Bridge Load Models
The major load components for highway bridges are deal load, live load, dynamic load, environmental loads (temperature, wind, earthquake), and other loads (collision, braking). In this paper, however, only the first three are considered. Consideration of live load involves not only the weight of trucks, but also the distribution factor (fraction of the total truck load per girder), and truck position within the roadway (curb distance). The load models are based on the available statistical data, surveys, inspection reports, and analytical simulations. The load variation is described by cumulative distribution function, mean value or bias factor (ratio of mean to nominal value), and coefficient of variation.
Dead load, DL, is the gravity load due to self-weight of the structural and nonstructural components permanently attached to the bridge. Therefore, it includes the weight of girders, deck slab, wearing surface, barriers, sidewalks, and diaphragms, when applicable. The statistical parameters for dead load were selected from the available literature (Nowak 1999). Four components are considered: DLi – weight of factory made elements, DL2 – weigh of cast-in-place
concrete, DL3 – weight of wearing surface (asphalt), and DL4 – weight of miscellaneous items (e. g., railing, luminaries). All components of dead load are treated as normal random variables. For DLi, the bias factor, X = 1.03, and coefficient of variation, V = 0.08; for DL2, X = 1.05, and V = 0.10; for DL4, X = 1.03—1.05, and V = 0.08~0.10,; and for asphalt wearing surface it is assumed that the mean thickness is 75 mm and V = 0.25.
The live load model was developed in conjunction with calibration of the AASHTO LRFD Code (Nowak and Hong 1991; Nowak 1993). The statistical parameters (mean values, bias factors and coefficients of variation) are derived for the maximum lane moments and shears. The multiple presence of trucks is considered by using the observed frequencies of occurrence of two vehicles in the same lane or side-by-side. For a single-lane loaded case, the ratio of the mean maximum 75-year moment to AASHTO HL-93 design moment varies from 1.3 for shorter spans (10 m) to 1.2 for longer spans (50 m), while coefficient of variation, V = 0.11 for all spans. For the two-lane loaded case, bias factor for each truck varies from 1.2 for shorter spans (10 m) to 1.0 for longer spans (50 m), while coefficient of variation, V = 0.11 for all spans.
The basic load combination includes dead load and live load (static and dynamic). Live load is represented in form of a design truck as shown in Figure 2. It is assumed that the gross vehicle weight (GVW) is a random variable, but the axle spacing and percentage of the total load per axle remain constant. The transverse position of the truck within the roadway (curb distance) is also treated as a random variable. An example of the probability density function (PDF) of the curb distance is shown in Figure 3, for two traffic lanes. Each curve represents a curb distance for a line of wheels, spaced at 1.8m for a truck.
^ 35 kN
4.3 m _ I _ 4.3 – 9.0 m _ |
Figure 3 Probability Density Functions (PDF) of the Curb Distance. Each PDF Represents a Line of
Truck Wheels (Tantawi 1986)
The variation in transverse traffic position is based on a survey on interstate highways in Southeastern Michigan. The PDF was approximated by a lognormal distribution with a coefficient of variation of 0.33. For a standard lane width of 3.63 m, the mean value of the distance from the lane edge to the centerline of the outermost vehicle wheel is equal to 0.91 m.
Dynamic load depends on roughness of the surface, dynamic properties of the bridge, and suspension system of the vehicle. Dynamic load factor is defined as the ratio of dynamic strain (or deflection) and static strain (deflection). Field tests conducted by Kim and Nowak (1997) and
Eom and Nowak (2001) showed that the dynamic load factor does not exceed 0.15 for a single truck and 0.10 for two heavily loaded trucks traveling side-by-side. Therefore, the mean dynamic load factor is conservatively taken as 0.10 with the coefficient of variation of 0.80.