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

Chapter 7 - Concentrically Loaded Compression Members

2006, 2008, 2011 T. Bartlett Quimby

Introduction

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

References


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Section 7.3

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

Last Revised: 11/04/2014

The flexural buckling strength for compact and non-compact sections (i.e. those sections that do not have slender elements as defined by SCM B4) limit state is found in SCM E3.  See the commentary on SCM page 16.1-292 for more discussion on this.

Since this limit state only applies for compact and non-compact sections, the SCM B4 criteria must be checked to make sure that the chosen section is not slender before applying this limit state.

The Limit State

The basic limit state follows the standard form.  The statement of the limit states and the associated reduction factor and factor of safety are given here:

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

The values of Pu and Pa are the LRFD and ASD factored loads, respectively, applied to the column. 

In this case, Pn is the nominal compressive strength of the member is computed using SCM equation E3-1:

Pn = FcrAg

Where:

  • Fcr is the flexural buckling stress.
  • Ag is the gross cross sectional area of the member.

The SCM has two formulas for determining the flexural buckling stress.  The first equation, E3-2, covers both the plastic and inelastic buckling regions of the typical buckling strength curve as shown in Figure 6.1.3.  The second equation, E3-3, covers the slender region.  Figure 7.3.1 shows how the SCM equations for Fcr vary with slenderness.

Figure 7.3.1
Fcr vs. Slenderness
Click on image for larger view

The criteria for selecting which formula to use is based on either the slenderness ratio for the member or the relationship between the Euler buckling stress and the yield stress of the material.  The selection, as found in SCM E3, can be stated as:

if (KL/r < 4.71*sqrt(E/Fy)) or (Fy / Fe < 2.25) then
    use SCM Equation E3-2
else
    use SCM Equation E3-3

The equations require you to compute the theoretical Euler buckling stress, Fe, for the member.  This can be done by using SCM equation E3-4 or by more advanced methods of elastic buckling analysis.  The other advanced methods for computing Fe are not covered in this text.

The effective length coefficient, K is taken as 1.00 for all purposes of this section if the demand side of the inequality (i.e. Pu or Pa) was determined using the Direct Analysis method, otherwise use the K computed using methods in SCM Appendix 7.

Sample Spreadsheet Calculation

The following spreadsheet example computes the nominal capacity of a W section column according to the requirements of SCM E3. Note that the value of KL is given.  This may have resulted from either a Direct Analysis or Effective Length Analysis--the method is not shown. The values in shaded cells were computed before reaching this point. 

W10X19   Fy = 50 ksi        
A992                
               
Check Local Buckling Criteria:  SCM Table B4.1        
Case Coeff. Ratio Actual Limit Act/Limit      
3 0.56 bf/2tf 5.09 13.49 0.377 Not Slender    
10 1.49 h/tw 35.4 35.88 0.987 Not Slender    
               
Use SCM E3            
               
Compute Global Slenderness Values          
Direction KL r KL/r          
  (ft) (in)            
Stong 30 4.14 86.96 <--- Controlling Value      
Weak 6 0.874 82.38          
               
Determine Pn              
Determine SCM E3 formula to use        
               
4.71sqrt(E/Fy) 113.43            
Controlling KL/r 86.96            
(KL/r)/limit 0.767 Use SCM Equation E3-2      
               
  Fe 37.85 ksi          
  Fcr 28.76 ksi          
  Ag 5.62 in^2          
  Pn 161.66 kips          
               
LRFD         ASD      
fc = 0.9       Wc = 1.67    
Pu  < 145.5 kips     Pa  < 96.8 kips  
CLF 1.311       CLF 0.806    
Ps,eq < 110.97 kips/connection   Ps,eq < 120.17 kips/connection

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