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Effects of bolt-plate arrangements on steel plate strengthened reinforced concrete beamsR.K.L. Su1, W.H. Siu2, S.T. Smith3Department of Civil Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, Chinaabstract：A structure that can behave in a ductile fashion under extreme events is of paramount importance due to safety considerations. Because of such importance, ductility performance of bolted side-plated (BSP) concrete beams under different bolt-plate arrangements is investigated experimentally through four large-scale tests on BSP beams. It is observed that bolt-plate arrangements have a dominant effect on the ductility performance of beams in terms of both the post-elastic strength enhancement (defined as the ratio between the peak strength and the yield strength of the beam), and the displacement ductility(defined as the ratio between displacements at the ultimate and notional yield stages). In order to ensure ductile beam behaviour, the concept of maximum allowable plate-force demand is introduced, of which the strength of additional plates should be kept below the balanced failure point, while sufficient shear strength of the bolt connections should be provided so that the strengthened beam will possess both sufficient strength enhancement and ductility.Keywords: Bolts Bi-linear Concrete beams Curvature Ductility Plate Strengthening1.IntroductionDue to deterioration of materials and demand for additional strength, retrofitting of existing beam structures is often needed. There are basically two methods for strengthening or stiffening existed reinforced concrete (RC) beams. The first method is to attach advanced composites, such as carbon fibre reinforced polymers or glass fibre reinforced polymers 1, onto the tension surface or the side faces of the members. These composites are generally capable of increasing the ultimate load resistance but are prone to peeling and edge debonding failure 2. The second method for strengthening or stiffening existed RC beams is to attach steel plates to the external surfaces of the structural components by means of bolting. This method can enhance both the flexural and shear performances of RC beams. A number of studies were carried out to investigate the flexural and shear behavior of bolted side-plated(BSP) beams 3-8 and coupling beams 9 as well as the behavior of the connecting bolt groups 10,11. However, as the allowable plateforce demand in the bolt-plate system has not been specified in these studies, the designed BSP beams may be over-reinforced when thick plates and strong bolts are used. It is well recognized that ductility is an important structural property which provides noticeable warning at the beginning of failure of the structure to users for evacuation. Although substantial research has shown that BSP beams are effective in providing additional strength, over-reinforced BSP beams could lead to un-desirable non-ductile failure 4. It is therefore imperative to develop retrofitting techniques that can enhance flexural strength and maintain sufficient ductility. With this consideration, four-point bending tests of five simply-supported RC and BSP specimens were conducted. All these specimens have the same RC geometries, but are strengthened with different bolt-plate arrangements. The bolt-plate arrangements of specimens were properly selected so that the present experimental study would cover both over-reinforced and under-reinforced BSP beams. The experimental data obtained was analyzed and the most appropriate strengthening system that can enhance flexural strength and maintain sufficient ductility has been identified. The proposed bolt plate arrangement can help designers to establish a ductile retrofitting scheme quickly and conveniently. It is noted that the investigation of the effect of bolt-plate arrangements on the partial interaction behavior of BSP beams is beyond the scope of this paper. The related experimental study can be found in the companion paper 12.Table 1 Summary of boll-plate arrangements of BSP specimens.Specimen SBSPSpecimen WBSPSpecimen WBWPSpecimen SBWPNo. of bolts on shear span83 35Strength of bolts on shear span Pb(kN)608228228380Plate size(mm *mm)6* 150 dp6 * 150 dp 6 * 75 dp6 * 75 dpPlate force at ultimate state in full interaction analysis Fp.fi (kN)605605302302Degree of shear connection (Pb Fp.fi) 1.000.380.751.26Fig.1. Test setup2. Experimental program2.1. Test setupA four-point bending test setup was adopted, as shown in Fig. 1.The beam specimens were simply-supported with a clear span of3600 mm. Load was applied by a 1000 kN hydraulic jack in the vertical direction, and divided into two equal point loads and exerted symmetrically onto the specimen through a transfer beam. With this arrangement, a pure bending zone with constant moment was created so that the flexural behavior under pure bending could be studied.2.2. Specimen detailsFive specimens were fabricated and tested. The RC details of all specimens are identical. As shown in Fig. 2, the size of the RC sections was 225 mm*350 mm deep. The specimens were under-reinforced by 3T16 tension bars, contributing to a steel percentage of 0.76%. Transverse reinforcement of T10-150 was applied throughout the span of the beam. This amount of longitudinal and transverse reinforcement would be sufficient to ensure that the specimens would fail in flexure in both un-strengthened and strengthened cases. This is desirable since the objective of this experimental study is to investigate the flexural responses of beams.Specimen NBNP is the control specimen without any strengthening measure. It serves as a control specimen and is used to demonstrate the structural performance of a RC beam prior to Strengthening.Four strengthened specimens were fabricated. Being identified as the major parameters affecting the performance of beams, the bolt-plate arrangements of these specimens were properly selected so that the behavior of beams under partial shear interaction in all cases could be captured in this study. Four different bolt-plate combinations including Strong Bolt Strong Plate(SBSP), Weak Bolt Strong Plate (WBSP), Weak Bolt Weak Plate(WBWP) and Strong Bolt Weak Plate (SBWP) are adopted and the detail arrangements of these specimens are summarized in Table 1 and illustrated in Fig. 2.Two different plate sizes, 6 mm *150 mm deep and 6 mm *75mmdeep mild steel plates on both side faces of specimens were chosen to be the Strong and Weak plate arrangements respectively. This is equivalent to 2.3% and 1.1% of the gross sectional area of concrete. The centroidal axis of the plates was set at 250 mm from the top of the beam and in the tension region of the beam. This arrangement can prevent buckling of steel plates which is out of the scope of the present study. Buckling of steel plates occurs when relatively deep plates are used of which the top parts would be subjected to compression 13,14. Adopting the current plate arrangement, the entire steel plate was below the mid-depth of the section and therefore the plate compression can be minimized and hence plate buckling can be avoided.In this study, the degree of shear connection is used to consider if a bolt arrangement is Strong or Weak. The degree of shear connection is defined mathematically asPb Fp.fi Where Pb and Fp.fi are the total strength of bolts on a shear span and the plate force at ultimate state under the case of full interaction respectively.To determine the degree of shear connection of all strengthened specimens, a non-linear full interaction section analysis was carried out. A non-linear stress-strain relationship was adopted for concrete and an elastic-plastic relationship was used to model the stress-strain relationship of steel plates and reinforcement. Incremental curvatures were applied to the section until the peak moment was solved. The plate force at ultimate state and the degree of shear connection of the strengthened specimens are listed in Table 1. The degree of shear connection of Specimens SBSP and SBWP are 1.00 and 1.26 respectively, implying that sufficient bolt forces have been provided. Thus the bolt arrangement is Strong. Conversely, the degree of shear connection of Specimens WBSP and WBWP are, respectively, 0.38 and 0.75, meaning that these specimens have Weak bolt arrangements.Specimens SBSP and WBSP were strengthened by the same size of plates, i.e. 6mm_150mmdeep steel plate strengthened on each side face of the beams, but with Strong and Weak bolt arrangements respectively. Specimens SBWP and WBWP have the same plate arrangement but with different degree of shear connections. By comparing these two pairs of specimens, the effect of strong and weak bolt arrangements on the behaviour of specimens could be studied. Meanwhile, the bolt arrangements of Specimens WBSP and WBWP are identical but with different plate arrangements. By comparing the results of these two specimens, the effect of plate geometry on the performance of the beams could be investigated. The concrete beams without plate strengthening were first fabricated. Holes for allowing future installation of a bolt-plate system were reserved in the concrete core using aluminium tubes with an internal diameter of 14 mm. The aluminium tube was permanently cast in the concrete core as it is expected that the change in stiffness due to the tube is very small compared with the shear stiffness of the bolt and would not significantly affect the experimental results. The bolt-plate system was installed at least 14 days after curing of concrete. By using this arrangement, the concrete core and the steel plate are interacted purely through the bolt anchors.Fig.2. RC and bolt-plate detail of BSP beamsFig.3. Dynamic set washer (a) diagrammatic illustration and (b) actual arrangement2.3Material propertiesA concrete mix containing maximum coarse aggregates of 10 mm and with target mean cube strength of 30 MPa at 28 days after casting was designed for the specimens. The constituents and the corresponding proportions of the concrete mix are shown in Table 2. For each specimen, three concrete cubes with dimensions 150 mm *150 mm* 150 mm were cast and compressive tests were carried out on the test day to obtain the compressive strength of cubes. There were slight variations in the average compressive strength of cube of specimens, but in general the average concrete compressive strength of cube was around 35 MPa, as shown in the Table 3.Table 2 Concrete mix adopted for producing a cubic meter of concrete.WaterCementFine10mm aggregate Kg/m3199.6278.91024.5837.6High yield steel reinforcement with characteristic yield strength of 460 MPa was used in this study. _16 bars were used as tension reinforcement while _10 reinforcing bars were used as hangers. Three samples were taken from each type of reinforcement. Tensile tests were carried out and the yield strength and Youngs modulus of these samples are summarized in Tables 4 and 5.Three strips of dimension 400 mm* 6 mm thick were taken from each of the 75 mm deep and 150 mm deep steel plates for tensile tests. The material properties of the steel plates are listed in Table 6.HAS-E anchor rods of 12 mm diameter 15 were used as the mechanical connectors of all specimens. The HAS-E rod is in Grade 5.8, with a minimum 5 mm galvanized surface. Dynamic set, instead of ordinary washer and nut was used in this study. A spherical washer, an injection washer and an ordinary nut were included in the dynamic set, as illustrated in Fig. 3. With this system, epoxy grouts can be easily injected into the gaps between connecting components and the bolt shaft, so that any undesirable slips due to the presence of gaps between components can be avoided. Bolt shear tests were conducted and an idealized load-deformation response of all anchor bolts (with appropriate key parameters) is presented in Fig. 4.Fig.4. Load-slip relationship of anchor bolts2.4. InstrumentationLinear Variable Direct Transducers (LVDTs) and Linear Displacement Transducers (LDTs) were installed, as illustrated in Fig. 5. Fig. 5. LVDT and LDT arrangements for the specimens.Table 3 Cube strength of concreteConcrete cube strength (MPa)Specimen NBNPSpecimen SBSPSpecimen WBSPSpecimen WBWPSpecimen SBWP135.534.53434.335.5236.2353734.135.533434.231.93735.0Average 35.234.634.335.135.3Table 4 Material properties of T-16 reinforcement.Yield strength（MPa）Youngs modulus（GPa）154518925251843540188Average537287Table 5 Material properties of T-10 reinforcement.Yield strength（MPa）Youngs modulus（GPa）15501852540194Average545190The LVDTs other than those in the constant moment zone were installed and pointed at the middle of the top flange. At the constant moment zone, installation at the middle of the top flange is not possible as a loading beam was present. In this case, pairs of LDTs were installed and the average of the readings was used to represent the displacement along the centroidal longitudinal axis of the beam, as illustrated in Fig. 5.Electric resistance strain gauges were attached on plates to measure the curvatures in various sections of the specimens. These strain gauges were installed along the direction of beam span at five different sections. Three sections were within the peak moment zone and two at the middle of the left and right shear spans, as illustrated in Fig. 6.Fig.6. strain gauges located on the steel plates of the specimens.2.5. Loading historyIn each test, the specimen was first incrementally loaded to 50% of the ultimate capacity of the beam as estimated by a full interaction sectional analysis. After that, the loading process was changed to a displacement-controlled mode in which incremental displacements were applied. The loading process was terminated at the instant when the post-peak loading in the beam was 85% of the peak load, or any of the two bolts in the specimen had fractured.3. Experimental results3.1. Moment-deformation responseThe moment-deformation responses of all specimens are shown in Fig. 7. For Specimen SBSP, which is strengthened with strong plate and strong bolt arrangements, the initial deformation response of the beam was elastic. The bottom reinforcement yielded when the applied moment reached 154 kN m, equal to 95% of the peak moment .Mu/ and the tangential stiffness of the beam dropped abruptly to 15% of the stiffness prior to yielding of the bottom reinforcement. The remaining stiffness was provided by both the axial interaction between concrete in compression and steel plate in tension and the flexure of steel plates. The stiffness kept constant up to the ultimate state (M = 161 kNm). After that, concrete crushed and the beam degraded gradually when further deformation was applied and the beam failed in concrete crushing when the mid-span deflection reached 55 mm.For Specimen WBSP, which has the same plate arrangement as Specimen SBSP, but with lesser bolts installed, the behaviour of the beam was governed by bolts. The elastic stage terminated when the applied moment reached 131 kNm(0.88Mu) due to yielding of the bottom reinforcement. At that instant, the tangential stiffness abruptly dropped to 26% of the stiffness just prior to yielding. The stiffness dropped gradually when the beam was deformed further and reached zero when the moment reached 147 kN m (0.99Mu). The gradual drop in stiffness was due to the stiffness drop in bolts as bolt slips increased. Two bolts on the same shear span and at the same side fractured consecutively beginning from the one closer to the support, when the mid-span deflection was 51mmand 54mm respectively.For Specimen WBWP, which was strengthened by the same Weak bolt arrangement with that of Specimen WBSP, but the Weak plate arrangement, the bottom reinforcement yielded at the end of the elastic stage when the moment reached 124 kN m(0.93Mu). The remaining stiffness was about 10% of the stiffness prior to yielding. The remaining stiffness sustained up to the failure point when the moment and deflection were 133 kNm and 50mm respectively. Failure of the beam was due to consecutive bolt fractures, which was similar to Specimen WBSP. For Specimen SBWP, which had the same Weak plate arrangement as that of Specimen WBWP but 60% more bolts to anchor the plates, the cracked elastic stiffness of SpecimenSBWP was 14% larger than that of Specimen WBWP. The bottom reinforcement yielded when the moment was equal to 124 kN m(0.86Mu). After yielding, a constant tangential stiffness, equal to 17% of its stiffness just prior to yielding, remained to resist further loading. When the applied load reached 145 kN, the Load-deflection curve changed gradually from an ascending trend to a descending trend and crushing of concrete began. The descending branch of Specimen SBWP was milder than Specimen SBSP and the residual strength in beam reached 85% of Mu at the point when the beam was further deformed by 22 mm. Fig.7. moment-deformation response of all specimens.3.2. Strength and ductilityCompared with the control specimen (Specimen NBNP), the strengthened specimens show various percentage of strengthening ranging from 32% to 59%. A summary of the strengthening performance of the specimens is given in Table 7. Among the four strengthened beams, Specimen SBSP, being strengthened with a Strong bolt and Strong plate arrangement, was the strongest with 59% additional strength over the control beam. Specimen WBSP, with the same Strong plate arrangement as Specimen SBSP, but with Weak bolts, achieved a 47% increase in strength. Even with half of the plate size as the Strong plate case, Specimen SBWP achieved a 43% increase in strength, which is comparable to Specimen SBSP. Specimen WBWP was the weakest among the four strengthened beams and achieved a 32% strength increase. This is much lower than that of Specimens WBSP and SBWP, which have the same bolt and plate arrangements respectively. The present experimental results indicate that the load-deformation responses of the specimens, as shown in Fig. 7, can be idealized by a bi-linear curve (see Fig. 8). The displacement ductility factor, which is defined as the ratio between the displacement at peak load _u and the notional yield displacement-y, was adopted to measure the ductility performance of the plated beams. As the strengthened beams considered are predominantly subjected to gravity loads, the strengthened beam would collapse when the applied gravity load is higher than the load-carrying capacity of the beam. The post-peak descending branch of the load-deflection curve would alter the rate of failure but could not avoid collapse of the beam. Because of that, the displacement at peak load u was chosen to represent the ultimate deformation of the BSP beams. As shown in Fig. 8, the notional yield displacement y is defined as the intersection of the two straight lines associated with the load-deflection curves at the elastic and post- elastic stages respectively. The displacement ductility factors of specimens were calculated using the above definitions and the results are given in Table 8. The four strengthened specimens have displacement ductility, ranging from 1.70 (Specimen SBSP) to 2.57(Specimen WBWP). The displacement ductility of all specimens were lower than the un-strengthened specimen as expected since the bolt-plate system acts as an additional reinforcement to the specimen and hence would reduce the displacement ductility of the BSP specimens. Substantial post-elastic strength enhancement could be found in Fig. 7. The degree of post-elastic strength enhancement is paramount impor
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