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Effective Length of Column given Maximum Stress for Column with Eccentric Load Formula

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

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

l_e - Effective Column Length?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?ε_column - Modulus of Elasticity of Column?I - Moment of Inertia?

Effective Length of Column given Maximum Stress for Column with Eccentric Load Example

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

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

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

58382.6917 = a \frac{sech (\frac{(6E-5 - (\frac{40}{0.6667})) \cdot 13}{40 \cdot 15000})}{\frac{\sqrt{\frac{40}{2 \cdot 0.0002}}}{2}}

58382.6917mm = a \frac{sech (\frac{(6E-5MPa - (\frac{40N}{0.6667m²})) \cdot 13m³}{40N \cdot 15000mm})}{\frac{\sqrt{\frac{40N}{2MPa \cdot 0.0002kg·m²}}}{2}}

58382.6917 = a \frac{sech (\frac{(6E-5 - (\frac{40}{0.6667})) \cdot 13}{40 \cdot 15000})}{\frac{\sqrt{\frac{40}{2 \cdot 0.0002}}}{2}}

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Effective Length of Column given Maximum Stress for Column with Eccentric Load Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

l e = a \frac{sech (\frac{(6E-5MPa - (\frac{40N}{0.6667m²})) \cdot 13m³}{40N \cdot 15000mm})}{\frac{\sqrt{\frac{40N}{2MPa \cdot 0.0002kg·m²}}}{2}}

Next Step Convert Units

∴

l e = a \frac{sech (\frac{(60Pa - (\frac{40N}{0.6667m²})) \cdot 13m³}{40N \cdot 15m})}{\frac{\sqrt{\frac{40N}{2E+6Pa \cdot 0.0002kg·m²}}}{2}}

Next Step Prepare to Evaluate

∴

l e = a \frac{sech (\frac{(60 - (\frac{40}{0.6667})) \cdot 13}{40 \cdot 15})}{\frac{\sqrt{\frac{40}{2E+6 \cdot 0.0002}}}{2}}

Next Step Evaluate

∴

l e = 58.3826916959103m

Next Step Convert to Output's Unit

∴

l e = 58382.6916959103mm

LAST Step Rounding Answer

∴

l e = 58382.6917mm

Effective Length of Column given Maximum Stress for Column with Eccentric Load Formula Elements

Variables

Functions

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

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

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

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)

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 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 Effective Length of Column given Maximum Stress for Column with Eccentric Load?

Effective Length of Column given Maximum Stress for Column with Eccentric Load evaluator uses Effective Column Length = 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))/(sqrt(Eccentric Load on Column/(Modulus of Elasticity of Column*Moment of Inertia))/2) to evaluate the Effective Column Length, Effective Length of Column given Maximum Stress for Column with Eccentric Load formula is defined as the length of a column that takes into account the maximum stress it can withstand when subjected to an eccentric load, providing a critical value for structural engineers to ensure the column's stability and safety. Effective Column Length is denoted by l_e symbol.

How to evaluate Effective Length of Column given Maximum Stress for Column with Eccentric Load using this online evaluator? To use this online evaluator for Effective Length of Column 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), Modulus of Elasticity of Column (ε_column) & Moment of Inertia (I) and hit the calculate button.

FAQs on Effective Length of Column given Maximum Stress for Column with Eccentric Load

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

The formula of Effective Length of Column given Maximum Stress for Column with Eccentric Load is expressed as Effective Column Length = 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))/(sqrt(Eccentric Load on Column/(Modulus of Elasticity of Column*Moment of Inertia))/2). Here is an example- 5.4E+6 = asech(((60-(40/0.66671))*13)/(40*15))/(sqrt(40/(2000000*0.000168))/2).

How to calculate Effective Length of Column 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), Modulus of Elasticity of Column (ε_column) & Moment of Inertia (I) we can find Effective Length of Column given Maximum Stress for Column with Eccentric Load using the formula - Effective Column Length = 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))/(sqrt(Eccentric Load on Column/(Modulus of Elasticity of Column*Moment of Inertia))/2). This formula also uses Square Root (sqrt)Hyperbolic Secant (sech), Inverse Trigonometric Secant (asech) function(s).

Can the Effective Length of Column given Maximum Stress for Column with Eccentric Load be negative?

No, the Effective Length of Column given Maximum Stress for Column with Eccentric Load, measured in Length cannot be negative.

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

Effective Length of Column given Maximum Stress for 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 Effective Length of Column given Maximum Stress for Column with Eccentric Load can be measured.

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Effective Length of Column given Maximum Stress for Column with Eccentric Load Formula

Effective Length of Column given Maximum Stress for Column with Eccentric Load Example

Effective Length of Column given Maximum Stress for Column with Eccentric Load Solution

Effective Length of Column given Maximum Stress for Column with Eccentric Load Formula Elements

Other formulas in Columns With Eccentric Load category

How to Evaluate Effective Length of Column given Maximum Stress for Column with Eccentric Load?

FAQs on Effective Length of Column given Maximum Stress for Column with Eccentric Load

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