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Least Radius of Gyration given Allowable Axial Compression Stress Formula

GoLeast Radius of Gyration given Allowable Axial Compression Stress Slenderness Ratio More 160 Formula

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

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}})))

r_least - Least Radius of Gyration Column?EAR - Effective Interest Rate?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?

Least Radius of Gyration given Allowable Axial Compression Stress Example

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Here is how the Least Radius of Gyration given Allowable Axial Compression Stress equation looks like with Values.

Here is how the Least Radius of Gyration given Allowable Axial Compression Stress equation looks like with Units.

Here is how the Least Radius of Gyration given Allowable Axial Compression Stress equation looks like.

-6.8386 = (0.20 \cdot ((\frac{6}{(\frac{2.7}{2.8 \cdot 10}) - 1}) \cdot (\sqrt{2.8 \cdot \frac{0.4}{4 \cdot 10.56}})))

-6.8386mm = (0.20 \cdot ((\frac{6}{(\frac{2.7MPa}{2.8 \cdot 10MPa}) - 1}) \cdot (\sqrt{2.8 \cdot \frac{0.4kN}{4 \cdot 10.56MPa}})))

-6.8386 = (0.20 \cdot ((\frac{6}{(\frac{2.7}{2.8 \cdot 10}) - 1}) \cdot (\sqrt{2.8 \cdot \frac{0.4}{4 \cdot 10.56}})))

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Least Radius of Gyration given Allowable Axial Compression Stress Solution

Follow our step by step solution on how to calculate Least Radius of Gyration given Allowable Axial Compression Stress?

FIRST Step Consider the formula

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}})))

Next Step Substitute values of Variables

∴

r least = (0.20 \cdot ((\frac{6}{(\frac{2.7MPa}{2.8 \cdot 10MPa}) - 1}) \cdot (\sqrt{2.8 \cdot \frac{0.4kN}{4 \cdot 10.56MPa}})))

Next Step Convert Units

∴

r least = (0.20 \cdot ((\frac{6}{(\frac{2.7E+6Pa}{2.8 \cdot 1E+7Pa}) - 1}) \cdot (\sqrt{2.8 \cdot \frac{400N}{4 \cdot 1.1E+7Pa}})))

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

r least = -0.00683857812580755m

Next Step Convert to Output's Unit

∴

r least = -6.83857812580755mm

LAST Step Rounding Answer

∴

r least = -6.8386mm

Least Radius of Gyration given Allowable Axial Compression Stress Formula Elements

Variables

Functions

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

Effective Interest Rate

The effective interest rate is the true rate of interest earned.

Symbol: EAR

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Effective Interest Rate

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 to find Least Radius of Gyration Column

Go Least Radius of Gyration given Allowable Axial Compression Stress Slenderness Ratio More 160

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

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 Least Radius of Gyration given Allowable Axial Compression Stress?

Least Radius of Gyration given Allowable Axial Compression Stress evaluator uses Least Radius of Gyration Column = (0.20*((Effective Interest Rate/((Specified minimum yield stress for column/(Factor of Safety*Allowable compression stress))-1))*(sqrt(Factor of Safety*Column Compressive load/(4*Modulus of Elasticity Column))))) to evaluate the Least Radius of Gyration Column, Least Radius of Gyration given Allowable Axial Compression Stress formula is defined as a measure of the minimum radius of gyration of a column, which is a critical parameter in determining the stability of a structural member under axial compressive loads, ensuring the safety and integrity of the structure. Least Radius of Gyration Column is denoted by r_least symbol.

How to evaluate Least Radius of Gyration given Allowable Axial Compression Stress using this online evaluator? To use this online evaluator for Least Radius of Gyration given Allowable Axial Compression Stress, enter Effective Interest Rate (EAR), 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 Least Radius of Gyration given Allowable Axial Compression Stress

What is the formula to find Least Radius of Gyration given Allowable Axial Compression Stress?

The formula of Least Radius of Gyration given Allowable Axial Compression Stress is expressed as Least Radius of Gyration Column = (0.20*((Effective Interest Rate/((Specified minimum yield stress for column/(Factor of Safety*Allowable compression stress))-1))*(sqrt(Factor of Safety*Column Compressive load/(4*Modulus of Elasticity Column))))). Here is an example- -6838.578126 = (0.20*((6/((2700000/(2.8*10000000))-1))*(sqrt(2.8*400/(4*10560000))))).

How to calculate Least Radius of Gyration given Allowable Axial Compression Stress?

With Effective Interest Rate (EAR), 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 Least Radius of Gyration given Allowable Axial Compression Stress using the formula - Least Radius of Gyration Column = (0.20*((Effective Interest Rate/((Specified minimum yield stress for column/(Factor of Safety*Allowable compression stress))-1))*(sqrt(Factor of Safety*Column Compressive load/(4*Modulus of Elasticity Column))))). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Least Radius of Gyration Column?

Here are the different ways to Calculate Least Radius of Gyration Column-

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

Can the Least Radius of Gyration given Allowable Axial Compression Stress be negative?

Yes, the Least Radius of Gyration given Allowable Axial Compression Stress, measured in Length can be negative.

Which unit is used to measure Least Radius of Gyration given Allowable Axial Compression Stress?

Least Radius of Gyration 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 Least Radius of Gyration given Allowable Axial Compression Stress can be measured.

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Least Radius of Gyration given Allowable Axial Compression Stress Formula

​GoLeast Radius of Gyration given Allowable Axial Compression Stress Slenderness Ratio More 160 Formula

Least Radius of Gyration given Allowable Axial Compression Stress Example

Least Radius of Gyration given Allowable Axial Compression Stress Solution

Least Radius of Gyration given Allowable Axial Compression Stress Formula Elements

Other Formulas to find Least Radius of Gyration Column

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

How to Evaluate Least Radius of Gyration given Allowable Axial Compression Stress?

FAQs on Least Radius of Gyration given Allowable Axial Compression Stress

Variable Name

GoLeast Radius of Gyration given Allowable Axial Compression Stress Slenderness Ratio More 160 Formula