孟子大剧院的结构设计分析

The 12th International Symposium on Structural EngineeringSTRUCTURAL DESIGN OF THE MENCIUS GRAND THEATREWei Liu, Dayi DingChina Wuzhou Engineering Co., Ltd. , Beijing 100053, P.R. ChinaAbstract: For The Mencius Grand Theatre, the issues of the theatre structural design were studied in this paper. Including selection of structural form and arrangement of structure, the control of calculation indicators, the achieving of the stalls structure and the cantilevered balcony structure, foundation design and so on. According to the design objects of the structure performance, the static and earthquake were analyzed with SATWE, MIDAS and PMSAP programs. The calculation assumptions and the theater model simplification were discussed. The seismic fortification measures were also investigated to intensify the concept design.Keywords: Theatre, floor discontinuous, performance-based design, seismic fortification measures1 INTRODUCTIONIn recent years, some grand theatres have been constructed in some cities of China. And some grand theatres are being planned to be designed and constructed. There are some design difficulties which are relatively typical in the theater structure design. Such as irregular plan, floor discontinuous, many split-level, cantilevered balcony, large-span roof structure and so on. In this paper, we’ll discuss these questions with The Mencius Grand Theatre for example, in order to be referenced by the next project.2 PROJECT PROFILEThe Mencius Grand Theatre is planned to be located in the city of Zoucheng of Shandong Province, which is the hometown of Mencius. It will be a modern standard theater with 1300 seats, which can meet the needs of domestic and foreign large-scale song and dance performances. Designed with other movie theaters, commercial center, underground garage and regional power centers, the building functions are very complex. There are 4 stories aboveground, and part of the area, 2 stories underground. The auditorium building height is 25.0m, and the stage building height is 32.4m, as shown in Figure 1, the total construction area is 35220m2. The main structural form is reinforced concrete frame - shear wall structure. The roof structural form of the auditorium(40.5m×40.5m) and the stage(33.3m×24.3m) are both steel truss with supporting structure. The whole structure bases on the natural foundation. Beam stiffened raft is adopted for the basement part, and the single column foundation and wall strip foundation are used for the rest part. The level of the building structure’s security is class 2. The designed service life is 50 years. Building seismicfortification classification is B.Figure 1. Structure section plan3 FOUNDATION DESIGNAccording to the survey report, the basement bearing stratum of natural foundation is intensely weathered granite， whose bearing capacity values f ak = 500kPa, and E s1-2 = 45MPa. As to the beam stiffened raft, the width of the floor beam is 0.6m, and the height is 1.5m. The thickness of the bottom plate is mainly 450mm, several is 600mm. Bottom elevation of the floor beams in the stage and auditorium part is -12.78m. And in the neighboring parking garage part is -8.08m. The basement wall at the border must bear the soil pressure caused by the higher elevation raft. No expansion joints lie in the basement, but post-poured strip width 800 - 1000mm will be set every 30 - 40 meters. Post-poured strip settings are shown in Figure 2a), other layers are the same. The single column foundation and wall strip foundation are used for the rest part. The differential settlement is controlled by 0.003L. Taking into account the beneficial effects on subsidence deformation, the single column foundation and wall strip foundation land at -4.000m, which is the same raft foundation bearing stratum. In the auditorium area, the stalls cause the arc column grid, and the basement of the regional power centers cause the partial column or the column pulling. All these lead to the poor regularity of the basement column gird. Foundation beams are set at the outer edge of the basement board, to unify the basement floor reinforcement. Based on previous experience, the crack width is not necessary to be checked for foundation beam and plate. Anti-floating design water level is 5.1m underground. Anti-float calculation should be done for stage area and auditorium area respectively, in order to meet the requirements of the local anti-floating.4 MAIN STRUCTURE DESIGN FEATURESAcoording to GB 50011-2010 code 10.1.6, a certain number of reinforced concrete shear wall should be set between hall and auditorium, and auditorium and stage, in order to strengthen the lateral stiffness. Seismic walls are set up around the stage, and also axis Y direction wall of the side stage, in order to strengthen the stiffness where there is no floor. Combined with the vertical transportation, the shear walls are also set up in the stairway surroundings. In addition, shear walls also lie in the position, where makes the shear wall layout of the entire structure is more balanced, as shown in Figure 2(b).As for floor structure selection, the cross beam floor is used when the column grid is regular, and the space between the beam is depend on the load magnitude. The one-way beam can divide plate flexible, and the floor is easy for construction, so it is used when the column grid is irregular. There are lots of region with no slab in the stage and side stage area, auditorium, rehearsal halls, cinema and film, multifunctional hall, lobby, etc.. There is more than 30 percent, or even 100% floor discontinuous, as shown in Figure 2(b). It’s not toward to set seismic joint for theater structure on account of the seismic design and the use function. As mentioned, seismic wall has been set to strengthen the rigidity of areas short of floor. Moreover, frame beams surrounding these areas are strengthen to pass the lateral force and enhance the rigidity of the layer. The structure torsional displacement ratio calculating the accidental eccentricity is controlled at less than 1.5.Figure 2. Structure planThe stage and auditorium roof structure form are both steel plane truss with supporting, which are located on the concrete wall or beam of the main structure. Through a combination of fixed pin support and sliding support, the horizontal thrust of the truss under vertical loads is minimized. The major earthquake and wind loads are transmitted to the shear wall, and the roof torsion is reduced. Gird and packway are set up from the bottom of the steel truss of the stage roof. Steel frame is suspended from the steel truss of the auditorium roof, which will meet the installation requirements of bridleways, sound bridge, the bridge of the surface light within the ceiling.Balcony and corridors in the Grand Theatre are cantilevered structure, usually in theater design with large-span prestressed concrete beam as the fulcrum of the cantilever structure to reduce the cantilever. Yet with no conditions to set the fulcrum in this project, minimizing the cantilever length of the balcony is necessary. The maximum cantilever length is 6.35m. There are generally three structure forms for the·561·auditorium: a) radial main beam, secondary beam and ladder board, it’s economical; b) annular main beam and gangboard; c) sleeper wall under the seats, it needs the secondary structure. The first structure is used here, and take steel reinforced concrete (SRC) truss as the radial cantilever components. It worth noting thar the calculation of the steel truss deflection should take into account the reduction of stiffness after concrete cracking. The reduction is even more than 60%. Profile steel is set in the concrete columns for the connection of the SRC truss. And it should be embedded in the solid side for the impact of the steel to the seismic performance. Postconstruction punching outlet holes in the ladder board below the chair is accurate and easy done.5 STRUCTURE CALCULATION5.1 LoadThe seismic precautionary intensity is 6 degrees (0.08g), based on “The auditing idea of the project seismic precautionary requirement”. Site category is class II. The design seismic group is group 2. The damping ratio is 0.05. In this project, we calculate the earthquake action by 7 degrees, and the seismic measures are also 7 degrees. The temperature range for the calculation of the roof steel truss structure is ± 30℃.5.2 Calculation Model SimplificationTheater structure is very complex, so the proper model simplification is very necessary for the calculation. The main simplification in this project include:1) The theatre structure has no standard layer in the traditional sense, but has many split-level. We simulate this structure by amending the elevation of the columns and beams. Another model with more layer to contrast with the anterior one, and get whichever is the adverse results of the calculation;2) The stalls and balcony are calculated in the overall model for reinforcement calculation. In the calculation of the overall displacement, the stalls and balcony are only taken as a load to simplify the model for their little function to seismic;3) The roof steel truss are separated from the main structure with the sliding supports, so its influence to the overall stiffness can be neglected. It can be input only as load in the overall model. The steel truss can be designed separately with Midas model, considering a combination of vertical load and temperature. It’s also checked in PMSAP model.5.3 Seismic CalculationThe static and multi-component earthquake were analyzed to ensure the bearing capacity of the structure. The elastic analysis under medium earthquake was to ensure that the key components do not yield under the earthquake. The elastic-plastic static analysis was to ensure the inelastic displacement angle of the structure can meet the basic specification requirements, and the structure will not fail under rare earthquake.5.4 Calculation Result5.4.1 Vibration modesTorsional vibration takes place in the third vibration mode. The first two modes are both translational vibration mode, and their period are very approximate.Table 1. The vibration mode periodMode Period Torsioncoefficient1 0.477 0.042 0.420 0.003 0.342 0.754 0.186 0.435 0.184 0.125.4.2 Layer displacement angle is very small. The control of layer maximum displacement to average displacement ratio is equal to control the structure torsion.6 SEISMIC STRENGTHENING MEASURES1) Adjust the location of the shear walls, that lead to the approximate vibration period on the two direction.2) The beams supporting the steel roof and the fireproof curtain should be given seismic fortification measures.3) The split-level place should adopt strengthening measures.4) The stress ratio of the main roof steel members should not be greater than 0.85.5) For the structural integrity, the floor in the weak parts should be strengthened, the beam should be strengthened where there is no floor.·562·7 CONCLUSIONSIn this paper, the issues of the theatre structural design were studied, the following conclusions may be drawn:1) The foundation design should meet the requirement of the local anti-floating.2) The roof steel structure always lie in the single walls around the stage or the auditorium, so reduce the horizontal thrustthe by the sliding support is favorable.3) The stalls and balcony structure adopt radial main beam, and take SRC truss as the radial cantilever component of balcony.4) Theater model simplification and multimodel compare are necessary.5) Seismic fortification measures are significant in the theatre structure. REFERENCESDong, W.Q., Wang, H.W., Ma, J. (2011). Structural Design of the Puer Theatre for Nationality. Building Structure, 41:10, 11-14. GB 50011-2010. (2010). Code for seismicdesign of buildings. Beijing: China Architecture and Building Press, China.Zhang, Y., Liu, M.G., Rui, M.Z., Wang, D.S., Qian, P. (2012). Structural Design of Tianjin Grangd Theatre. Building Structure, 42:5, 119-124.·563·。