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In the current bridge design specifications of China [

To overcome the challenges, many efforts [

One objective of this paper is to describe a methodology to handle truck load and earthquake load combinations. Earthquake load is modeled using seismic risk analysis. Truck load is modeled using Stationary Poisson processes based on the BHMS and statistical analysis. Two numerical examples of truck load and earthquake load combinations are used to illustrate the methodology.

A number of variables describe the effects that earthquakes have on bridges, such as the intensity of acceleration, the rate of earthquake occurrences, the natural period of the bridge, the seismic response coefficient, and the response modification factor. In order to explain the methodology of load combinations, only the intensity of acceleration and the rate of occurrence are chosen as the main variables.

Based on the Poisson process assumption, the probability of exceedance (

For more than one potential seismic source zone, suppose the parameters of the earthquake are random distributions and the probability over 1 year is a stable Poisson process. Based on the total probability theorem, the probability of exceeding a given earthquake intensity

The earthquake intensity could be acceleration, velocity, or displacement. For acceleration,

Because of the uncertainties of direction impact of potential seismic source zones, for

For disperse potential seismic source areas, the probability of the

The South China belt.

Based on (

Annual exceedance probability of PGA.

Assume that the probability density of earthquake load intensity in time

Studies on truck load have been difficult historically, principally because weighing equipment was lacking and the data are correspondingly rare [

Nowak [

Layout of monitoring sites.

Histogram of the monitoring sites.

Curve fitting of truck load density.

For a typical bridge, the truck load will consist of a varying number of trucks on the bridge. The probability function for such a bridge can be obtained using following analysis. Assume

Based on total probability theory and Poisson processes, the truck load intensity function for an interval

The intensity of dead load is usually defined as a time independent variable, and that of truck load is a time dependent variable, both of whom follow normal distributions [

As mentioned above, earthquake load and time-variable truck load are assumed to be Poisson processes, each with same distribution and time duration. Based on these assumptions, as mentioned earlier load processes can be converted to a small

Dirac Delta function is introduced to deal with the characteristics of

Based on (

To further simplify the discussion without losing generality, the probability of two loads occurring simultaneously is neglected. Thus (

Although in our study emphasis is given to formulate the “demand” to establish load combinations, all events must address a capacity issue of the bridge. For example, the earthquake load and truck load combination on a bridge column can either consider the vertical load or the column base shear load. Theoretically, (

determine truck load and earthquake load distributions over a particular period;

using Poisson processes, convert earthquake load and truck load distributions over a particular period to a sufficiently small interval

using (

using (

Using the method of load combination described in the preceding section, a simple example of horizontal load combination is presented here. Profiles of the typical bridge are shown in Figures

Longitudinal profile of the typical bridge.

Transverse profile of the typical bridge.

Probability curve of each truck load effect.

Truck load probability density curve for varied number of trucks.

Probability of passing truck number simultaneously in

Combined probability curves for truck load in earthquake load duration.

Probability curves for earthquake load in 100 years.

Probability density of load combination in 100 years.

Cumulative probability of load combination in 100 years.

Truck and earthquake load effects are the base moment caused by trucks and earthquakes, respectively. Figure

From the results shown in Figure

Example

Vertical truck load probability density curves for varied number of trucks.

Probability of passing truck number simultaneously in

Probability density of vertical load combination in 100 years.

Cumulative probability of vertical load combination in 100 years.

Probability density of dead, truck, and earthquake load combination.

Probability curves of dead, truck, and earthquake load combination.

Figures

This paper describes a method to combine earthquake load and truck load in the service life of bridges. The following conclusions can be drawn.

Given the more than 70% seismic areas in China, earthquake load is a main consideration for bridge design in the southeast coastal areas of China. The earthquake load probability curve is obtained using seismic risk analysis.

Using measured truck load data from BHMS, multimodal characteristics of truck load are analyzed. The truck load density of each truck is obtained by curve fitting. Considering that truck load may consist of varying numbers of trucks, truck load is calculated through traffic analysis.

In this method, the maximum value of combined load is defined as

The shape of the earthquake and truck load combination is similar to that of truck load alone, but the curve is displaced to the right, which means the mode and mean value of truck and earthquake load combination in this example is larger than that of truck load alone. This also illustrates that truck load is more sensitive to bridge design and over most ranges truck load is larger than earthquake load in this area.

The curve from direct load combined over 100 years is further away from the curve obtained using the method in the paper, with the direct combination of truck load and earthquake load over 100 years giving much larger values. It is not suggested that this method be used in bridge design considerations.

Because dead load is combined with truck and earthquake load along the direction of gravity, the dead load contributes a substantial portion in vertical load combinations.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This study is jointly funded by Basic Institute Scientific Research Fund (Grant no. 2012A02), the National Natural Science Fund of China (NSFC) (Grant no. 51308510), and Open Fund of State Key Laboratory Breeding Base of Mountain Bridge and Tunnel Engineering (Grant no. CQSLBF-Y14-15). The results and conclusions presented in the paper are of the authors and do not necessarily reflect the view of the sponsors.