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

GoDeflection at Free End of Column with Eccentric load Formula

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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. Check FAQs

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

δ - Deflection of Free End?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?e_load - Eccentricity of Load?

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

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

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

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

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

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

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

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

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Convert Units

∴

δ = (\frac{0.012m}{1 - \cos (1m \cdot \sqrt{\frac{40N}{2E+6Pa \cdot 0.0002kg·m²}})}) - 0.0025m

Next Step Prepare to Evaluate

∴

δ = (\frac{0.012}{1 - \cos (1 \cdot \sqrt{\frac{40}{2E+6 \cdot 0.0002}})}) - 0.0025

Next Step Evaluate

∴

δ = 0.201111961236572m

Next Step Convert to Output's Unit

∴

δ = 201.111961236572mm

LAST Step Rounding Answer

∴

δ = 201.112mm

Deflection at Free End given Deflection at Section of Column with Eccentric load Formula Elements

Variables

Functions

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

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

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

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 Deflection of Free End

Go Deflection at Free End of Column with Eccentric load

δ = e load \cdot (\sec (L \cdot \sqrt{\frac{P}{ε column \cdot I}}) - 1)

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

FAQs on Deflection at Free End given Deflection at Section of Column with Eccentric load

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

The formula of Deflection at Free End given Deflection at Section of Column with Eccentric load is expressed as 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. Here is an example- 201112 = (0.012/(1-cos(1*sqrt(40/(2000000*0.000168)))))-0.0025.

How to calculate Deflection at Free End 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) & Eccentricity of Load (e_load) we can find Deflection at Free End given Deflection at Section of Column with Eccentric load using the formula - 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. This formula also uses Cosine (cos), Square Root (sqrt) function(s).

What are the other ways to Calculate Deflection of Free End?

Here are the different ways to Calculate Deflection of Free End-

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

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

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

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

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

​GoDeflection at Free End of Column with Eccentric load Formula

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

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

Deflection at Free End given Deflection at Section of Column with Eccentric load Formula Elements

Other Formulas to find Deflection of Free End

Other formulas in Columns With Eccentric Load category

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

FAQs on Deflection at Free End given Deflection at Section of Column with Eccentric load

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GoDeflection at Free End of Column with Eccentric load Formula