Design of structures and foundations for vibrating machines.
The lack of methods for rigorous dynamic analysis of foundations and structures for vibrating machines has resulted in below optimum performance and in some cases reduction of life of machines, structures and foundations. The costs and complexities of these machines make it necessary to conduct proper geotechnical site investigations. and dynamic analyses to obtain the response of the soil, foundation and structure as a system to excitation. In order to highlight the use of dynamic analyses, the response of the foundations and structures were compared to the "rule of thumb" which is based on mass ratio. Furthermore sensitivity analyses were carried out comprising the following variables: • Shear modulus of soil, G • Poisson's ratio of soil,Y • Type of structure (ie raft, table top and multi-storey) • Stiffness of structure • Stiffness of foundation The fundamentals of structural dynamics have not been dealt with in this dissertation. The dynamic analyses were carried out using a finite element analysis program called Strand 7. The results were typical of a finite element analysis, giving stresses, strains, deflections, amplitudes, frequencies and velocities of vibration. The traditional "elastic halfspace model" is deficient as it does not account for soil comprising various layers. The theory has been based on an isolated circular footing. Most foundations are located in soils with layered mediums, are rectangular and in some cases are affected by the interaction of foundations in close proximity. Furthermore there is a need to account for the non-linear effects and properties of soil. It is therefore becoming more attractive to adopt mathematical models of soils using finite elements, where the visco-elastoplastic properties of soils can be realized and modeled. Furthermore the finite element method overcomes limitations such as layering and shapes or foot-prints of foundations. The "rule of thumb" or mass ratio method of design procedure is as follows:- • firstly the requirements of stresses and serviceability must be satisfied. This is usual in a statically loaded system. the ratio of the machine mass to that of the foundation together with the structure should be greater than 3 in the case of a revolving machine and 5 in the case of a reciprocating machine. • in order to obtain uniform settlement of the foundation the distance of the combined centre of gravity of the machine and foundation from the centre of area in contact with the soil is limited to 5% of the corresponding dimension of the foundation. It is evident that the mass ratio lacks accuracy in that there are several parameters that are required to describe the satisfactory performance of a system such as amplitude, frequency and velocity of vibration. The finite element method allows for calibration of the model to account for the real behaviour of the system. Calibration is generally conducted using sensitive transducers called accelerometers. The accelerometers produce power spectral density (PSD) graphs from which deflections and stresses can be back calculated. The deflections and stresses are compared with calculated deflections and stresses. Descriptions of the methods of analysis followed by presentation of results, discussions and interpretations have been included. To motivate the use of dynamic analyses case histories have been presented and discussed. Finally the dissertation concludes with findings of the study together with recommendations for the way forward in terms of research.