Chapter 3 - Tension Members
© 2006, 2007, 2008, 2011 T. Bartlett Quimby
Tension Member Overview
Last Revised: 07/30/2011
It is now time to actually learn how to design something! We start with tension members because they are relatively simple. There are only a few limit states to worry about.
Now that we are ready, please turn to SCM Chapter D (SCM page 16.1-26) and let's get started.
Controlling Limit States
In SCM Chapter D we look at three limit states that relate to the member itself. We will then look to SCM Chapter J to look at some connection related limit states at apply to connecting elements and/or end conditions of general tension members.
The SCM Chapter D limit states that we will consider are:
In SCM Chapter J we will look at the limit states of:
As discussed in an earlier chapter, limit states represent conditions that limit the usefulness of a member. Generally only one of the limit states will control the design. All must be checked to ensure that your member is adequate for its intended purpose. The following sections present the limit states as implemented by the AISC specification. The example problems show how the limits are applied.
A brief overview of the limit states is presented here.
Figure 3.1.1 illustrates "failures" associated with the various strength based limit states. You can click on each of the drawings to get a larger view with more annotations.
Figure 3.1.1(a) shows the end of a W section attached to a short connecting plate. The other drawings in the set illustrate the various strength based failure limit states for the W section.
Note that the connecting plate shown is a separate member and has its own set of limit states that used to define it's tensile strength. For this example, we will only focus on the capacity of the W section.
Tension yielding is illustrated in Figure 3.1.1(b). This failure mode looks at yielding on the gross cross sectional area, Ag, of the member under consideration. Consequently, the critical area is located away from the connection as shown. Strength of the section equals the gross area, Ag, times the minimum yield stress, Fy, of the member.
Tensile rupture occurs in the next section of the W section at the connection. In this case we have two potential failure paths that see the full force of the member. These are shown in Figures 4.1.1(c) and 4.1.1(d). It is common to have multiple potential failure paths. Each valid path must be investigated. Tensile rupture is complicated by the need to get the forces out of the flanges, through the web, and into the bolts. This means that we need to account for the stress concentrated in and around the bolts. This will be discussed in further detail later. The capacity of each failure path equals the effective net area, Ae, times the tensile stress, Fu, of the member.
Block shear occurs when a "block" of the member is "torn" out as depicted in Figures 4.1.1(e) and 4.1.1(f). Block shear is characterized by a failure that includes both tension (i.e. normal to the force) and shear (i.e. parallel to the force) failure planes. Like tensile rupture, there are frequently multiple valid failure paths that must be investigated. The capacity of each failure path is a sum of the capacities of each of the failure surfaces in the path. Each tension area capacity equals the tension area (either gross or net) times a tensile stress (yield or ultimate). Each shear area capacity equals the shear area (either gross or net) times a shear stress (yield or ultimate).
The three strength based limit states shown here are three of the four possible failures to be considered for the W section. Bolt bearing, the fourth strength limit state, is not reasonably shown in these figures and is treated later. The limit state that results in the lowest capacity for the member controls the capacity of the member.
Note that the capacity of the connection is the lowest of the capacity of the two connected members or the fasteners. This chapter deals with the capacity of the connected members, not the fasteners. The fasteners are addressed in chapter 5.