Advances in Steel Structures - part 51 potx

480 J. IV. Zhang et al. Zhang et al. (1999) compared the accuracy of these three yield line patterns in predicting the test results. The triangular pattern (Figure 2) was identified by Zhang et al. (1999) as the most suitable for use in design as long as the width ratio between the steel plate and the slab k2 (or k3 denoting the width ratio between the patch load and the slab for the RC control slab SB 1) is not too large (Table 3). Although the triangular pattern is not as accurate as the most complicated pattern assumed in Zhang et al. (1999), it is simpler than the latter and conservative for all applicable slabs (SB 1-SB4). YIELD LINE ANALYSIS OF RECTANGULAR SLABS Yield Line Pattern The above comparisons between yield line analyses and tests show that the yield line method can predict the ultimate strength of plated slabs closely and is suitable for design use. In order for the method to be more generally applicable, a yield line analysis of rectangular slabs adopting the triangular yield line pattern is briefly presented in this section. A more detailed description of this analysis can be found in Teng et al. (1999). In this analysis, the rectangular slab is assumed to have an aspect ratio of less than 2 and to be symmetrically bonded with a steel plate and subjected to a central patch load. In order for the triangular yield line pattern to be the critical pattern, it is further assumed that the longer direction of the slab coincides with that of the steel plate. Only isotropic steel reinforcement with equal sagging and hogging yield moments is considered. Due to symmetry, only a quarter of a rectangular plated RC slab is considered, as shown in Figure 3. This quarter of the plated slab is then divided into four rigid regions A, B, C and D by yield lines. The negative yield line on the top surface of the slab is assumed to be inclined to the slab edges at an angle of 45 degrees. aJ2 s o~ ~ A bd2 t'q >_ ~5 C ~ Figure 3 Yield Line Pattern for a Rectangular Plated Slab Virtual Work Equation Before proceeding to the detailed derivation, it is necessary to define some notation. The width and length of the slab are a~ anda 2 respectively, while those of the steel plate are b~ and b 2 . The location of the negative yield line is determined by k~ = s / a~. The steel plate-to-slab width and length ratios are denoted by k 2 and k 4 respectively. That is, k 2 = b 1 / a~ and k 4 = b 2 / a z . The aspect ratio of the slab a 2 / a~ is denoted by k s . Rectangular Two-Way RC Slabs Bonded with a Steel Plate 481 Based on geometrical compatibility requirements, the rotations of the rigid regions A, B, and C around their own rotational axes are respectively found to be 0 A =2/(a~-b~), 0 B =I/H and 0 c = 2/(a 2 -b2). Here H is the perpendicular distance from the plate comer to the adjacent negative yield line, and can be found using simple geometric relations as H = a+,~[(l - k 2 - 2k, ) + ks O - k4 )l/ 4 . (t) Based on the virtual work principle, the expressions of extemal virtual workE e and intemal virtual work Eg can be found without difficulty: Ee = Pu x 1.0 = P. (2) -2k 1 1-2k 1 8k t Ei = 4mp 5 +~+ ] (3) kl-k 2 ks0-k4) O-kz-2k,)+ksO-k4) where m.,, denotes the yield moment per unit length of the unplated part of the slab. Combination of Eqns 2 and 3 then yields the desired ultimate load Pu as I -2k 1 1-2k 1 8k l P. = 4mp 5 +~+ ] (4) kl-k+ ks(l-k4) O-k2-2kl)+ksO-k4) Minimization of Pu with respect to k t and ignoring the contribution of the hogging moment in this minimization leads to 1 k I - -~(1-k 2 ,-l O-k4)k 5 -420-k2)(l-k4)ks) (5) which can be substituted into Eqn. 4 to find the minimum value of Pu. Eqns 4 and 5 include square plated slabs as a special case. For the case of k 5 = 1 and k 2 = k 4 which corresponds to the case of a square slab bonded symmetrically with a square plate, Eqns 4 and 5 reduce to Eqns 6 and 7 below: where 1-k 1-k 2+2kl z ] P,, =8mp (l_k_kzXl_k2) (6) k, : 2-'f2 (l-k2) (7) 2 DESIGN PROCEDURE The main task in designing the steel plate for strengthening a given RC slab is to determine the size of the required steel plate provided the thickness of the steel plate required to prevent failure in the 482 J.W. Zhang et al. central plated part is determined by a suitable method. A discussion of this issue is given in Teng et al. (1999). To this end, the strength P,c of the existing RC slab needs to be found first, using Puc =4mpT (8) where I ks-T ~ 1-T~ 4T~] r= + k 5 -k 3 T 2 (9) T~ = 1- 2k 3 + k 5 - T 2 (10) T 2 = ~/2(1-k3)(k 5 -k3) (11) Eqn. 8 is obtained from Eqn. 4 by replacing k 2 with k 3 and k 4 with k3/k 5 respectively, with k 3 = c/a~. For convenient use in design, the strengths of unplated slabs are tabulated in Table 4 in a dimensionless manner. TABLE 4 DIMENSIONLESS STRENGTHS euc / mp OF UNPLATED RC SLABS k3 0.05 0.10 0.15 0.20 0.25 0.30 k 5 1.0 1.2 1.4 1.6 1.8 2.0 10.36 10.48 10.83 11.30 11.86 12.47 10.83 10.92 11.27 11.77 12.35 12.99 11.35 11.41 11.76 12.28 12.89 13.57 11.94 11.95 12.31 12.85 13.50 14.21 12.61 12.56 12.92 13.49 14.18 14.94 13.37 13.26 13.62 14.22 14.95 15.76 Once the existing strength Puc is known and the required strength Pa of the strengthened slab is specified, the strengthening ratio required fl is calculated as fl = Pd (12) Puc For design use, the strength of the plated slab can be predicted by the following modified form of Eqn. 4: 4mplk -2kl 1-2k ~ 8kl )1 +~+ - (13) Pd " Ifig 51-k2 k50-k4) O-k2-2kl)-~t-k50-k4 where the term ~ is introduced to account for the differences between the test results and the yield line analysis. For square slabs, the value of ~t can be found using the following empirical formula obtained by curve-fitting the results of Table 3: = 1.63k 3 - 1.18k 2 + 0.37k 2 + 0.80 (14) Rectangular Two-Way RC Slabs Bonded with a Steel Plate 483 For rectangular plated slabs, ~ is expected to be a function of both k 2 and k 4. As experimental results are only available for square plated slabs, a conservative approach for rectangular slabs is to adopt the greater of k 2 and k 4 for k 2 in Eqn. 14 to find the value of ~. Combination of Eqns 8, 12, 13 and 14 results in the following expression for /3 for a given steel plate size chosen to strengthen the slab 1 Iks-D 1-D 4D 1 13 = ~-T-~ 1-k 2 + (1 - k4)k ~ +~D 1 (15) in which D =(1-k2)+O-k4)k 5 -D, (16) D, = 420-k2 Xl-k4)k5 (17) For convenience in design use, the values of fl can be tabulated. An example is shown in Table 5. TABLE 5 STRENGTHENING RATIO fl OF PLATED RC SLABS k5 1.0 1.2 1.4 1.6 1.8 2.0 k 2 (k 4 =0.60, k 3 =0.10) 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 1.727 1.769 1.818 1.876 1.946 2.032 2.140 2.187 2.251 1.660 1.710 1.768 1.838 1.922 2.025 2.155 2.228 2.323 1.602 1.659 1.726 1.806 1.901 2.019 2.166 2.259 2.379 1.556 1.619 1.693 1.780 1.886 2.014 2.175 2.285 2.424 1.520 1.588 1.668 1.762 1.875 2.013 2.185 2.307 2.46'1 1.493 1.565 1.650 1.749 1.868 2.014 2.195 2.327 2.493 Such tables enable a simple determination of fl once the dimensions of the slab and the plate are known, or the determination of the steel plate size to arrive at a given value of ft. Although Eqns 13 and 15 may be applicable to slabs with a very large steel plate as was used in the square test slab SB5 since a modification factor ~ has been included, it is necessary at this point of the time to restrict the application of these formulas to slabs with a bonded steel plate satisfying the following conditions: 0.3 < k 2 < 0.7 (18) 0.3 _< k 4 < 0.7 (19) The lower bound is to ensure that punching shear failure does not become critical while the upper bound is to prevent a yield line pattern different from that assumed in Figure 3 to become critical. The above limitations allow plates up to half the size of the slab to be used in strengthening, which are already capable of producing a large strength increase. These limits are to be further justified in future work. 484 J.W. Zhang et al. CONCLUSIONS This paper has been concemed with the strength of two-way rectangular RC slabs bonded with a steel plate subject to a central patch load. Based on experimental observations of the formation of yield lines in square plated slabs and the previous success of the yield line method for these slabs, a yield line analysis of rectangular two-way plated RC slabs has been presented. Finally, a design procedure based on the yield line analysis has been proposed for practical use, which incorporates an empirical modification factor based on the experimental results. Experiments on rectangular plated slabs are required to validate the proposed design method. ACKNOWLEDGEMENTS The work described here forms part of the project "Strengthening of Reinforced Concrete Slabs by Plate Bonding" carried out in the Department of Civil and Structural Engineering, The Hong Kong Polytechnic University in collaboration with the Department of Structural Engineering, Southeast University. The authors wish to thank Professors Z.T. Lu of Southeast University and J.M. Ko of The Hong Kong Polytechnic University for their support to this collaborative project and The Hong Kong Polytechnic University for the financial support provided through a central research grant (G- $567). The authors would also like to thank Messrs Zheng Xian-Yuan and Mr Chen Mao-Lin for their assistance in the experimental work. REFERENCES Civil Engineers Australia. (1995). Epoxy Adhesive Used to Bond Steel Plates. Civil Engineers Australia Sep., 55. Erki M.A. and Hefferman P.J. (1995). Reinforced Concrete Slabs Externally Strengthened with Fibre-Reinforced Plastic Materials. Non-Metallic (FRP) Reinforcement for Concrete Structures, L. Taerwe ed., E & FN Spon, 509-516. Kong, F.K. and Evans, H.R.(1987). Reinforced and Prestressed Concrete, 3rd Edition, Chapman and Hall, London. Godfrey J. and Sharkey P. (1996). Plate Bonding to Strengthen Hall Floor. Construction Repair July/August, 39-40. Johansen K. W. (1962). YieM Line Theory, Cement and Concrete Association, London. Jones L.L. and Wood R.H. (1967). Yield Line Analysis of Slabs, American Publishing Company, Inc., USA. Teng J.G., Zhang J.W. and Wong Y.L. (1999). Strength of Two-Way Rectangular RC Slabs Externally Bonded with a Steel Plate. To Be Published. Zhang J.W., Teng J.G., Wong Y.L. and Lu Z.T. (1999). Behaviour of Two-way RC Slabs Externally Bonded with a Steel Plate. To Be Published. Bridges This Page Intentionally Left BlankThis Page Intentionally Left BlankThis Page Intentionally Left BlankThis Page Intentionally Left BlankThis Page Intentionally Left BlankThis Page Intentionally Left BlankThis Page Intentionally Left BlankThis Page Intentionally Left BlankThis Page Intentionally Left BlankThis Page Intentionally Left BlankThis Page Intentionally Left BlankThis Page Intentionally Left BlankThis Page Intentionally Left BlankThis Page Intentionally Left Blank Structural Performance Measurements and Design Parameter Validation for Tsing Ma Suspension Bridge C.K. Lau 1 W.P. Mak I K.Y. Wong 1 Deputy Director Chief Engineer Senior Engineer W.Y. Chan' K.L. Man' K.F. Wong 2 Engineer Engineer System Analyst 'Highways Department, The Government ofHong Kong Special Administrative Region 2E&M Section, Tsing Ma Management Limited ABSTRACT An intensive bridge monitoring system has been installed on the Tsing Ma Suspension Bridge for monitoring the structural performance and evaluating the health (safety) conditions of the bridge. After more than two years of operation, the system has collected and archived a substantial amount of data. Numerous works for data processing, analysis and interpretation have been carried out to assess the structural performance of the bridge as well as to validate the various bridge design parameters. This paper presents the findings from the measured results including: wind, temperature, traffic and bridge responses. The measured results are then used to compare with the design parameters of the bridge for evaluating the current loading and health conditions. KEYWORDS bridge monitoring system, measurement, design parameters, load monitoring, response monitoring INTRODUCTION The Tsing Ma Suspension Bridge, which forms a key part of the most essential strategic transportation network (road and railway) linking the Hong Kong International Airport to the urban areas of Hong Kong, was opened to traffic on 22 May 1997. Figure 1 shows the location of Tsing Ma Bridge in the Tsing Ma Control Area. In order to monitor and evaluate the structural health and performance of the bridge, Highways Department of the Government of the Hong Kong Special Administrative Region has devised and implemented an intensive structural monitoring system on the bridge, named as Wind And Structural Health Monitoring System (WASHMS) [1 and 2]. The system collects environmental and applied loads information (such as wind, temperature, seismic and traffic) and structural response records of the bridge (such as vibrations, displacements and strains) in a continuos manner from 487 488 C.K. Lau et al. approximately 350 sensors installed at different locations of the bridge. According to the nature of the signals to be collected, these sensors are divided into seven groups, namely, anemometer, temperature measurement assembly, accelerometer, strain gauge, level sensing system, displacement transducer and weigh-in-motion system. Figure 2 shows the layout of the sensory system in Tsing Ma Bridge. WIND LOAD MONITORING The Tsing Ma Suspension Bridge was designed to resist a maximum steady wind speed of 50 m/s plus a maximum fluctuating wind speed of 80 m/s (3-second gust). Such design parameters are based on a wind return period of 1 in 120 years. A summary of the design wind speeds and corresponding horizontal wind loaded lengths for Tsing Ma Suspension Bridge is given in Table 1. TABLE 1 STRUCTURAL DESIGN WIND SPEEDS FOR BRIDGE DECK WITH AND WITHOUT HIGHWAY AND RAILWAY LIVE LOADS (120 YEARS RETURN PERIOD) Design Wind Speeds for Deck without Highway and Railway Live Load Design Wind Speeds for Deck with combined Highway and Railway Live Load Design Wind Speeds for Deck with Railway Live Load only Hourly Mean Wind Speed at Deck Level 50m/s 25 m/s 28 m/s Maximum 3-second Wind Speed Horizontal Wind Loaded Length 20morless 100m 600m 1000m 80m/s 72m/s 65 m/s 63 m/s 2000m 60 m/s 44m/s 38 m/s 34 m/s 33 m/s 33 m/s 50 m/s 43 m/s 39 m/s 38 m/s 37 m/s The above information was derived from the wind data obtained from an observation station at Waglan Island which is located some 5 kilometres to the south-east of Hong Kong Island. As the topographical conditions of the bridge site and that of Waglan Island are different, it is necessary to verify the above wind design parameters. The bridge deck was designed for aerodynamic stability according to the parameters given in Table 2. TABLE 2 DESIGN CRITICAL WIND SPEEDS FOR AERODYNAMIC STABILITY CHECK Angle of Incidence Design Critical Wind Speeds (One-minute Mean Wind Speed) Bridge Deck Alone Bridge Deck with Traffic and Trains -5 ~ 31 m/sec 25 m/sec -2.5 ~ 50 m/sec 40 m/sec 0 o 74 m/sec 50 m/sec 2.5 ~ 50 m/sec 40 m/sec 5 ~ 31 m/sec 25 m/sec (Note : Wind speeds in 1 in 200 years return period were used in the design in deriving the critical wind speeds for checking the bridge's aerodynamic stability) Wind measurement data for Tsing Ma Suspension Bridge are given by 6 No. anemometers respectively installed at the tower top of the bridge (2 No.), mid-span at deck level (2 No.) and Ma Wan side-span deck level (2 No.). The measured wind data are used to derive (a) wind rose diagrams Structural Performance Measurements for Tsing Ma Suspension Bridge 489 of hourly mean wind speeds and 3-second gust wind speeds - showing wind speeds, wind directions and frequencies of occurrence and (b) wind structure - including 3-second gust wind speed and hourly mean wind speed, gust factors, turbulence intensities and wind spectrum. Some typical wind monitoring results for the bridge obtained in the past two years are given in Figure 3 to Figure 6. TEMPERATURE MONITORING The structural design for temperature load of the bridge is based on two parameters, namely effective bridge temperature and differential temperature. Effective bridge temperatures are functions of total solar radiation and values of shade air temperature, whilst differential temperature is a function of total solar radiation and extreme ranges of shade air temperature. The parameters for the design of steel and composite bridges are based on theoretical approaches and experimental data adopted for the design of concrete bridges under Hong Kong climatic conditions[3]. It is thus necessary to verify the original design parameters by measuring the temperature distribution of the bridge. A total of 115 temperature sensors are installed at various locations of the bridge deck to measure respectively the ambient air temperature, structural steel temperature including steel sections, main suspension cables, steel cladding and asphalt temperature. The bridge is designed for temperature values with a 120-year return period and the corresponding designed maximum and minimum coincident effective bridge temperature are given in Table 3. TABLE 3 DESIGNED MAXIMUM/MINIMUM EFFECTIVE TEMPERATURE FOR TSING MA SUSPENSION BRIDGE Design Max Effective Temp (oc) Deck 46 Main Cables 50 Suspenders 50 Design Min Effective Temp (oc) -2 -2 -2 Towers 36 2 Figure 7 is a summary of the annual temperature variation on Tsing Ma Suspension Bridge during the past two years. Six different curves are presented in the plot, namely (i) mean effective temperature, (ii) maximum effective temperature, (iii) minimum effective temperature, (iv) mean ambient temperature, (v) maximum ambient temperature and (vi) minimum ambient temperature. The lowest mean ambient temperature was recorded in December and a value of 13.5 ~ was recorded. The highest mean ambient temperature was recorded in August and a value of 34.5 ~ was recorded. It is noted that during the period of low temperature, i.e., at night, values of effective temperature and ambient temperature run very closely to each other as there is no solar energy gained by the structure. However, during the hottest period of the measurement, i.e., during noon time and in the summer season, values of effective temperature are about 8 to 12 ~ higher than the recorded ambient temperature. The highest effective temperature measured on the bridge was 44.5 ~ which was recorded in July 1998. This value is close to the design threshold limit of 46 ~ An interesting point to note however concerning the temperature in the year 1998 is that it is the warmest year since 1884 (according to the information from Hong Kong Observatory). DISPLACEMENT MONITORING Longitudinal movement of the bridges at the expansion joint is mainly affected by the temperature of the structure. The designed maximum longitudinal movement value for Tsing Ma Suspension Bridge . be predicted by the following modified form of Eqn. 4: 4mplk -2 kl 1-2 k ~ 8kl )1 +~+ - (13) Pd " Ifig 5 1- k2 k50-k4) O-k 2-2 kl )-~ t-k50-k4 where the term ~ is introduced to account for. minimization leads to 1 k I - -~ (1-k 2 ,-l O-k4)k 5 -4 20-k2)(l-k4)ks) (5) which can be substituted into Eqn. 4 to find the minimum value of Pu. Eqns 4 and 5 include square plated slabs as. as I -2 k 1 1-2 k 1 8k l P. = 4mp 5 +~+ ] (4) kl-k+ ks(l-k4) O-k 2-2 kl)+ksO-k4) Minimization of Pu with respect to k t and ignoring the contribution of the hogging moment in this minimization