Reliability Analysis for Code Development

In the 1960s, the philosophy of the code specifications was based on the allowable stress principles (ASD, Allowable Stress Design). The structure was supposed to behave elastically, and the uncertainties were taken into account by a safety factor which divided the maximum stress according to the limit state considered. However, since these safety factors were selected subjectively, the risk of failure associated with that decision was unknown. Therefore, this practice has become impractical from the economical and safety point of view.

During the 1960s and 1970s, different natural disasters took place around the world causing extensive loss of human lives and economical damage. The evidence of deficiencies in design specifications revealed the need for the elaboration of codes based in a different design philosophy. More rational code definitions were defined identifying the basic limit states that any structure should achieve: safety under high load scenarios

and comfort during normal load conditions. This approach became the basis of most of the structural design specifications even for current codes.

In 1978, Ellingwood, Galambos, MacGregor and Cornell developed a set of design specifications using advanced reliability analysis methods and statistical data (Ellingwood, 1985). The fundamental concept of this design procedure is the basis of the Partial Factor Method, which is considered a “Simplified Probabilistic Design” method (Vrounwenvelder, 2001). In this method, a structural failure occurs if the load effects are larger than the resistance capacity of the element or system, and since both of these variables are considered random, a probability-based criterion may be applied. The issue consisted in defining the target probabilities considered as “safe” for design, in order to find the appropriate threshold between safety and economy. Several current structural design standards such as the AISC’s LRFD Specifications for Steel Structures, ASCE Standard 16 on LRFD for Engineered Wood Construction, American Concrete Institute Standard 318, and the International Building Code 2000, are based on these principles.

Initially, the partial factors that account for uncertainties in loads and resistances were defined based only on past experiences and the observed behavior of the structures. However, current systems demand more accurate methods to determine these factors, since high uncertainties may carry catastrophic consequences which are unacceptable in today’s practice. The probabilistic analyses satisfy this requirement and enhance the confidence level of the structures.

Some new code specifications address the structural design problem from the performance-based point of view, which is the final target of the evolution of the design codes. Vision 2000, FEMA 356 (FEMA, 2000a), FEMA 350 (FEMA, 2000b), ATC-40 (ATC, 1996) and NEHRP (FEMA, 2003) are some examples of this new trend in the code developments, principally for seismic design. The designer needs to define a structural performance objective which consists of different intensity load scenarios that control the design of structural and no-structural members. The definition of the loads and the capacities are based on probabilistic analyses according to real conditions.

Specific research works on the calibration of code specifications for steel bridges have been done by several authors (Nowak, 1995; Nowak, 2004; Barker & Zacher, 1997; Czarnecki & Nowak, 2006). In these studies, the probabilistic definitions of loads and

capacities have been addressed during the service stage of the bridge. In particular, Nowak et. al. (2006) calibrated the resistance factors for steel curved bridges including construction stages using three representative structures. The authors concluded that the resistance factors used for straight bridges are valid for curved bridges and that the construction stage is very important for curved bridges because of the significant variation of stresses during this phase.

Eamon et. al. (2000) presented a reliability-based criterion for wood bridges in the Load and Resistance Factor Design (LRFD) format. Load and resistance models were developed based on statistical analyses of test results. The limit state considered was the flexural capacity where the failure is limited by the moment of rupture. A wide range of reliability indexes was exhibited principally due to significant differences between code- predicted stresses and analytical results. The authors concluded that more accurate design approximations based on experimental and analytical results are required to improve the reliability for a wood bridge code.

Galambos (2004) determined the theoretical reliability of steel beams, columns and beam-columns designed according to the projected 2005 AISC specifications. The reliability indices were evaluated based on contemporary material properties and recent experimental strength data. It was concluded that the notional reliability of the proposed specification is identical to the one exhibited by the LRFD Specifications of 1986.

White and Jung (2008) evaluated the lateral-torsional and flange local buckling (LTB & FLB) predictions from 2004 AASHTO and 2005 AISC provisions versus uniform bending experimental test results. The reliability indices were estimated where the corresponding values for FLB were shown to be larger than those for LTB. These specifications were also evaluated using the results obtained from moment gradient experimental tests (White & Kim, 2008). In this work, the estimated reliability indices for FLB of end-loaded segments were found to be similar to those determined by White and Jung (2008) in most cases. For LTB, the reliability indices for end-loaded segments with moderate to large unbraced lengths were slightly larger than the values estimated from the uniform bending tests.