CNC Machining Design Guide

Optimize your designs, reduce machining time, and lower your costs.

NASA Tech Briefs

Innovations developed by NASA and its industry partners in a wide array of fields.


How OEM's can make their parts better, faster, and more efficient.

Injection Molding Design Guide

Guide for high quality and cost-effective plastic injection molding.

more free magazines
Calculator Introduction

This calculator computes the critical load of the specified column. In addition, the boundary condition factor and the effective length of the column are also calculated.

Both theoretical and engineering results are presented. The theoretical critical load is obtained directly from the elastic buckling theory. The boundary conditions are considered to be perfect as specified. The engineering critical load is used in column design, where the ideal boundary conditions are approximated.

Note: 1. The critical load is good for long columns, in which the buckling occurs way before the stress reaches the compression strength of the column material.
  2. For the classification of short, intermediate, and long columns, please refer to the column introduction or to thecolumn design calculator for structural steel.
  3. The boundary conditions for the column can be a combination of the following terminations:

  Young's Modulus (E):    
  Area Moment of Inertia (I):    
  Length of Column (L):    
  Boundary Conditions:    
  Theoretical Critical Load (Fcr):  6.43 × 106  lbf
  Theoretical Boundary Condition Factor:  1.00  
  Theoretical Effective Length (LeffT):  12.5  ft
  Engineering Critical Load (Fcr):  6.43 × 106  lbf
  Engineering Boundary Condition Factor:  1.00  
  Engineering Effective Length (LeffE):  12.5  ft
Equations behind the Calculator

The formula for the critical buckling load is derived in the elastic buckling section and summarized in the critical load section.

The critical load (Extended Euler's formula) for a column is given by,

where E is the Young's modulus, I is the area moment of inertia of the cross section, and Leff is the effective length of the column, which depends on the length of column as well as its boundary conditions.