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

Chapter 8 - Bending Members

2006, 2007, 2008, 2011 T. Bartlett Quimby

Introduction


Flexure


Shear


Deflection


Misc. Limit States


Beam Design

Chapter Summary

Example Problems

Homework Problems

References


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Section 8.2.3

Flexural Yielding Limit State

Last Revised: 07/30/2011

As described in the section on flexural limit state behavior, the flexural yielding limit state represents that absolute maximum nominal moment that a section can support.  At this condition the section is fully yielded.  The limit state for strong axis bending in I-shaped member is found in SCM F2.1 and for weak axis bending in SCM F6.  Other situations are covered in other sections of SCM Chapter F and are similar to those presented here.

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
Mu < fbMn Ma < Mn/Wb
Req'd Mn = Mu/fb < Mn Req'd Mn = Mu Wb < Mn
Mu / (fbMn< 1.00 Ma / (Mn/Wb) < 1.00
fb = 0.90 Wb = 1.67

The values of Mu and Ma are the LRFD and ASD factored loads, respectively, applied to the flexural member. 

In this case Mn is the nominal flexural yielding strength of the member.  For doubly symmetric compact I-shaped members and channels bent about their major axis:

Mnx = Mpx= FyZx for strong axis bending (SCM equation F2-1)

Mny = Mpy = min(FyZy, 1.6FySy) for weak axis bending (SCM equation F6-1)

Where:

  • Mp is the plastic flexural strength of the member.
  • Fy is the material yield stress.
  • Z is the plastic section modulus for the axis of bending being considered.
Sample Spreadsheet Calculation

The following spreadsheet example computes the flexural capacity, about each principle axis, for a typical W section.  The input values are in the grey shaded cells and the results in the yellow highlighted cells.

Flexural Yielding             
             
Section: W10X49     Steel: A992    
  Zx 60.4 in4   Fy 50 ksi
  Zy 28.3 in4        
  Sy 18.7 in3        
             
    Mnx = 251.7 ft-k    
    Mny = 117.9 ft-k    

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