SEISMIC ANALYSIS OF STEPBACK AND SETBACK BUILDINGS

Abstract

Plain land in hills is scare and therefore sloping land is being increasingly used for buildings. Economic development of hilly areas, have a marked effect on the buildings in terms of style, material and method of construction. Stone, wooden load bearing buildings are common in hilly areas. Traditionally, the hill buildings are constructed in stone masonry with mud mortar. Loss of lives and property are mainly due to damage of these buildings during earthquakes. The existing r.c.c. buildings have performed well. Therefore r.c. framed buildings are getting popular in hilly areas. In hilly areas, many multistoreyed r.c. framed buildings rests on hill slope. The various floors of the building stepback towards the hill slope and at the same time the building may have setback also. The stepping back of the building towards hill slope result into unequal column heights at the same floor level. Building constructed on hill slope poses special structural and constructional problems. The various floors of the building on hill slope may be supported on two types of columns (i) columns resting on the floors below and (ii) columns resting on the sloping ground. These buildings are highly irregular and asymmetric. The centres of mass of various floors of the building on hill slope lies on different vertical axes and so is its centre of stiffness unlike symmetrical buildings. Most of the hill areas falls in active seismic belts. These buildings are subjected to severe torsion in addition to lateral shears under the action of earthquake loads. The non uniform soil profile on the hill slope result into different soil properties at different levels. It may result into unequal settlement of foundations and local failure of slope. Landslides and unstable slope creates problem to buildings on hill slope causing total collapse. Not much studies have been made on the various problems facing hill buildings. Climatic conditions and heavy rains is a big problem for buildings in hill areas. This thesis looks into the solution of some of the special problems related to buildings on hills. To capture the real behaviour of buildings on hill slope 3D modelling of the building is required. In the present study two different 3D modelling of the structure have been taken for seismic analysis. In the rigorous method of dynamic analysis, the floor slab of the building is taken as flexible and the building has been modelled as having 6 d.o.f. per node. The mathematical model consists of 3D frame elements, r.c.c. panels, brick masonry infills, r.c.c. slabs, interface elements. Special attention has been given to the nonlinear modelling of the various components of buildings. The r.c. beam/column section has been analysed using nonlinear stress-strain relation for concrete and an elasto-plastic model for steel. The regression analysis is used to fit a third degree polynomial to the points obtained from the actual analysis of the r.c. cross section. The irregular buildings such as on hill slopes are subjected to severe torsional moment and lateral shears under the action of earthquake loads in addition to bending moments and axial forces. The yielding of the frame members takes place under the combined action of the bending moments, axial force, torsional moment and shears. The presently available yield criteria take interaction of some of the components of forces, all components are not considered in the available yield criteria. To study the inelastic behaviour of the buildings on hill slope subjected to severe torsion and shears in addition to bending moments, axial forces requires the yield criteria which consider the interaction of all the six components of forces. Therefore in the present study effort has been made to develop a yield criterion considering the interaction of all the six components of forces. In case of r.c.c. panel elements, concrete is modelled as an isotropic material under biaxial stress condition and the material modelling for different phenomenon such as cracking, yielding and crushing of concrete and yielding of steel are modelled using available models. The brick masonry elements has been modelled considering crushing and cracking condition. The interface elements have been modelled considering separation and slippage. The tension and compression at the interface determines the separation and contact. While in contact, the normal and shear stress at the interface determines the slippage at the interface. To analyse the structure in the inelastic range the frame elements have been modelled by lumped plasticity theory. The algorithm predicts the formation and disappearance of plastic hinges. Ductility is an important parameter in earthquake resistant design of buildings. To study the ductility requirement of r.c. members, an inelastic analysis is necessary. Ductility of a member cannot be realistically determined unless appropriate inelastic degrading stiffness model is used. Therefore degrading modified Takeda's model has been implemented. On unloading the plastic hinge, stiffness degradation has been considered for all the six components as the yield criteria used in the present study takes interaction of all the six components of forces. Ductility requirement of all the yielded members have been evaluated. There is a gradual deterioration of stiffness of the structure due to plastic hinges formed and cracking, yielding and crushing of r.c.c panels, cracking and crushing of brick masonry infills. The results of inelastic analysis obtained from present study compares well with the available experimental results in the literature. It is observed in the present study that in the buildings which are subjected to severe torsion and lateral shears in addition to bending moments and axial loads, the yielding of r.c. members takes place at a lower load factor as compared to buildings which are not subjected to severe torsion and lateral shears. In the simplified method of dynamic analysis the floor system is considered as rigid under lateral loads, then the building modelling is much simplified and can be modelled as 3 d.o.f. per floor at the centre of gravity of the floor i.e. two translation and one rotation about vertical axis passing through centre of gravity. The model consists of frame elements and infill panels. Building on hill slope is characterised by the location of centre of mass of different floors lying on different vertical axes, and so is the case with the centre of stiffness. The existing methods of dynamic analysis of such irregular buildings are too complicated to be used in the design offices. Therefore a simplified method for seismic analysis of these buildings based on transformation of mass and stiffnesses of various floors about a arbitrarily choosen common vertical reference axis is developed. The mass of different floors lying on different vertical axes gets transferred to common vertical reference axis and so is the stiffness ofvarious floors. In this modelling the overall size of the problem gets reduced tremendously requiring much less time for data preparation and computational effort. In this modelling accidental eccentricity can be taken into account by simply shifting the centre of mass of the floor equal to accidental eccentricity. The results obtained from this method compares well with 6 d.o.f./node analysis with rigid floor diaphragm. Afew real building problems having stepback configurationon hill slope have been studied for its seismic response using the two methods of analyses. It has been found that the results of free vibration time periods, mode shapes, inter storey column shears, ground column shears and infill shears, lateral floor displacements obtained by simplified method are comparable to the results obtained by rigorous method. Code of Practices(UBC,NBCC,NZS etc.) recommends 3D dynamic analysis for irregular buildings such as on hill slopes. Although many computer codes are available for seismic analysis of irregular buildings, still there is a need of simplified method for seismic analysis of stepback and setback buildings such as that on hill slope to be used in design offices, which gives an insight into the real behaviour of hill buildings under seismic conditions. It is suggested to adopt the simplified method for 3D dynamic analysis of irregular buildings in the Code of Practices. It has also been observed that the base shear concept is not applicable in these types of buildings. A procedure for stability analysis of the slope with building loads has been developed based on limit plastic equilibrium using simplified Bishop's method. The IV building loads in the form of vertical loads, horizontal loads and bending moments transferred at the foundation level to the hill slope has been considered in addition to the self weight of the sliding mass of the soil. The dry/wet condition of the material of the hill slope can be considered in the analysis. The minimum factor of safety against sliding failure of slope is evaluated by taking various trial slip circles automatically in the computer program. The different layers of the soil in the slope can be taken into account considering different properties of the soil mass. Earthquake effects can be considered in the analysis. It is found from the study that the stability of slope depends on the type of loads, location of loads, configuration of the building transferring the load, drainage condition of the area. It is found that the stepback type configuration of building gives better stabilising effect as compared to combination of stepback and setback. The stability of slope decreases with earthquake loads. Buildings on flat ground adjacent to hill slope should be so configured that heavier part of the load should be transferred at uphill side of the slope otherwise there is a chance of local failure. Taking foundation deeper on upstream side of slope increases the stability of slope. The reduction in pressure due to building loads enhances the stability of slopes and can be achieved by providing strip foundation across the slope for all the columns in one row. It has been observed that factor of safety against sliding of slope increases with increase in distance of location of footing from free edge of slope. The distance between the two column loads also affects the factor of safety. Proper drainage arrangement should be provided around the building complexes so as to avoid soil erosion and landslides. The results of inelastic analysis of real buildings on hill slope having stepback configuration shows that the plastic hinges forms in the members located on periphery of the building and mostly are in columns. It shows that the stepback buildings are torsionally unbalanced. The ductility requirement has been evaluated for the yielded members and it is found that the ductility demand is higher for members located at the outer periphery. The too short and too long columns at the same floor level in these buildings are the worst affected and are to be avoided. Soil structure interaction study has been carried out for few cases of hill buildings. It is observed that for loose and medium soil with shear wave velocity up to 300m/sec, the free vibration time periods increases from 1 to 5% as compared to fixed base condition. For dense soil with shear wave velocity 600m/sec and above, the results of free vibration time periods are almost the same as that of fixed base condition. It is also observed that ductility demand of the yielded members increases, where the buildings are supported on the loose and medium soil base. A few different configuration of buildings on hill slope (i.e. regular frame building on flat ground, setback building on flat ground, stepback building on sloping ground, stepback and setback building on sloping ground) have been studied from structural and stability considerations under the action of dead, live, and earthquake loads. It has been found that there is not much difference in the structural behaviour and member forces for these configurations under the action of dead and live loads. But under the action of earthquake load the behaviour of different configurations of the buildings is quite different. It advocates the use of different configurations in different situations so as to get the better structural performance and economical design of buildings on hill slope. A combination of stepback and setback type configuration of building gives better response as compared to stepback configuration only because of neutralizing effect of torsion. It has been observed that ductility requirement of r.c. members in stepback configuration is more as compared to combination of stepback and setback configuration building. Incidentally the outer profile of a combination of stepback and setback configuration building follows the natural profile of hill slope, which is architecturally more acceptable. Therefore a combination of stepback and setback configuration of buildings are recommended for construction in hill areas.