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**1. Abstract:**

Many connection elements are modeled as rectangular members under various combinations of loads. The traditional method of combing loads using beam theory needs to be updated to fulfill the strength design philosophy due to the fact that the strength design is now used for steel members and connections. This paper has reviewed existing equations on the plastic interaction of rectangular members and has also provided new derivations where existing research is not available. Under any possible loading combination, an interaction equation is developed for strength design of rectangular connection elements.

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**2. Introduction**

Connections are divided into elements and modeled as structural members with predictable behavior for design purpose. Many connection elements can be modeled as rectangular members under various combinations of load, such as, shear, flexural, torsional and axial loads. Loads have been, traditionally, combined using beam equations with a first-yield criterion; however, a plastic strength approach is more appropriate for connections designed to the AISC Specification, which is based on a strength design philosophy.The purpose of this paper is to determine the strength of rectangular connection elements subjected to various loads acting at the same time. An interaction equation is developed for strength design of rectangular connection elements under any possible loading combination. Due to the extensive research available on the plastic interaction of rectangular members, this paper has reviewed existing equations on the plastic interaction of rectangular members and has also provided new derivations where existing research is not available.

### 3. Rectangular Connection Elements

Figure 1a shows a moment connection of rectangular flange plates under axial tension and compression loads. The inelastic material behavior will allow load redistribution in ductile connection elements. This redistribution of loads allows the flange plates to be designed based on the simplified assumption of axial load only.Figure 1b shows a single-plate connection subjected to a constant shear load and a maximum moment at the face of the column. In some cases, these connections must also carry a large axial load. Because the moment, shear and axial loads occur at the same location on the connection element, the load interaction must be accounted for. Torsional stress is typically neglected in design, but tests by Moore and Owens (1992), Sherman and Ghorbanpoor (2002) and Goodrich (2005) have shown presence of torsional stresses.

The bracket, gusset and hanger connections in Figures 1c through 1e are additional examples of rectangular connection elements subjected to strong-axis bending in addition to shear and/or axial loads. Figure 1f shows the prying action of a flange, which is a rectangular connection element in weak-axis bending. In this case, the effect of the shear force is usually small and is neglected in practice.

### 4. Von Mises Criterion

Several theories have been proposed to predict the behavior of materials under multi-axial states of stress. Von Mises’ criterion is considered the most accurate for predicting the initiation of
Figure 1. Rectangular Connection elements: (a) moment connection; (b) single-plate connection; (c) bracket; (d) gusset plate; (e) hanger plate; (f) prying at flange.

yield in ductile metals when loaded by various combinations of normal and shear stresses. The general von Mises stress is shown in Equation 1a.

For plane stress, von Mises’ equation reduces to

Where

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