Shear Stress Calculation and Distribution in Variable Cross Sections of Box Girders with Corrugated Steel Webs Man Zhou, Ph.D. 1 ; Jiandong Zhang 2 ; Jitao Zhong, Ph.D. 3 ; and Yong Zhao, Ph.D. 4 Abstract: Based on the condition of static equilibrium and the equivalent law of shearing stress of an infinitesimal segment, this paper provides a strict derivation of the general formula for shearing stress in a nonuniform box girder with corrugated steel webs in the elastic stage. The derived formula is applied to investigate the stress distribution in concrete flanges and corrugated steel webs. Additional shear stress was found to be caused by the bending moment, and the axial force should be included in calculations from the effect of variable cross sections, which are quite different from that of the uniform cross sections. Moreover, because the additional shear stress of the bending moment is self- balanced, the shear force distribution can be adjusted between the concrete slabs and steel webs. Research shows that shear stress decreases markedly in the webs, whereas the shear stress apparently increases in the inclined bottom flange in the action of the bending moment. This study also found and explained the phenomenon that shear stress in the lower surface of the inclined bottom flange is not zero. In the elastic stage, the proposed formula is in good agreement with the results of the three-dimensional (3D) finite-element analysis for a cantilever beam. This example shows that the classic method of material mechanics is no longer suitable for the calculation of a nonuniform beam. Finally, because the formula is too complex to be extensively executed by engineers, two simplified calculation methods are put forward considering the equivalent force principle, and the simplified calculation methods are proved to be valid and applicable according to the contrasting results with the nonuniform mathematical formula. DOI: 10.1061/(ASCE)ST.1943-541X.0001477. © 2016 American Society of Civil Engineers. Author keywords: Variable cross section; Corrugated steel web; Shear stress; Self-balanced stress; Stress distribution; Simplified calculation method; Analysis and computation. Introduction In 1975, the idea of using corrugated steel webs (CSWs) as op- posed to traditional flat webs was put forward for the first time by Campenon Bernard (Clichy, France) of France. Soon after, the first composite box girder with CSWs, the Cognac Bridge, was constructed in France in the late 1980s. Since the 1980s, a new type of steel prestressed concrete (PC) composite structure has been used, the prestressed concrete box girder with CSWs. With the advantages of outstanding mechanical behavior, simple construction, and remarkable economic performance, this new type of structure instantly attracted the increasing interest of engineers (Cheyrezy et al. 1990; Lebon 1998). Many countries have erected bridges of this type since the PC box girder with CSWs was introduced, such as the new superstructure type for bridges by ACSI in 1988 (Zhong 2006). Specifically, this new type of bridge received wide application in Japan since the bridge of the box girder with CSWs was successfully first built in 1993. With the rapid development of scientific research and practice, a series of bridges of this type was built in Japan. To date, Japan has the most PC box girder bridges with CSWs in the world (He et al. 2012; Jiang et al. 2014). In recent years, as the manufacturing processes, construction technology, and design theory of the box girder with CSWs have increasingly matured, this type of bridge has begun to offer signifi- cant competition to the modern larger span bridges. Generally, beams of variable depth are inevitably used, considering the ration- ality of economy and technology. Many scholars have conducted extensive practical and theoretical research on the shear deforma- tion and shear buckling of the I-girder and box girders with CSWs (Elgaaly et al. 1996; Luo et al. 1996; Aravena and Edlund 1987; Höglund et al. 1997; Sayed-Ahmed et al. 2001, 2007; Yamazaki 2001; Abbas et al. 2002; Driver et al. 2006; Yi et al. 2008). How- ever, most of the research efforts focus on uniform components, and few previous studies have focused on the analytic expression and distribution laws of shear stress in beams of variable cross sections. Previous research achievements by domestic and foreign researchers are presented below. Based on the results of multiple group experiments, Hamilton (1993) and Sayed-Ahmed (2005) suggested that shear forces were resisted mainly by the CSWs and that the structural damage was caused by shear buckling of webs. Johnson (1997) found that stress in the CSWs is generated almost solely by vertical shear, shrinkage, and creep, and prestressing temperature changes in the concrete slabs have little influence on the folded webs. Rosignoli (1999) concluded that the longitudinal bending moment is resisted mostly by axial forces in the concrete flanges and that the shear forces are resisted mostly by the steel webs in a prestressed composite struc- ture (PCS). Japanese scholars have conducted extensive fundamen- tal research in this field. Through the experiment of a simply 1 Key Laboratory of Concrete and Prestressed Concrete Structures of Ministry of Education, College of Civil Engineering, Southeast Univ., 2 Sipailou, Nanjing 210096, China (corresponding author). E-mail: [email protected] 2 Professor, Key Laboratory of Concrete and Prestressed Concrete Struc- tures of Ministry of Education, College of Civil Engineering, Southeast Univ., 2 Sipailou, Nanjing 210096, China. E-mail: [email protected] 3 Key Laboratory of Concrete and Prestressed Concrete Structures of Ministry of Education, College of Civil Engineering, Southeast Univ., 2 Sipailou, Nanjing 210096, China. E-mail: [email protected] 4 Dept. of System Consulting, Aimnext Inc., Minato-Ku, Tokyo 105-0013, Japan. E-mail: [email protected] Note. This manuscript was submitted on January 27, 2015; approved on November 24, 2015; published online on January 27, 2016. Discus- sion period open until June 27, 2016; separate discussions must be sub- mitted for individual papers. This paper is part of the Journal of Structural Engineering, © ASCE, ISSN 0733-9445. © ASCE 04016022-1 J. Struct. Eng. J. Struct. Eng., 2016, 142(6): 04016022 Downloaded from ascelibrary.org by Southeast University on 01/11/19. Copyright ASCE. For personal use only; all rights reserved.
Shear Stress Calculation and Distribution in Variable Cross Sections of Box Girders with Corrugated Steel Webs
Jun 24, 2023
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