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

✖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.ⓘ Compressive Yield Stress [σ_c]			+10% -10%
✖Critical Load On Column is the greatest load that will not cause lateral deflection (buckling).ⓘ Critical Load On Column [P]			+10% -10%
✖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.ⓘ Column Cross Sectional Area [A_sectional]			+10% -10%
✖Johnson's formula constant is defined as the constant that depends on the material of column.ⓘ Johnson's formula constant [r]			+10% -10%
✖Least Radius of Gyration Column is the smallest value of the radius of gyration is used for structural calculations.ⓘ Least Radius of Gyration Column [r_least]			+10% -10%

✖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.ⓘ Effective Length of Column According to Johnson's Parabolic Formula [L_eff]

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Formula

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Effective Length of Column According to Johnson's Parabolic Formula

Formula

`"L"_{"eff"} = ("σ"_{"c"}-("P"/"A"_{"sectional"}))/("r"*(1/"r"_{"least"}))`

Example

`"3263.412mm"=("420N/m²"-("5N"/"1.4m²"))/("6"*(1/"47.02mm"))`

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

STEP 0: Pre-Calculation Summary

Formula Used

Effective Column Length = (Compressive Yield Stress-(Critical Load On Column/Column Cross Sectional Area))/(Johnson's formula constant*(1/Least Radius of Gyration Column))
L_eff = (σ_c-(P/A_sectional))/(r*(1/r_least))
This formula uses 6 Variables

Variables Used

Effective Column Length - (Measured in Meter) - 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.
Compressive Yield Stress - (Measured in Pascal) - 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.
Critical Load On Column - (Measured in Newton) - Critical Load On Column is the greatest load that will not cause lateral deflection (buckling).
Column Cross Sectional Area - (Measured in Square Meter) - 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.
Johnson's formula constant - Johnson's formula constant is defined as the constant that depends on the material of column.
Least Radius of Gyration Column - (Measured in Meter) - Least Radius of Gyration Column is the smallest value of the radius of gyration is used for structural calculations.

STEP 1: Convert Input(s) to Base Unit

Compressive Yield Stress: 420 Newton per Square Meter --> 420 Pascal (Check conversion here)
Critical Load On Column: 5 Newton --> 5 Newton No Conversion Required
Column Cross Sectional Area: 1.4 Square Meter --> 1.4 Square Meter No Conversion Required
Johnson's formula constant: 6 --> No Conversion Required
Least Radius of Gyration Column: 47.02 Millimeter --> 0.04702 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L_eff = (σ_c-(P/A_sectional))/(r*(1/r_least)) --> (420-(5/1.4))/(6*(1/0.04702))

Evaluating ... ...

L_eff = 3.26341190476191

STEP 3: Convert Result to Output's Unit

3.26341190476191 Meter -->3263.41190476191 Millimeter (Check conversion here)

FINAL ANSWER

3263.41190476191 ≈ 3263.412 Millimeter <-- Effective Column Length

(Calculation completed in 00.004 seconds)

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National Institute Of Technology (NIT), Hamirpur

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Birsa Institute of Technology (BIT), Sindri

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< 11 Johnson's Parabolic Formula Calculators

Effective Length of Column According to Johnson's Parabolic Formula

Go Effective Column Length = (Compressive Yield Stress-(Critical Load On Column/Column Cross Sectional Area))/(Johnson's formula constant*(1/Least Radius of Gyration Column))

Least Radius of Gyration According to Johnson's Parabolic Formula

Go Least Radius of Gyration Column = (Johnson's formula constant*(Effective Column Length))/(Compressive Yield Stress-(Critical Load On Column/Column Cross Sectional Area))

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

Go Johnson's formula constant = (Compressive Yield Stress-(Critical Load On Column/Column Cross Sectional Area))/(Effective Column Length/Least Radius of Gyration Column)

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

Go Column Cross Sectional Area = Critical Load On Column/(Compressive Yield Stress-(Johnson's formula constant*(Effective Column Length/Least Radius of Gyration Column)))

Critical Load on Column According to Johnson's Parabolic Formula

Go Critical Load On Column = (Compressive Yield Stress-(Johnson's formula constant*(Effective Column Length/Least Radius of Gyration Column)))*Column Cross Sectional Area

Compressive Yield Stress According to Johnson's Parabolic Formula

Go Compressive Yield Stress = Critical Load On Column/Column Cross Sectional Area+Johnson's formula constant*Effective Column Length/Least Radius of Gyration Column

Cross-Sectional Area According to Johnson's Parabolic Formula given Slenderness Ratio

Go Column Cross Sectional Area = Critical Load On Column/(Compressive Yield Stress-(Johnson's formula constant*(Slenderness Ratio)))

Constant Depending on Material of Column According to Terms Slenderness Ratio

Go Johnson's formula constant = (Compressive Yield Stress-(Critical Load On Column/Column Cross Sectional Area))/(Slenderness Ratio)

Slenderness Ratio According to Johnson's Parabolic Formula

Go Slenderness Ratio = (Compressive Yield Stress-(Critical Load On Column/Column Cross Sectional Area))/(Johnson's formula constant)

Critical Load on Column According to Johnson's Parabolic Formula given Slenderness Ratio

Go Critical Load On Column = (Compressive Yield Stress-(Johnson's formula constant*Slenderness Ratio))*Column Cross Sectional Area

Compressive Yield Stress According to Johnson's Parabolic Formula given Slenderness Ratio

Go Compressive Yield Stress = Critical Load On Column/Column Cross Sectional Area+Johnson's formula constant*Slenderness Ratio

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

What is slenderness ratio in column?

The slenderness ratio of a reinforced concrete (RC) column is the ratio between the length of the column, its lateral dimensions, and end fixity. The slenderness ratio is calculated by dividing the column length by its radius of gyration. The slenderness ratio differentiates the short column from the long or slender column.

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

Effective Length of Column According to Johnson's Parabolic Formula calculator 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 calculate the Effective Column Length, The Effective length of column according to Johnson's parabolic formula formula is defined as the distance between successive inflection points or points of zero moment. Effective Column Length is denoted by L_eff symbol.

How to calculate Effective Length of Column According to Johnson's Parabolic Formula using this online calculator? To use this online calculator 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. Here is how the Effective Length of Column According to Johnson's Parabolic Formula calculation can be explained with given input values -> 3.3E+6 = (420-(5/1.4))/(6*(1/0.04702)).

FAQ

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

The Effective length of column according to Johnson's parabolic formula formula is defined as the distance between successive inflection points or points of zero moment and is represented as L_eff = (σ_c-(P/A_sectional))/(r*(1/r_least)) or Effective Column Length = (Compressive Yield Stress-(Critical Load On Column/Column Cross Sectional Area))/(Johnson's formula constant*(1/Least Radius of Gyration Column)). 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, Critical Load On Column is the greatest load that will not cause lateral deflection (buckling), 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, Johnson's formula constant is defined as the constant that depends on the material of column & Least Radius of Gyration Column is the smallest value of the radius of gyration is used for structural calculations.

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

The Effective length of column according to Johnson's parabolic formula formula is defined as the distance between successive inflection points or points of zero moment is calculated using 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 calculate Effective Length of Column According to Johnson's Parabolic Formula, you need 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). With our tool, you need to enter the respective value for Compressive Yield Stress, Critical Load On Column, Column Cross Sectional Area, Johnson's formula constant & Least Radius of Gyration Column and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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