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Deflection at Free End of Column with Eccentric load Formula

GoDeflection at Free End given Deflection at Section 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 = e load \cdot (\sec (L \cdot \sqrt{\frac{P}{ε column \cdot I}}) - 1)

δ - Deflection of Free End?e_load - Eccentricity of Load?L - Column Length?P - Eccentric Load on Column?ε_column - Modulus of Elasticity of Column?I - Moment of Inertia?

Deflection at Free End of Column with Eccentric load Example

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

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

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

-18.7596 = 2.5 \cdot (\sec (5000 \cdot \sqrt{\frac{40}{2 \cdot 0.0002}}) - 1)

-18.7596mm = 2.5mm \cdot (\sec (5000mm \cdot \sqrt{\frac{40N}{2MPa \cdot 0.0002kg·m²}}) - 1)

-18.7596 = 2.5 \cdot (\sec (5000 \cdot \sqrt{\frac{40}{2 \cdot 0.0002}}) - 1)

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Deflection at Free End of Column with Eccentric load Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

δ = 2.5mm \cdot (\sec (5000mm \cdot \sqrt{\frac{40N}{2MPa \cdot 0.0002kg·m²}}) - 1)

Next Step Convert Units

∴

δ = 0.0025m \cdot (\sec (5m \cdot \sqrt{\frac{40N}{2E+6Pa \cdot 0.0002kg·m²}}) - 1)

Next Step Prepare to Evaluate

∴

δ = 0.0025 \cdot (\sec (5 \cdot \sqrt{\frac{40}{2E+6 \cdot 0.0002}}) - 1)

Next Step Evaluate

∴

δ = -0.018759610370341m

Next Step Convert to Output's Unit

∴

δ = -18.759610370341mm

LAST Step Rounding Answer

∴

δ = -18.7596mm

Deflection at Free End 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

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

Column Length

Column length refers to the distance between its two ends, typically measured from the base to the top, crucial as it influences the column’s stability and load-bearing capacity.

Symbol: L

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Column Length

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

sec

Secant is a trigonometric function that is defined ratio of the hypotenuse to the shorter side adjacent to an acute angle (in a right-angled triangle); the reciprocal of a cosine.

Syntax: sec(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 given Deflection at Section of Column with Eccentric load

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

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

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)

Go Modulus of Elasticity given Deflection at Section of Column with Eccentric Load

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

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

Deflection at Free End of Column with Eccentric load evaluator uses Deflection of Free End = Eccentricity of Load*(sec(Column Length*sqrt(Eccentric Load on Column/(Modulus of Elasticity of Column*Moment of Inertia)))-1) to evaluate the Deflection of Free End, Deflection at Free End of Column with Eccentric load formula is defined as the maximum displacement of the column's free end due to the eccentric load, which affects the column's stability and structural integrity, and is a critical parameter in designing columns to withstand external loads. Deflection of Free End is denoted by δ symbol.

How to evaluate Deflection at Free End of Column with Eccentric load using this online evaluator? To use this online evaluator for Deflection at Free End of Column with Eccentric load, enter Eccentricity of Load (e_load), Column Length (L), 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 Free End of Column with Eccentric load

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

The formula of Deflection at Free End of Column with Eccentric load is expressed as Deflection of Free End = Eccentricity of Load*(sec(Column Length*sqrt(Eccentric Load on Column/(Modulus of Elasticity of Column*Moment of Inertia)))-1). Here is an example- -18759.61037 = 0.0025*(sec(5*sqrt(40/(2000000*0.000168)))-1).

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

With Eccentricity of Load (e_load), Column Length (L), Eccentric Load on Column (P), Modulus of Elasticity of Column (ε_column) & Moment of Inertia (I) we can find Deflection at Free End of Column with Eccentric load using the formula - Deflection of Free End = Eccentricity of Load*(sec(Column Length*sqrt(Eccentric Load on Column/(Modulus of Elasticity of Column*Moment of Inertia)))-1). This formula also uses Secant (sec), 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=(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

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

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

Which unit is used to measure Deflection at Free End of Column with Eccentric load?

Deflection at Free End 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 of Column with Eccentric load can be measured.

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Deflection at Free End of Column with Eccentric load Formula

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

Deflection at Free End of Column with Eccentric load Example

Deflection at Free End of Column with Eccentric load Solution

Deflection at Free End 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 of Column with Eccentric load?

FAQs on Deflection at Free End of Column with Eccentric load

Variable Name

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