Effective Length of Column given Crippling Load and Rankine's Constant Calculator

✖Column Crushing Stress is a special type of localized compressive stress which occurs at the surface of contact of two members that are relatively at rest.ⓘ Column Crushing Stress [σ_c]			+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]			+10% -10%
✖Crippling Load is the load over which a column prefers to deform laterally rather than compressing itself.ⓘ Crippling Load [P]			+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%
✖Rankine's Constant is the constant of Rankine's empirical formula.ⓘ Rankine's Constant [α]			+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 given Crippling Load and Rankine's Constant [L_eff]

⎘ Copy

👎

Formula

LaTeX

Reset

👍

Download Euler and Rankine's Theory Formulas PDF PDF Image

Effective Length of Column given Crippling Load and Rankine's Constant Solution

STEP 0: Pre-Calculation Summary

Formula Used

Effective Column Length = sqrt((Column Crushing Stress*Column Cross Sectional Area/Crippling Load-1)*(Least Radius of Gyration Column^2)/Rankine's Constant)
L_eff = sqrt((σ_c*A/P-1)*(r_least^2)/α)
This formula uses 1 Functions, 6 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

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.
Column Crushing Stress - (Measured in Pascal) - Column Crushing Stress is a special type of localized compressive stress which occurs at the surface of contact of two members that are relatively at rest.
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.
Crippling Load - (Measured in Newton) - Crippling Load is the load over which a column prefers to deform laterally rather than compressing itself.
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.
Rankine's Constant - Rankine's Constant is the constant of Rankine's empirical formula.

STEP 1: Convert Input(s) to Base Unit

Column Crushing Stress: 750 Megapascal --> 750000000 Pascal (Check conversion here)
Column Cross Sectional Area: 2000 Square Millimeter --> 0.002 Square Meter (Check conversion here)
Crippling Load: 588.9524 Kilonewton --> 588952.4 Newton (Check conversion here)
Least Radius of Gyration Column: 47.02 Millimeter --> 0.04702 Meter (Check conversion here)
Rankine's Constant: 0.00038 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L_eff = sqrt((σ_c*A/P-1)*(r_least^2)/α) --> sqrt((750000000*0.002/588952.4-1)*(0.04702^2)/0.00038)

Evaluating ... ...

L_eff = 3.00000005533691

STEP 3: Convert Result to Output's Unit

3.00000005533691 Meter -->3000.00005533691 Millimeter (Check conversion here)

FINAL ANSWER

3000.00005533691 ≈ 3000 Millimeter <-- Effective Column Length

(Calculation completed in 00.004 seconds)

You are here -

Home » Physics » Strength of Materials » Column And Struts » Mechanical » Euler and Rankine's Theory » Effective Length of Column given Crippling Load and Rankine's Constant

Credits

Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

Anshika Arya has created this Calculator and 2000+ more calculators!

Verified by Payal Priya

Birsa Institute of Technology (BIT), Sindri

Payal Priya has verified this Calculator and 1900+ more calculators!

< Euler and Rankine's Theory Calculators

Crushing Load by Rankine's Formula

LaTeX Go Crushing Load = (Rankine’s Critical Load*Euler’s Buckling Load)/(Euler’s Buckling Load-Rankine’s Critical Load)

Crippling Load by Euler's Formula given Crippling Load by Rankine's

LaTeX Go Euler’s Buckling Load = (Crushing Load*Rankine’s Critical Load)/(Crushing Load-Rankine’s Critical Load)

Crippling Load by Rankine's

LaTeX Go Rankine’s Critical Load = (Crushing Load*Euler’s Buckling Load)/(Crushing Load+Euler’s Buckling Load)

Crushing Load given Ultimate Crushing Stress

LaTeX Go Crushing Load = Column Crushing Stress*Column Cross Sectional Area

< Rankine's Formula Calculators

Cross-Sectional Area of Column given Crippling Load and Rankine's Constant

LaTeX Go Column Cross Sectional Area = (Crippling Load*(1+Rankine's Constant*(Effective Column Length/Least Radius of Gyration Column)^2))/Column Crushing Stress

Crippling Load given Rankine's Constant

LaTeX Go Crippling Load = (Column Crushing Stress*Column Cross Sectional Area)/(1+Rankine's Constant*(Effective Column Length/Least Radius of Gyration Column)^2)

Crippling Load by Rankine's

LaTeX Go Rankine’s Critical Load = (Crushing Load*Euler’s Buckling Load)/(Crushing Load+Euler’s Buckling Load)

Cross-Sectional Area of Column given Crushing Load

LaTeX Go Column Cross Sectional Area = Crushing Load/Column Crushing Stress

Effective Length of Column given Crippling Load and Rankine's Constant Formula

LaTeX Go

Effective Column Length = sqrt((Column Crushing Stress*Column Cross Sectional Area/Crippling Load-1)*(Least Radius of Gyration Column^2)/Rankine's Constant)
L_eff = sqrt((σ_c*A/P-1)*(r_least^2)/α)

What is Effective Length of Column?

The Effective Length of a Column is the length between points of inflection (zero bending moment) in a buckling column. It represents the length of an equivalent pinned-pinned column that would buckle in the same manner as the actual column, taking into account the column's end support conditions.

How to Calculate Effective Length of Column given Crippling Load and Rankine's Constant?

Effective Length of Column given Crippling Load and Rankine's Constant calculator uses Effective Column Length = sqrt((Column Crushing Stress*Column Cross Sectional Area/Crippling Load-1)*(Least Radius of Gyration Column^2)/Rankine's Constant) to calculate the Effective Column Length, The Effective Length of Column given Crippling Load and Rankine's Constant formula is defined as a measure of the reduced length of a column that takes into account the crippling load and Rankine's constant, providing a more accurate representation of the column's behavior under compressive loads in structural analysis. Effective Column Length is denoted by L_eff symbol.

How to calculate Effective Length of Column given Crippling Load and Rankine's Constant using this online calculator? To use this online calculator for Effective Length of Column given Crippling Load and Rankine's Constant, enter Column Crushing Stress (σ_c), Column Cross Sectional Area (A), Crippling Load (P), Least Radius of Gyration Column (r_least) & Rankine's Constant (α) and hit the calculate button. Here is how the Effective Length of Column given Crippling Load and Rankine's Constant calculation can be explained with given input values -> 3E+6 = sqrt((750000000*0.002/588952.4-1)*(0.04702^2)/0.00038).

FAQ

What is Effective Length of Column given Crippling Load and Rankine's Constant?

The Effective Length of Column given Crippling Load and Rankine's Constant formula is defined as a measure of the reduced length of a column that takes into account the crippling load and Rankine's constant, providing a more accurate representation of the column's behavior under compressive loads in structural analysis and is represented as L_eff = sqrt((σ_c*A/P-1)*(r_least^2)/α) or Effective Column Length = sqrt((Column Crushing Stress*Column Cross Sectional Area/Crippling Load-1)*(Least Radius of Gyration Column^2)/Rankine's Constant). Column Crushing Stress is a special type of localized compressive stress which occurs at the surface of contact of two members that are relatively at rest, 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, Crippling Load is the load over which a column prefers to deform laterally rather than compressing itself, Least Radius of Gyration Column is the smallest value of the radius of gyration is used for structural calculations & Rankine's Constant is the constant of Rankine's empirical formula.

How to calculate Effective Length of Column given Crippling Load and Rankine's Constant?

The Effective Length of Column given Crippling Load and Rankine's Constant formula is defined as a measure of the reduced length of a column that takes into account the crippling load and Rankine's constant, providing a more accurate representation of the column's behavior under compressive loads in structural analysis is calculated using Effective Column Length = sqrt((Column Crushing Stress*Column Cross Sectional Area/Crippling Load-1)*(Least Radius of Gyration Column^2)/Rankine's Constant). To calculate Effective Length of Column given Crippling Load and Rankine's Constant, you need Column Crushing Stress (σ_c), Column Cross Sectional Area (A), Crippling Load (P), Least Radius of Gyration Column (r_least) & Rankine's Constant (α). With our tool, you need to enter the respective value for Column Crushing Stress, Column Cross Sectional Area, Crippling Load, Least Radius of Gyration Column & Rankine's Constant and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Effective Column Length?

In this formula, Effective Column Length uses Column Crushing Stress, Column Cross Sectional Area, Crippling Load, Least Radius of Gyration Column & Rankine's Constant. We can use 1 other way(s) to calculate the same, which is/are as follows -

Effective Column Length = sqrt((pi^2*Modulus of Elasticity Column*Moment of Inertia Column)/(Euler’s Buckling Load))

Home

FREE PDFs

🔍 Search