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Effective Column Length given Allowable Axial Compression Stress Formula

GoEffective Column Length given Allowable Axial Compression Stress, SL Ratio Greater than 160 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 eff = (\frac{(\frac{F yw}{f s \cdot F a}) - 1}{0.20 \cdot ((\sqrt{f s \cdot \frac{P compressive}{4 \cdot ε column}}))}) \cdot r least

L_eff - Effective Column Length?F_yw - Specified minimum yield stress for column?f_s - Factor of Safety?F_a - Allowable compression stress?P_compressive - Column Compressive load?ε_column - Modulus of Elasticity Column?r_least - Least Radius of Gyration Column?

Effective Column Length given Allowable Axial Compression Stress Example

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Here is how the Effective Column Length given Allowable Axial Compression Stress equation looks like with Values.

Here is how the Effective Column Length given Allowable Axial Compression Stress equation looks like with Units.

Here is how the Effective Column Length given Allowable Axial Compression Stress equation looks like.

-41254.1898 = (\frac{(\frac{2.7}{2.8 \cdot 10}) - 1}{0.20 \cdot ((\sqrt{2.8 \cdot \frac{0.4}{4 \cdot 10.56}}))}) \cdot 47.02

-41254.1898mm = (\frac{(\frac{2.7MPa}{2.8 \cdot 10MPa}) - 1}{0.20 \cdot ((\sqrt{2.8 \cdot \frac{0.4kN}{4 \cdot 10.56MPa}}))}) \cdot 47.02mm

-41254.1898 = (\frac{(\frac{2.7}{2.8 \cdot 10}) - 1}{0.20 \cdot ((\sqrt{2.8 \cdot \frac{0.4}{4 \cdot 10.56}}))}) \cdot 47.02

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Effective Column Length given Allowable Axial Compression Stress Solution

Follow our step by step solution on how to calculate Effective Column Length given Allowable Axial Compression Stress?

FIRST Step Consider the formula

L eff = (\frac{(\frac{F yw}{f s \cdot F a}) - 1}{0.20 \cdot ((\sqrt{f s \cdot \frac{P compressive}{4 \cdot ε column}}))}) \cdot r least

Next Step Substitute values of Variables

∴

L eff = (\frac{(\frac{2.7MPa}{2.8 \cdot 10MPa}) - 1}{0.20 \cdot ((\sqrt{2.8 \cdot \frac{0.4kN}{4 \cdot 10.56MPa}}))}) \cdot 47.02mm

Next Step Convert Units

∴

L eff = (\frac{(\frac{2.7E+6Pa}{2.8 \cdot 1E+7Pa}) - 1}{0.20 \cdot ((\sqrt{2.8 \cdot \frac{400N}{4 \cdot 1.1E+7Pa}}))}) \cdot 0.047m

Next Step Prepare to Evaluate

∴

L eff = (\frac{(\frac{2.7E+6}{2.8 \cdot 1E+7}) - 1}{0.20 \cdot ((\sqrt{2.8 \cdot \frac{400}{4 \cdot 1.1E+7}}))}) \cdot 0.047

Next Step Evaluate

∴

L eff = -41.2541898052361m

Next Step Convert to Output's Unit

∴

L eff = -41254.1898052361mm

LAST Step Rounding Answer

∴

L eff = -41254.1898mm

Effective Column Length given Allowable Axial Compression Stress 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_eff

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Effective Column Length

Specified minimum yield stress for column

Specified minimum yield stress for column represents the minimum tensile stress or yield stress required by the flexural member, say, web.

Symbol: F_yw

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Specified minimum yield stress for column

Factor of Safety

Factor of Safety expresses how much stronger a system is than it needs to be for an intended load.

Symbol: f_s

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Factor of Safety

Allowable compression stress

Allowable compression stress is the maximum stress (tensile, compressive or bending) that is allowed to be applied on a structural material.

Symbol: F_a

Measurement: PressureUnit: MPa

Note: Value can be positive or negative.

Formulas to find Allowable compression stress

Column Compressive load

Column Compressive load is the load applied to a column that is compressive in nature.

Symbol: P_compressive

Measurement: ForceUnit: kN

Note: Value should be greater than 0.

Formulas to find Column Compressive load

Modulus of Elasticity Column

Modulus of Elasticity 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 Column

Least Radius of Gyration Column

Least Radius of Gyration Column is the smallest value of the radius of gyration is used for structural calculations.

Symbol: r_least

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Least Radius of Gyration Column

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)

Other Formulas to find Effective Column Length

Go Effective Column Length given Allowable Axial Compression Stress, SL Ratio Greater than 160

L eff = 1.2 - (\frac{F a}{σ c'}) \cdot (800 \cdot r least)

Other formulas in Formula By I.S. Code For Mild Steel category

Go Allowable Axial Compression Stress for Slenderness Ratio 0 to 160

F a = \frac{\frac{F yw}{f s}}{1 + (0.20 \cdot ((\frac{EAR}{r least}) \cdot (\sqrt{f s \cdot \frac{P compressive}{4 \cdot ε column}})))}

Go Minimum Yield Stress for Allowable Axial Compression Stress for Slenderness Ratio between 0 to 160

F yw = F a \cdot (1 + (0.20 \cdot ((\frac{EAR}{r least}) \cdot (\sqrt{f s \cdot \frac{P compressive}{4 \cdot ε column}})))) \cdot f s

How to Evaluate Effective Column Length given Allowable Axial Compression Stress?

Effective Column Length given Allowable Axial Compression Stress evaluator uses Effective Column Length = (((Specified minimum yield stress for column/(Factor of Safety*Allowable compression stress))-1)/(0.20*((sqrt(Factor of Safety*Column Compressive load/(4*Modulus of Elasticity Column))))))*Least Radius of Gyration Column to evaluate the Effective Column Length, Effective Column Length given Allowable Axial Compression Stress formula is defined as a measure of the effective length of a column in a structure, considering the allowable axial compression stress, yield strength, and other factors, to ensure the stability and safety of the structure under various loads. Effective Column Length is denoted by L_eff symbol.

How to evaluate Effective Column Length given Allowable Axial Compression Stress using this online evaluator? To use this online evaluator for Effective Column Length given Allowable Axial Compression Stress, enter Specified minimum yield stress for column (F_yw), Factor of Safety (f_s), Allowable compression stress (F_a), Column Compressive load (P_compressive), Modulus of Elasticity Column (ε_column) & Least Radius of Gyration Column (r_least) and hit the calculate button.

FAQs on Effective Column Length given Allowable Axial Compression Stress

What is the formula to find Effective Column Length given Allowable Axial Compression Stress?

The formula of Effective Column Length given Allowable Axial Compression Stress is expressed as Effective Column Length = (((Specified minimum yield stress for column/(Factor of Safety*Allowable compression stress))-1)/(0.20*((sqrt(Factor of Safety*Column Compressive load/(4*Modulus of Elasticity Column))))))*Least Radius of Gyration Column. Here is an example- -41254189.805236 = (((2700000/(2.8*10000000))-1)/(0.20*((sqrt(2.8*400/(4*10560000))))))*0.04702.

How to calculate Effective Column Length given Allowable Axial Compression Stress?

With Specified minimum yield stress for column (F_yw), Factor of Safety (f_s), Allowable compression stress (F_a), Column Compressive load (P_compressive), Modulus of Elasticity Column (ε_column) & Least Radius of Gyration Column (r_least) we can find Effective Column Length given Allowable Axial Compression Stress using the formula - Effective Column Length = (((Specified minimum yield stress for column/(Factor of Safety*Allowable compression stress))-1)/(0.20*((sqrt(Factor of Safety*Column Compressive load/(4*Modulus of Elasticity Column))))))*Least Radius of Gyration Column. This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Effective Column Length?

Here are the different ways to Calculate Effective Column Length-

Effective Column Length=1.2-(Allowable compression stress/Value obtained from Secant Formula)*(800*Least Radius of Gyration Column)

Can the Effective Column Length given Allowable Axial Compression Stress be negative?

Yes, the Effective Column Length given Allowable Axial Compression Stress, measured in Length can be negative.

Which unit is used to measure Effective Column Length given Allowable Axial Compression Stress?

Effective Column Length given Allowable Axial Compression Stress is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Effective Column Length given Allowable Axial Compression Stress can be measured.

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Effective Column Length given Allowable Axial Compression Stress Formula

​GoEffective Column Length given Allowable Axial Compression Stress, SL Ratio Greater than 160 Formula

Effective Column Length given Allowable Axial Compression Stress Example

Effective Column Length given Allowable Axial Compression Stress Solution

Effective Column Length given Allowable Axial Compression Stress Formula Elements

Other Formulas to find Effective Column Length

Other formulas in Formula By I.S. Code For Mild Steel category

How to Evaluate Effective Column Length given Allowable Axial Compression Stress?

FAQs on Effective Column Length given Allowable Axial Compression Stress

Variable Name

GoEffective Column Length given Allowable Axial Compression Stress, SL Ratio Greater than 160 Formula