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Least Radius of Gyration According to Johnson's Parabolic Formula 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{r \cdot (L eff)}{σ c - (\frac{P}{A sectional})}

r_least - Least Radius of Gyration Column?r - Johnson's formula constant?L_eff - Effective Column Length?σ_c - Compressive Yield Stress?P - Critical Load On Column?A_sectional - Column Cross Sectional Area?

Least Radius of Gyration According to Johnson's Parabolic Formula Example

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Here is how the Least Radius of Gyration According to Johnson's Parabolic Formula equation looks like with Values.

Here is how the Least Radius of Gyration According to Johnson's Parabolic Formula equation looks like with Units.

Here is how the Least Radius of Gyration According to Johnson's Parabolic Formula equation looks like.

43.2247 = \frac{6 \cdot (3000)}{420 - (\frac{5}{1.4})}

43.2247mm = \frac{6 \cdot (3000mm)}{420N/m² - (\frac{5N}{1.4m²})}

43.2247 = \frac{6 \cdot (3000)}{420 - (\frac{5}{1.4})}

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Strength of Materials » fx Least Radius of Gyration According to Johnson's Parabolic Formula

Least Radius of Gyration According to Johnson's Parabolic Formula Solution

Follow our step by step solution on how to calculate Least Radius of Gyration According to Johnson's Parabolic Formula?

FIRST Step Consider the formula

r least = \frac{r \cdot (L eff)}{σ c - (\frac{P}{A sectional})}

Next Step Substitute values of Variables

∴

r least = \frac{6 \cdot (3000mm)}{420N/m² - (\frac{5N}{1.4m²})}

Next Step Convert Units

∴

r least = \frac{6 \cdot (3m)}{420Pa - (\frac{5N}{1.4m²})}

Next Step Prepare to Evaluate

∴

r least = \frac{6 \cdot (3)}{420 - (\frac{5}{1.4})}

Next Step Evaluate

∴

r least = 0.0432246998284734m

Next Step Convert to Output's Unit

∴

r least = 43.2246998284734mm

LAST Step Rounding Answer

∴

r least = 43.2247mm

Least Radius of Gyration According to Johnson's Parabolic Formula 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

Open Variable

Johnson's formula constant

Johnson's formula constant is defined as the constant that depends on the material of column.

Symbol: r

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Johnson's formula constant

Open Variable

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 should be greater than 0.

Formulas to find Effective Column Length

Open Variable

Compressive Yield Stress

Compressive yield stress is stress which causes a material to exhibit a specified deformation. Usually determined from the stress-strain diagram obtained in a compression test.

Symbol: σ_c

Measurement: PressureUnit: N/m²

Note: Value should be greater than 0.

Formulas to find Compressive Yield Stress

Open Variable

Critical Load On Column

Critical Load On Column is the greatest load that will not cause lateral deflection (buckling).

Symbol: P

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Critical Load On Column

Open Variable

Column Cross Sectional Area

Column Cross Sectional Area is the area of a two-dimensional shape that is obtained when a three dimensional shape is sliced perpendicular to some specified axis at a point.

Symbol: A_sectional

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Column Cross Sectional Area

Open Variable

Other formulas in Johnson's Parabolic Formula category

Go Critical Load on Column According to Johnson's Parabolic Formula

P = (σ c - (r \cdot (\frac{L eff}{r least}))) \cdot A sectional

Go Compressive Yield Stress According to Johnson's Parabolic Formula

σ c = \frac{P}{A sectional} + r \cdot \frac{L eff}{r least}

Go Cross-Sectional Area of Column According to Johnson's Parabolic Formula

A sectional = \frac{P}{σ c - (r \cdot (\frac{L eff}{r least}))}

Go Constant Depending on Material of Column According to Johnson's Parabolic Formula

r = \frac{σ c - (\frac{P}{A sectional})}{\frac{L eff}{r least}}

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How to Evaluate Least Radius of Gyration According to Johnson's Parabolic Formula?

Least Radius of Gyration According to Johnson's Parabolic Formula evaluator uses Least Radius of Gyration Column = (Johnson's formula constant*(Effective Column Length))/(Compressive Yield Stress-(Critical Load On Column/Column Cross Sectional Area)) to evaluate the Least Radius of Gyration Column, Least Radius of Gyration According to Johnson's Parabolic Formula is a measure of the minimum radius of gyration of a column, which is a critical parameter in structural analysis, used to determine the stability and strength of a column under compressive loads. Least Radius of Gyration Column is denoted by r_least symbol.

How to evaluate Least Radius of Gyration According to Johnson's Parabolic Formula using this online evaluator? To use this online evaluator for Least Radius of Gyration According to Johnson's Parabolic Formula, enter Johnson's formula constant (r), Effective Column Length (L_eff), Compressive Yield Stress (σ_c), Critical Load On Column (P) & Column Cross Sectional Area (A_sectional) and hit the calculate button.

FAQs on Least Radius of Gyration According to Johnson's Parabolic Formula

What is the formula to find Least Radius of Gyration According to Johnson's Parabolic Formula?

The formula of Least Radius of Gyration According to Johnson's Parabolic Formula is expressed as Least Radius of Gyration Column = (Johnson's formula constant*(Effective Column Length))/(Compressive Yield Stress-(Critical Load On Column/Column Cross Sectional Area)). Here is an example- 43224.7 = (6*(3))/(420-(5/1.4)).

How to calculate Least Radius of Gyration According to Johnson's Parabolic Formula?

With Johnson's formula constant (r), Effective Column Length (L_eff), Compressive Yield Stress (σ_c), Critical Load On Column (P) & Column Cross Sectional Area (A_sectional) we can find Least Radius of Gyration According to Johnson's Parabolic Formula using the formula - Least Radius of Gyration Column = (Johnson's formula constant*(Effective Column Length))/(Compressive Yield Stress-(Critical Load On Column/Column Cross Sectional Area)).

Can the Least Radius of Gyration According to Johnson's Parabolic Formula be negative?

Yes, the Least Radius of Gyration According to Johnson's Parabolic Formula, measured in Length can be negative.

Which unit is used to measure Least Radius of Gyration According to Johnson's Parabolic Formula?

Least Radius of Gyration According to Johnson's Parabolic Formula 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 According to Johnson's Parabolic Formula can be measured.

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