FormulaDen.com

Physics Chemistry Math Chemical Engineering Civil Electrical Electronics Electronics and Instrumentation Materials Science Mechanical Production Engineering Financial Health

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

GoModulus 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

Fx Copy

LaTeX Copy

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

ε_column - Modulus of Elasticity of Column?σ_max - Maximum Stress at Crack Tip?P - Eccentric Load on Column?A_sectional - Cross-Sectional Area of Column?S - Section Modulus for Column?e - Eccentricity of Column?l_e - Effective Column Length?I - Moment of Inertia?

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

With values

With units

Only example

Here is how the Modulus of Elasticity given Maximum Stress for Column with Eccentric Load equation looks like with Values.

Here is how the Modulus of Elasticity given Maximum Stress for Column with Eccentric Load equation looks like with Units.

Here is how the Modulus of Elasticity given Maximum Stress for Column with Eccentric Load equation looks like.

1.1E-8 = \frac{{(a \frac{sech (\frac{(6E-5 - (\frac{40}{0.6667})) \cdot 13}{40 \cdot 15000})}{200})}^{2}}{\frac{40}{0.0002}}

1.1E-8MPa = \frac{{(a \frac{sech (\frac{(6E-5MPa - (\frac{40N}{0.6667m²})) \cdot 13m³}{40N \cdot 15000mm})}{200mm})}^{2}}{\frac{40N}{0.0002kg·m²}}

1.1E-8 = \frac{{(a \frac{sech (\frac{(6E-5 - (\frac{40}{0.6667})) \cdot 13}{40 \cdot 15000})}{200})}^{2}}{\frac{40}{0.0002}}

Tip: Use pencil ( Pencil

) icon above to edit Input Values and Units.

Calculate

Recalculate

Solution

Copy

Reset

You are here -

Home » Category

Physics » Category

Mechanical » Category

Strength of Materials » fx Modulus of Elasticity given Maximum Stress for Column with Eccentric Load

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

Follow our step by step solution on how to calculate Modulus of Elasticity given Maximum Stress for Column with Eccentric Load?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

ε column = \frac{{(a \frac{sech (\frac{(6E-5MPa - (\frac{40N}{0.6667m²})) \cdot 13m³}{40N \cdot 15000mm})}{200mm})}^{2}}{\frac{40N}{0.0002kg·m²}}

Next Step Convert Units

∴

ε column = \frac{{(a \frac{sech (\frac{(60Pa - (\frac{40N}{0.6667m²})) \cdot 13m³}{40N \cdot 15m})}{0.2m})}^{2}}{\frac{40N}{0.0002kg·m²}}

Next Step Prepare to Evaluate

∴

ε column = \frac{{(a \frac{sech (\frac{(60 - (\frac{40}{0.6667})) \cdot 13}{40 \cdot 15})}{0.2})}^{2}}{\frac{40}{0.0002}}

Next Step Evaluate

∴

ε column = 0.0106516834051866Pa

Next Step Convert to Output's Unit

∴

ε column = 1.06516834051866E-08MPa

LAST Step Rounding Answer

∴

ε column = 1.1E-8MPa

Modulus of Elasticity given Maximum Stress for 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

Maximum Stress at Crack Tip

Maximum stress at crack tip refers to the highest stress concentration that occurs at the very tip of a crack in a material.

Symbol: σ_max

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Maximum Stress at Crack Tip

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

Cross-Sectional Area of Column

Cross-sectional area of column is the area of the shape we get when we cut through the column perpendicular to its length, helps in determining the column’s ability to bear loads and resist stresses.

Symbol: A_sectional

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Cross-Sectional Area of Column

Section Modulus for Column

Section modulus for column is a geometric property of a cross-section that measures the ability of a section to resist bending and is crucial for determining the bending stress in structural elements.

Symbol: S

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Section Modulus for Column

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.

Formulas to find Eccentricity of Column

Effective Column Length

Effective column length, often that represents the length of a column that influences its buckling behavior.

Symbol: l_e

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Effective Column Length

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

sech

The hyperbolic secant function is a hyperbolic function that is the reciprocal of the hyperbolic cosine function.

Syntax: sech(Number)

asech

The hyperbolic secant function is defined as sech(x) = 1/cosh(x), where cosh(x) is the hyperbolic cosine function.

Syntax: asech(Number)

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 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})}

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 Maximum Stress for Column with Eccentric Load?

Modulus of Elasticity given Maximum Stress for Column with Eccentric Load evaluator uses 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)) to evaluate the Modulus of Elasticity of Column, Modulus of Elasticity given Maximum Stress for Column with Eccentric Load formula is defined as a measure of the ratio of stress and strain within the proportional limit of a column subjected to eccentric loading, providing a critical value for structural integrity and stability analysis. Modulus of Elasticity of Column is denoted by ε_column symbol.

How to evaluate Modulus of Elasticity given Maximum Stress for Column with Eccentric Load using this online evaluator? To use this online evaluator for Modulus of Elasticity given Maximum Stress for Column with Eccentric Load, enter Maximum Stress at Crack Tip (σ_max), Eccentric Load on Column (P), Cross-Sectional Area of Column (A_sectional), Section Modulus for Column (S), Eccentricity of Column (e), Effective Column Length (l_e) & Moment of Inertia (I) and hit the calculate button.

FAQs on Modulus of Elasticity given Maximum Stress for Column with Eccentric Load

What is the formula to find Modulus of Elasticity given Maximum Stress for Column with Eccentric Load?

The formula of Modulus of Elasticity given Maximum Stress for Column with Eccentric Load is expressed as 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)). Here is an example- 9.2E-17 = ((asech(((60-(40/0.66671))*13)/(40*15))/(0.2))^2)/(40/(0.000168)).

How to calculate Modulus of Elasticity given Maximum Stress for Column with Eccentric Load?

With Maximum Stress at Crack Tip (σ_max), Eccentric Load on Column (P), Cross-Sectional Area of Column (A_sectional), Section Modulus for Column (S), Eccentricity of Column (e), Effective Column Length (l_e) & Moment of Inertia (I) we can find Modulus of Elasticity given Maximum Stress for Column with Eccentric Load using the formula - 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)). This formula also uses Hyperbolic Secant (sech), Inverse Trigonometric Secant (asech) 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=Eccentric Load on Column/(Moment of Inertia*(((arcsec((Deflection of Free End/Eccentricity of Load)+1))/Column Length)^2))

Can the Modulus of Elasticity given Maximum Stress for Column with Eccentric Load be negative?

No, the Modulus of Elasticity given Maximum Stress for Column with Eccentric Load, measured in Pressure cannot be negative.

Which unit is used to measure Modulus of Elasticity given Maximum Stress for Column with Eccentric Load?

Modulus of Elasticity given Maximum Stress for 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 Maximum Stress for Column with Eccentric Load can be measured.

Let Others Know

✖

Facebook

Twitter

Copied!

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

​GoModulus 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

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

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

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

FAQs on Modulus of Elasticity given Maximum Stress for Column with Eccentric Load

Variable Name

GoModulus 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