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

Chapter 3 - Tension Members

© 2006, 2007, 2008, 2011 T. Bartlett Quimby

Section 3.3

Tensile Yielding of a Member

Last Revised: 11/04/2014

Tensile yielding is the first of the strength based limit states that we consider in this text.  As you will recall from your mechanics course, the stress and strain in a tension member, away from end connections, is assumed to be uniform throughout the member as long as the force is concentric with the member.   For a tension member, this means that the entire member can yield and experience permanent elongation if the force in the member is high enough.  Permanent deformation is not a desirable state, so the limit state of tensile yielding is introduced to guard against this form of "failure" to satisfy the needs of the structure.

Tensile yielding is considered away from the connections in the mid part of the member.  Figure 3.3.1 shows the general region of concern for a flat plate member.

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:

The values of P_u and P_a are the LRFD and ASD factored loads, respectively, applied to the member.  In this case P_n is the nominal tensile yielding strength of the member.

Nominal Tensile Yielding Strength, P_n:

P_n is computed using SCM equation D2-1 and is in force units.  As you will recall from mechanics, for an axial force member, the force in the member equals the normal stress times the cross sectional area of the member.  In this case, we multiply the gross cross sectional area, A_g, by the yield stress, F_y to determine force that would cause the member to yield in tension. 

The maximum force a member can resist is commonly referred to as the STRENGTH of a member.

As shown in the SCM overview given in chapter 1, the values for F_y and F_u can be found in SCM Tables 2-4 through 2-6 as appropriate. 

A_g is the gross cross sectional area of the member and is defined in SCM section B4.3a.  You should read that section now. This area is normal to the axis of the member.  A_g is tabulated in the section property tables of Part 1 of the SCM for all rolled shapes.  For other members A_g needs to be computed.

Example 3.1 shows how this limit state is applied.  As you follow the example you will notice that the member is adequate for LRFD but not for ASD.  You will want to read the observations in the example problem to find out why this is so.

Sample Spreadsheet P_n Computation

There are probably many ways to arrange this computation, but here is one.  The shown spreadsheet both computes the "capacity" of the member (in terms of P_s,eq) and checks the capacity against the demand, or required strength, (P_u or P_a).  Generally you will do either one or the other, not both.  The values in the shaded cells are either entered manually or computed elsewhere and linked to these locations.  Note that this spreadsheet only ANALYZES a given member.  For design problems where the member size is unknown, you will need use a little algebra to solve the limit state equation for the required A_g then make decisions from there.  In the end, however, you need to show that your final selection satisfies the limit state using some calculation similar to the one shown here.

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