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

GoEffective Column Length given Allowable Axial Compression Stress 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 = 1.2 - (\frac{F a}{σ c'}) \cdot (800 \cdot r least)

L_eff - Effective Column Length?F_a - Allowable compression stress?σ_c' - Value obtained from Secant Formula?r_least - Least Radius of Gyration Column?

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

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Here is how the Effective Column Length given Allowable Axial Compression Stress, SL Ratio Greater than 160 equation looks like with Values.

Here is how the Effective Column Length given Allowable Axial Compression Stress, SL Ratio Greater than 160 equation looks like with Units.

Here is how the Effective Column Length given Allowable Axial Compression Stress, SL Ratio Greater than 160 equation looks like.

260.1874 = 1.2 - (\frac{10}{400.25}) \cdot (800 \cdot 47.02)

260.1874mm = 1.2 - (\frac{10MPa}{400.25MPa}) \cdot (800 \cdot 47.02mm)

260.1874 = 1.2 - (\frac{10}{400.25}) \cdot (800 \cdot 47.02)

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

Follow our step by step solution on how to calculate Effective Column Length given Allowable Axial Compression Stress, SL Ratio Greater than 160?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

L eff = 1.2 - (\frac{10MPa}{400.25MPa}) \cdot (800 \cdot 47.02mm)

Next Step Convert Units

∴

L eff = 1.2 - (\frac{1E+7Pa}{4E+8Pa}) \cdot (800 \cdot 0.047m)

Next Step Prepare to Evaluate

∴

L eff = 1.2 - (\frac{1E+7}{4E+8}) \cdot (800 \cdot 0.047)

Next Step Evaluate

∴

L eff = 0.260187382885696m

Next Step Convert to Output's Unit

∴

L eff = 260.187382885696mm

LAST Step Rounding Answer

∴

L eff = 260.1874mm

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

Variables

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

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

Value obtained from Secant Formula

Value obtained from secant formula is the stress value on the column of mild steel.

Symbol: σ_c'

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Value obtained from Secant Formula

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

Other Formulas to find Effective Column Length

Go Effective Column Length given Allowable Axial Compression Stress

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

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

Go Allowable Axial Compression Stress for Slenderness Ratio greater than 160

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

Go Least Radius of Gyration given Allowable Axial Compression Stress

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

How to Evaluate Effective Column Length given Allowable Axial Compression Stress, SL Ratio Greater than 160?

Effective Column Length given Allowable Axial Compression Stress, SL Ratio Greater than 160 evaluator uses Effective Column Length = 1.2-(Allowable compression stress/Value obtained from Secant Formula)*(800*Least Radius of Gyration Column) to evaluate the Effective Column Length, Effective Column Length given Allowable Axial Compression Stress, SL Ratio Greater than 160 formula is defined as a measure of the effective length of a column in a structural system, considering the allowable axial compression stress and the slenderness ratio, which is essential in designing stable and safe structures, particularly in mild steel construction. Effective Column Length is denoted by L_eff symbol.

How to evaluate Effective Column Length given Allowable Axial Compression Stress, SL Ratio Greater than 160 using this online evaluator? To use this online evaluator for Effective Column Length given Allowable Axial Compression Stress, SL Ratio Greater than 160, enter Allowable compression stress (F_a), Value obtained from Secant Formula (σ_c') & Least Radius of Gyration Column (r_least) and hit the calculate button.

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

What is the formula to find Effective Column Length given Allowable Axial Compression Stress, SL Ratio Greater than 160?

The formula of Effective Column Length given Allowable Axial Compression Stress, SL Ratio Greater than 160 is expressed as Effective Column Length = 1.2-(Allowable compression stress/Value obtained from Secant Formula)*(800*Least Radius of Gyration Column). Here is an example- 260187.4 = 1.2-(10000000/400250000)*(800*0.04702).

How to calculate Effective Column Length given Allowable Axial Compression Stress, SL Ratio Greater than 160?

With Allowable compression stress (F_a), Value obtained from Secant Formula (σ_c') & Least Radius of Gyration Column (r_least) we can find Effective Column Length given Allowable Axial Compression Stress, SL Ratio Greater than 160 using the formula - Effective Column Length = 1.2-(Allowable compression stress/Value obtained from Secant Formula)*(800*Least Radius of Gyration Column).

What are the other ways to Calculate Effective Column Length?

Here are the different ways to Calculate Effective Column Length-

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

Can the Effective Column Length given Allowable Axial Compression Stress, SL Ratio Greater than 160 be negative?

Yes, the Effective Column Length given Allowable Axial Compression Stress, SL Ratio Greater than 160, measured in Length can be negative.

Which unit is used to measure Effective Column Length given Allowable Axial Compression Stress, SL Ratio Greater than 160?

Effective Column Length given Allowable Axial Compression Stress, SL Ratio Greater than 160 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, SL Ratio Greater than 160 can be measured.

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

​GoEffective Column Length given Allowable Axial Compression Stress Formula

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

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

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

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

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GoEffective Column Length given Allowable Axial Compression Stress Formula