INELASTIC SEISMIC RESPONSE OF R. C. FRAMED BUILDINGS WITH A SOFT STOREY

Abstract

The provision of adequate and easily accessible parking space is one of the challenges in the design of multi-storey buildings. The common practice is either to go for basement parking or to keep the ground storey open and free of infills. The open ground storey configuration is also inevitable for having large unhindered circulation areas in shopping plazas. This type of building support is termed as stilt. Stilt construction results in a stiffness discontinuity in the ground storey thus making it what is called a 'soft storey'. The soft storey has an advantage that it reduces earthquake forces due to the increase in natural period of vibration of structure. However, the price of this force reduction is paid in the form of increased structural displacements and inter-storey drift, thus entailing a significant P-A effect, which is a threat to the stability of the structure. The failure of r. c. buildings with soft storeys in past earthquakes have been a matter ofgreat concern to all. The Bhuj earthquake (2001) in India also revealed that the soft ground storey was one of the main reasons for extensive damage to r. c. buildings especially in Ahmedabad which is located about 300 km away from the epicentre. It is recognised that this type of failure results from a combination of several other unfavourable reasons, such as torsion, excessive mass on upper floor, P-A effect and lack of ductility in the bottom storeys. These factors lead to local stress concentrations accompanied by large plastic deformations. Therefore, the soft storeys require special attention in the analysis and design. Prediction of seismic and pushover response of such structures is highly cumbersome and is a matter ofactive research. In the present work, a mathematical model for the prediction of inelastic static and dynamic response of a framed building with and without infills including the soil structure interaction has been proposed. A computer code in FORTRAN language has been developed for the analysis of framed buildings incorporating all the above. Several parametric studies have been under taken by considering the irregularity in the distribution of infills on the behaviour ofthe r. c. framed building. 11 To simulate the behaviour of buildings under the action of various kinds of loadings, different elements of a building have been carefully modelled. The basic member geometry and the prescribed failure criteria of the material define the stress-strain relation, to establish the member nonlinear behaviour. The contribution of individual members is then assembled to get the overall structural behaviour. In this study, finite element modelling is used for the building-frame-infill system. The infilled frame structure is modelled as a 3D assemblage of r. c. beams, 4-noded flat shell elements to idealise the floor, 4-noded inplane rectangular elements to model the masonry infills, and 4-noded joint elements to represent the frame infill interface. The elastic stiffness matrix of a 3D beam-column element with two rigid ends has been used. The elasto-plastic stiffness matrix for beam-column element having plastic hinge at its one or both ends has been derived in this study by using the plasticity theory. The yielding ofthe frame members (beam-column element) takes place under the combined action of two bending moments, axial force, torsional moment and shears at a section. Effects of axial forces on member stiffness (P-A effect) are also included. Using available concrete model, the elasto-plastic stiffness matrix of beam/column element has been generated. The effect of degradation of r. c. section due to development of a plastic hinge and their disappearance has been established by using modified Takeda's model. Each floor slab is assumed to behave elastically and has been discretized by a single 4-noded flat shell element. In the case of r. c. panel elements, the concrete is modelled as an isotropic material under biaxial stress condition and the material modelling for different phenomenon such as cracking, yielding, crushing of concrete and yielding of steel have been suitably incorporated. The effects of tension stiffening, aggregate interlock and dowel action are also considered using simple models available in the literature. The brick masonry elements have been modelled as an isotropic material under biaxial stresses and the nonlinearity due to crushing and cracking are incorporated. For the masonry infill, smeared crack model has been adopted. For brick masonry infill panel in compression, the material has been assumed to be linearly elastic until in failure, and on crushing stiffness has been reduced to nearly zero. In tension cracking, the stress and stiffness normal to crack have been reduced to a very small value. The interface between the r. c. beam/column element and the adjacent brick masonry infill element has been modelled using a four-noded interface element. The interface elements have been modelled to incorporate slip and separation at the interface. The tension and compression at the interface determines the separation and contact respectively. While in contact, the normal and shear stresses at the interface determines the slippage at the interface. The stress-strain relationship has been assumed to be elastic-perfectly plastic following the Mohr-Coulomb yield criterion. In the present formulation, for reasons of simplicity, the spring analogy has been used to model the foundation-soil system to account for the soil structure interaction. In the present study, the foundation consists of spread footing and the soil is represented by linear springs. The step-by-step (incremental-iterative) approach procedure has been used for the solution of the resulting nonlinear system. Newmark's predictor-corrector implicit scheme is used to solve the equation ofmotions for an elasto-plastic dynamic system. Theory of plasticity has been used to develop a general procedure suitable for static and dynamic analysis for 3D problems. The inelastic procedure estimates the continuously deteriorating stiffness of the frame, panel and interface due to on-set of plasticity in the frame members and cracking, yielding and crashing in the panels, and separation and sliding at the interface. In the static analysis, because of the ill-conditioned nature of the tangent stiffness matrix in the neighbourhood of a load limit point, solution convergence is extremely difficult; as a result the conventional incremental/iterative method fails to trace the response beyond the limit point. In the present study, to get this response, the use of arc-length algorithm has been implemented to capturethe complete load-displacement response ofr. c. framed buildings. For the pushover analysis, the effect of the localised nonlinearity occurring in the framed building on the distribution of the incremental lateral forces is quite important IV and this effect has been investigated. Finally, yet another computer programme has been developed to define the performance point from the building capacity curve and demand curve using the capacity spectrum method. A new formula has been introduced to calculate energy dissipation by hysteretic damping (area enclosed by hysteretic loop, ED); the value ofED is used to estimate hysteretic damping. Thevalidation of the proposed formulation and the computer program has been made by analysing different types of building frames picked up from the available literature and necessary comparison with the experimental and theoretical results reported in the literature have been made. The comparison of the results has been made with respect to load deflection behaviour, yield location, time history response and ultimate loads. The results predicted by the developed computer program are found to compare well with those obtained experimentally. Validation for the arc-length method has also been carried out with the published analytical andexperimental results. Using the proposed mathematical model and the computer program developed, an extensive parametric study has been carried out with respect to nonlinear static pushover analyses and seismic evaluation of a 2D frame. The framed building parameters investigated in the present work relate to different configurations of infills in the elevation with Constant Lateral Force Distribution Procedure (Ai) and Mode Adoptive Pushover Analysis Procedure (MAP). The effect of the two masonry infill configurations (regular and irregular infill) on the global seismic response of r. c. framed building has been studied through numerical simulation. Also, the effect of initial design basis of a frame, namely strong column-weak beam (SC-WB) and strong beam-weak column (SB-WC) on the global seismic response has been investigated. The effect of soil structure interaction has been studied for the framed building with softground storey andwith uniform infills for both SC-WB and the SBWC designs. The hysteretic damping value obtained from new formula has been validated by comparing with the results reported in the literature. Excellent agreement has been observed. The results of the pushover analysis imply that the distribution of the applied lateral forces after the building yields is much different from that before the yielding, especially in building with the soft storey. For the bare frame and fully infilled the pushover analysis results are not much different for Ai and MAP distributions. The maximum base shear obtained for the frame with SB-WC was almost 55 per cent of the maximum base shear obtained for SC-WB for each configuration of the infilled examined. The presence of infills and irregularity in their arrangement in elevation has a very little effect on the seismic response provided the frame is designed as strong column-weak beam. VI