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

GoModulus of Elasticity given Deflection at Free End 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 \cos (1 - (\frac{δ c}{δ + e load}))}{x})}^{2})})

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

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

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

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

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

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

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

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

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

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

ε column = (\frac{40N}{0.0002kg·m² \cdot ({(\frac{a \cos (1 - (\frac{12mm}{201.112mm + 2.5mm}))}{1000mm})}^{2})})

Next Step Convert Units

∴

ε column = (\frac{40N}{0.0002kg·m² \cdot ({(\frac{a \cos (1 - (\frac{0.012m}{0.2011m + 0.0025m}))}{1m})}^{2})})

Next Step Prepare to Evaluate

∴

ε column = (\frac{40}{0.0002 \cdot ({(\frac{a \cos (1 - (\frac{0.012}{0.2011 + 0.0025}))}{1})}^{2})})

Next Step Evaluate

∴

ε column = 2000000.38458075Pa

Next Step Convert to Output's Unit

∴

ε column = 2.00000038458075MPa

LAST Step Rounding Answer

∴

ε column = 2MPa

Modulus of Elasticity given Deflection at Section 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 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

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

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

cos

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

Syntax: cos(Angle)

acos

The inverse cosine function, is the inverse function of the cosine function. It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio.

Syntax: acos(Number)

Other Formulas to find Modulus of Elasticity of Column

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

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

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

Modulus of Elasticity given Deflection at Section of Column with Eccentric Load evaluator uses 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))) to evaluate the Modulus of Elasticity of Column, Modulus of Elasticity given Deflection at Section of Column with Eccentric Load formula is a measure of the ratio of stress and strain on a column when it is subjected to an eccentric load, providing insight into the column'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 Section of Column with Eccentric Load using this online evaluator? To use this online evaluator for Modulus of Elasticity given Deflection at Section of Column with Eccentric Load, enter Eccentric Load on Column (P), Moment of Inertia (I), Deflection of Column (δ_c), Deflection of Free End (δ), Eccentricity of Load (e_load) & Distance b/w Fixed End and Deflection Point (x) and hit the calculate button.

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

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

The formula of Modulus of Elasticity given Deflection at Section of Column with Eccentric Load is expressed as 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))). Here is an example- 1.4E-7 = (40/(0.000168*(((acos(1-(0.012/(0.201112+0.0025))))/1)^2))).

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

With Eccentric Load on Column (P), Moment of Inertia (I), Deflection of Column (δ_c), Deflection of Free End (δ), Eccentricity of Load (e_load) & Distance b/w Fixed End and Deflection Point (x) we can find Modulus of Elasticity given Deflection at Section of Column with Eccentric Load using the formula - 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))). This formula also uses Cosine (cos), Inverse Cosine (acos) 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*(((arcsec((Deflection of Free End/Eccentricity of Load)+1))/Column Length)^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 Section of Column with Eccentric Load be negative?

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

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

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

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

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

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

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

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

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

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

Variable Name

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

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