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Modulus of Elasticity given Deflection at Free End of Column with Eccentric Load Formula

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

GoModulus of Elasticity given Maximum Stress for Column with Eccentric Load Formula

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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. Check FAQs

ε column = \frac{P}{I \cdot ({(\frac{a r c \sec ((\frac{δ}{e load}) + 1)}{L})}^{2})}

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

Modulus of Elasticity given Deflection at Free End of Column with Eccentric Load Example

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Here is how the Modulus of Elasticity given Deflection at Free End of Column with Eccentric Load equation looks like with Values.

Here is how the Modulus of Elasticity given Deflection at Free End of Column with Eccentric Load equation looks like with Units.

Here is how the Modulus of Elasticity given Deflection at Free End of Column with Eccentric Load equation looks like.

2.4506 = \frac{40}{0.0002 \cdot ({(\frac{a r c \sec ((\frac{201.112}{2.5}) + 1)}{5000})}^{2})}

2.4506MPa = \frac{40N}{0.0002kg·m² \cdot ({(\frac{a r c \sec ((\frac{201.112mm}{2.5mm}) + 1)}{5000mm})}^{2})}

2.4506 = \frac{40}{0.0002 \cdot ({(\frac{a r c \sec ((\frac{201.112}{2.5}) + 1)}{5000})}^{2})}

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Strength of Materials » fx Modulus of Elasticity given Deflection at Free End of Column with Eccentric Load

Modulus of Elasticity given Deflection at Free End of Column with Eccentric Load Solution

Follow our step by step solution on how to calculate Modulus of Elasticity given Deflection at Free End of Column with Eccentric Load?

FIRST Step Consider the formula

ε column = \frac{P}{I \cdot ({(\frac{a r c \sec ((\frac{δ}{e load}) + 1)}{L})}^{2})}

Next Step Substitute values of Variables

∴

ε column = \frac{40N}{0.0002kg·m² \cdot ({(\frac{a r c \sec ((\frac{201.112mm}{2.5mm}) + 1)}{5000mm})}^{2})}

Next Step Convert Units

∴

ε column = \frac{40N}{0.0002kg·m² \cdot ({(\frac{a r c \sec ((\frac{0.2011m}{0.0025m}) + 1)}{5m})}^{2})}

Next Step Prepare to Evaluate

∴

ε column = \frac{40}{0.0002 \cdot ({(\frac{a r c \sec ((\frac{0.2011}{0.0025}) + 1)}{5})}^{2})}

Next Step Evaluate

∴

ε column = 2450570.52196348Pa

Next Step Convert to Output's Unit

∴

ε column = 2.45057052196348MPa

LAST Step Rounding Answer

∴

ε column = 2.4506MPa

Modulus of Elasticity given Deflection at Free End of Column with Eccentric Load Formula Elements

Variables

Functions

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

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

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

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

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)

arcsec

Inverse trigonometric secant – Unary function.

Syntax: arcsec(x)

Other Formulas to find Modulus of Elasticity of Column

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})})

Go Modulus of Elasticity given Maximum Stress for Column with Eccentric Load

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

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

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

How to Evaluate Modulus of Elasticity given Deflection at Free End of Column with Eccentric Load?

Modulus of Elasticity given Deflection at Free End of Column with Eccentric Load evaluator uses Modulus of Elasticity of Column = Eccentric Load on Column/(Moment of Inertia*(((arcsec((Deflection of Free End/Eccentricity of Load)+1))/Column Length)^2)) to evaluate the Modulus of Elasticity of Column, Modulus of Elasticity given Deflection at Free End of Column with Eccentric Load formula is defined as a measure of the ratio of stress and strain of a material, specifically in columns subjected to eccentric loads, providing insight into the material's ability to resist deformation under such conditions. Modulus of Elasticity of Column is denoted by ε_column symbol.

How to evaluate Modulus of Elasticity given Deflection at Free End of Column with Eccentric Load using this online evaluator? To use this online evaluator for Modulus of Elasticity given Deflection at Free End of Column with Eccentric Load, enter Eccentric Load on Column (P), Moment of Inertia (I), Deflection of Free End (δ), Eccentricity of Load (e_load) & Column Length (L) and hit the calculate button.

FAQs on Modulus of Elasticity given Deflection at Free End of Column with Eccentric Load

What is the formula to find Modulus of Elasticity given Deflection at Free End of Column with Eccentric Load?

The formula of Modulus of Elasticity given Deflection at Free End of Column with Eccentric Load is expressed as Modulus of Elasticity of Column = Eccentric Load on Column/(Moment of Inertia*(((arcsec((Deflection of Free End/Eccentricity of Load)+1))/Column Length)^2)). Here is an example- 3E-6 = 40/(0.000168*(((arcsec((0.201112/0.0025)+1))/5)^2)).

How to calculate Modulus of Elasticity given Deflection at Free End of Column with Eccentric Load?

With Eccentric Load on Column (P), Moment of Inertia (I), Deflection of Free End (δ), Eccentricity of Load (e_load) & Column Length (L) we can find Modulus of Elasticity given Deflection at Free End of Column with Eccentric Load using the formula - Modulus of Elasticity of Column = Eccentric Load on Column/(Moment of Inertia*(((arcsec((Deflection of Free End/Eccentricity of Load)+1))/Column Length)^2)). This formula also uses Secant (sec), Inverse Trigonometric Secant (arcsec) function(s).

What are the other ways to Calculate Modulus of Elasticity of Column?

Here are the different ways to Calculate Modulus of Elasticity of Column-

Modulus of Elasticity of Column=(Eccentric Load on Column/(Moment of Inertia*(((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=((asech(((Maximum Stress at Crack Tip-(Eccentric Load on Column/Cross-Sectional Area of Column))*Section Modulus for Column)/(Eccentric Load on Column*Eccentricity of Column))/(Effective Column Length))^2)/(Eccentric Load on Column/(Moment of Inertia))

Can the Modulus of Elasticity given Deflection at Free End of Column with Eccentric Load be negative?

No, the Modulus of Elasticity given Deflection at Free End of Column with Eccentric Load, measured in Pressure cannot be negative.

Which unit is used to measure Modulus of Elasticity given Deflection at Free End of Column with Eccentric Load?

Modulus of Elasticity given Deflection at Free End of Column with Eccentric Load is usually measured using the Megapascal[MPa] for Pressure. Pascal[MPa], Kilopascal[MPa], Bar[MPa] are the few other units in which Modulus of Elasticity given Deflection at Free End of Column with Eccentric Load can be measured.

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Modulus of Elasticity given Deflection at Free End of Column with Eccentric Load Formula

​GoModulus of Elasticity given Deflection at Section of Column with Eccentric Load Formula

​GoModulus of Elasticity given Maximum Stress for Column with Eccentric Load Formula

Modulus of Elasticity given Deflection at Free End of Column with Eccentric Load Example

Modulus of Elasticity given Deflection at Free End of Column with Eccentric Load Solution

Modulus of Elasticity given Deflection at Free End of Column with Eccentric Load Formula Elements

Other Formulas to find Modulus of Elasticity of Column

Other formulas in Columns With Eccentric Load category

How to Evaluate Modulus of Elasticity given Deflection at Free End of Column with Eccentric Load?

FAQs on Modulus of Elasticity given Deflection at Free End of Column with Eccentric Load

Variable Name

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

GoModulus of Elasticity given Maximum Stress for Column with Eccentric Load Formula