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Deflection at Section of Column with Eccentric Load Formula

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GoDeflection at Free End given Moment at Section of Column with Eccentric load Formula

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GoDeflection at Section of Column with Eccentric Load given Moment at Section Formula

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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. Check FAQs

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

δ_c - Deflection of Column?δ - Deflection of Free End?e - Eccentricity 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?

Deflection at Section of Column with Eccentric Load Example

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

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

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

895.8872 = (201.112 + 15000) \cdot (1 - \cos (1000 \cdot \sqrt{\frac{40}{2 \cdot 0.0002}}))

895.8872mm = (201.112mm + 15000mm) \cdot (1 - \cos (1000mm \cdot \sqrt{\frac{40N}{2MPa \cdot 0.0002kg·m²}}))

895.8872 = (201.112 + 15000) \cdot (1 - \cos (1000 \cdot \sqrt{\frac{40}{2 \cdot 0.0002}}))

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Home » Physics » Mechanical » Strength of Materials » Deflection at Section of Column with Eccentric Load

Deflection at Section of Column with Eccentric Load Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

δ c = (201.112mm + 15000mm) \cdot (1 - \cos (1000mm \cdot \sqrt{\frac{40N}{2MPa \cdot 0.0002kg·m²}}))

Next Step Convert Units

∴

δ c = (0.2011m + 15m) \cdot (1 - \cos (1m \cdot \sqrt{\frac{40N}{2E+6Pa \cdot 0.0002kg·m²}}))

Next Step Prepare to Evaluate

∴

δ c = (0.2011 + 15) \cdot (1 - \cos (1 \cdot \sqrt{\frac{40}{2E+6 \cdot 0.0002}}))

Next Step Evaluate

∴

δ c = 0.895887171324175m

Next Step Convert to Output's Unit

∴

δ c = 895.887171324175mm

LAST Step Rounding Answer

∴

δ c = 895.8872mm

Deflection at Section of Column with Eccentric Load Formula Elements

Variables

Functions

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.

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.

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.

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.

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.

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.

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.

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)

Credits

Creator Image

Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

Anshika Arya has created this Formula and 2000+ more formulas!

Verifier Image

Verified by Payal Priya

Birsa Institute of Technology (BIT), Sindri

Payal Priya has verified this Formula and 1900+ more formulas!

Other Formulas to find Deflection of Column

Go Deflection at Free End given Moment at Section of Column with Eccentric load

δ c = (\frac{M}{P}) - (e load + δ)

Go Deflection at Section of Column with Eccentric Load given Moment at Section

δ c = - (\frac{M}{P}) + δ + e

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

See More

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

Deflection at Section of Column with Eccentric Load evaluator uses Deflection of Column = (Deflection of Free End+Eccentricity 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)))) to evaluate the Deflection of Column, Deflection at Section of Column with Eccentric Load formula is defined as a measure of the lateral displacement of a column under an eccentric load, which affects the column's stability and structural integrity, and is critical in designing columns to withstand external loads. Deflection of Column is denoted by δ_c symbol.

How to evaluate Deflection at Section of Column with Eccentric Load using this online evaluator? To use this online evaluator for Deflection at Section of Column with Eccentric Load, enter Deflection of Free End (δ), Eccentricity of Column (e), 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) and hit the calculate button.

FAQs on Deflection at Section of Column with Eccentric Load

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

The formula of Deflection at Section of Column with Eccentric Load is expressed as Deflection of Column = (Deflection of Free End+Eccentricity 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)))). Here is an example- 884859.6 = (0.201112+15)*(1-cos(1*sqrt(40/(2000000*0.000168)))).

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

With Deflection of Free End (δ), Eccentricity of Column (e), 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) we can find Deflection at Section of Column with Eccentric Load using the formula - Deflection of Column = (Deflection of Free End+Eccentricity 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)))). This formula also uses Cosine (cos), Square Root (sqrt) function(s).

What are the other ways to Calculate Deflection of Column?

Here are the different ways to Calculate Deflection of Column-

Deflection of Column=(Moment of Force/Eccentric Load on Column)-(Eccentricity of Load+Deflection of Free End)
Deflection of Column=-(Moment of Force/Eccentric Load on Column)+Deflection of Free End+Eccentricity of Column

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

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

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

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 Deflection at Section of Column with Eccentric Load can be measured.

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