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

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Effective Column Length can be defined as the length of an equivalent pin-ended column having the same load-carrying capacity as the member under consideration. 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?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.

5412.4069 = a \frac{sech (\frac{(6E-5 - (\frac{40}{1.4})) \cdot 13}{40 \cdot 15000})}{\frac{\sqrt{\frac{40}{2 \cdot 0.0002}}}{2}}

5412.4069mm = a \frac{sech (\frac{(6E-5MPa - (\frac{40N}{1.4m²})) \cdot 13m³}{40N \cdot 15000mm})}{\frac{\sqrt{\frac{40N}{2MPa \cdot 0.0002kg·m²}}}{2}}

5412.4069 = a \frac{sech (\frac{(6E-5 - (\frac{40}{1.4})) \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}{1.4m²})) \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}{1.4m²})) \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}{1.4})) \cdot 13}{40 \cdot 15})}{\frac{\sqrt{\frac{40}{2E+6 \cdot 0.0002}}}{2}}

Next Step Evaluate

∴

L e = 5.41240687177984m

Next Step Convert to Output's Unit

∴

L e = 5412.40687177984mm

LAST Step Rounding Answer

∴

L e = 5412.4069mm

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

Variables

Functions

Effective Column Length

Effective Column Length can be defined as the length of an equivalent pin-ended column having the same load-carrying capacity as the member under consideration.

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 due to the applied nominal stress.

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 is the load that causes direct stress as well as 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 for a given cross-section used in the design of beams or flexural members.

Symbol: S

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Section Modulus for Column

Eccentricity

Eccentricity is the distance from point of application of resultant to center of base.

Symbol: e

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Eccentricity

Modulus of elasticity of column

Modulus of elasticity of column is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it.

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 is the measure of the resistance of a body to angular acceleration about a given 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 (a crippling + e load - δ c)

Go Eccentricity given Moment at Section of Column with Eccentric Load

e = (\frac{M}{P}) - a crippling + 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))/(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 (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))/(sqrt(Eccentric load on column/(Modulus of elasticity of column*Moment of Inertia))/2). Here is an example- 5.4E+6 = asech(((60-(40/1.4))*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 (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))/(sqrt(Eccentric load on column/(Modulus of elasticity of column*Moment of Inertia))/2). This formula also uses Square Root FunctionHyperbolic Secant Function, Inverse trigonometric secant 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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