The uneven topology of hilly terrain does not afford plane land in adequate measure for construction of buildings along the same pattern and scale as the plains. The constraints so imposed have led to the adoption of constructional forms and architectural features dictated both by the topography as well as local cultural norms. The added restriction of adoption of locally available materials and expertise has led to a limited number of building forms, such as the setback and the combined stepback-setback forms finding traditional acceptance. With the passage of time and the improved economic situation in general, even in remote areas, the adoption of contemporary materials has replaced the use of locally available material significantly. The architectural metamorphosis is not as pronounced, leaving the present-day forms still following traditional lines, albeit on a grander scale. The various floors of such buildings stepback toward the hill slope and at the same time the building may have setback also. The stepping back of building towards hill slope may result in unequal column heights at the same floor (Kumar and Paul, 1997).
Due to the varied configuration of buildings in hill areas, these buildings become highly irregular and asymmetric. Buildings on hill slope are highly irregular due to their configuration and asymmetry due to variation in mass and stiffness distribution on different vertical axis at each floor (Kumar and Paul, 1999). These irregular and asymmetric buildings are subjected to severe torsional moment and lateral shears under the action of earthquake loads in addition to bending moments and axial forces (Kumar and Paul, 1994a and 1994b). The soil-structure interaction affects the response of the structure, so for more realistic behavior of structure, the flexibility of the soil is to be taken into account. These types of buildings are asymmetrical in one direction (Y-direction), while it is symmetrical in other direction (Y-direction). The mass and the stiffness increases along the height. The stepback buildings usually have a number of storeys reducing successively at the bottom in each bay, along the direction of the slope, while maintaining a constant roof level. This leads to unequal column heights at the foundation level, which again varies depending on the sloping ground profile on which the columns are founded. The setback-stepback buildings, on the other hand, do not have a constant roof level but maintain the same number of storeys in each bay (usually). This building form also has columns, and their foundations are organized in the same manner as the stepback buildings. The IS: 1893, Part 1(2002) recommend 3D-model dynamic analysis (response spectrum analyses and time history analyses) for irregular buildings higher than 12 m in zone IV and V, and those greater than 40 m in height in zone II and III. The center of mass and the center of rigidity do not coincide on the same floor, and their locations vary from floor to floor. The eccentricity varies floor-wise. The torsional behavior of these types of buildings will change from floor to floor, therefore a three-dimensional analysis is more or less essential to obtain realistic results.
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