Modulus of Elasticity of Column given Crippling Stress Solution

STEP 0: Pre-Calculation Summary
Formula Used
Modulus of Elasticity Column = (Crippling Stress*Effective Column Length^2)/(pi^2*Least Radius of Gyration Column^2)
εc = (σcrippling stress*Leff^2)/(pi^2*rL^2)
This formula uses 1 Constants, 4 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Modulus of Elasticity Column - (Measured in Pascal) - Modulus of Elasticity Column is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it.
Crippling Stress - (Measured in Pascal) - Crippling Stress is the stress in column due to crippling load.
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.
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
Crippling Stress: 0.02 Megapascal --> 20000 Pascal (Check conversion here)
Effective Column Length: 2500 Millimeter --> 2.5 Meter (Check conversion here)
Least Radius of Gyration Column: 50 Millimeter --> 0.05 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
εc = (σcrippling stress*Leff^2)/(pi^2*rL^2) --> (20000*2.5^2)/(pi^2*0.05^2)
Evaluating ... ...
εc = 5066059.18211689
STEP 3: Convert Result to Output's Unit
5066059.18211689 Pascal -->5.06605918211689 Megapascal (Check conversion here)
FINAL ANSWER
5.06605918211689 5.066059 Megapascal <-- Modulus of Elasticity Column
(Calculation completed in 00.020 seconds)

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14 Estimation of Effective Length of Columns Calculators

Radius of Gyration given Effective Length and Crippling Load
Go Least Radius of Gyration Column = sqrt((Column Crippling Load*Effective Column Length^2)/(pi^2*Modulus of Elasticity Column*Column Cross Sectional Area))
Effective Length of Column given Crippling Stress
Go Effective Column Length = sqrt((pi^2*Modulus of Elasticity Column*Least Radius of Gyration Column^2)/Crippling Stress)
Effective Length of Column given Crippling Load for any type of End Condition
Go Effective Column Length = sqrt((pi^2*Modulus of Elasticity Column*Moment of Inertia Column)/(Column Crippling Load))
Modulus of Elasticity of Column given Crippling Stress
Go Modulus of Elasticity Column = (Crippling Stress*Effective Column Length^2)/(pi^2*Least Radius of Gyration Column^2)
Modulus of Elasticity given Crippling Load for any type of End Condition
Go Modulus of Elasticity Column = (Column Crippling Load*Effective Column Length^2)/(pi^2*Moment of Inertia Column)
Moment of Inertia given Crippling Load for any type of End Condition
Go Moment of Inertia Column = (Column Crippling Load*Effective Column Length^2)/(pi^2*Modulus of Elasticity Column)
Least Radius of Gyration given Slenderness Ratio
Go Least Radius of Gyration Column = Length of Column/Slenderness Ratio
Actual Length given Slenderness Ratio
Go Length of Column = Slenderness Ratio*Least Radius of Gyration Column
Effective Length of Column given Actual Length if One End is Fixed Other is Hinged
Go Effective Column Length = Length of Column/(sqrt(2))
Actual Length of Column given Effective Length if One End is Fixed Other is Hinged
Go Length of Column = sqrt(2)*Effective Column Length
Actual Length of Column given Effective Length if One End is Fixed Other is Free
Go Length of Column = Effective Column Length/2
Effective Length of Column given Actual Length if One End is Fixed Other is Free
Go Effective Column Length = 2*Length of Column
Actual Length of Column given Effective Length if Both Ends of Column are Fixed
Go Length of Column = 2*Effective Column Length
Effective Length of Column given Actual Length if Both Ends of Column are Fixed
Go Effective Column Length = Length of Column/2

3 Modulus of elasticity Calculators

Modulus of Elasticity of Column given Crippling Stress
Go Modulus of Elasticity Column = (Crippling Stress*Effective Column Length^2)/(pi^2*Least Radius of Gyration Column^2)
Modulus of Elasticity given Crippling Load for any type of End Condition
Go Modulus of Elasticity Column = (Column Crippling Load*Effective Column Length^2)/(pi^2*Moment of Inertia Column)
Moment of Inertia given Crippling Load for any type of End Condition
Go Moment of Inertia Column = (Column Crippling Load*Effective Column Length^2)/(pi^2*Modulus of Elasticity Column)

Modulus of Elasticity of Column given Crippling Stress Formula

Modulus of Elasticity Column = (Crippling Stress*Effective Column Length^2)/(pi^2*Least Radius of Gyration Column^2)
εc = (σcrippling stress*Leff^2)/(pi^2*rL^2)

What is meant by Effective Length of a Column also define Slenderness Ratio?

The effective length of the column is the length of an equivalent column of the same material and cross sectional area with hinged ends and having the value of the crippling load equal to that of the given column. The least radius of gyration is the radius of gyration where the least moment of inertia is considered.

How to Calculate Modulus of Elasticity of Column given Crippling Stress?

Modulus of Elasticity of Column given Crippling Stress calculator uses Modulus of Elasticity Column = (Crippling Stress*Effective Column Length^2)/(pi^2*Least Radius of Gyration Column^2) to calculate the Modulus of Elasticity Column, The Modulus of Elasticity of Column given Crippling Stress is defined as the measure of the stiffness of a material. in other words, it is a measure of how easily any material can be bend or stretch. Modulus of Elasticity Column is denoted by εc symbol.

How to calculate Modulus of Elasticity of Column given Crippling Stress using this online calculator? To use this online calculator for Modulus of Elasticity of Column given Crippling Stress, enter Crippling Stress crippling stress), Effective Column Length (Leff) & Least Radius of Gyration Column (rL) and hit the calculate button. Here is how the Modulus of Elasticity of Column given Crippling Stress calculation can be explained with given input values -> 0.021199 = (20000*2.5^2)/(pi^2*0.05^2).

FAQ

What is Modulus of Elasticity of Column given Crippling Stress?
The Modulus of Elasticity of Column given Crippling Stress is defined as the measure of the stiffness of a material. in other words, it is a measure of how easily any material can be bend or stretch and is represented as εc = (σcrippling stress*Leff^2)/(pi^2*rL^2) or Modulus of Elasticity Column = (Crippling Stress*Effective Column Length^2)/(pi^2*Least Radius of Gyration Column^2). Crippling Stress is the stress in column due to crippling load, 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 & Least Radius of Gyration Column is the smallest value of the radius of gyration is used for structural calculations.
How to calculate Modulus of Elasticity of Column given Crippling Stress?
The Modulus of Elasticity of Column given Crippling Stress is defined as the measure of the stiffness of a material. in other words, it is a measure of how easily any material can be bend or stretch is calculated using Modulus of Elasticity Column = (Crippling Stress*Effective Column Length^2)/(pi^2*Least Radius of Gyration Column^2). To calculate Modulus of Elasticity of Column given Crippling Stress, you need Crippling Stress crippling stress), Effective Column Length (Leff) & Least Radius of Gyration Column (rL). With our tool, you need to enter the respective value for Crippling Stress, Effective Column Length & 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.
How many ways are there to calculate Modulus of Elasticity Column?
In this formula, Modulus of Elasticity Column uses Crippling Stress, Effective Column Length & Least Radius of Gyration Column. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Modulus of Elasticity Column = (Column Crippling Load*Effective Column Length^2)/(pi^2*Moment of Inertia Column)
  • Modulus of Elasticity Column = (Column Crippling Load*Effective Column Length^2)/(pi^2*Moment of Inertia Column)
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