Nonlinear Behavior Of Singlebox Multi-cell Composite Box-girder With Corrugated Steel Webs Under Torsion

Composite box-girder with corrugated steel webs（CBGCSW）is a new type of composite bridge formed by corrugated steel webs（CSWs）instead of concrete webs,which has certain advantages in terms of lighter self-weight,non-cracking of webs,less prestressing loss,increasing spanning capacity,and improving material utilization.Currently,to meet the rapidly growing traffic demand,more and more CBGCSWs employ multi-cell form to provide more traffic lanes,called single-box multi-cell CBGCSW（SBMC-CBGCSW）,and even this new type of bridge with 10-cell has been built in China.Previous literature suggests that the employment of thin CSWs will lead to a remarkable reduction in torsional stiffness of CBGCSW,with a decrease of approximately 60%.Even worse,when the wide or curved SBMC-CBGCSWs are subjected to the eccentric load or wind load,the torsional problem will be more prominent and dominant,so the torsional response of such bridges should be fairly investigated to guarantee their safety.In order to clearly reveal the torsional performance of SBMC-CBGCSW,a combination of experiment,finite element analysis and theory is used to systematically study the entire response of SBMC-CBGCSW subjected to pure torsion.The main research work and conclusions are as follows:（1）In this paper,experimental study on six scaled specimens,including 1-cell CBGCSW,3-cell CBGCSW and 5-cell CBGCSW,subjected to pure torsion is conducted to understand the effect of the thickness of CSWs,number of cells and spacing of CSWs on the full torsional response of SBMC-CBGCSW.The failure mode,cracking patterns,and buckling patterns of specimens are presented,and the torsional behavior of SBMC-CBGCSW,such as torque-torque curve and shear strain,during the entire load process is analyzed.Experimental research shows:（a）All specimens exhibit ductile failure,and all the outermost CSWs reach their yield strength before the steel bars.The failure of specimens is due to the spalling of concrete.The angle of diagonal cracks approximately ranges from 32°to 45°,while the angle of buckling of all specimens ranges from 23°to 37°,shaping a spiral shape in space;（b）Thicker CSWs can delay the cracking of concrete and significantly increase the ultimate torque of CBGCSWs.In addition,the thickness of CSWs has a direct impact on the sparsity of the distribution of diagonal cracks and the degree of buckling of CSWs;（c）With the increase of the number of cells and the distance between inner CSW and symmetric axis of box-girder,the degree of buckling of CSWs is reduced and the diagonal cracks can develop well.In addition,the yield torque and ultimate torque of SBMC-CBGCSW can be significantly improved,while the two factors have limited contribution to the cracking torque;（d）For SBMC-CBGCSW,before the cracking of concrete,the external torque is mainly resisted by the concrete slabs and the outermost CSWs,while in the nonlinear stage,especially after the yield of outermost CSWs,the inner CSWs are still in the elastic stage,playing a greater effect to the total torque;（e）The pure torsional behavior of CBGCSW,including single-cell and multi-cell,can generally be divided into four stages:the pre-cracking stage,the elastic-plastic stage,the yield stage and the decline stage;（2）A new shear strain relationship between inner CSWs and outside CSWs obtained from experimental results,which is in terms of the distance between CSWs,twist and number of cells,is proposed in this study to estimate the contribution of the inner CSWs to the torsional performance of SBMC-CBGCSW by theory.The new relationship can be applied in both linear and nonlinear analysis;（3）Finite element analysis（FEA）models corresponding to the scaled multi-cell specimens are created to model the torsional behavior of SBMC-CBGCSW,such as the angle of diagonal cracks,torque-twist curves,and shear strains of CSWs and concrete slabs.Then,the comparisons of FEA and experimental data show that the FEA models adopted in this study are in good agreement with experimental results,which indicates that these FEA models are capable of simulating the torsional performance of SBMC-CBGCSW;（4）A parametric study is performed to investigate the effect of influencing factors,such as the effective prestressing(f_pi),the ratio of width to height（B/H）,the ratio of width to span length（B/L）,the ratio of width to thickness of slab（B/T）,and the number of cells（n）,on the torsional performance of SBMC-CBGCSW.The parametric study suggests:（a）The main role of the prestressing is to delay the cracking of concrete and increase the cracking torque,but it cannot increase the ultimate torque;（b）the yield torque and ultimate torque of 5-cell CBGCSW are roughly inversely proportional to B/H;（c）the ultimate torque improves linearly with the increase of B/L in a certain range,whereas B/L has little impact on the yield torque;（d）while the ultimate torque decreases linearly with increasing B/T,the yield torque improves slightly with increasing B/T;（e）the yield torque and ultimate torque linearly improve with the increase of the number of cells in given range;（5）when R_{d 2}=0.9 and R_d3=0.5-0.55,5-cell CBGCSW will achieve optimum torsional performance.In addition,the CSWs near the outermost CSWs have a greater effect on the torsional behavior of SBMC-CBGCSW than the innermost CSWs.It also should be noted that when the distance between CSWs is small,there will be an effect of changing the number of boxes,reducing the torsional resistance of SBMC-CBGCSW;（6）Based on the rotating-angle softened truss model for torsion（RA-STMT）,this paper has proposed a modified softened truss model to compute the full performance of single-box single-cell CBGCSW under pure torsion,called the modified RA-STMT（MRA-STMT）,which considers the effect of concrete in tension and the effective thickness of shear flow zone of concrete slab,and takes into account the new three-stage average stress coefficients influenced by the correction of effective thickness of shear flow zone,the new two-stage shear strain relationship between concrete slabs and CSWs,and the torsional deformation coordination of whole cross section.The comparisons between the predicted results of MRA-STMT and test data in this paper verify the accuracy and rationality of the theoretical model.In addition,the comparisons between MRA-STMT and the other softened truss models and the softened membrane model show that the MRA-STMT model has a high precision in computing the torsional response of single-box single-cell CBGCSW,and it can achieve the same prediction accuracy as the more advanced softened membrane model.Meanwhile,and MRA-STMT in this paper has the advantages of relatively simple model and high solution efficiency;（7）The contribution of the inner CSWs in SBMC-CBGCSW is estimated by introducing the shear strain relationship between CSWs.The MRA-STMT for analyzing the torsional behavior of single-box single-cell CBGCSW is extended to predict the torsional response of SBMC-CBGCSW.Thus,a unified model for predicting the torsional behavior of CBGCSW,including single-cell and multi-cell,subjected to pure torsion is proposed（still called MRA-STMT）.Then,the torque-torque curve and shear strain predicted by MRA-STMT are compared with the experimental data and finite element results to verify the applicability and accuracy of the proposed model.In addition,the pure torsional response of SBMC-CBGCSW predicted by MRA-STMT is also compared with that of SMMT,which shows that the proposed MRA-STMT has high accuracy and can be used to predict the torsional performance of SBMC-CBGCSW under pure torsion;（8）Based on MRA-STMT and combining with relevant standards,the simplified formulas for calculating the cracking torque and ultimate torque of SBMC-CBGCSW are proposed,and they are proved by the test data and the results predicted by MRA-STMT,which shows that the simplified formulas can be used in engineering applications.Finally,based on the simplified calculation formula for predicting ultimate torque,the design process and calculation example of SBMC-CBGCSW under pure torsion are given.