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

✖Johnson's formula constant is defined as the constant that depends on the material of column.ⓘ Johnson's formula constant [r]			+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 Column Length [L_eff]			+10% -10%
✖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%

✖Least Radius of Gyration Column is the smallest value of the radius of gyration is used for structural calculations.ⓘ Least Radius of Gyration According to Johnson's Parabolic Formula [r_least]

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

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

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

STEP 1: Convert Input(s) to Base Unit

Johnson's formula constant: 6 --> No Conversion Required
Effective Column Length: 3000 Millimeter --> 3 Meter (Check conversion here)
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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_least = (r*(L_eff))/(σ_c-(P/A_sectional)) --> (6*(3))/(420-(5/1.4))

Evaluating ... ...

r_least = 0.0432246998284734

STEP 3: Convert Result to Output's Unit

0.0432246998284734 Meter -->43.2246998284734 Millimeter (Check conversion here)

FINAL ANSWER

43.2246998284734 ≈ 43.2247 Millimeter <-- Least Radius of Gyration Column

(Calculation completed in 00.007 seconds)

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< Johnson's Parabolic Formula Calculators

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

LaTeX 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

LaTeX 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

LaTeX 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

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

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

LaTeX Go

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

Least Radius of Gyration According to Johnson's Parabolic Formula calculator 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 calculate 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 calculate Least Radius of Gyration According to Johnson's Parabolic Formula using this online calculator? To use this online calculator 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. Here is how the Least Radius of Gyration According to Johnson's Parabolic Formula calculation can be explained with given input values -> 43224.7 = (6*(3))/(420-(5/1.4)).

FAQ

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

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 and is represented as r_least = (r*(L_eff))/(σ_c-(P/A_sectional)) or Least Radius of Gyration Column = (Johnson's formula constant*(Effective Column Length))/(Compressive Yield Stress-(Critical Load On Column/Column Cross Sectional Area)). Johnson's formula constant is defined as the constant that depends on the material of column, 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 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.

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

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 is calculated using Least Radius of Gyration Column = (Johnson's formula constant*(Effective Column Length))/(Compressive Yield Stress-(Critical Load On Column/Column Cross Sectional Area)). To calculate Least Radius of Gyration According to Johnson's Parabolic Formula, you need 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). With our tool, you need to enter the respective value for Johnson's formula constant, Effective Column Length, Compressive Yield Stress, Critical Load On Column & Column Cross Sectional Area 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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