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Design Proposal for Luyang Sea Crossing in Phase I Project of Yang Shan Deepwater Port Chapter XIChapter XIV Static Analysis and Calculation 14.1 IntroductionThe proposed Lu Yang Sea Crossing bridge is located between Dajishan mountain and Tanxushan mountain, at the northern sea area of Hangzhouwan bay which lies on the inner edge of continental shelf of Donghai sea. Its total length is about 30 km, connecting south with Xiaoyangshan mountain of Qiyu archipelago in norther Zhejiang province, north with Lu Chao port of Shanghai Nanhui county. This report details an analysis on the proposed bridge scheme of five-span, spatial single plan cable stayed bridge (80+103+380+103+80) with vase shape tower, using 28 meter wide, 3.8 meter high box girder. Concrete pier with box section is used in middle span, dual column pier with box section is for side pir and single column pier for auxiliary pier.Despite 380 meter long main span of the bridge and its maximum 188.5 meter long cantilever during construction as well as its 140.2 meter high tower above the top of pilecap, to ensure the wind resistant capacity during operation and construction and the seismic resistant capacity during operation, a related comprehensive study has been performed considering the following adverse climate condtions at the proposed site: a. Complicated climate due to its location at the south edge of northern subtropical zone , an area in east Asia where monsoon prevails. b. Frequent active tropical cyclone and gale with maximum average 10-minute speed once every 100 years as large as 42.16 m/s. c. Peak seismic dynamic acceleration as high as 0.1g. Below lists all work performed along with conclusions and assessments14.1.1 Work performed1. Basic wind design speed, standard wind design speed and allowable wind design speed for girder flutter2. Determination of seismic resistance standard3. Structural dynamical characteristics analysis4. Wind resistance stability check for main girder5. Other problems related to wind resistance6. Seismic response of structure14.1.2Conclusions and assessments1. Basic wind design speed V10 = 42.16 m/sBasic wind design speed at operation stage:Main girder:VD(girder)=51.0 m/s;Tower:VD=60.3 m/s;Basic wind design speed at operation stage:Main girder:VD(girder at construction)=42.84 m/s;Tower:VD(tower at construction)=50.7 m/s;Allowable wind design speed for girder flutter:At operation stage:Vcr=80.0 m/s;At construction stage:Vcr=66.3 m/s;2. Determination of seismic resistance standardPeak seismic parameter :0.1g;Seismic parameter: PGA=0.15g,Kh=0.15;(for structure strength check)PGA=0.20g,Kh=0.20; (for structure deflection check)3. Structure dynamic characteristics analysis and calculation of critical wind speed for girder flutterTable 1: Structure dynamic characteristics analysis and calculation of critical wind speed for main girder flutter at operation and construction stages:Working StateBasic frequency of vertical bending（Hz）Basic frequency of lateral bending（Hz）Torsional basic frequency（Hz）Vcr1(m/s)Vcr2(m/s)Vcr (m/s)Vcrs (m/s)Operation0.39760.35600.80192.02174.6179.680.0/Max. Cantilever during construction 0.41040.26160.90102.20181.2201.8/66.3Note：- Ratio of torsional to bending frequency；Vcr1 - Critical wind speed of bending torsion coupled flutter；Vcr2 - Critical wind speed of separate-flow torsional flutterFrom results listed above, all the calculated critical wind speed for girder flutter both at operation stage and construction stage are greater than 150 m/s, exceeding the allowable wind design speed for girder flutter which is 80.0 m/s at operation stage and 66.3 m/s at construction stage. Therefore, it can be concluded that either at operation or construction stage the proposed bridge is stable to withstand the wind.4. Structure seismic resistance analysisUsing the method of Response Spectrum, seismic response analysis for each critical section was performed with input of peak seismic parameter as 0.15g for medium earthquake; 0.2g for big earthquake;and seismic magnifying coef. for grade III site which is specified in Chinese code JTJ004-89 Seismic Resistance Design Code for Highway Works. Per above seismic response analysis, the maximum moment is listed below:Longitudinal moment in tower:788700KN-MLateral moment in tower:670500KN-MLateral moment in side pier:32170KN-MLateral moment in auxiliary pier:114100KN-MLateral moment in main girder:265100KN-MAfter calculation check, the structure is proven to be capable of resisting earthquake and bearable for all seismic response in all its components.The perimeter friction and horizontal resistance of pile used in tower and pier foundation at potential liquefaction later should be reduced per requirement of relevant code. Further investigation should be performed on the two unseen fissures crossing the proposed bridge location.14.2 Applied codes and references1 JTJ021-89General Code for Highway Bridge and Culvert DesignIssued by Transportation Ministry of P.R.C2 JTJ004-89Seismic Resistance Design Code for Highway WorksIssued by Transportation Ministry of P.R.C3 Guide to Wind Resistance Design of Highway BridgesPublished by Peoples Transportation Publishing House, 19964 JTJ027-96Design Code for Highway Cable Stayed Bridge (Trial)Trade Standard of P.R.C5 Handbook for Wind Resistance Design for Highway BridgeBy Japan Road Consortium, 19916 Volume 3, of Solicitation Document for Lu Yang Sea Crossing Bridge of Shanghai Deepwater Port Project, Phase I, Nov.,200114.3 Basic wind design speed, standard wind design speed and allowable wind design speed for test for girder flutter14.3.1 Basic wind design speedSite location and meteorological data The proposed Lu Yang Sea Crossing bridge is located between Dajishan mountain and Tanxushan mountain, at the northern sea area of Hangzhouwan bay which lies at the inner edge of continental shelf of Donghai sea. Its total length is 28.136 km, connecting south with Xiaoyangshan mountain(Xiaochengzishan in Yang Shan deepwater port) of Qiyu archipelago in norther Zhejiang province, north with Lu Chao port (close to Nanhuizui 4KM away from the east of Lu Chao Port Passenger Station) of Shanghai Nanhui county, running through Xiaowugui, Dawugui, Kezhushan. It is known from reference 1.6 that monsoon is the typical meteorologic feature of this area. The yearly wind information is listed as below:Most probable wind direction:northward and southeastPrimary wind direction:NNENESecondary wind direction:SESSEGale most probable direction:northward and southeast slightly slant to southwardMaximum wind speed and its direction surveyed at Dajishan station and Xiaoyangshan station are :Survey StationMaximum Wind SpeedWind DirectionDajishan35.0 m/sNNEXiaoyangshan27.0 m/sSSEGale statistics data from Dajishan station(81.0 meter high above ground) are:Wind ForceYearly Occurrence frequencyGreater than Grade 765.8 daysGreater than Grade 830 daysGreater than Grade 93 daysGale statistics data from Xiaoyangshan station in recent two years are:Greater than Grade 724.3 days (45 daysduring 2-year long survey)Tropical cyclone statistics in this region show that probably occurred period for tropical cyclone is from May to November and July, August and September are the seasons when cyclone is most likely to happen, with frequency equal to 78% days of whole year. Statistics for cyclone surveyed from 1960 to 1995 show:Cyclone ForceTotal OccurrenceAverage YearlyYearly Max. = Grade 71293.6times7times= Grade 8892.4= Grade 126once every six yearsInfluenced by the tropical cyclone in the area, prevailing wind direction is northward. Based on the gale direction surveyed by Xiaoyangshan station and the prevailing direction of tropical cyclone dominant in this area, the angle between gale and bridge axis is less than 45 degree, similar with the angle between tropical cyclone and bridge axis, both angle are oblique. 14.3.2 Basic wind design speedConsidering that the proposed Lu Yang Sea Crossing bridge is a cable stayed bridge with main span of 380 meters, and its service life is designed to be 100 years, the basic wind design speed should use maximum 10-minute average wind speed (V10) of the wind in recent 100 years which should be surveyed at the elevation of 10 meter above open ground . From table 2-4 in reference 1.6, the required wind speed is 42.16 m/s. In the meantime, from the national wind pressure chart, the maximum 10-minute average speed V20 of wind surveyed at elevation of 20 meters above open ground in recent 100 years is 35.8 m/s (basic wind pressure Wo=800 Pa). Based on the assumption that wind speed varies linearly with the height, the required wind speed V10 can be obtained from V20. By calculation V10 is 29.9 m/s. Surface roughness factor K4 can be set to 1.4 for the reason that the bridge is 30 KM long spanning the sea. Then by taking into account of K4 factor, the final V10 is modified to be 36.6 m/s. Further, Taking into consideration that the site is crossing the sea which is not clearly identified on the national wind pressure chart, wind speed V10 is finally conservatively determined to be 42.16 m/s to assure the wind resistance capacity of bridge.14.3.3 Standard wind design speedFrom reference 1.3, the standard wind design speed at the operation stage is:Standard wind design speed for main girder: VD(girder)= K1.V10=51.0 m/sStandard wind design speed for tower: VD(tower)= K4.V10=60.3 m/sHowever, from reference 1.6, the given 10-minute average maximum wind speed surveyed at 40 meter high in recent 100 years is 48.43 m/s, the stardard wind design speed for girder VD is determined conservatively to be 51.0 m/s. For tower and girder at construction stage, the standard wind design speed in recent only years can be used, which are:Standard wind design speed for girder at construct: VD(girder/const)=0.84.V10=42.84 m/sStandard wind design speed for tower at construct:VD(tower/cons)= 0.84.V10=50.7 m/s14.3.3 Allowable wind design speed for girder flutterFrom reference 1.3, the allowable wind design speed for girder flutter can be obtained through the following formula:Vcr=Kf VD(girder)where : K-incorporated safety factor considering the test deviation in wind tunnel and the uncertain factors from the design and construction. K=1.2;f - Modification coef. considering wind pulse impact and horizontal related factors, f =1.29;Therefore the allowable wind design speed for girder flutter at the operation stage can be obtained to be 80.0 m/s (Vcr=80.0 m/s) and 66.3 m/s for girder at construction stage. (V=0.84Vcr=66.3m/s)14.4 Determination of seismic resistance standardEstablishing a safe, economical and reasonable seismic resistance standard is foremost for the seismic design of long span cable stayed bridge. Considering the important role the huge bridge plays in connecting Shanghai and Yangshan deep water port, earthquake related safety evaluation should be performed per the requirement stated in item 17 of Chinese Law of Seismic Resistance and Disaster Elimination. However the seismic parameter for the proposed site cannot be obtained due to the lack of evaluation conclusions in reference 1.6 regarding to the earthquake safety on the site. The national standard Chinese Earthquake Parameter Map (GB18306-2001) has been issued on Feb. 2, 2001 by national quality supervision bureau and will be effective Aug. 1, 2001. From this map, the desired parameters for Shanghai Nanhui and Shensi of Zhejiang province are 0.1g; According to the China Seismic Response Spectrum Eigenperiod Division Map, the eigenpriod of seismic response spectrum for these two areas is 0.35s.The bridge is located at the loose stratum of the 4th century with thickness of between 160 and 220 meter varying with the elevation of sea bottom. It is known from reference 1.6 that the site is classified as to site of grade III.Since the bridge is an important huge bridge with total length of 28.136 kilometer, the service life of the bridge is designed to be 100 years. Following the design principle for earthquake resistance which says “no damage for small earthquake, repairable for medium earthquake and no collapse for big earthquake”, the seismic parameter for small, medium and big earthquake should respectively be that of 63%, 10% and 2%3% of passage probability of 100-year used probability. Referring to the seismic parameter provided in reference 1.6, the peak seismic acceleration specified in the Chinese Seismic Parameter Map can not be used since its corresponding probability is 10% of passage probability of 50 years. For the same reoccurrence period, the seismic parameter can be obtained as below provided both the earthquake resistance of the structural and the economy are satisfied.(1) Seismic parameter used for checking structure strength: PGA=0.15g, Kh=0.15;(2) Seismic parameter used for checking structure deflection:PGA=0.20g, Kh=0.20;(3) Grade III site, Eigenperiod of response spectrum is 0.45s.14.5 Structure dynamic characteristics analysis14.5.1 Calculation modelA fish spine like spatial model was employed in dynamic analysis. See figure 1 and figure 2 for model simulating bridge status at both operation stage and construction stage with longest cantilever. 14.5.2 Boundary restraintsSee table 2 below for boundary restraint at both operation and construction stage. Table 2 Boundary restraints at operation and construction stageComponentOperationConstructionxyzxyzxyzxyzPile fixed point of tower foundation 111111111111Joint of tower and girder011100111101Pile fixed point of side and auxiliary pier foundation111111111111Joint of girder and side/auxiliary pier011100011100Note: x、y、z longitudinal, lateral and vertical linear displacement constraint x、y、z。Rotation constraint along longitudinal, lateral and vertical axis. 1-constrained，0-free。14.5.3 Dynamic characteristics analysisSee table 3 for main mode features at operation stage. It can be obtained from the mode shape digram (Fig. 2) that:(1). Side pier and auxiliary pier has strongly restricted the lateral and vertical vibration of main girder which is favorable to the structure wind resistance. Since there is no longitudinalconstraint between pier and main girder, the side pier and auxiliary pier have weak restriction to the longitudinal vibration of the main girder.(2) The structure is designed to be a floating system by freeing the longitudinal displacement constraint at the points where main girder and tower or piers are connected. So designed system, whose longitudinal movement becomes its first mode with natural period to be 8.9s, is favorable in reducing the seismic response with considerably large displacement. (3) The main girder, 28 meter wide and 3.8 meter high, produces larger lateral rigidity than vertical rigidity. However because the structure adopts the single plan cable which can be viewed as vertical elastic support, the entire vertical rigidity of the structure becomes larger than lateral rigidity, which is demonstrated in the mode shape diagram showing lateral bending mode precedes vertical bending mode.(4)The vase type tower with its foundation, 140.2 meter high measured from the top of pile cap is a flexible structure. So the modes of lateral bending both in the same and opposite faces in the tower come comparatively earlier, which is No.6 and No.5 mode.(5) The main girder is a closed box section with 28 meter wide deck. The girder itself does have a large torsion rigidity. However as the structure is single plan cable stayed which contributes almost no torsion rigidity, the entire structure torsion rigidity is contributed by main girder alone. So the structure torsion frequency is only 0.8019 HZ.(6)No.2 mode is most favorable to lateral seismic response of the girder. No.6 mode is most favorable to lateral seismic response of the tower footing.No.1 mode is most favorable to longitudinal seismic response of the tower footing.(7) The mode related to structure wind resistance is the mode where girder vibration dominates. No.2 mode is the mode which is related to the lateral girder buffeting and No.3 mode is the mode related to the vertical girder buffeting and vortex-excited vibration, while No.3 and No.8 mode are the modes related to girder self-excited vibration whose frequency ratio of torsion to bending is 2.02. (=2.02)Although the bridge is single plan cable stayed, it still achieves high frequency ratio of torsion to bending, providing high wind resistance stability by using closed box section for main girder which helps increase the girder weight and torsion rigidity. Main girder adopts nearly flat and streamline box girder (width/height=7.4) which is helpful to increasing the critical wind speed for girder flutter, reducing the vortex-excited vibration amplitude and buffeting.The maximum cantilever length at construction stage is 188.5 meter. The mode features at this working state is listed in table 4 and its corresponding mode shape diagram is shown as Fig.4. From the diagram it can be obtained that becaus