TRA NSPORTATI ON RESEA RCH R ECOR D 1291 315 Reliability Analysis for Wood Bridges ANDRZEJ s. NOWAK A probabilistic approach for analysis of wood bridges is discussed . Load and resistance parameters are treated as random variables. The statistical models are derived on the basis of truck surveys, test data, and analysis. The mean maximum 75-year live load is calculated for single- and two-lane bridges. For low-volume roads, the maximum moments can be reduced by about 10 percent. Resistance is considered for timber stringers, glued-laminated (glulam) girders, and stressed decks. A considerable variation of modulus of rupture (MOR) is observed for sawn lumber. The degree of variation of MOR is considerably reduced in case of glulam girders and tressed decks. Reliability is a convenient mea- sure of tructural performance. Reliability indices are caiculated for three structural types. The effect of traffic volume is negligible for timber stringers, but it can be considered for glulam girders and stressed decks. Wood is an attractive material for bridge construction. It can be used successfully on low-volume roads. Very promising are new structural systems, including glued-laminated (glu- Iam) girders and stressed decks. They allow for the use of low-grade local materials and are suitable for designs and repair or rehabilitation projects. However, there is a need for a rational basis for the development of design criteria. Traditionally, a considerable variation of mechanical prop- erties such as modulus of rupture (MOR) and modulus of elasticity (MOE) led to low values of the allowable stresses. Introduction of new technologies, including glulam girders and stressed decks, requires a new approach to the design and evaluation of wood structures. Load and resistance parameters are random variables. Therefore , reliability is a convenient measure of the structural performance that also provides a rational basis for comparison between wood and other structural materials. The parameters involved in the design and evaluation of wood bridges are reviewed and a probabilistic basis for the development of load and resistance factors is developed. The load model is based on the available truck survey data. Resist- ance parameters are derived from test data and simulations. The procedure is formulated for calculation of reliability indices for sawn stringers, glulam girders and stressed decks, as shown in Figure 1. BRIDGE LOADS Bridge load components include dead load, live load, dynamic load, environmental loads and others (collision). A combi- nation of the first three components is considered. University of Michigan, 2370 G. G. Brown Building , Ann Arbor, Mich . 48109. Dead Load In case of wood bridges, dead load is usually a small portion of the total load. The major components of dead load, D, are the weight of the structural members and the weight of asphalt (if any). The density of wood, which varies depending on species and moisture, is assumed equal to 60 lb/ft 3 for hardwood and 40 lb/ft 3 for softwood. Dead load is normally distributed . The statistical parameters of D are presented in Table 1 (J). Live Load Live load, L, covers a range of forces produced by vehicles moving on the bridge. The effect of live load depends on many parameters , including span length, truck weight, axle loads, axle configuration, position of the vehicle on the bridge (transverse and longitudinal), number of vehicles on the bridge (multiple presence), and stiffness of structural members. The maximum live load effect also depends on the time period considered. Bridges are usually designed for an economic life of 50 to 75 years. Shorter periods of time are considered in case of serviceability limit states. The development of the live load model requires an exten- sive data base, weigh-in-motion (WIM) measurements, or truck surveys. The model described in the following para- graphs is based on the results of the truck survey performed by the Ontario Ministry of Transportation in 1975 (2). About 10,000 heavy trucks were measured (only heavily loaded vehi- cles were included). Moments were calculated for various simple spans. The calculations were performed for trucks and axle configura- tions, with about 10 configurations per vehicle. For spans from 10 to 100 ft, the results are shown in Figure 2 on normal probability paper. The vertical scale is the inverse normal probability function . Any distribution represented by a straight line on normal probability paper is a normal function. There- fore, the shape of obtained distributions indicates the type. The moments are divided by the design values, for the HS- 20 truck (3). The maximum 75-year moment can be estimated by extrap- olation. The surveyed trucks represent about 2 weeks' traffic on an Interstate highway. In 75 years, there will be about 1,500 times more vehicles. Let N be the number of trucks and axle configurations. For a 2-week period, N = 100,000, and for 75 years N = 150 ,000,000 . The corresponding prob- ability of occurrence, PN, is equal to the inverse of the number of vehicles, PN = l/N. The corresponding inverse normal distribution, Z, is Z = <1>- 1 (PN) (1) where <I> is the standard normal distribution function.