Structural design code calibration using reliability-based cost optimization

Structural design codes provide minimum requirements to assure at least a certain level of safety. Codes may need some revisions due to availability of new data on random variables such as material or loading and improvements in analytical tools used in the design process, access to new or better construction materials, or changing demand on the use of the structure. In current Load and Resistance Factor Design (LRFD) practice, the code calibration is carried out by using predefined target (reliability) levels. Defining the target safety level is not clear since codes involve multiple load combinations including combination of time dependent loads, and a dilemma arises as to which target safety index should be used in calibrating load factors for these combinations.; This study investigates use of reliability based cost optimization in calibration of design codes. Load factors that make the total expected cost a minimum are the optimum load factors and the corresponding safety index is the optimum safety index for each load case. No predefined target safety levels are used herein; however, the contribution of the current code in the calibration process is satisfied by deducing the failure cost that a current level of safety implies in the current code. The most basic gravity load combination is chosen to deduce the failure cost. First Order Reliability Method (FORM) is used for reliability analysis, and the combination of time dependent loads is derived with the Ferry-Borges Method. Since application of Ferry-Borges method requires independency between load events, the part coming from the time independent modeling uncertainties are separated herein from the time dependent part and calculations are carried out by combining the Ferry-Borges Method with a Nested Reliability Analysis. The approach is illustrated with application to a bridge design specification including dead, live, wind and earthquake load combinations. Optimum total cost including failure cost and safety indices are compared to existing code format. A recommended load factor table is presented as a product of the calibration process.