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))
Leff = (σc-(P/Asectional))/(r*(1/rleast))
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
Leff = (σc-(P/Asectional))/(r*(1/rleast)) --> (420-(5/1.4))/(6*(1/0.04702))
Evaluating ... ...
Leff = 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 00.020 seconds)

Credits

Creator Image
Created by Anshika Arya
National Institute Of Technology (NIT), Hamirpur
Anshika Arya has created this Calculator and 2000+ more calculators!
Verifier Image
Verified by Payal Priya
Birsa Institute of Technology (BIT), Sindri
Payal Priya has verified this Calculator and 1900+ more calculators!

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

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

​LaTeX ​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))
Leff = (σc-(P/Asectional))/(r*(1/rleast))

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, 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 Leff 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 c), Critical Load On Column (P), Column Cross Sectional Area (Asectional), Johnson's formula constant (r) & Least Radius of Gyration Column (rleast) 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?
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 and is represented as Leff = (σc-(P/Asectional))/(r*(1/rleast)) 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?
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 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 c), Critical Load On Column (P), Column Cross Sectional Area (Asectional), Johnson's formula constant (r) & Least Radius of Gyration Column (rleast). 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.
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!