## 1 Introduction  
Compared with conventional concrete box girders, a composite box girder with corrugated steel webs has several advantages, including that it is lightweight, has a convenient construction process, improved prestress efficiency, and lower probability of developing web cracks. When a corrugated steel web is used to replace the concrete web of box girders, the reduction of the web thickness reduces the torsional stiffness of the box girder. Previous studies have shown that the reduction in the torsional stiffness is approximately 60-70% [1]. Therefore, torsional loads, such as those resulting from eccentric loads, could have a more prominent effect on composite box girders with corrugated steel webs. This effect may, in turn, impact the structural safety of those girders. In recent years, several research studies have been introduced to calculate the torsional performance of composite box girders with corrugated steel webs [2; 3; 4; 5]. Among them, [PERSON] et al. [6] and [PERSON] et al. [7] derived differential equations based on [PERSON]'s second theory to calculate the torsion and distortion of composite box girders with corrugated steel webs. [PERSON] et al. [8; 9] applied the softened truss theory to the torsion analysis of composite box girders with corrugated steel webs and proposed the corresponding torsion design method. [PERSON] et al. [10] proposed an improved softened truss analysis model that fully considered the tensile characteristics of the concrete, and the model was validated by physical tests, as well as a finite element analysis. [PERSON] et al. [1] developed an analytical model to determine the torsional stress of composite box girders on the basis of two stakes, and the whole torque/twist curve of composite box girders with corrugated steel webs under pure torque was obtained. [PERSON] et al. [11; 12] and [PERSON] et al. [13] studied the torsional mechanism and the torsional strength by using a torsional test of a Prestressed Concrete (PC) composite box girder model with corrugated steel webs. [PERSON] et al. [14; 15] applied the softened membrane under shear action to the torsion member and proposed the softened membrane model under the pure torsion action. [PERSON] et al. [16] established a full-range analytical model for PC composite box girders with corrugated steel webs based on the theory of the softened membrane. Among the above theoretical analyses, the analysis based on [PERSON]'s second theory is the most common. This theory is simple, easy to understand, and mature, and the calculation results can meet the requirements of engineering error [3]. When analyzing the torsional effect of composite box girders with corrugated steel webs by using [PERSON]'s second theory, the composite section is converted into the section of the same material according to the ratio of the shear modulus of the steel and concrete, and then calculate it as a thin-walled box girder. However, the elastic modulus of the converted section is not completely equal, and the elastic modulus of the web is different from that of the top and bottom flanges, which leads to a large difference between the calculated results and the actual results of the box girder [17; 18]. The above studies mainly focused on traditional composite box girders with corrugated steel webs; however, there are fewer studies related to improved composite box girders with corrugated steel webs with a steel bottom plate instead of the conventional concrete bottom plate [19; 20; 21]. This type of box girder has several advantages, including its light weight, good seismic performance, low cost, and the reduced probability of developing bottom cracks. However, the reduction of the thickness of the bottom plate also reduces the torsional stiffness of the section, and, therefore, the torsional stress of the box girder may be impacted under the eccentric load. This paper provides a methodology to calculate the torsional stress in a single-box multi-cell-improved composite box girder with corrugated steel webs.