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Cracking Mechanism and Simplified Design Method for Bottom Flange in Prestressed Concrete Box Girder Bridge Yiqiang Xiang1 Guobin Tang2 and Chengxi Liu3 Abstract Serious cracking has occurred frequently in the bottom flange of box girders during construction in recent years This paper aims at studying the cracking mechanism and countermeasures The stress field in the bottom flange associated with the bottom continuity tendon is presented and the propagation of cracks during tensioning is simulated by nonlinear analysis according to the actual construction sequence A cracking mode which is not easy to detect in field investigation is illustrated through numerical and theoretical study It is caused by the deficient shear strength of the bottom flange attributed to the void in tendon ducts Based on numerical results and field investigation four types of cracking in the bottom flange are proposed and discussed and a simplified design method is recommended for control of cracking DOI 10 1061 ASCE BE 1943 5592 0000151 2011 American Society of Civil Engineers CE Database subject headings Bridges girder Box girders Concrete Flanges Cracking Design Author keywords Bridge engineering PC box girder Bottom flange Cracking mechanism Simplified design method Introduction Prestressed concrete box girder bridges were developed in Europe in the 1950s and today are widely used in both mid and long span bridge construction with the advantage of economy and aesthetics Toward the 1970s the balanced cantilever construction method imported from Germany began to be used in China In the past 20 years this technique has been well developed and a large number of continuous and rigid frame bridges have been built using this method in China such as the Shibanpo Bridge 330 m and the Sutong Auxiliary Bridge 268 m However some effects that are especially critical in structures are poorly understood or even completely ignored Consequently defects such as cracks still appear in concrete box girder bridges Podolny 1985 Chatelain et al 1990 In box girder bridges cracks usually occur in the flanges or webs after the traffic opening and have been studied for a long time In addition to the cracking after traffic opening the cracking during the construction becomes more and more common in box girder bridges using the balanced cantilever technique This new cracking appears in the bottom flange while prestressing the bottom continuity tendons and takes the form of longitudinal cracking spalling of concrete cover and delamination of the flange Peng 2008 It was generally ascribed to the construction deficien cies arising from poor or substandard workmanship Podolny1985 He 2001 Podolny 1985 found that the cracking resulted from downward radial force associated with curved tendons which was unexpected in the design If the longitudinal ducts were used with an insufficient number of supporting chairs or ties or if they were deflected downward by the weight of the wet concrete being placed or by workmen walking in the fresh concrete the duct profile would have an angle break or cusp at each joint As a con sequence an excessive downward radial forcewas induced and the risk of local spalling and bursting of intrados of the bottom flange arose Nevertheless not all the cracking suffered from tendon mis alignment Li 1997 During an investigation of a continuous box girder bridge little deviation of tendons was discovered after incis ing the concrete of the bottom flange Recently studies on the cause and retrofit of this cracking have been widely reported Qualitative and quantitative methods were used to analyze the cause of crack ing However the conclusions on the cracking was different Ac cording to their results either vertical tension stress Podolny 1985 Guo 2005 or transverse stress Wei et al 2007 Wang et al 2008 of the bottom flange was probably the most fundamental reason for cracking Although the radial force as the direct load causing the cracking has been widely accepted the cracking mechanism under radial force remains debatable It is partly attributed to the obscure cracking process in the bottom flange during the tensioning of the tendons Because the bottom flange lies beneath the box girder only severe cracks can be investigated but initial cracking is not easy to detect According to the field investigation Pan 2008 di vided these cracks into two main groups longitudinal cracking and delamination of the flange base whereas Peng 2008 extended the spalling as the third type of cracking In this paper based on the numerical and theoretical analysis four types of cracking of the bottom flange are presented and the relationship among them is studied A new cracking type is detailed and the cracking mechanism is discussed based on the nonlinear analysis with the actual construction sequence In addition a simplified design method learning from similar structure is proposed for cracking control 1Dept of Civil Engineering Zhejiang Univ Hangzhou Zhejiang 310058 China E mail Xiangyiq 2Dept of Civil Engineering Zhejiang Univ Hangzhou Zhejiang 310058 China corresponding author E mail tangguobin 3Dept of Civil Engineering Zhejiang Univ Hangzhou Zhejiang 310058 China E mail sd1207465 Note This manuscript was submitted on November 18 2009 approved on June 14 2010 published online on July 10 2010 Discussion period open until August 1 2011 separate discussions must be submitted for in dividual papers This paper is part of the Journal of Bridge Engineering Vol 16 No 2 March 1 2011 ASCE ISSN 1084 0702 2011 2 267 274 25 00 JOURNAL OF BRIDGE ENGINEERING ASCE MARCH APRIL 2011 267 J Bridge Eng 2011 16 267 274 Downloaded from ascelibrary org by Changsha Univ Of Sci all rights reserved Stress Field Associated with Curved Tendons Mechanism of the Curved Tendon The curvature of the longitudinal tendons induces radial forces dur ing the prestressing and it is the direct load acting on concrete cover at the bottom flange Fig 1 shows a segment ds of the curved tendon in the flange with a spatial location r fx s y s z s gt Assuming that there is a tensile force of Tsat the middle of thesegment theforceatbothendsofthesegmentis Ts 1 2 dTs ds ds The pn ps and pmare equivalent loads in three directions of the tendon The n denotes a unit vector in the direction of tendon curvature and the s and m are the orthogonal vectors in the normal plane The equilibrium equation may be es tablished as Ts 1 2 dTs ds ds s 1 2 ds ds ds Ts 1 2 dTs ds ds s 1 2 ds ds ds pns psn pmm ds 0 1 By introducing ds ds n the above equation may be expressed as Tskn dTs ds s pnn pss pmm 2 Using the scalar form Eq 2 can be simplified as pn Ts ps dTs ds pm 0 3 where isthecurvatureofthetendon InEq 3 twotypesofforceare accompaniedbystressing theyareradialforcepnand tangential force ps However as the value of coefficient of friction between tendon and duct is usually from 0 15 to 0 30 the three dimensional 3D finite element model FEM study indicates the stress caused by the psis not more than 5 of that caused by the pn Consequently thetangentialforcemaybeneglectedinthisstudy Stress Field of the Bottom Flange during Construction The bridge considered in this paper is a three span cast in place continuous box girder bridgewith a total length of 180 m as shown in Fig 2 The main span is 80 m long with a 18 m beeline segment at midspan and a circle arc segment Fig 3 is the typical section at an interior pier and midspan The box girder is built using the can tilever method and there are 30 bottom continuity tendons in the midspan which are anchored in 12 blisters at the bottom flange as illustrated in Fig 4 The posttensioned tendon anchorage system for 12 strands of a 15 24 mm diameter according to ASTM A416 has been selected for bottom continuity tendons The design applied load in the anchorage device is 2 344 kN and it is applied to the 12 strands by means of a multiple jack simultaneously which induces the same lengthening to all the strands and transfers the load to the anchorage when the wedges grip the strands in the anchorage head After closure of the center span joint the bottom continuity tendons are installed When the tendons are being stressed crack ing occurs in the flange in Zone A followed by a rapid splitting of the concrete cover Fig 5 shows the details of reinforcement in T T s s ds ds d 2 1 r x z n m o y T s s ds ds dT 2 1 p s s p m p n Fig 1 Equivalent loads of curved tendons Fig 2 General layout details Fig 3 Cross sections of the bridge at interior piers and midspan 268 JOURNAL OF BRIDGE ENGINEERING ASCE MARCH APRIL 2011 J Bridge Eng 2011 16 267 274 Downloaded from ascelibrary org by Changsha Univ Of Sci all rights reserved Zone A The reinforcement form as shown in Fig 5 is quite common in box girder design in China Alinear3Dmodelisdevelopedforthestressfieldintheconstruc tion stage The SOLID45 element is used to model the concrete whereas the LINK8 element is used for prestressed tendons The element birth and death capability is employed to simulate the con structionprogress Thebirthanddeathofelementsandactivationand deactivation of tendons are performed according to the construction phase Theprestressingeffectofbottomcontinuitytendonsissolved bytheprinciple ofequivalentload The equivalentloadsdetermined by Eq 3 are applied to the ducts according the construction steps Fig 6 shows the stress conditions of the box girder from the numerical analysis As indicated in Fig 6 a there is an adverse tensile stress field in Zone A where the maximum principal tensile stresses exceed the concrete tensile strength This tensile stress is quite small during the construction of the cantilever part but rap idly increases during the tensioning of the bottom continuity ten dons Figs 6 b and 6 c indicate the transverse and vertical stress of the flange in Zone A respectively The maximum transverse ten sile stress is 4 95 MPa and the vertical stresses normally do not exceed 0 51 MPa In the flange longitudinal cracks occur along the ducts first rather than laminar cracks at the ribs during the pre stressing After longitudinal cracking the stress field of the flange be comes more complicated because of stress redistribution As these initial cracks usually cannot be discovered with tensioning of other tendons the cracks may propagate rapidly and lead to serious failure In this case a nonlinear analysis has to be promoted to clarify the cracking mechanism Nonlinear Analysis of the Cracking of Bottom Flange FEM Model A solid model of the whole bridge may not be necessary to study the flange cracking because greater costs effort and more time are involved For an effective nonlinear model the basic assumption of simple frame analysis SFA is adopted Kurian and Menon 2005 A 3D scale solid model is established by modeling the cross section as a frame of unit width with imaginary supports at the web loca tions By taking advantage of the symmetry half the frame has been discretized using ANSYS with proper boundary conditions A solid element SOLID65 is used to model the concrete The element has eight nodes with three degrees of freedom at each node It is capable of simulating the plastic deformation and crack ing in three orthogonal directions The plain bars and tendons are represented by the 3D line elements Two nodes are required for these elements At each node the degrees of freedom are identical to those for the SOLID65 which represents the concrete The combination of these two elements can describe the box girder behavior Ideally in the present analysis the reinforcement bars are assumed to be perfectly bonded to the surrounding concrete Fig 7 shows the mesh of the model and both discrete reinforce ment and smeared reinforcement have been used in the mesh All the prestressed tendons and plain bars in the bottom flange adopt truss bars as discrete reinforcement connecting solid element nodes whereas the other bars in the top flange and webs are smeared in the solid elements This model can help confirm the cracking process as well as provide a valuable supplement to the field investigations of behavior 4 N214 N20 2 N19 2 N19a 2 N19b 2 N18 2 N18a 2 N18b 2 N17 2 N17a 2 N17b 2 N22 2 N22a Fig 4 Bottom continuity tendons and anchorage blister in midspan Fig 5 Geometry and reinforcement bar details in the bottom plate of Section A A Fig 6 Stress of box girder after bottom continuity tendons tensioning unit MPa a the first principal stress b the transverse stress of bottom flange in Zone A c the vertical stress of bottom flange in Zone A Fig 7 Finite element mesh division of the half box girder JOURNAL OF BRIDGE ENGINEERING ASCE MARCH APRIL 2011 269 J Bridge Eng 2011 16 267 274 Downloaded from ascelibrary org by Changsha Univ Of Sci all rights reserved Material Models In accordance with the Solid65 element linear isotropic and multi linear isotropic material properties are required to properly model concrete The multilinear isotropic material uses the Von Mises failure criterion along with the Willam and Wamke model to define the failure of the concrete Fig 8 a shows the uniaxial stress strain curve of concrete that will be used in this study The relation in compression is a parabola followed by the linear softening branch until the ultimate compres sivestrain Hognestad et al 1955 Using the two stress strain pairs 0 0 and fc Ec and zero slope of the stress strain curve at fc one can obtain the following parabolic relationship c fc 2 c 0 c 0 2 for c 0 4 c fc 1 0 15 c 0 cu 0 for 0 c s 2 d the governing failure mecha nism will be delamination with Eq 10 giving the radial force required to delaminate the ribs Fig 17 shows the plot of radial force q normalized to ft d against the ratio of concrete cover c to duct diameter d for the relations given by Eqs 9 and 10 which correspond to the expressions for the radial force required for spalling and delamina tion respectively of the bottom flange Also the radial force required for the longitudinal cracking is illustrated by 3D finite element analysis For any value of c d longitudinal cracking initially occurs at the bottom surface of the flange Depending on the geometric configuration of the concrete cover and ducts spacing the radial force q resulting from further tensioning induces the concrete cover to fail in three modes longitudinal cracking fol lowed by spalling longitudinal cracking followed by delamination or longitudinal cracking followed by shear failure of ribs For the example illustrated in Fig 17 where the ratio of duct spacing s to diameter d is set to 3 the failure of the bottom flange will manifest itself as longitudinal cracking followed by delamination for c d 0 5 as longitudinal cracking followed by spalling for c d 0 5 Simplified Design Method In the previous sections the writers have attempted to delineate the causes of cracking in the bottom flange of a box girder For crack ing control engineers should reevaluate the design method of the bottom flange AASHTO LRFD 2004 details provisions for ten don confinement in section 5 10 and it focuses on the spalling of curved webs The Chinese bridge design specification also makes similar provisions However more attention should be paid to other cracking patterns in bottom flange during design and construction The following section proposes some countermeasures for cracking control in the bottom flange Fig 14 Spalling of bottom flange in a box girder bridge q Spalling Fig 15 Calculation model of spalling q q Delamination Fig 16 Delamination of ribs 0 1 2 3 4 5 6 0 00 40 81 21 62 02 4 c d q ft d Longitudinal Cracking Spalling Delamination s d 3 Fig 17 Radial force required for different failure modes of bottom flange 272 JOURNAL OF BRIDGE ENGINEERING ASCE MARCH APRIL 2011 J Bridge Eng 2011 16 267 274 Downloaded from ascelibrary org by Changsha Univ Of Sci all rights reserved Transverse Action from Bottom Continuity Tendon To further compound the problem the effect of curved tendons should be incorporated in design practice From Eq 3 the equiv alent loads of tendons can be obtained and acted on the bottom flange Based on the SFA method the transverse action can be determined It should be noted that the bending movement and shear force from the radial force adopted hereinneed to be combined with other construction loads The load factors for tendon force may reference the specifications in Article 3 4 3 AASHTO LRFD 2004 Transverse Bending Design The bottom flange of the box girder is usually designed as a rein forced concrete structure Consequently there is a risk of cracking and longitudinal cracks have occurred in a number of box girders However nonlinear results indicate that longitudinal cracking re mains stable during further tensioning and it has little effect on the bearing capacity At the strength limit state the failure is still caused by the crush of concrete or the yield of steel In addition the ducts have little influence on transverse bending performance Therefore the transverse bending design of the bottom flange under radial force may refer to the common reinforced concrete structure design For longitudinal cracking control measures to control the radial force should be adopted in the preliminary design such as mini mizing the curvature of the bottom flange or adding flange thick ness Xiang and Tang 2009 Transverse Shear Design Because of the ducts the shearing performance of the bottom flange is different from that without ducts There are obvious de fects in shear transfer such as the discontinuity of concrete and it should not be neglected in the design Nonetheless there is no specification for this type of structure in either AASHTO LRFD 2004 or Chinese codes D62 2004 MCPRC 2004 However this problem may be solved by introducing the analy sis results of a concrete hollow floor system The concrete hollow floor system as shown in Fig 18 has been promoted and applied in Chinese building structures recently It has a similar structure con figuration to the bottom flange of a box