## 1 Introduction
The same triangular distribution of shear connectors was also employed by [PERSON] and [PERSON] [8] to derive the expressions of interface slip. Even though the triangular distribution can effectively cut down the interface slip, the method is too complicated to be applied in practical engineering. Simultaneously, [PERSON] et al. [9] presented an analytical solution for the interface slip of composite beams through stepwise distribution of connectors, although this distribution was inconvenient for application in practical engineering, since it needs to be resolved anew for each load case. These research results show that the distribution type of the shear connectors has a significant impact on the interface slip of composite beams. Despite the fact that the triangular distribution and stepwise distribution of shear connectors can reduce interface slips, it may be inconvenient to apply them in practice, as mentioned above. Furthermore, their application was restricted to simple load cases only (i.e., uniformly distributed load or point load at mid-span), because no analytical solutions were provided for composite beams with more than two distribution types under other complicated load cases. With the progress in the development of computing tools and computers, finite element methods have become a powerful and useful tool for the analysis of a wide range of engineering problems, since they are convenient and universal in terms of dealing with any combination of loading and constraint conditions. Thus, lots of one-dimensional, two-dimensional and three-dimensional finite element models have been developed for the finite element analysis of composite beams. Two-dimensional and three-dimensional composite beam elements have been used quite often in  
or other aspects of the system behavior. In addition, these works adopted the continuous bond model for interface connection, but in practical engineering, the two components of composite beams are often connected in a discrete way by means of shear connectors. With the help of the finite element method, this paper proposes an optimal layout method for shear connectors that adopts a stepwise uniform distribution of shear connectors, i.e., 2-stepped rectangular distribution, 3-stepped rectangular distribution and 5-stepped rectangular distribution, in order to approximate a triangular distribution [7]. A one-dimensional composite element model with discrete shear connectors is developed for the finite element analysis of composite beams. A composite beam element model with 4 degrees of freedom per node is constructed in accordance with the Euler-Bernoulli theory, and the corresponding element stiffness matrix is derived by utilizing the total potential energy method and considering the effect of interface slip. After being validated by comparing the results obtained from the developed element with those of the closed-form solutions and experimental results, the developed element is applied to analyze the impact of distribution type of shear connectors on the interface slip. On the basis of the numerical results, an optimal layout method for shear connectors is proposed for simply supported composite beams under four different types of load without increasing the total number of shear connectors. The rest of the paper is divided into four main sections. First, on the basis of the Euler-Bernoulli theory, the composite beam element is constructed, and this is followed by a validation study using finite element analysis and the results of closed-form solutions and experiments. Afterwards, the problem of how to obtain an optimal layout method based on the developed element is discussed. Finally, some conclusive remarks are summarized.