.0002kg·m²}})}) - 0.2011m

Next Step Prepare to Evaluate

∴

e = (\frac{0.012}{1 - \cos (1 \cdot \sqrt{\frac{40}{2E+6 \cdot 0.0002}})}) - 0.2011

Next Step Evaluate

∴

e = 0.00249996123657184m

Next Step Convert to Output's Unit

∴

e = 2.49996123657184mm

LAST Step Rounding Answer

∴

e = 2.5mm

Eccentricity given Deflection at Section of Column with Eccentric load Formula Elements

Variables

Functions

Eccentricity of Column

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.

Symbol: e

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Eccentricity of 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

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

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

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

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

cos

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

Syntax: 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.

Syntax: sqrt(Number)

Other Formulas to find Eccentricity of Column

Go Eccentricity given Moment at Section of Column with Eccentric Load

e = (\frac{M}{P}) - δ + δ c

Go Eccentricity given Maximum Stress for Column with Eccentric Load

e = \frac{(σ max - (\frac{P}{A sectional})) \cdot S}{\frac{P \cdot \sec (l e \cdot \sqrt{\frac{P}{ε column \cdot I}})}{2}}

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 Eccentric Load given Deflection at Section of Column with Eccentric Load

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

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

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

FAQs on Eccentricity given Deflection at Section of Column with Eccentric load

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

The formula of Eccentricity given Deflection at Section of Column with Eccentric load is expressed as 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. Here is an example- 189612 = (0.012/(1-cos(1*sqrt(40/(2000000*0.000168)))))-0.201112.

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

With 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) we can find Eccentricity given Deflection at Section of Column with Eccentric load using the formula - 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. This formula also uses Cosine (cos), Square Root (sqrt) function(s).

What are the other ways to Calculate Eccentricity of Column?

Here are the different ways to Calculate Eccentricity of Column-

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)

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

No, the Eccentricity given Deflection at Section of Column with Eccentric load, measured in Length cannot be negative.

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

Eccentricity given Deflection at Section of Column with Eccentric load is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Eccentricity given Deflection at Section of Column with Eccentric load can be measured.

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Eccentricity given Deflection at Section of Column with Eccentric load Formula

​GoEccentricity given Moment at Section of Column with Eccentric Load Formula

​GoEccentricity given Maximum Stress for Column with Eccentric Load Formula

Eccentricity given Deflection at Section of Column with Eccentric load Example

Eccentricity given Deflection at Section of Column with Eccentric load Solution

Eccentricity given Deflection at Section of Column with Eccentric load Formula Elements

Other Formulas to find Eccentricity of Column

Other formulas in Columns With Eccentric Load category

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

FAQs on Eccentricity given Deflection at Section of Column with Eccentric load

Variable Name

GoEccentricity given Moment at Section of Column with Eccentric Load Formula

GoEccentricity given Maximum Stress for Column with Eccentric Load Formula