Wind loading and dynamic response of air-supported roof structures
This thesis is concerned with defining, theoretically, approximate values of wind loading and predicting dynamic response of air-supported structures subject to suddenly applied loads. Wind loading on air-supported structures is a phenomenon involving significant mutual interaction between inertial, elastic and aerodynamic forces. The aerodynamic forces described by fluid mechanics equations are examined in the first part of the thesis, Chapters 2 to 6. Chapter 2 contains a brief discussion of wind as a flow of air around rigid bodies. This review is followed by an introduction to modern wind engineering, and then by discussion on the theoretical and/or experimental methods to assess wind response of flexible structures. Under the simplifying assumption of three-dimensional potential flow of an incompressible, inviscid, steady air flow, the three-dimensional pressure coefficient distribution on an open-sided paraboloid shallow shell roof is examined in Chapter 5, employing three versions of a vortex-lattice method. The modified Hedman method with horseshoe vortices in the plane z=0, and a boundary condition of tangential flow applied on the body of the shell yielded the best results. In the Appendix to Chapter 5 a real flow solution based on the 'SIMPLE' algorithm is investigated for a numerical example of a thin shell submerged in steady flow - a two-dimensional approximation of the section employed in Chapter 5. For a 3D structure which cannot be adequately represented by 2D model a simple 3D potential flow solution is likely to yield more accurate pressure distributions than a sophisticated 2D real flow analysis. The wind tunnel tests described in Chapter 6 were conducted on a thin, rigid eliptic paraboloid subject to two flow conditions: uniform flow, and in the thick turbulent boundary layer. The theoretical results predicted fairly well the mean pressure distribution on the shell in uniform flow, except on the rearmost part of the model, where separation occurred. In the case of the turbulent boundary layer flow, discrepancies in mean pressure coefficient distributions are of the same order as for uniform flow. However, as the turbulent boundary layer flow is a much more complicated phenomenon than the theoretical description of potential flow, the above conclusion cannot be generalized without further work. The vortex-lattice method, due to its simplicity, can be easily incorporated into any structurefluid interactive scheme accounting for both static and quasi-dynamic behaviour, and an assessment of dynamic response is essential for the design of large air-supported structures. The second part of the thesis, Chapters 7 to 12, is concerned with the structural response of air-supported structures; with special emphasis on the dynamic response following sudden release of a loading system. Chapter 7 gives a review of methods of analysis for pneumatic structures; those experiencing strong geometric nonlinearities are especially focused. The dynamic relaxation method with kinetic damping is discussed in Chapter 8 with respect to the static analysis of pneumatic structures; structural idealization depending on the fabric patterning, type of loading and kind of membrane material being used. Two series of model tests are described; both employing fairly large scale pneumatic domes. The first test model constructed using an orthotropic woven fabric is subject to centrally placed suddenly applied loading. The second test model constructed with very lightweight polythene is subject to suddenly released loading, both central and asymmetric. For this case the internal air and added mass effects become dominant. Explicit dynamic analysis using a centred finite difference scheme is employed in Chapter 9 to analyse the response of pneumatic structures; and in particular to assess the response of the test structures. The influence of surrounding air is included as far as internal air stiffening is considered. For the suddenly unloaded dome, a revised, more efficient numerical scheme is developed, where checking for buckling is carried out at each time step, but creep strains, updated stiffness matrices and unit pressure vectors are calculated at less frequent intervals. In Chapter 10 the tests on the impulsively loaded and unloaded pneumatic domes are described. Dome membrane properties are established from static and dynamic tests on specimens. For dynamic tests a new procedure is devised, to model more closely the state of stresses, by including twodimensional stresses in the testing area of the specimen. Still and movie cameras were used in the static and dynamic tests on the pneumatic domes to record deflection. The results were analysed by means of photogrammetric techniques. The static results compare very well with theoretical predictions. The theoretical dynamic trace for the apex nodal deflection of the impulsively centrally loaded dome differs only slightly from experimental results. The heavy central load influences greatly the response. Discrepancies between theoretical and experimental dynamic responses of the very lightweight and suddenly unloaded dome are however large. The main area of error is caused by improper modelling behaviour of the surrounding air which should be treated as an intrinsic part of the structure. A coupled fluid-structure explicit dynamic analysis, including membrane and air modelling, is presented in Chapter 11. The behaviour of irrotational, inviscid, compressible fluid is described from a Lagrangian point of view. Although only the simplest axisymmetric case is considered, the amount of computing is enormous, hence the procedure cannot, at present, be advocated for use in practice. In Chapter 12 the added mass effect due to vibrating air is discussed. A method to account for virtual mass in shallow pneumatic structures, based on potential incompressible flow and discrete source distributions, is presented and included in the numerical explicit dynamic procedure. The results for the centrally unloaded dome show a great improvement in terms of frequencies, with only a small increase in computing time compared with the numerical scheme of Chapter 9. The discrete source distribution method to calculate added mass effects can be easily extended to any shape of pneumatic structure, and when combined with an explicit dynamic analysis can provide a useful scheme for calculating frequencies and the approximate dynamic response of air-supported structures.