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Calculator Introduction

This calculator is designed specifically for structural steel columns. Columns made by other materials (e.g. aluminum alloys) should use other formulas.

Given the material properties (Young's modulus E, yield stress sy, proportional limit spl) and the column geometry (effective length Leff and radius of gyration r), this calculator will compute the allowable stress with respect to a given safety factor.

Note: 1. The proportional stress is equal to the yield stress minus the maximum compression residual stress sres left over from any hot or cold forming operation,

spl = sy - sres

Typically, the proportional stress is 50% to 100% of the yield stress,

spl = (0.5 ~ 1)·sy.
  2. Radius of gyration , where I is the area moment of inertia of the cross section and A is the cross section area.
  3. If a safety factor less than the AISC-recommended value (which ranges from 1.67 to 1.92) is entered, the calculator will use the larger ASIC value. ASIC stands for the American Institute of Steel Construction
  Young's Modulus (E):    
  Yield Stress (sy):    
  Proportional Limit (spl):    
  Effective Length of the column (Leff):    
  Radius of Gyration (r):    
  Safety Factor (SF):    
  Allowable Stress (sallow):  237  MPa
  Safety Factor (SF):  1.69  
  Slenderness Ratio (Leff / r):  5.00  
  Critical Slenderness Ratio (SRc):  99.3  
Equations behind the Calculator
The formulas used in this calculator are based on the Guide to Stability Design Criteria for Metal Structures by the Structural Stability Research Council. Anyone designing metal columns should consult this guide or other well estabilshed publications.

The column is classified as either long or short/intermediate, and two different formulas are used in these two regions.

The critical slenderness ratio SRc separates long columns from short/intermediate columns. Basically, SRc corresponds to the case when the stress due to the axial load reaches the proportional limit and the critical load at the same time.

If Leff / r < SRc, the column is considered short/intermediate. Inelastic buckling is likely to be the cause of failure, where the stress exceeds the proportional limit before reaching the critical load. The ASIC safety factor and resulting allowable stress are given by,

If Leff / r > SRc, the column is considered long. Elastic buckling in accordance with Euler's formula is expected. The ASIC safety factor and resulting allowable stress are given by,

If the safety factor specified by the user is larger than the ASIC safety factor in the above formulas, the user's value will be used in calculating the allowable stress.