Applications of reliability concepts to timber engineering

This paper describes the use of reliability based procedures in the formulation of structural design standards in Australia. These procedures are the use of formal Monte Carlo simulations and closed form solutions. Examples of applications include aspects of design codes, quality control procedures and building regulations. INTRODUCTION Reliability concepts and procedures, although of intense academic interest, are rarely applied to the type of constructions covered by engineering design codes and building regulations. Nevertheless, during the past two decades there have been quite a few instances where simple probabilistic and reliability concepts have been usefully developed and/or applied for this purpose within Australia. The criterion used in the Australian risk studies was either to compare a risk with acceptable values or alternatively to choose a cost optimised risk. Three types of probability procedures have been used. These are as follows: (i) Approximate computations of failure probabilities; (ii) Approximate closed form solutions of reliability criteria; (iii) Exact solutions using Monte Carlo simulation. The notation to be used in this paper includes the following: Pr( ) = probability of an event occurring FR(x) = Pr(R < x) = cumulative frequency distribution of R GR(x) = Pr(R > x) = complementary frequency distribution of R pF = probability of failure VR = coefficient of variation of R R = element strength S = applied load effect on an element mean = average value. SAFETY ASSOCIATED WITH DESIGN CODES During the Standards Australia conversion of Australian structural design codes to limit states format, the target safety levels of both working stress and limit states design codes were examined. The safety was based on an estimate of pF,50, the probability of failure in-service during a 50 year period. pF,50 = Pr{R< (D + L + W)50} (1) where R denotes the structural load capacity and (D + L + W)50 denotes the peak value of the applied dead plus live plus wind load effect in a 50-year period. 1 Chief Research Scientist, CSIRO Building, Construction and Engineering, PO Box 56, Highett, Victoria 3190, Australia The analyses were undertaken using the Lind-Hasofer-Rackwitz-Fiessler algorithm (Leicester 1985) and the detailed procedures followed those outlined in the seminal report by Ellingwood et al. (1980). Lam Pham and Peter Kleeman played leading roles in these studies. The results are stated in terms of a safety index β defined by