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Slenderness Ratio given Allowable Axial Compression Stress Formula

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The Slenderness ratio is the ratio of the length of a column and the least radius of gyration of its cross section. Check FAQs

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

λ - Slenderness Ratio?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?

Slenderness Ratio given Allowable Axial Compression Stress Example

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Here is how the Slenderness Ratio given Allowable Axial Compression Stress equation looks like with Values.

Here is how the Slenderness Ratio given Allowable Axial Compression Stress equation looks like with Units.

Here is how the Slenderness Ratio given Allowable Axial Compression Stress equation looks like.

-877.3754 = \frac{(\frac{2.7}{2.8 \cdot 10}) - 1}{0.20 \cdot ((\sqrt{2.8 \cdot \frac{0.4}{4 \cdot 10.56}}))}

-877.3754 = \frac{(\frac{2.7MPa}{2.8 \cdot 10MPa}) - 1}{0.20 \cdot ((\sqrt{2.8 \cdot \frac{0.4kN}{4 \cdot 10.56MPa}}))}

-877.3754 = \frac{(\frac{2.7}{2.8 \cdot 10}) - 1}{0.20 \cdot ((\sqrt{2.8 \cdot \frac{0.4}{4 \cdot 10.56}}))}

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Slenderness Ratio given Allowable Axial Compression Stress Solution

Follow our step by step solution on how to calculate Slenderness Ratio given Allowable Axial Compression Stress?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Convert Units

∴

λ = \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}}))}

Next Step Prepare to Evaluate

∴

λ = \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}}))}

Next Step Evaluate

∴

λ = -877.375368039899

LAST Step Rounding Answer

∴

λ = -877.3754

Slenderness Ratio given Allowable Axial Compression Stress Formula Elements

Variables

Functions

Slenderness Ratio

The Slenderness ratio is the ratio of the length of a column and the least radius of gyration of its cross section.

Symbol: λ

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Slenderness Ratio

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

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 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 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

How to Evaluate Slenderness Ratio given Allowable Axial Compression Stress?

Slenderness Ratio given Allowable Axial Compression Stress evaluator uses Slenderness Ratio = ((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))))) to evaluate the Slenderness Ratio, Slenderness Ratio given Allowable Axial Compression Stress formula is defined as a measure of the structural efficiency of a column, which is a critical parameter in determining the load-carrying capacity of a column under axial compression, and is used to ensure the safety and stability of structures. Slenderness Ratio is denoted by λ symbol.

How to evaluate Slenderness Ratio given Allowable Axial Compression Stress using this online evaluator? To use this online evaluator for Slenderness Ratio 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) and hit the calculate button.

FAQs on Slenderness Ratio given Allowable Axial Compression Stress

What is the formula to find Slenderness Ratio given Allowable Axial Compression Stress?

The formula of Slenderness Ratio given Allowable Axial Compression Stress is expressed as Slenderness Ratio = ((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))))). Here is an example- -877.375368 = ((2700000/(2.8*10000000))-1)/(0.20*((sqrt(2.8*400/(4*10560000))))).

How to calculate Slenderness Ratio 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) we can find Slenderness Ratio given Allowable Axial Compression Stress using the formula - Slenderness Ratio = ((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))))). This formula also uses Square Root (sqrt) function(s).

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Slenderness Ratio given Allowable Axial Compression Stress Formula

Slenderness Ratio given Allowable Axial Compression Stress Example

Slenderness Ratio given Allowable Axial Compression Stress Solution

Slenderness Ratio given Allowable Axial Compression Stress Formula Elements

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

How to Evaluate Slenderness Ratio given Allowable Axial Compression Stress?

FAQs on Slenderness Ratio given Allowable Axial Compression Stress

Variable Name