A Beginner's Guide to the Steel Construction Manual, 14th ed.

Chapter 7 - Concentrically Loaded Compression Members

2006, 2008, 2011 T. Bartlett Quimby


Slenderness Limit State

Limit State of Flexural Buckling for Compact and Non-compact Sections

Limit State of Flexural Buckling for Slender Sections

Limit State of Bolt Bearing on Holes

Selecting Sections

Chapter Summary

Example Problems

Homework Problems


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Section 7.7

Compression Member Summary

Last Revised: 11/04/2014

Compressive strength is limited by:

  • Material Strength
  • General Buckling
  • Local Buckling

Strength Limit States:

All strength limit states take the form:

Pu < fcPn Pa < Pn/Wc
Req'd Pn = Pu/fc < Pn Req'd Pn = Pa Wc < Pn
Pu / (fcPn< 1.00 Pa / (Pn/Wc) < 1.00
fc = 0.90 Wc = 1.67

Which is:  FORCE on a column < STRENGTH of a column

The STRENGTH of a Column is computed by:

The nominal capacity of the column, Pn = Fcr Ag

Limit State Specification Critical Stress, Fcr Typical Design Variables
Flexural Buckling E3 (Q=1), E7 If (KL/r) < 4.71 sqrt(E/QFy)
QFy/Fe < 2.25

Then: Fcr = [.658(QFy/Fe)] QFy

Else: Fcr = .877 Fe

Member selection (Ag and slenderness parameters), KL, support conditions
  • Fe = p2 E / (KL/r)2 = Euler Critical Buckling Stress

  • Q =1 for compact and non-compact sections

  • Q = Qs Qa for slender sections

  • Qs:  Slenderness factor for unstiffened elements (SCM E7.1).  A function of the slenderness (b/t) of the unstiffened element.
  • Qa:  Slenderness factor for stiffened elements (SCM E7.2).  Different equations for flanges of square and rectangular sections, circular sections, and other uniformly compressed elements.
  • KL = Effective Length.  The choice of K will depend on how the demand side of the inequality was computed.

Slenderness Limit State (SCM E2)

This serviceability limit state is not binding, but a good suggestion:   (KL/r) < 200

Computing Effective Length (SCM Commentary 7.2)

Principles of Mechanics are used to determine the effective length of columns.  The effective length is a function of the overall member length, length between lateral braces, end support condition, and the arrangement of these factors relative to each principle axis. 

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