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

GoLeast Radius of Gyration given Allowable Axial Compression Stress 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 = \frac{L eff}{800 \cdot (1.2 - (\frac{F a}{σ c'}))}

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

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

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Here is how the Least Radius of Gyration given Allowable Axial Compression Stress Slenderness Ratio More 160 equation looks like with Values.

Here is how the Least Radius of Gyration given Allowable Axial Compression Stress Slenderness Ratio More 160 equation looks like with Units.

Here is how the Least Radius of Gyration given Allowable Axial Compression Stress Slenderness Ratio More 160 equation looks like.

3.1914 = \frac{3000}{800 \cdot (1.2 - (\frac{10}{400.25}))}

3.1914mm = \frac{3000mm}{800 \cdot (1.2 - (\frac{10MPa}{400.25MPa}))}

3.1914 = \frac{3000}{800 \cdot (1.2 - (\frac{10}{400.25}))}

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

Follow our step by step solution on how to calculate Least Radius of Gyration given Allowable Axial Compression Stress Slenderness Ratio More 160?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

r least = \frac{3000mm}{800 \cdot (1.2 - (\frac{10MPa}{400.25MPa}))}

Next Step Convert Units

∴

r least = \frac{3m}{800 \cdot (1.2 - (\frac{1E+7Pa}{4E+8Pa}))}

Next Step Prepare to Evaluate

∴

r least = \frac{3}{800 \cdot (1.2 - (\frac{1E+7}{4E+8}))}

Next Step Evaluate

∴

r least = 0.00319144694875611m

Next Step Convert to Output's Unit

∴

r least = 3.19144694875611mm

LAST Step Rounding Answer

∴

r least = 3.1914mm

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

Variables

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 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

Other Formulas to find Least Radius of Gyration Column

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}})))

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

Least Radius of Gyration given Allowable Axial Compression Stress Slenderness Ratio More 160 evaluator uses Least Radius of Gyration Column = Effective Column Length/(800*(1.2-(Allowable compression stress/Value obtained from Secant Formula))) to evaluate the Least Radius of Gyration Column, Least Radius of Gyration given Allowable Axial Compression Stress Slenderness Ratio More 160 formula is defined as the minimum radius of gyration of a column that can withstand axial compression stress without buckling, considering the slenderness ratio and allowable stress values for mild steel as per I.S. Code. Least Radius of Gyration Column is denoted by r_least symbol.

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

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

What is the formula to find Least Radius of Gyration given Allowable Axial Compression Stress Slenderness Ratio More 160?

The formula of Least Radius of Gyration given Allowable Axial Compression Stress Slenderness Ratio More 160 is expressed as Least Radius of Gyration Column = Effective Column Length/(800*(1.2-(Allowable compression stress/Value obtained from Secant Formula))). Here is an example- 3191.447 = 3/(800*(1.2-(10000000/400250000))).

How to calculate Least Radius of Gyration given Allowable Axial Compression Stress Slenderness Ratio More 160?

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

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=(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)))))

Can the Least Radius of Gyration given Allowable Axial Compression Stress Slenderness Ratio More 160 be negative?

Yes, the Least Radius of Gyration given Allowable Axial Compression Stress Slenderness Ratio More 160, measured in Length can be negative.

Which unit is used to measure Least Radius of Gyration given Allowable Axial Compression Stress Slenderness Ratio More 160?

Least Radius of Gyration given Allowable Axial Compression Stress Slenderness Ratio More 160 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 Slenderness Ratio More 160 can be measured.

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

​GoLeast Radius of Gyration given Allowable Axial Compression Stress Formula

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

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

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

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

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GoLeast Radius of Gyration given Allowable Axial Compression Stress Formula