## 1 Introduction  
Fiber-reinforced-polymer (FRP) composites are among the most promising alternatives to steel and concrete due to their light weight, high durability, and high strength. Glass-fiber-reinforced polymer (GFRP) decks are of interest because of their economy and applicability to bridges. They have significant advantages over concrete and steel owing to their durability and corrosion resistance. Thus, they have longer service life and lower maintenance costs. Moreover, GFRP decks have significantly lower dead loads than conventional concrete decks owing to their light weight. Therefore, slimmer bridge pier designs can be produced, and existing bridge walkways can be economically expanded, even without retrofitting the substructures. Furthermore, construction is significantly shortened due to the easy installation of FRP decks [1, 2, 3, 4].  
When designing a GFRP bridge deck, structural safety and serviceability under bidirectional bending due to design wheel loads should be considered. Generally, GFRP decks have higher strength than normal decks made of steel or reinforced concrete. Therefore, safety requirements are easily satisfied within an adequate factor of safety. However, their low stiffness means that deflection limits under service loads govern the design.  
Particularly, the local behavior of adhesive joints in GFRP decks should be investigated because they are the primary cause of pavement cracks and durability problems. Individual pultruded GFRP deck units are connected through adhesive bonding to form a deck system [5]. The improper design of adhesive joints results in excessive deformation at the joints, causing local tensile cracking in the adhesive and reflective cracking in asphalt pavements under service loads [6; 7]. Weak axis bending of the deck system significantly affects the behavior of adhesive joints. To the authors' knowledge, only a few studies on the weak-axis bending of deck systems have been reported, and these did not consider the behavior of the adhesive joints [8; 9; 10]. Our previous study described the failure modes in the adhesive joints of purturbed GFRP decks under weak-axis bending, including failures of adhesive and deck substrates [11]. Finite element (FE) analyses and tests were conducted on adhesively connected GFRP decks with hollow trapezoidal sections called \"Delta Deck TG200\" (TG200 hereafter) as beam specimens.  
In this study, an FE analysis of an adhesively connected GFRP bridge deck under bidirectional bending due to traffic wheel loads was performed. Three-dimensional solid elements, which simulated the actual shape and material properties of the deck tubes and adhesive layers, were utilized in the FE analyses. To investigate the behavior of the adhesive joints in the deck system, the FE model of a deck system should represent the connection details, such as the joint geometries and material properties, of adhesive and deck substrates. Figure 1 shows the configurations of the section and adhesive layer in TG200. The connections between the TG200 deck tubes had a tongue-and-groove (TG) shape with stepped lap joints. This study describes the requirements for limit state design; introduces a solid-element FE model and the assumed material properties of the deck substrate and adhesive; verifies the serviceability in terms of global deflection of the deck and local deformation of the adhesive joints; and verifies the safety of the adhesive and deck substrate at the joints against the four different failure modes introduced by [PERSON] et al. [11]: (1) tensile failure of adhesive at joint edge of bonded flanges (TAF), (2) tensile failure of adhesive between vertical webs (TAW), (3) shear failure of adhesive between flanges (SAF), and (4) failure of deck substrate at discontinuous dimension in section (FSD).  
Figure 1: _Cont._