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Effective Length of Column According to Johnson's Parabolic Formula 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 = \frac{σ c - (\frac{P}{A sectional})}{r \cdot (\frac{1}{r least})}

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

Effective Length of Column According to Johnson's Parabolic Formula Example

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Here is how the Effective Length of Column According to Johnson's Parabolic Formula equation looks like with Values.

Here is how the Effective Length of Column According to Johnson's Parabolic Formula equation looks like with Units.

Here is how the Effective Length of Column According to Johnson's Parabolic Formula equation looks like.

3263.4119 = \frac{420 - (\frac{5}{1.4})}{6 \cdot (\frac{1}{47.02})}

3263.4119mm = \frac{420N/m² - (\frac{5N}{1.4m²})}{6 \cdot (\frac{1}{47.02mm})}

3263.4119 = \frac{420 - (\frac{5}{1.4})}{6 \cdot (\frac{1}{47.02})}

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Effective Length of Column According to Johnson's Parabolic Formula Solution

Follow our step by step solution on how to calculate Effective Length of Column According to Johnson's Parabolic Formula?

FIRST Step Consider the formula

L eff = \frac{σ c - (\frac{P}{A sectional})}{r \cdot (\frac{1}{r least})}

Next Step Substitute values of Variables

∴

L eff = \frac{420N/m² - (\frac{5N}{1.4m²})}{6 \cdot (\frac{1}{47.02mm})}

Next Step Convert Units

∴

L eff = \frac{420Pa - (\frac{5N}{1.4m²})}{6 \cdot (\frac{1}{0.047m})}

Next Step Prepare to Evaluate

∴

L eff = \frac{420 - (\frac{5}{1.4})}{6 \cdot (\frac{1}{0.047})}

Next Step Evaluate

∴

L eff = 3.26341190476191m

Next Step Convert to Output's Unit

∴

L eff = 3263.41190476191mm

LAST Step Rounding Answer

∴

L eff = 3263.4119mm

Effective Length of Column According to Johnson's Parabolic Formula 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 should be greater than 0.

Formulas to find Effective Column Length

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

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

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

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

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 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}}

How to Evaluate Effective Length of Column According to Johnson's Parabolic Formula?

Effective Length of Column According to Johnson's Parabolic Formula evaluator uses Effective Column Length = (Compressive Yield Stress-(Critical Load On Column/Column Cross Sectional Area))/(Johnson's formula constant*(1/Least Radius of Gyration Column)) to evaluate the Effective Column Length, Effective Length of Column According to Johnson's Parabolic Formula formula is defined as a measure of the effective length of a column in a structural system, taking into account the column's sectional area, radius, and least radius, to determine its buckling load and stability. Effective Column Length is denoted by L_eff symbol.

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

FAQs on Effective Length of Column According to Johnson's Parabolic Formula

What is the formula to find Effective Length of Column According to Johnson's Parabolic Formula?

The formula of Effective Length of Column According to Johnson's Parabolic Formula is expressed as Effective Column Length = (Compressive Yield Stress-(Critical Load On Column/Column Cross Sectional Area))/(Johnson's formula constant*(1/Least Radius of Gyration Column)). Here is an example- 3.3E+6 = (420-(5/1.4))/(6*(1/0.04702)).

How to calculate Effective Length of Column According to Johnson's Parabolic Formula?

With Compressive Yield Stress (σ_c), Critical Load On Column (P), Column Cross Sectional Area (A_sectional), Johnson's formula constant (r) & Least Radius of Gyration Column (r_least) we can find Effective Length of Column According to Johnson's Parabolic Formula using the formula - Effective Column Length = (Compressive Yield Stress-(Critical Load On Column/Column Cross Sectional Area))/(Johnson's formula constant*(1/Least Radius of Gyration Column)).

Can the Effective Length of Column According to Johnson's Parabolic Formula be negative?

No, the Effective Length of Column According to Johnson's Parabolic Formula, measured in Length cannot be negative.

Which unit is used to measure Effective Length of Column According to Johnson's Parabolic Formula?

Effective Length of Column 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 Effective Length of Column According to Johnson's Parabolic Formula can be measured.

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Effective Length of Column According to Johnson's Parabolic Formula Formula

Effective Length of Column According to Johnson's Parabolic Formula Example

Effective Length of Column According to Johnson's Parabolic Formula Solution

Effective Length of Column According to Johnson's Parabolic Formula Formula Elements

Other formulas in Johnson's Parabolic Formula category

How to Evaluate Effective Length of Column According to Johnson's Parabolic Formula?

FAQs on Effective Length of Column According to Johnson's Parabolic Formula

Variable Name