## 122 Available Structural Design Concepts

Before introducing the reliability-based design concept in structural engineering, it may be informative to study different deterministic structural design concepts used in the recent past. The fundamental concept behind any structural design is that the resistance of a structural element, joint, or the structure as a whole should be greater than the load or combinations of loads that may act during its lifetime with some conservatism or safety factor built in. The level of conservatism is introduced in the design in several ways depending on the basic design concept being used. In the ASD approach, the basic concept is that the allowable stresses should be greater than the unfactored nominal loads or load combinations expected during its lifetime. The allowable stresses are calculated using a safety factor. In other words, the nominal resistance Rn is divided by a safety factor to compute the allowable resistance Ra, and safe design requires that the nominal load effect Sn is less than Ra. In the ultimate strength design method [10], the loads are multiplied by certain load factors to determine the ultimate load effects and the members are required to resist various design combinations of the ultimate load. In this case, the safety factors are used in the loads and load combinations.

It is well known that the loads that may act on a structure during its lifetime are very unpredictable and different levels of unpredictability or uncertainty exist for each load. The uncertainty associated with predicting dead load is expected to be lower than that of live, wind, or seismic load. Since different assumptions are made in developing the beam and column theories, the theoretical prediction of the resistance or strength of beams and columns is expected to have different levels of uncertainty. In the ASD approach, the safety factor is introduced in predicting resistance, and the loads are assumed at their nominal values ignoring the different levels of uncertainty in predicting them. In the ultimate strength design concept, conservatism is introduced by using different load factors. Conceptually, the use of load- and resistance-related safety factors may not assure a uniform underlying risk for different structural elements, for example, beams, columns, and slabs, or under different loading conditions (e.g., dead, live, wind, or seismic loads). In the LRFD or reliability-based design concept, conservatism is introduced by using both load and resistance factors and satisfying an underlying risk, combining the desirable features of both the ASD and ultimate design concepts. Essentially, the LRFD approach uses safety factors to estimate both the resistance and load under the constraint of an underlying risk. Since satisfying an underlying risk is the main objective of the reliability-based design concept, this assures uniform risk for the structure and may produce a more economical design than other deterministic design concepts.

Like the LRFD format, the reliability-based design concept can be represented in its basic form as where Q, is the ¿th nominal load effect, g is the load factor corresponding to Q,, Rn is the nominal resistance, and f is the resistance factor corresponding to Rn. The load factor g and the resistance factor f account for the uncertainties in the parameters related to the loads and resistance. The mathematical expressions for these factors will be derived in Section 12.4. These factors are derived based on reliability analysis of simple ''standard'' structures such as simple beams, centrally loaded columns, tension members, high-strength bolts, and fillet welds [11], and are calibrated to achieve levels of reliability similar to conventional ASD procedures such as the 1989 AISC specification [2].

One of the most important objectives of the reliability-based design approach is that it provides a reasonable platform to compare different design alternatives by considering the realistic behavior of structures and the uncertainty in the design variables satisfying some underlying design criteria. It tries to reduce the scatter in the underlying risk of different members designed according to the ASD concept. Thus, the risk-consistent load factors used in LRFD help to economize the design. Since dead load has less uncertainty than live load, it should have a smaller load factor. But in the ASD procedure, the dead and live loads have the same load factor of 1. In evaluating the strength or resistance, theoretically predicted values generally do not match experimental results. The strength of a beam is more predictable than column strength. The support conditions and the buckling behavior of a column make its strength prediction more uncertain, indicating that beams and columns should have different capacity reduction factors to satisfy the same underlying risk. This is common-sense logic, and reliability or risk-based design is expected to be superior to ASD.

ASD is essentially a deterministic design concept. A casual evaluation of the LRFD code indicates that it is also deterministic in nature; only the prescribed load and resistance factors are based on reliability analysis. This information may not be of any practical significance to a typical practicing engineer.

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