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 8.5.1

Web Local Yielding

Last Revised: 07/30/2011

The web local yielding limit state assumes that the entire applied force/reaction passes through a critical area of web located at the top of the fillet that connects the flange to the web and equals the thickness of the web times a distance that equals the actual bearing distance plus a distance of 2.5k on each side of the bearing length, where the length is available.  Figure 8.5.1.1 shows how this is applied both at the end of a beam and on somewhere away from an end of the beam.

Figure 8.5.1.1
Web Local Yielding Parameters
Click on hotlinks in image for larger views

Note that, at the end of the beam, there is less material available in the web (i.e. the length of the critical area is shorter) than when away from the end of the beam.  Consequently there is not as much strength available near the end of the beam as there is when away from the end of the beam.

The maximum stress that can occur on this area is taken to be the steel yield stress, Fy.  Thus the maximum force that can be applied equals the critical area times the yield stress.

As a designer, once a beam is chosen and the reaction is known, the only variable you have direct control over (without adding bearing stiffeners) is the actual bearing length lb.

Bearing stiffeners, similar to shear stiffeners except they are in contact with the flange where the load is applied, distribute the shear reaction over the depth of the web.  The critical area can be increased by the addition of bearing stiffeners, which are discussed in a different section of this text.

The Limit State

SCM J10.2 covers web local yielding due to concentrated point loads applied to the flange.

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
Ru < fRn Ra < Rn/W
Req'd Rn = Ru / f < Rn Req'd Rn = Ra  W < Rn
Ru / (fRn< 1.00 Ra / (Rn/W) < 1.00
f = 1.00 W = 1.50

The values of Ru and Ra are the LRFD and ASD factored loads, respectively, applied to the beam. 

In this case Rn is the nominal web yielding strength of the member is computed using SCM equations J10-2 and J10-3 re-arranged here slightly:

Rn = FyAcr

Where:

  • Fy is the tensile yield stress of the beam steel.
  • Acr is the critical cross sectional area at the top of the fillet that connects the web and flange of the member.
    • For forces applied away from the end of the beam, Acr = (5k + lb) tw
    • For forces applied at the end of the beam, Acr = (2.5k + lb) tw
  • lb is the actual bearing length on the flange.  This is the length of contact with the supporting or supported element.
  • k is the distance from the face of the flange to the top of the fillet that connects the web to the flange.  This value is tabulated in the W shape section property tables.

This limit state is to be checked at each location where a concentrated force is applied transverse to the axis of a member.  This typically occurs at support reaction locations and where the beam supports a column or beam reaction applied to the top of the top flange.

Sample Spreadsheet Calculation

The given spreadsheet example computes the reaction capacity, Rn, as controlled by local web yielding for a typical W section. The input values are in the grey shaded cells and the results in the yellow highlighted cells.

Web Local Yielding    
SCM J10.2      
         
Section W12x65      
Steel: A992      
Fy 50 ksi    
lb 5 in    
       
Tabulated Section Properties    
tw 0.39 in     
k 1.2 in    
       
Location End Mid    
Ae 3.12 4.29 in2  
Rn 156 214.5 k <---- Answer

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