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ISET Journal of Earthquake Technology, Paper No. 495, Vol. 45, No. 1-2, March-June 2008, pp. 13–2928th ISET Annual LectureFOUNDATIONS FOR INDUSTRIAL MACHINES ANDEARTHQUAKE EFFECTSK.G. BhatiaCenter for Applied DynamicsD-CAD Technologies, New DelhiABSTRACTImprovement in manufacturing technology has provided machines of higher ratings with bettertolerances and controlled behaviour. These machines give rise to considerably higher dynamic forces andthereby higher stresses and, in return, demand improved performance and safety leaving no room forfailures. This paper highlights need for a better interaction between foundation designer and machinemanufacturer to ensure improved machine performance. The paper also describes the designaids/methodologies for foundation design. Various issues related to mathematical modeling andinterpretations of results are discussed at length. Intricacies of designing vibration isolation system forheavy-duty machines are also discussed. Influences of dynamic characteristics of foundation elements,viz., beams, columns, and pedestals etc. on the response of machine, along with some case studies, arealso presented. The paper also touches upon the effects of earthquakes on machines as well as on theirfoundations. Use of commercially available finite element packages, for analysis and design of thefoundation, is strongly recommended, but with caution.KEYWORDS:Machine Foundation, Dynamic Response, Seismic Qualification, Design Aids,Vibration IsolationINTRODUCTIONThe dynamics of machine-foundation system is an involved task in itself and consideration ofearthquake effects further adds to its complexity. The performance, safety and stability of machinesdepend largely on their design, manufacturing and interaction with environment. In principle machinefoundations should be designed such that the dynamic forces of machines are transmitted to the soilthrough the foundation in such a way that all kinds of harmful effects are eliminated (Barkan, 1962;Bhatia, 1984, 2006, 2008; Major, 1980; Prakash and Puri, 1988; Srinivasulu and Vaidyanathan, 1980). Inthe past, simple methods of calculation were used, most often involving the multiplication of static loadsby an estimated dynamic factor and the result being treated as an increased static load without anyknowledge of the actual safety factor. Because of this uncertainty, the value of the adopted dynamic factorwas usually too high, although practice showed that during operation harmful deformations did result inspite of using such excessive factors. This necessitated a deeper scientific investigation of dynamicloading. A more detailed study became urgent because of the development of machines of highercapacities (Bhatia, 1984).Machines of higher ratings gave rise to considerably higher stresses thereby posing problems withrespect to performance and safety. This called for development partly in the field of vibration techniqueand partly in that of soil mechanics. Hence new theoretical procedures were developed for calculating thedynamic response of foundations (Bhatia, 2006).Based on the scientific investigations carried out in the last few decades it has been established that itis not enough to base the design only on the vertical loads multiplied by a dynamic factor, even if thisfactor introduces a dynamic load many times greater than the original one. It should be remembered thatoperation of the machines generates not only vertical forces, but also forces acting perpendicular to theaxis; it is thus not enough to take into account the vertical loads only and to multiply those by a selecteddynamic factor (Bhatia, 2006, 2008). It has also been found that the suitability of machine foundationsdepends not only on the forces to which they will be subjected to, but also on their behaviour, when

14Foundations for Industrial Machines and Earthquake Effectsexposed to dynamic loads, which depends on the speed of the machine and natural frequency of thefoundation. Thus a vibration analysis becomes necessary. Each and every machine foundation doesrequire detailed vibration analysis providing insight into the dynamic behaviour of foundation and itscomponents for satisfactory performance of the machine. The complete knowledge of load-transfermechanism from the machine to the foundation and also the complete knowledge of excitation forces andassociated frequencies are a must for the correct evaluation of machine performance.All machine foundations, irrespective of the size and type of machine, should be regarded asengineering problems and their designs should be based on sound engineering practices. Dynamic loadsfrom the machines causing vibrations must be duly accounted for to provide a solution, which istechnically sound and economical. Though advanced computational tools are available for preciseevaluation of dynamic characteristics of machine-foundation systems, their use in design offices, whichwas limited in the past, has now been found to be quite common. A machine-foundation system can bemodeled either as a two-dimensional structure or as a three-dimensional structure.For mathematical modeling and analysis, valid assumptions are made keeping in view the following: The mathematical model should be compatible with the prototype structure within a reasonabledegree of accuracy. The mathematical model has to be such that it can be analysed with the available mathematical tools. The influence of each assumption should be quantitatively known with regard to the response of thefoundation.Vibration isolation techniques have also been used to reduce vibrations in the machines. Isolationleads to reduction in the transmissibility of the exciting forces from the machine to the foundation andvice-versa. Use of vibration isolation devices is one of the methods by which one can achieve satisfactoryperformance, which in turn can result in minimizing failures and reduce downtime on account of highvibrations. However, for equipment on elevated foundations, it is desirable to have support structurestiffness sufficiently higher than the overall stiffness of isolation system in order to get the desiredisolation efficiency (Bhatia, 2008). The support structure, a 3-D elevated structural system, possessesmany natural frequencies. The vibration isolation system, comprising the machine, inertia block and theisolation devices, also has six modes of vibration having specific stiffness values corresponding to eachmode of vibration. It is of interest to note that the lateral stiffness of an elevated structure is very muchlower than its vertical stiffness. If this lower (lateral) stiffness is comparable to the stiffness of isolators, itcertainly affects the overall stiffness and thereby the response of the machine-foundation system. Hence,the lateral stiffness of the support structure must also be computed and considered while selecting theisolators. Finally it may be desirable to carry out detailed dynamic analysis of the complete systemincluding the substructure.MACHINE-FOUNDATION SYSTEMThe main constituents of a typical machine-foundation system are machine: rotary machines, reciprocating machines, impact machines; foundation: block foundations, or frame foundations; and support medium: soil continuum, or a soil-pile system, or a substructure that, in turn, is supportedover the soil continuum or soil-pile system.Dynamic forces are (i) internally generated forces by the machine itself, or (ii) externally applied forces(that are applied directly to the machine, or transmitted through the support medium/foundation).Figure 1 shows the schematic of dynamics between various elements of a machine-foundationsystem. It is seen that all the three constituents of the machine-foundation system, viz., machine,foundation and soil, contribute to the frequency of the system. This system, when subjected to dynamicforces (whether internally generated, externally applied, or transmitted through the soil), results inresponse of the system.MODELING AND ANALYSISEvery foundation designer should remember that he/she is dealing with machines weighing severaltonnes and is required to design the foundations having dimensions of several meters but with amplitudesrestricted to only a few microns. The designer, therefore, must clearly understand the assumptions,

ISET Journal of Earthquake Technology, March-June 200815approximations, and simplifications made during the modeling and must recognize their influence on theresponse. It is this aspect that makes modeling and analysis a very important part of FrequencySystemResponseSafetyCheckYesSoilO.K.Fig. 1 Schematic diagram of a machine-foundation system subjected to dynamic loadsFor the purpose of analysis, the machine-foundation system is represented by an appropriatemathematical model with the basic objective that the model should be compatible with the prototype. Foreach mathematical representation, a host of assumptions and approximations are made. The extent ofcomplexity introduced in the mathematical model directly influences the reliability of results. In addition,simplifications/approximations are also introduced to meet the limitations of the analytical tools. In otherwords, mathematical representation not only depends on the machine and foundation parameters but alsodepends on the analysis tools.1. Manual Computational Method1.1 Block FoundationsFor the machines on block foundations, it is good enough to use simple formulations (which areequations of motion considering block as a rigid body supported on an elastic medium, i.e., soil). Whereasmajority of the machine and foundation aspects are well taken care of by these procedures, there are someaspects, as given below, that cannot be fully managed by these manual computational methods.1.2 Foundation EccentricityIf foundation eccentricity is higher than the permissible value, the vertical mode of vibration will nolonger remain uncoupled from the lateral and rotational modes (Barkan, 1962; Bhatia, 2008). It isundoubtedly easy to write equations of motion for such uncoupled modes, but getting closed-formsolutions for those equations is not that simple, and computations may turn out to be complex. Further,getting transient response history may be a tedious task, though it is possible to evaluate transientresponse at any of the defined frequencies.It is therefore recommended to use finite element (FE) analysis, wherever feasible, in order to includeall these aspects. Further, this gives improved reliability on account of lesser number of

16Foundations for Industrial Machines and Earthquake Effectsapproximations/assumptions. This also permits visualization of animated mode shapes, and viewing ofresponse amplitude build-up and stress concentration locations.1.3 Frame FoundationsThe formulations used for manual computations cover only standard/ideal frames, i.e., frame beam isrectangular in cross-section having machine mass at its center. Analysis of a single portal frame is basedon the premise that longitudinal beams of a frame foundation are flexible enough to permit transverseframes to vibrate independently (Barkan, 1962; BIS, 1992). These procedures are only for very idealcases, and most of the real-life machine foundations do not fall under this category. Some of the aspectsthat cannot be suitably accounted for by the manual computational methods (Bhatia, 2008; Ramdasa etal., 1982) are haunches, machine mass at off-center locations of the beam, beams extended as cantilevers on one side/both sides of the frame beam, beams inclined in elevation supporting heavy machine mass, no frame beam at column locations, higher-order frame-column vibration frequencies, presence of solid thick deck within the frames, and depression/recess in the top deck.Based on many design studies carried out by the author, it has been observed that1. Variation in natural frequencies of a frame obtained manually compared to the FE method is of theorder of 10% to 20% (Bhatia, 2008).2. FE analysis confirms the presence of three-to-four additional frequencies between the first and secondvertical modes as computed manually. These additional frequencies lie well within the operatingrange of the medium-RPM machines and may significantly contribute to the response.3. In recognition of the higher reliability of the FE method, and the fact that manual computations giveresults that are in variance by 10% to 20% compared to the FE analysis, it has been suggested that nocorrections need to be applied on account of either frame centerline dimensions or inclusion ofhaunches, etc.; all corrections put together will easily get absorbed by the available margins (Bhatia,2008).It is, therefore, recommended to use FE analysis with appropriate element types for the modeling of framefoundation. It is, however, recommended to use the manual analytical approach to evaluate free-vibrationresponse for each frame to get a first-hand feeling of the frequency range of frames vis-à-vis the operatingfrequency and their sub- and super-harmonics.2. Finite Element MethodFinite element method is the most commonly accepted analysis tool for the solution of engineeringproblems. Effective pre- and post-processing capabilities make modeling and interpretation of resultssimple. It is relatively easy to incorporate changes, if any, and to redo the analysis without much loss oftime. Viewing of the animated mode shapes and dynamic response makes understanding of the dynamicbehaviour of the machine foundation system relatively simpler. Design of machine foundation involvesthe consideration of machine, foundation and soil together as a system, subjected to applied or generateddynamic forces. Development of a specific FE-based package for the design of machine foundation isgenerally not feasible on account of (a) tight project schedules and (b) validation of results. Use ofcommercially available packages is more effective for des