Slenderness Ratio 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%

✖The Slenderness ratio is the ratio of the length of a column and the least radius of gyration of its cross section.ⓘ Slenderness Ratio According to Johnson's Parabolic Formula [λ]

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Formula

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Slenderness Ratio According to Johnson's Parabolic Formula

Formula

`"λ" = ("σ"_{"c"}-("P"/"A"_{"sectional"}))/("r")`

Example

`"69.40476"=("420N/m²"-("5N"/"1.4m²"))/("6")`

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Slenderness Ratio According to Johnson's Parabolic Formula Solution

STEP 0: Pre-Calculation Summary

Formula Used

Slenderness Ratio = (Compressive Yield Stress-(Critical Load On Column/Column Cross Sectional Area))/(Johnson's formula constant)
λ = (σ_c-(P/A_sectional))/(r)
This formula uses 5 Variables

Variables Used

Slenderness Ratio - The Slenderness ratio is the ratio of the length of a column and the least radius of gyration of its cross section.
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.

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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

λ = (σ_c-(P/A_sectional))/(r) --> (420-(5/1.4))/(6)

Evaluating ... ...

λ = 69.4047619047619

STEP 3: Convert Result to Output's Unit

69.4047619047619 --> No Conversion Required

FINAL ANSWER

69.4047619047619 ≈ 69.40476 <-- Slenderness Ratio

(Calculation completed in 00.020 seconds)

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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

Slenderness Ratio According to Johnson's Parabolic Formula Formula

Slenderness Ratio = (Compressive Yield Stress-(Critical Load On Column/Column Cross Sectional Area))/(Johnson's formula constant)
λ = (σ_c-(P/A_sectional))/(r)

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 Slenderness Ratio According to Johnson's Parabolic Formula?

Slenderness Ratio According to Johnson's Parabolic Formula calculator uses Slenderness Ratio = (Compressive Yield Stress-(Critical Load On Column/Column Cross Sectional Area))/(Johnson's formula constant) to calculate the Slenderness Ratio, The Slenderness ratio according to Johnson's parabolic formula formula is defined as the quotient between the height and the width of a building. In structural engineering, slenderness is used to calculate the propensity of a column to buckle. Slenderness Ratio is denoted by λ symbol.

How to calculate Slenderness Ratio According to Johnson's Parabolic Formula using this online calculator? To use this online calculator for Slenderness Ratio 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) and hit the calculate button. Here is how the Slenderness Ratio According to Johnson's Parabolic Formula calculation can be explained with given input values -> 69.40476 = (420-(5/1.4))/(6).

FAQ

What is Slenderness Ratio According to Johnson's Parabolic Formula?

The Slenderness ratio according to Johnson's parabolic formula formula is defined as the quotient between the height and the width of a building. In structural engineering, slenderness is used to calculate the propensity of a column to buckle and is represented as λ = (σ_c-(P/A_sectional))/(r) or Slenderness Ratio = (Compressive Yield Stress-(Critical Load On Column/Column Cross Sectional Area))/(Johnson's formula constant). 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.

How to calculate Slenderness Ratio According to Johnson's Parabolic Formula?

The Slenderness ratio according to Johnson's parabolic formula formula is defined as the quotient between the height and the width of a building. In structural engineering, slenderness is used to calculate the propensity of a column to buckle is calculated using Slenderness Ratio = (Compressive Yield Stress-(Critical Load On Column/Column Cross Sectional Area))/(Johnson's formula constant). To calculate Slenderness Ratio 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). 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 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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