RELIABILITY-BASED SELECTION OF STANDARD STEEL BEAMS

Abstract

A reliability-based design approach using sensitivity analysis is presented for the selection of standard steel beams subjected to concentrated and or distributed loads, assuming lognormal probability density function. Serviceability criteria of bending stress, transverse deflection, and web maximum shear stress are considered. The load, strength, and geometric parameters are considered to be log normal in distribution. Equations are developed for the coefficients of variation for the mentioned serviceability criteria so as to determine design reliability. Deterministic design equations are transformed into probabilistic ones by replacing the traditional “safety factor” with a “reliability factor”. The reliability factor is determined from a specified reliability goal and the coefficients of variation in design models and parameters. Design examples are presented and results are compared with solutions based on the traditional ASD (Allowable Stress Design) method. Two of the four design examples have identical solutions with the ASD method. The third example result is practically the same as that of ASD method, except that the beam is slightly lighter. The fourth example has a similar result as the ASD method but the beam is deeper. The deeper beam solution stems from the use of both bending stress and deflection serviceability criteria in the new approach while only the bending stress criterion was used in the ASD method. All the chosen beams indicate a reliability of at least 99.73% for bending stress and at least 95.22% reliability for deflection. In all the chosen beams, the web maximum shear stress has a reliability factor of at least 4.91, making shear failure improbable. The agreement between the results of these different methods is amazingly interesting. All computations in the study were done on Microsoft Excel Spreadsheet, demonstrating that probabilistic design can be done with inexpensive computer resource and not too advanced analytical skills. This study shows that acceptable design solutions can be achieved by modification of deterministic or traditional design method through probabilistic consideration of “design or safety factor”. From the very favorable comparison of the results between the new approach and ASD method, it appears reasonable to conclude that the method proposed in this paper is satisfactory for the probabilistic design of standard steel beams. The covs for practical design applications should be based on data from material vendors and historical data on loads. Engineering companies providing design services would have such data and a simple statistical analysis will give realistic cov values for use in their design practice.