Calculation and investigation of causes of Transvaal Water Park cover collapse
A range of expert’s studies devoted to the analysis of structural strength of Transvaal Water Park building have been conducted so far. However, none of these studies definitely indicated the cause of collapse of this building.
As the main tool to determine stressedly-deformed state and dynamic properties of the structure under different loads, a finite element numeric method was used in these studies, realized in various program systems: LIRA, SCAD, ANSYS and STADIO. Finite element models formed from beam and shell elements were used to determine stressedly-deformed state of the cover structure with a system of support pillars. Strength characteristics of reinforced concrete were specified to model a reinforced concrete shell of the cover. These finite element models included from several dozens to a hundred thousand elements.
Real cover was made as reinforced concrete shell of variable thickness having inhomogeneous reinforcement and a system of cross reinforced ribs. In modeling of such complex structure, the above mentioned degree of discretization does not make it possible to take into consideration any local features of stressedly-deformed state of the structure conditioned by nonlinear behavior of concrete and reinforcement system realized in the structure.
For more accurate determination of local features it was decided: to build a finite element model of cover with modeling of support contour and adjacent to it shell areas by solid elements; define all reinforcement installed in the concrete by beam elements in accordance with the drawings; define a “thin” part of the shell (thickness=70 mm) and supporting ribs by two-dimensional shell elements; define rib reinforcement by beam elements; take account of nonlinear behavior of material with different compression and tension characteristics for concrete; model the structure of support pillars by shell elements with a detailed elaboration of connections and support joints. As a result, a model was developed, consisting of about 2 million elements, 20 times above a detailed elaboration of the structure in the models presented earlier in the calculations of expert organizations. Number of joints in the model =1,851,000, number of elements =1 894 000.
LLC Hexa was the first to use this combined method of concrete and reinforcement modeling in the study of the water park structure. A simplified roof model was used in all previous calculations and examinations.
The model of pillars with connections is also different from the model used in the analysis of expert organizations. Simplified framing models used in the calculations of expert organizations lead to 450% inaccuracy in the results of force analysis. Such inaccuracy resulted from the fact that compliance of pillar shell was not taken into account in the model.
The calculations were made for successive loading of the structure:
The calculations and analyses performed in this study include:
Initially, it was considered whether it was reasonable to solve the problem of large-span sloping shell loading in the linear-elastic setting. For this purpose, calculations for loading with permanent load (“weight” load) were performed for the models:
Nonlinear behavior of concrete under tension and compression was taken into consideration in the calculations by defining an elasto-plastic material model. Link connections of top pillar points with the support contour of the shell were defined.
Comparison of design data shows significant difference in maximum displacements of the cover determined for models with linear and elasto-plastic properties of concretel.
When geometric nonlinearity is taken into account in the calculation for the linear-elastic concrete model it is possible to determine the areas of large local deflections of the shell, but deflection values are understated: 65 mm for the linear-elastic model, 144 mm for the linear-plastic model. In the calculations performed in the design of the construction under study, nonlinear behavior of concrete was not taken into account thus resulting, as shown above, in significantly understated estimate of shell deflections.
Calculation studies of effect produced on stressedly-deformed state of the structure by changes in concrete properties were conducted.
The use of concrete with better elasticity and strength properties in the cover structure reduces deflections of the shell and stresses in the reinforcement.
Results of calculations under snow load
Initially, the properties of В35 concrete strength (initial modulus of elasticity Еb = 34,500 MPa) were defined for the elements modeling concrete. With uniformly distributed snow load 90 kg/m² (design value of snow load is 180 kg/m²), maximum tensile stresses in the reinforcement exceeded yield point Rsn= 500 MPa (standard resistance for A500C reinforcement). It should be noted that creep of concrete is not taken into account in the calculation.
Maximum deflections under the above given load achieve 300 mm.
Stresses in concrete exceed yield points (standard resistances) to compression and tension. Principal stresses in concrete achieve 27.5 MPa (standard value is 25.5 MPa). The zone of plastic deformations in concrete covers a significant area of the shell.
The entire red zone is exposed to cracking in concrete.
“Weight + snow 30 kg/m²” load. Concrete modulus of elasticity Еb = 23000 MPa
Stresses are right on size thus refuting experts’ assertion of loss in bearing capacity of pillars and side connections. We found that even if one pillar is excluded from the use, no significant (catastrophic) changes occur in the structure.
The design data given above show that determination of stressedly-deformed state of the structure under study with no account taken of geometric and physical nonlinearities results in significant understating of maximum shell deflections and maximum stresses both in concrete and reinforcement.
If the analysis of structural strength similar to that described above was performed at the stage of design and final decision-making, it would be more reasonable to assert that all design errors were detected.
Hexa Company to order of KURORTPROJECT CJSC, 2007.
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