## 51 Introduction

The steel design methods used in the United States are allowable stress design (ASD), plastic design (PD), and load and resistance factor design (LRFD). In ASD, the stress computation is based on a first-order elastic analysis, and the geometric nonlinear effects are implicitly accounted for in the member design equations. In PD, a first-order plastic-hinge analysis is used in the structural analysis. PD allows inelastic force redistribution throughout the structural system. Since geometric nonlinearity and gradual yielding effects are not accounted for in the analysis of PD, they are approximated in member design equations. In LRFD, a first-order elastic analysis with amplification factors or a direct second-order elastic analysis is used to account for geometric nonlinearity, and the ultimate strength of beam-column members is implicitly reflected in the design interaction equations. All three design

methods require separate member capacity checks including the calculation of the K-factor. In the following, the characteristics of the LRFD method are briefly described.

The strength and stability of a structural system and its members are related, but the interaction is treated separately in the current American Institute of Steel Construction (AISC)-LRFD Specification [1]. In current practice, the interaction between the structural system and its members is represented by the effective length factor. This aspect is described in the following excerpt from SSRC Technical Memorandum No. 5 [2]:

Although the maximum strength of frames and the maximum strength of component members are interdependent (but not necessarily coexistent), it is recognized that in many structures it is not practical to take this interdependence into account rigorously. At the same time, it is known that difficulties are encountered in complex frameworks when attempting to compensate automatically in column design for the instability of the entire frame (for example, by adjustment of column effective length). Therefore, SSRC recommends that, in design practice, the two aspects, stability of separate members and elements of the structure and stability of the structure as a whole, be considered separately.

This design approach is marked in Figure 5.1 as the indirect analysis and design method.

In the current AISC-LRFD Specification [1], first- or second-order elastic analysis is used to analyze a structural system. In using first-order elastic analysis, the first-order moment is amplified by B1 and B2 factors to account for second-order effects. In the Specification, the members are isolated from a structural system, and they are then designed by the member strength curves and interaction equations as given in the Specifications, which implicitly account for the second-order effects, inelasticity, residual stresses, and geometric imperfections [3]. The column curve and the beam curve were developed by a curve-fit to both theoretical solutions and experimental data, while the beam-column interaction equations were determined by a curve-fit to the so-called ''exact'' plastic-zone solutions generated by Kanchanalai [4].

In order to account for the influence of a structural system on the strength of individual members, the effective length factor is used as illustrated in Figure 5.2. The effective length method generally provides a good design of framed structures. However, several difficulties are associated with the use of the effective length method, which are as follows:

1. The effective length approach cannot accurately account for the interaction between the structural system and its members. This is because the interaction in a large structural system is too complex to be represented by the simple effective length factor K. As a result, this method cannot accurately predict the actual strengths required of its framed members.

FIGURE 5.1 Analysis and design methods. Copyright 2005 by CRC Press

Framed member

Effective length factor

Structural system

Framed member

Effective length factor

Structural system

FIGURE 5.2 Interaction between a structural system and its component members.

2. The effective length method cannot capture the inelastic redistributions of internal forces in a structural system, since the first-order elastic analysis with B1 and B2 factors accounts only for second-order effects and not the inelastic redistribution of internal forces. The effective length method provides a conservative estimation of the ultimate load-carrying capacity of a large structural system.

3. The effective length method cannot predict the failure modes of a structural system subject to a given load. This is because the LRFD interaction equation does not provide any information about failure modes of a structural system at the factored loads.

4. The effective length method is not user friendly for a computer-based design.

5. The effective length method requires a time-consuming process of separate member capacity checks involving the calculation of K-factors.

With the development of computer technology, two aspects, the stability of separate members and the stability of the structure as a whole, can be treated rigorously for the determination of the maximum strength of the structures. This design approach is shown in Figure 5.1 as the direct analysis and design method. The development of the direct approach to design is called ''advanced analysis'' or, more specifically, "second-order inelastic analysis for frame design.'' In this direct approach, there is no need to compute the effective length factor, since separate member capacity checks encompassed by the specification equations are not required. With the current available computing technology, it is feasible to employ advanced analysis techniques for direct frame design. This method was considered impractical for design office use in the past. The purpose of this chapter is to present a practical, direct method of steel frame design, using advanced analysis, that will produce almost identical member sizes as those of the LRFD method.

The advantages of advanced analysis in design use are outlined as follows:

1. Advanced analysis is another tool used by structural engineers in steel design, and its adoption is not mandatory but will provide a flexibility of options to the designer.

2. Advanced analysis captures the limit state strength and stability of a structural system and its individual members directly, so separate member capacity checks encompassed by specification equations are not required.

3. Compared to the LRFD and ASD, advanced analysis provides more information of structural behavior by direct inelastic second-order analysis.

4. Advanced analysis overcomes the difficulties due to incompatibility between the elastic global analysis and the limit state member design in the conventional LRFD method.

5. Advanced analysis is user friendly for a computer-based design, but the LRFD and ASD methods are not, since they require the calculation of the K-factor along with the analysis to separate member capacity checks.

6. Advanced analysis captures the inelastic redistribution of internal forces throughout a structural system, and allows an economic use of material for highly indeterminate steel frames.

7. It is now feasible to employ advanced analysis techniques that were considered impractical for design office use in the past, since the power of personal computers and engineering workstations is rapidly increasing.

8. Member sizes determined by advanced analysis are close to those determined by the LRFD method, since the advanced analysis method is calibrated against the LRFD column curve and beam-column interaction equations. As a result, advanced analysis provides an alternative to the LRFD.

9. Since advanced analysis is a structure-based analysis and design approach, it is more appropriate for performance-based fire and seismic design than conventional member-based design approaches [5].

Among various advanced analyses, including plastic zone, quasi-plastic hinge, elastic-plastic hinge, notional-load plastic hinge, and refined plastic-hinge methods, the refined plastic-hinge method is recommended since it retains the efficiency and simplicity of computation and accuracy for practical use. The method is developed by imposing simple modifications on the conventional elastic-plastic hinge method. These include a simple modification to account for the gradual sectional stiffness degradation at the plastic-hinge locations and to include the gradual member stiffness degradation between two plastic hinges.

The key considerations of the conventional LRFD method and the practical advanced analysis method are compared in Table 5.1. While the LRFD method does account for key behavioral effects implicitly in its column strength and beam-column interaction equations, the advanced analysis method accounts for these effects explicitly through stability functions, stiffness degradation functions, and geometric imperfections, which are discussed in detail in Section 5.2.

Advanced analysis holds many answers about the real behavior of steel structures and, as such, the authors recommend the proposed design method to engineers seeking to perform frame design with efficiency and rationality, yet consistent with the present LRFD Specification. In the following sections, we will present a practical advanced analysis method for the design of steel frame structures with LRFD. The validity of the approach will be demonstrated by comparing case studies of actual members and frames with the results of analysis/design based on exact plastic-zone solutions and

Key considerations |

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