FORMULAS FOR COLUMN BUCKLING CALCULATIONS

The formulas and parameters used in "Compression Member Calculator" are given below. According to the input parameters entered, column categorization is done by the calculator and suitable formulas are selected from the list of equations given below for the design of compression member.

Effective length constants used for the design of compression member are also given in this page for different end conditions of compression member.



Calculation Steps and List Of Equations for Compression Member Design:

Step Parameter/Condition Symbol Equation
1 Radius of gyration k Equation for radius of gyration
2 Eccentricity ratio er
3 Slenderness ratio S Equation for slenderness ratio
4 Effective slenderness ratio  Seff Equation for effective slenderness ratio
5 If er=0 and Seff > (2π2E/Sy)^0.5 then go to step 6
6 Force (according to Euler column formula) Pcr Euler column formula
7 If er=0 and Seff ≤(2π2E/Sy)^0.5 then go to step 8
8 Force (according to Parabolic/J.B. Johnson formula) Pcr Parabolic/J.B. Johnson formula
9 If er≠0 and S>0.282(AE/P)^0.5 then go to step 10
10 Force (according to secant formula)* Pcr Secant formula
11 If er≠0 and S≤0.282(AE/P)^0.5 then go to step 12
12 Force (according to stress formulas)* Pcr

* Note: After calculation, er=0 assumption is made and step 5 and step 7 is revisited. Pcr is calculated with er=0 assumption (in step 6 or step 8 according to conditions), then smaller value is selected by the calculator.


List of Parameters :

Symbol Parameter
I Area moment of inertia
A Area of the cross-section
L Length of the column
C Effective length constant
Sy Yield strength
Syc Compressive yield strength
e Eccentricity – Distance between central axis of column and line of action of the force
c Perpendicular distance to neutral axis

Effective Length Constant :

Boundary Conditions Theoretical Suggested Engineering
Free-Free 1.0 1.2
Pinned-Free 1.0 1.2
Pinned-Pinned 1.0 1.0
Guided-Free 2.0 2.1
Guided-Pinned 2.0 2.0
Guided-Guided 1.0 1.2
Fixed-Free 2.0 2.1
Fixed-Pinned 0.707 0.8
Fixed-Guided 1.0 1.2
Fixed-Fixed 0.5 0.65

Supplements:

Link Usage
Compression member design The calculator which calculates parameters of the compression member (column) for different end conditions and loading types.

Reference: