# 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 2 Eccentricity ratio er 3 Slenderness ratio S 4 Effective slenderness ratio Seff 5 If er=0 and Seff > (2π2E/Sy)^0.5 then go to step 6 6 Force (according to Euler column formula) Pcr 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 9 If er≠0 and S>0.282(AE/P)^0.5 then go to step 10 10 Force (according to secant formula)* Pcr 11 If er≠0 and S≤0.282(AE/P)^0.5 then go to step 12 12 Force (according to stress formulas)* Pcr

##### 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.