Effect of beam joinery on bridge structural stability
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Abstract
In this paper, we analyze the load deflection behavior of the superstructure elements of beam bridges under two different beam–beam connection designs. We present a mathematical model for beam–bridge structural analysis and apply the finite element method to solve the problem. We investigate the effects of beam–beam connection design on the response and behavior of the bridge system. We also present the effect of liveloads and deadloads on structural deformation, stress, and internal strain energy. We perform computer modeling of the beam bridge using ANSYS 19.2.
Keywords
Beam–beam connection Beam bridge Structure analysis Liveload force Deadload force1 Introduction
Bridges have always been an important part of our communities since the beginning of human civilization. The main objective of bridge construction is providing passages over natural barriers such as rivers and valleys, or infrastructures such as roads and railways. In modern bridge engineering, bridges can be classified by several different approaches, such as functions, materials, and types of structural elements. The notable bridge types include beam bridges, truss bridges, cantilever bridges, arch bridges, and suspension bridges [6]. The beam bridge is the most common form that has been used more extensively than others. Beam bridges or girder bridges are the simplest and also the oldest type of bridges. Similarly to many kinds of physical structures such as ships or building, they involve two components, superstructure and substructure. The superstructure refers to the beam itself, where the live load such as traffic loads are endured, and the substructure refers to a supporting structure to the bridge such as foundation, abutment, and piers where the live loads, dead load, and other loads are tolerated [14]. In their most basic form, beam bridges usually consist of a relatively short horizontal beam with supports at each end.
The use of structural modeling and analysis plays a crucial role in predicting and determining the loaddeflection behavior. For evaluation of existing bridges, structural models such as lumpedparameter models (LPMs), structural component models (SCMs), and finite element models (FEMs) are used to study the internal forces, stresses, and fracture of structures under various load conditions. Especially, the finite element method has been remarkably used in the area of structural analysis over the past 60 years. The finite element analysis (FEA) is also used in an accuracy assessment of the design rules [16]. A growing body of research has numerically investigated the structural performance of different types of bridges and their components exposed to various loadings using FEMs. A study on the ultimate load behavior of slab on a steel stringer bridge superstructure using a threedimensional nonlinear finite element analysis based on the ABAQUS software was conducted by Barth and Wu [2].
Brackus et al. [3] used both experimental and numerical models to determine the load distribution between the steel girders and the precast deck panels. They found that the loaddeflection data obtained from their numerical analysis corresponded very well with experimental results. Cobo del Arco and Aparicio [4] formulated a set of governing equations to study the deflection behavior of suspension bridges under concentrated loading. Nakamura, Tanaka, and Kazutoshi [13] carried out a static analysis of a new type of bridge called the cablestayed bridge with concrete filled steel tubes (CFT) arch ribs. They compared structural deformation between the cablestayed CFT arch bridge and a conventional steel cablestayed bridge at various ultimate loads. It was found that the cablestayed CFT arch bridge has higher flexural rigidity with less deflection than the conventional bridge.
The superstructure of the bridge usually consists of multiple spans to prevent any possible cracking. Due to the importance of the connections of bridge elements, a great deal of research has been carried out, based on both experimental and numerical models, to study the behavior of beamtocolumn connections and beamtobeam connections. Mashaly et al. [11] studied numerically the behavior of beamtocolumn joints in steel frames subjected to lateral loads using a 3D finite element model. Zhu and Li [19] used beamtocolumn welded connections in steel structures to study the resistance of steel structure after a fire. Jia et al. [8] performed experiments to investigate the effects of gusset stiffeners at the beamwebtocolumnweb joint on seismic performance of the beam–column connections in existing piers with welded box sections. Liu et al. [9] investigated experimentally the weld damage behavior using various local welded connections representing beamtocolumn connections under monotonic and cyclic loads. As the beamtobeam connection plays a tremendous part in the deformation of the bridge, several studies [5, 18] on beamtobeam connections have been carried out. Dessouki et al. [5] performed bolt force analysis using two different designs of endplate configurations, four bolts and multiple rows extended end plates, for Ibeam extended endplate moment connection. Yam et al. [18] analyzed the block shear strength and behavior of coped beams with welded end connections using the finite element model. However, no attempt has been done on the structural analysis of the beam bridge with main beam connections.
Hence the objective of this paper is to study the loaddeflection behavior of beam bridges with connections on the main beams. A finite element model of the beam bridge structure is presented to analyze the structural behavior of the beam bridge with main beam connections under deadload and liveload forces. The model is used to conduct a parametric study on two different designs of the connections including the full beam–beam and the half beam–beam geometries. Effects of the connection design on bridge behavior are investigated. We also present the total deformation, distributions of equivalent (von Mises) stresses, and internal strain energy obtained from the domain with different beamtobeam connection geometries.
2 Governing equation

Each Ibeam is pinned to its support.

The bases of all footings do not experience any deflection, that is, \(\underline{u} = \underline{0}\).
3 Finite element simulation
Model parameters. Properties of materials at temperature 22°C
Material  Density kg⋅m^{−3}  Isotropic Elasticity  Reference 

Concrete (unconfined compression strength 2.0E+7 Pa)  2286  Young’s modulus 2.3E+10 Pa  Murray (2007) [12] 
Poisson’s ratio 0.15  
Bulk modulus 1.1E+10 Pa  
Shear modulus 1E+10 Pa  
Asphalt concrete  Patel et al. (2011) [15]  
 semidense  2360  Young’s modulus 6.98E+8 Pa  
Poisson’s ratio 0.4  
Bulk modulus 7.48E+8 Pa  
Shear modulus 2.49E+8 Pa  
 dense  2330  Young’s modulus 2.17E+9 Pa  
Poisson’s ratio 0.4  
Bulk modulus 1.693E+9 Pa  
Shear modulus 7.75E+8 Pa  
Structural Steel  7860  Young’s modulus 2.05E+11 Pa  Luecke et al. (2005) [10] 
Poisson’s ratio 0.288  
Bulk modulus 1.6667E+11 Pa  
Shear modulus 7.96E+10 Pa 
Live load. Weights (Kg) of three different classes of trucks
Class  Light truck  Medium truck  Heavy truck 

1  0–2722  6361–7257  11,794–14,969 
2  2723–4536  7258–8845  >14,969 
3  4537–6360  8846–11,793 
Structural analysis. Loaddeflection behavior of bridge structure with different shaped geometries of the main beam connection
Load–deflection behavior (MIN, MAX)  Half beam–beam shaped geometry  Halffull beam–beam shaped geometry 

Total deformation (mm)  (0, 0.1545)  (0, 0.489) 
Equivalent (von Mises)  
Stress (MPa)  (0.1289, 0.4796)  (0.5949, 8.837) 
Total Energy (mJ)  (0, 5674)  (0, 2.527E+4) 
4 Conclusion
The computer bridge model was developed to study the effect of beam–beam connection geometry on the loaddeflection behavior of beam bridges. Two designs of halffull beam–beam shape and half beam–beam shape were chosen in this study. The results indicate that the model with halffull beam–beam connection design leads to higher values of bridge deformation, (von Mises) stress, and total strain energy compared with the bridge model with half beam–beam connections. The results of this research may help structural engineers in the optimization of the main Ibeam connection system design.
Notes
Authors’ contributions
The main idea of this paper was proposed by YHW and NK. DW prepared the manuscript initially and performed all the steps of the proofs in this research. All authors read and approved the final manuscript.
Funding
The first author would like to thank for the 2018 SAE summer scholarship from the faculty of Science and Engineering, Curtin University, Perth WA, Australia. The second author would like to thank for partial financial support from the Centre of Excellence in Mathematics, Commission on Higher Education, Thailand. The last author would like to thank the Australia research council for the financial support and WA Main Road for providing some data for the work.
Competing interests
The authors declare that they have no competing interests.
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