# Estimation of Live Load Distribution Factor for a PSC I Grider Bridge in an Ambient Vibration Test
## 1 Introduction  
Bridges are major facilities on roads that constitute the core of social infrastructures. They are built to secure stability and usability during their service lives. A bridge with excellent construction quality and materials can safely perform its functions during its design lifetime and service life when the external environment does not change significantly. Over time, however, bridges are damaged by various factors, such as changes in the traffic environment and deterioration of materials. Thus, it is necessary to extend their lifetime and secure safety and usability through proper maintenance [1; 2; 3; 4]. Consequently, evaluating the integrity of bridges is an important maintenance task for securing safety [5; 6; 7; 8; 9; 10; 11]. At present, inspections and safety diagnoses are regularly performed for the maintenance of bridges, and the load-carrying capacity of bridges is evaluated to identify their performance degradation and level of deterioration [12; 13; 14]. In general, the vehicle loading test is conducted to evaluate the load-carrying capacity of a bridge [15; 16; 17]. The overlap and symmetric behavior of a bridge can be identified by measuring the live load distribution factor (LLDF) using the vehicle loading test. When there is no connecting structure between the girders of a bridge, bending occurs only in the girders under the loads. In bridges, however, load transfer structures are installed in a direction perpendicular to the bridge axis to connect the girders. Therefore, even if a load is applied to a girder, the load is shared by the neighboring girders due to the load transfer structure connected in the lateral direction. In this instance, the degree of load transfer depends on the stiffness of theload transfer structure and the spacing between girders. This makes LLDF an important element in bridge maintenance [18; 19; 20]. The procedure for updating the finite element model mostly involves finding the most suitable structural parameter that can minimize the error between the measurement and analysis results by solving the optimization problem. Various types of responses, such as displacement, natural frequency, and mode shape, can be considered as references in matching the actual structure and the finite element model [21; 22; 23; 24; 25]. Dynamic characteristics for the natural frequency and mode shape can be measured using the ambient vibration test. The finite element model updated only with dynamic characteristics, however, is not sufficient to reproduce the static displacement of the target bridge. Static displacement is a good indicator in correcting the stiffness characteristics of a finite element model, but it cannot perform mass correction [26; 27; 28]. In this sense, the reliability of the finite element model of the target structure for structural performance evaluation can be improved if static displacement is supplemented by dynamic characteristics [29; 30; 31; 32]. To measure static displacement, however, traffic control is required on bridges in use because loading must be performed at designated positions using vehicles whose details are known. For girder bridges, LLDF can be used instead of static displacement because LLDF represents the load-sharing behavior of girders for vehicle loads. Therefore, LLDF can be used in updating the finite element model that represents the stiffness characteristics of the target bridge. Many studies have been conducted on the LLDF of bridges and results have consequently been published. LLDF was expressed as a function of the spacing between girders and the bridge span using the finite element analysis of a plate girder bridge [33]. A vehicle loading test was conducted on a post-tensioned box girder bridge, and the finite element model was updated using the results obtained. A study was conducted to evaluate the influence of various parameters, such as the span length, girder spacing, railing, slope, and deck thickness of a bridge, on LLDF using the updated finite element model [34].