**Bishnu Gupt Gautam , Yi-Qiang Xiang \* , Zheng Qiu and Shu-Hai Guo**

College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China; bishnu@zju.edu.cn (B.G.G.); qiuzheng\_zju@126.com (Z.Q.); 15158016702@163.com (S.-H.G.) **\*** Correspondence: xiangyiq@zju.edu.cn; Tel.: +86-571-8820-8700

Received: 23 February 2019; Accepted: 19 March 2019; Published: 22 March 2019

**Abstract:** Accelerated construction in the form of steel–concrete composite beams is among the most efficient methods to construct highway bridges. One of the main problems with this type of composite structures, which has not yet been fully clarified in the case of continuous beam, is the crack zone initiation that gradually expands through the beam width. In the current study, a semi-empirical model was proposed to predict the size of cracks in terms of small box girder deflection and intensity of load applied on the structure. To this end, a set of steel–concrete composite small box girders were constructed by the use of steel fibrous concrete and experimentally tested under different caseloads. The results were then used to create a dataset of the box girder response in terms of beam deflection and crack width. The obtained dataset was then utilized to develop a simplified formula providing the maximum width of cracks. The results showed that the cracks initiated in the hogging moment region when the load exceeded 80 kN. Additionally, it was observed that the maximum cracked zone occurred in the center of the beam due to the maximum negative moment. Moreover, the crack width of the box girder at different loading cases was compared with the test results obtained from the literature. A good agreement has been found between the proposed model and experiment results.

**Keywords:** static behavior; studs; deflection; finite element model; composite beam; crack width
