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The IUP Journal of Structural Engineering :
Free and Forced Vibration Interactive Analysis of a Framed Structure Under Varying Soil Medium
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The interactive dynamic response of the framed structure significantly depends on the type of soil medium and its properties. The dynamic interrelationship between the response of a structure and the characteristic of soil medium is termed as the interaction effect. The finite element method has been employed to estimate the effect of soil media on the dynamic response of framed structure, including the interaction effect. A six-storey framed structure with raft foundation and soil medium has been considered as a system. The soil continuum and raft foundation have been discretized using four-noded isoparametric elements, and the superstructure by two-noded beam elements. The free vibration interaction analysis on this system estimated the natural frequency and modal behavior of the system under various types of soils. The forced vibration interaction analysis has been performed to estimate the interaction effect on the dynamic response of the structure in terms of stress and strain. The property of soil medium has been varied by varying Young's modulus and constant Poisson's ratio, while the other conditions have been achieved by varying Poisson's ratio and constant Young's modulus. It has been observed from the compared dynamic interactive and non-interactive analysis that varying soil medium significantly affects the natural frequency and mode shapes of the framed structure. The variation of natural frequency is in the range of 20-30%. In the interactive case, additional mode shapes are induced due to additional degree of freedom, compared to non-interactive case. The varying soil properties have also affected the interactive static and dynamic stresses of the system at the junction of foundation-soil medium significantly, compared to the structure-foundation interface.

 
 

The response of a structure and the characteristic of foundation medium confer the interactive behavior of the system. During an earthquake, seismic waves are transmitted through soil from the origin of disturbance to the structure, the wave motion of the soil excites the structure, which in turn modifies the input-motion by its movement relative to the ground. This interaction phenomenon is called soil-foundation-superstructure interaction or simply soil-structure interaction (Wolf, 1985). The interaction phenomenon is generally affected by the mechanism of energy exchange between the soil and the structure, and the primary influence on the building is to modify the natural period of vibration and hence the response in terms of stress and strain (Chopra, 2003).

An analysis for estimating the dynamic response of a structure, including soil-structure interaction, generally involves the application of such methods as elastic wave propagation method, finite element method and the mass-spring method. A perfect bond at the contact surface between the soil and structure is assumed in all these methods. Depending on the material properties of the soil medium, the source of dynamic excitation and the particular type of foundation considered, the response of the structural system can be quite different. Soil structure interaction represents an integrated system. However, this complex problem is always analyzed in separate parts. This simplification is generally necessary because of the intrinsic complexities of treating soil-structure interaction as a whole, as each of the sub systems, by itself, represents a vast field of possible mechanical idealization and a wide choice of physical and geometric parameters (Wolf, 1985).

Two different approaches to the problem are commonly found: (1) applying rigorous model to the super structure where the soil is considered as a rigid base; and (2) applying rigorous mechanical model to the soil without coupling it to the superstructure just considering a raft on a simple two-dimensional frame resting on the deformable soil (Chopra and Gutierrez, 1974). Dumanoglu and Severn (1976) worked on the influence of foundation media on the response of the structure to earthquake, considering the spring model. Wong and Luco (1978) studied the dynamic response of rectangular foundation to obliquely incident seismic waves. Gupta and Penzien (1982) worked on developing a hybrid model for the analysis of soil structure interaction under dynamic condition. Further, studies on the effect of soil on the structure under wind and earthquake (Novak, 1974) as well as on the soil-structure interaction due to damping were also taken up (Novak and Hifnawy, 1983). Recently, Wang and Cheng (2008) worked on the modal analysis for evaluating the response of the structure.

 
 

Structural Engineering Journal, Free Vibrations, Forced Vibrations, Soil-structure interactions, Framed Structures, Finite Element Method, Natural Frequencies, Poisson's Ratio, Elastic Wave Propagation, Mass-Spring Method, Modal Dynamic Analysis, Mechanical Models, Natural Circular Frequencies, Isoparametric Elements.