Influence on Durability of Concrete Slab in Composite Bridge due to Use of Elastic Supports Joang-Jin PARK Shigeyuki MATSUI Hiroshi HIGASHIYAMA Keizo EGASHIRA Abstract: When existing simple span bridges are converted into a continuous span rigid support conditions have to be changed to elastic supports in order to absorb and distribute the energy of large horizontal motion due to earthquake loading. However, development of reaction force and additional stresses on the slab due to the unequal displacement of the elastic supports have been overlooked. In this study, a simple span bridge specimen is tested and analyzed to investigate stress increase of the concrete slab when the rigid supports are replaced by the elastic supports to accommodate the structural conversion under the elastic support is also discussed.. Durability of concrete slab Key Words : elastic supports, structural conversion, durability of concrete slab 1. Introduction Expansion joints are designed to absorb horizontal displacement and rotation of the beam end due to the temperature change, moving vehicular load,...etc. However, expansion joints are very often damaged due to the repeated loading of moving vehicles. If damaged, the expansion joints become the sources for several problems. Uncomfortable ride, noise, and structural vibration as vehicles pass over the broken joints trouble riders as well as residents in the vicinity of the structure. Corrosion due to water penetrated through the damaged expansion joints is also a factor for shortening the service life of the structure. Moreover, *1 D epartment bf Civil Engineering, Osaka University, Research Fellow *2 D epartment of Civil Engineering, Osaka University, Dr., Professor *3 D epartment of Civil Engineering, Osaka University, Ph.D. Student *4 D epartment of Bridge Design, repairing of damaged joints can not be performed without regulating the traffic flow. In any view, expansion joints in the simple span bridge structures have been one of the troublesome parts. One of the advantages of a continuous bridge over the simple span bridges is that there are fewer number of expansion joints which cause the above stated problems. When existing simple span bridges are converted to the continuous spans, changes in the vertical reaction due to the live load and distribution of horizontal reactions to all supports have to be adjusted. Detailed specifications are provided in the Highway Bridge Design Manual for Seismic Design[l]. When girders and I or concrete slabs are connected, support conditions have to be changed as illustrated in Fig. 1. Vertical spring constant for the support has to be selected on the base of the vertical reaction so that the change of the reactions after the conversion would not be large enough to cause over-stress of the bridge piers[2]. Harumoto Corporation 71
Steel Construction Engineering Vol. 5 No, l8(june 1998) Fig.l Structural Conversion of Simply Supported In the process of the conversion, effect of the vertical elastic supports on the concrete slab due to the live (traffic) load has not been studied thoroughly, assuming that the stress level for the continuous bridge structures would be reduced. In contrary, an additional stress on the concrete slab is presumed due to uneven settlement of elastic supports. Only a preliminary study of the increase of transverse stress on the concrete slab due to elastic supports has been reported so far[3]. As a more extensive study, a composite bridge specimen on three-steel-girders was set up to test the slab behavior due to the change of the support conditions. Tests were conducted by changing the support conditions from rigid to elastic and the results of both test and numerical analysis are reported in this paper. 2. Set-up of the Test Specimen Spans to a Continuous Structure Tests were conducted on a composite simple span bridge specimen composed of pre-cast concrete slabs on three-steel-girders. The test specimen is shown in Fig. 2. Scale of the test specimen is 114 in the transverse direction and 118 in the longitudinal direction to an actual bridge currently being converted to a continuous structure. The assembly for the test specimen was performed in the following order; (1) placement of the pre-cast slabs on the main girders (2) connection of the pre-cast concrete slabs at the.joint, and (3) placement of elastic supports under the girders. Properties for the precast concrete slabs are given in Table 1. Strain gages in the longitudinal direction (x direction) were stuck on the bottom surface of the section a `a. Strains in the transverse direction (y direction) were measured along the sections b-b, cc and d `d between the steel girder G 1 and G2. Loading positions are marked as 'A' to 'G' along the sections b `b, c `c and d `d. Fig. 2 Test Specimen Table 1 Material Properties of Concrete Slab Tests were performed under the three different support conditions. First, test was carried out on the rigid supports (pin and roller support). Rubber Bearings (R.B.) with different thickness were used as elastic supports for the two following tests. The results of loading on `A' to 'C' were used to compare the variations of shear strain with respect to the support conditions while axial strain distributions in the bottom surface of the concrete slab were compared by the 72
results of loading on 'D' to 'G'. Axial strain i n the transverse direction on the top surface of the concrete slab was also studied when loading was applied at 'A'. 3. Selection of the Elastic Support Stiffness As the preliminary step to study the behavior of the concrete slab when th e structural type was changed, suitable support stiffhess for the test specimen was sought b y calculating the reactions at the interior supports under the applied load of 1,000 kgf. R eactions at the elastic supports L and R for the bridge model shown in Fig. 3 are calculated with respect to the support stiffness and the result is shown in Fig. 4. Fig. 3 Structural Model to Find Suitable Support Stiffness value is 72,100 kgf/cm. The model (Fig. 3) used for the calculation of reaction forces is 1/4 model whose scale is the same as the test specimen in the transverse direction. The selected support stiffness is also about 1 /4 of the actual support stiffness (300,000 kgf/cm used in the practice[2]. As a comparable bearing, one that has twice the vertical stiffness of the previous selection was also chosen. The chosen stiffness was 142,000 k gf/cm. This value was a little stiffer than the critical value of about 110,000 kgf/cm, above which the reaction of support R (Fig. 3) was negative. For the convenience of presentation, elastic bearing with the stiffness of 72,100 kgf/cm will be called 'soft support' and 'hard support' for that of 142,000 kgflcm. The designed elastic supports were made at a factory and also were subjected to the test to calibrate their force-displacement relationship. The test set-up is as given in Fig. 5. Test and design properties of the elastic bearing materials are given in Table 2. Fig. 5 Test Set-up for the Elastic Supports Fig. 4 Vertical Spring Constant vs. Reaction at the Interior Supports Since the reaction force of 500 kgf is that of the simple span structure before the conversion under the applied force of 1,000 k gf, the support stiffness that would provide the same reaction (500 kgf ) after the conversion is searched. From Fig. 4, the reaction force of 500 kgf at the support L can be recognized when the stiffness of the supports is about 70,000 kgflcm. The chosen Spring constant obtained from the experiment is showing about 8 11 % of difference to that of the design values. These amounts of difference are normal because each bearing material is hand-made upon order. The result obtained from the test was used as input data for the numerical analysis of the test specimen. Table 2 Properties of the Elastic Support. 73
Steel Construction Engineering Vol. 5 No. 18(June 1998) 4. Test and Numerical Analysis 4.1 Strain Distribution along the Longitudinal Direction One example of the no joint methods for converting simple span structures to the continuous structure is shown in Fig. 6. This type of connection develops an actual behavior as it is a continuous structure against horizontal forces such as temperature and earthquake loading while it behaves as a simple span structure for the live (traffic) load. It is because the connection does not permit the transmission of end rotation to the adjacent span[5]. Fig. 7(a) Longitudinal Strain Distribution on the Bottom Surface (Section a-a), Loading on 'D' Fig. 7(b) Longitudinal Strain Distribution on the Bottom Surface (Section a-a), Loading on 'E' Fig. 6 Connection Mechanism of Transverse Girders Using P.C. Strand Fig. 7 is the comparison of the strain distribution obtained from the tests on the bottom surface of the concrete slab along the section a `a with respect to the support conditions from rigid to elastic ones. The loading positions for each of Figs. 7 (a)'(d) are 'D' `'G' in Fig. 2, respectively and the Fig 7(c) Longitudinal Strain Distribution on the Bottom Surface (Section a-ja), Loading on 'P applied load is 1,000 kgf. The longitudinal strain distribution in Fig. 7 shows compression (negative strain value) at some distance away from the load while high tension (positive strain value) is shown near the loading position. This is because the whole section acts as a composite section. In other words, strain due to the plate bending action of the concrete slab is larger than the strain resulting from the beam theory. Fig. 7 shows only a small variation of strain values (less than 5 %) along the Fig. 7(d) Longitudinal Strain Distribution on the Bottom Surface (Section a-a), Loading on 'G' 74
longitudinal direction when the support conditions are changed from rigid to elastic supports. The observation of the longitudinal strain distribution points out that the usage of elastic supports may be practized without causing any additional stress in the longitudinal direction. Fig. 8(a) Transverse Strain Distribution on the Bottom Surface (Section c `c), Loading on 'D' 4.2 Strain Distribution along the Transverse Direction Fig. 8 is the comparisons of strain distribution on the bottom surface of the concrete slab along the sections c `c and d-d with respect to the different support conditions from rigid to elastic ones. The loading positions for each of Figs. 8 (a) `(d) are 'D' 'F' in Fig. 2, respectively. Applied load is 1,000 kgf. Strain increase from 64x106 to 76x10-6 (refer to Fig. 8(d)) is about 18% growth which can be attributed to the Fig. 8(b) Transverse Strain Distribution on the Bottom Surface (Section c `c), Loading on 'E' Fig. 8(c) Traisverse Strain Distribution on the Bottom Surface (Section d `d), Loading on 'F' Fig. 8(d) Transverse Strain Distribution on the Bottom Surface (Section d `d), Loading on 'G' increase of moment (MXX) as the support condition is changed from rigid to soft elastic bearing. This increase of moment is due to a larger differential displacement between two main girders when elastic supports are used [3]. The deformation of the concrete slab under the rigid and elastic support conditions are shown in Fig. 9 while the settlement of the supports obtained from the analysis is given in Tables 3 and 4, respectively. The positions of the load for the analysis are 'D' and 'E', for each of Table 3 and 4. Table 3 indicates a small difference of displacement between the supports S 1 and S2 regardless of the support conditions. This agrees well with the Figs. 8(a) and (c) where the variation of the strain distributions in the transverse direction is small with respect to the support condition. A small amount of relative displacement between the supports S 1 and S2 is because the applied load is evenly distributed to each support when the load is placed at the center between two girders. Table 4 shows much larger amount of relative displacement when the load is applied toward the side on 'E'. This is in 75
Steel Construction Engineering Vol. 5 No. 18(June 1998) accordance with Figs. 8(b) and (d) which show the increase of strain from 10 to 20% in the transverse direction on the bottom surface of the concrete slab. This increase of strain in the transverse direction is not in the order that can be ignored and one has to noticed the possible increase of stress when elastic support conditions are to be used. Transverse strain distributions on the top surface of the concrete slab along the section b `b, when the load is applied at 'A', are also compared with respect to the different support conditions. Fig. I 0 shows the strain distributions in the transverse direction obtained from the numerical analysis. The test results under the rigid support condition (marked x in Fig. 10) is presented to validate the numerical result. What has to be noticed from Fig. 10 is not the increase of compression at the loading position (y=37.5cm) but the increase of tension on the concrete slab above the middle girder (y=9ocm). Strain from 8.7x 1016 under the rigid support to 10.3x106 under the soft elastic support represents 17% of increase in tensile force which, in given time, may cause the development of cracks on the top surface of the concrete slab. Fig. 9 Deformation Shape of Concrete Slab Table 3 Displacement from the Analysis of Support Obtained (Loading Position 'D') Fig. 10 Transverse Strain Distribution on the Top Surface, Section(b `b), Loading on 'A' Table 4 Displacement from the Analysis of Support Obtained (Loading Position 'E') Fig. 11 Influence Line for the Transverse Strain on the Top Surface of the Concrete Slab at y=90 cm 76
Fig. 11 is influence lines of the transverse strain on the top surface of the concrete slab above the middle girder G2 (y=9ocm) which obtained from the analysis. Each line in Fig. 11 represents different support conditions from rigid to elastic ones. The lines for the soft and hard elastic support materials show about the same values while that for the rigid support shows much different course. From this figure, which is obtained with one concentrated load applied across the section b-b, increase of tensile strain when the load is applied on the girder G1 can be understood. The maximum increase of tensile strain is caused when the actual truck is loaded as shown below in Fig. 12. Since there are certain problems with the development of cracks on the top surface of the concrete slab, a careful verification should be carried out before the field practice. Problems concerning the development of crack on the top surface of concrete slab has been reported by Matsui [6]. stress is the main factor causing the fatigue failure of the concrete slab [6]. Figs. 13 (a) `(c)represent the distributions of horizontal shear strain (ċxy) along the section b `b with respect to each support condition when loaded at the position ' A', 'B' and 'C', respectively. The notations for the shear strains are given in Fig. 14. Figs. 13 (a) and (c) indicate about 20% increased horizontal shear strain when the supports are changed from rigid to elastic ones while Fig. 13 (b) does not show much of change in its values when the load is applied at the position 'B'. Fig. 13(a) Horizontal Shear Strain(c) Distribution on the Bottom Surface(Section b~b), Loading on 'A' Fig. 12 Loading Position Which Will Cause the Maximum Increase of Tensile Strain on the Top Surface of the Concrete Slab Fig. 13(b) Horizontal Shear Strain(c) Distribution on the Bottom Surface(Section b~b),loading on 'B' 4.3 Shear Strain Distribution on the Concrete Slab Both horizontal and vertical shear strains are obtained through the numerical analysis. Comparison of the shear strain is conducted because of possible increase of torsion on the concrete slab due to the use of elastic support. Moreover, a quantitative study on the fatigue life of the concrete slab is performed because of the fact that shear Fig. 13 (c) Horizontal Shear Strain(c) Distribution on the Bottom Surface (Section b-b),loading on 'C' 77
Steel Construction Vol. 5 No. 18(June 1998) Engineering Increase of horizontal shear strain is due to the increase of torsion by an eccentric loading. Horizontal shear strain tends to increase under the elastic support when the load is applied near the girder. Horizontal shear strain remains unchanged with respect to the support condition if the load is positioned at the mid-length between girders as the case of Fig.13 (b). Fig. 14 Notation for the Shear Strain Fig. 15 (a) `(c) represent the vertical shear strain (c) yzalong the section b `b with respect to the different support conditions when the load is applied on the positions 'A' and 'C', respectively. General tendency ', B' for Fig. 15 is about the same as Fig. 13 showing an average of 15% increased value when the load is applied on 'A' and 'C'. This increase of vertical strain is directly due to Fig. 15(a) Vertical Shear Strain(E) Distribution on the Bottom Surface (Section b'-b), Loading on 'A' the change of moment in the transverse direction which is caused by uneven support displacement. Loading applied at the mid - length between two girders as the position ' B' causes little difference of the displacement between the elastic supports located on the both sides of the load. Fig. 15 also displays the same tendency as Fig. 8, which shows strain distribution in the Fig. 15(b) Vertical Shear Strain(E) Distributi on on the Bottom Surface (Section b-b), Loading on 'B' transverse direction. Fig. 16 (a)-(c) show the vertical shear strain (~~Z) along the section b-b with respect to the support conditions when the load is applied on the positions 'A', 'B' and 'C', respectively. The change of the vertical shear strain (c) is caused by the increase of bending moment in the longitudinal direction when the support conditions are changed from rigid to elastic support. In accordance with this fact, vertical shear strain (c) also indicates small changes regardless of loading position when the support condition is changed. Fig. 15(c) Vertical Shear Strain(c) Distribution o n the Bottom Surface(Section b-sb), Loading on 'C' 4.4 Estimation of Fatigue Life Because vertical shear stress (Eye) influences the fatigue failure, it is desired to study the service life of the structure under the different support 78
Fig. 16(a) Vertical Shear Strain(c the Bottom Surface (Section b `b) 1) Distribution on, Loading on 'A' Fig. 16(b) Vertical Shear Strain(E 1) Distribution on the Bottom Surface (Section b `b), Loading on 'B' Fatigue service life of the test specimen obtained under the rigid support when subjected to the wheel-running -Machine can be represented using Eq. (1) in the following manner; where, (4) Q rigid : shear force of concrete slab under the rigid support Nrigid : number of loading cycles under the rigid support. Fig. 16(c) Vertical Shear Strain() Distribution on the Bottom Surface (Section b `b), Loading on 'C' conditions. The fatigue life can be obtained through the following equation [6]; Log =-0.07835 logn + log C (1) where, Q : shear force due to the applied load Psx : punching shear capacity of the concrete slab as a beam-like condition due to the full depth transverse cracks N : number of loading cycles C : a constant.. Fatigue service life of the test specimen obtained under the soft support when subjected to the wheel-running -Machine can be represented in the same manner; where, Q soft : shear force of concrete slab under the soft support Nsoft : number of loading cycles under the soft support. From Eqs. (4) and (5), NSO ft can be written as; (5) ( 6) Punching shear capacity (P u) after the d evelopment of transverse cracks can be Vertical shear strain (c r) in Fig. 15 shows an average of 15 % increase when the support is changed from rigid to soft elastic calculated as (2)B =b+2 dd (3)where, tension maximum side. shear strength ~smax: of concrete6tmax: tensile strength of concret : d 79
Steel Construction Engineering Vol. 5 No. 18(June 1998) support. Fatigue service life of the concrete slab under the soft elastic support can be obtained by applying an equivalent shear farce of 1.15XQrigid (i.e. Qsoft=l.15x Qrigid). With this equivalent shear force, Eq. (6) yields Nsoft = 0.17 Nrigid. Above result indicates that the service life due to the increase of vertical shear stress in case when elastic supports are used is 116 of that under the rigid support condition. 5. Conclusion A simple span bridge specimen was tested to study the behavior of the slab due to the change of the support conditions from rigid to elastic one, which accommodates structural conversion from simple spans to a continuous structure. The test as well as numerical analysis results indicate about 10 to 20 % of strain increase in the transverse direction when rigid support conditions are changed to that of the elastic ones. Vertical and horizontal shear strains also increase due to uneven displacement of the elastic supports. The followings are observed as a result of this study; (1) change of strain in the longitudinal direction is small and may be ignored. (2) change of strain in the transverse direction is over l0% and the effect is large when the load is applied near the girder (3) increase of tensile strain on the top surface of the concrete slab is also observed due to the use of elastic supports (4) increase of horizontal shear strain due to the growth of torsion in the concrete slab is observed to be large when the support conditions are changed (5) vertical shear strain also increases directly affecting the fatigue life of the concrete slab. Elastic supports are used to accommodate the conversion of the simple spans to the continuous structure and to prevent damages from earthquake. This usage of elastic supports exposes the slab to a higher stress level which, in turn causes a faster fatigue deterioration due to traffic loads. Therefore, a careful verification should be carried out before the field practice. Acknowledgement A great appreciation is due to Mr. Hiroshi Ota and Kiyoshi Kirikawa without whose help this test would not have been completed. Kawaguchi Metal Industries Co., LTD provided rubber bearing which was indispensable material for this study. The authors also thank Kouzai Club in Japan, Matsuo Bridge and Harumoto Corporation for their financial funding for this study. References 1. Ministry of Construction : Highway Bridge Design Manual for Seismic Design(Draft), Civil Engineering Research Centre, 1992 (in Japanese). 2. Otoguro, Y. and Uno, H. : Connection Method of Connecting Girder-Webs, J. of Bridge and Foundation Engineering, Vol. 28, pp. 172-173,1994 (in Japanese). 3. Park, J., Matsui, S., Higashiyama, H., and Egashira, K. : Effect of Change of Boundary Condition from Rigid to Elastic Supports on Slab Behavior, Proceedings of the Japan Concrete Institute, Vol. 19, pp.1479-1484,1997. 4. Satoshi, Yamamoto : No-Joint Methods for Existing Highway Bridges, J. of Bridge and Foundation Engineering, Vol.28, pp. 163-166, 1994 (in Japanese). 5. Shinkai, M. and Ueda, T.: The Jointless Work of Multi Simple Span Bridges in Chuo Expressway, J. of Bridge and Foundation Engineering, Vo1.28, pp. 174-175,1994(in Japanese). 6. Shigeyuki, Matsui : New Technologies for Durable Highway Bridge Slabs in Japan, Proceeding of International Seminar on New Technologies for Bridge Management, Dec.6,1996.