This chapter presents a brief review of literature available on the subject “torsional effects on irregular buildings under seismic loads”. Efforts were made to collect related research material. Review of literature encompass research papers on the topic in general and specifically aims at latest trend to control asymmetry, design requirements, configuration requirements, torsional irregularity, performance of irregular buildings, and behaviour of appropriate structural system. At the end of the chapter, selection of lateral force procedures is also described.
2.2 RELATED RESEARCH WORK
Latest available research papers are studied related to subject of thesis. Few of research papers are described here under
1) Torsional irregularity of any structure can be determined by calculating the deflections at the ends in every storey. Codes and guidelines give the definite numbers or coefficients to limit the excess torsion in irregular structures. In this paper adequacy of code provisions regarding the torsional irregularity coefficient is checked and concerned over limits are expressed. For this particular research works different groups of buildings are made with different changes in plans such as position of shear walls, number of grids and number of storey etc. Four groups are made namely A, B, C and D with different locations of shear walls in plan.
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At first, variation of torsional irregularity with respect to number of grids is investigated. Analysis has been performed for each variation of gridlines in a particular group and conclusions carried out. Graphs are plotted by changing the number of grids lines in each group A, B, C and D against irregularity coefficients. It is observed from theses graphs that in each particular group A, B, C or D there exist different numbers of grid lines against which maximum results are obtained in that particular group. Maximum value of irregularity coefficient is determent in group C in which shear walls is away from the gravity center but not at the edges. Irregularity coefficient reach a maximum value for certain number of grid lines then decrease by increasing the number of axis.
In second stage, torsional irregularity coefficient is calculated by changing the number of storeys. General trend which graphs shows that with increasing the number of storey for any particular structures, keeping position of shear walls and number of axis same, torsional irregularity coefficient decreases. Curves for structure group C for 1, 2, 4, 6, 8 and 10 storey shows that lesser number of storey yields more critical results because as the number of stories increases center of rigidity shifts toward center causing lesser torsion consequently gives less critical results.
In the last, position of walls is changed to determine the effects on the torsional irregularity coefficient. Graphs are plotted for each individual structural group against the torsional irregularity coefficient. Curves of different storeys predict the lesser the number of storeys more critical will the results. By changing the location of the shear walls in any particular key plan indicate that critical results are obtain for shear wall placed in between the center and edges of the structures. (Guany Ozmen, 2004)
2) Parametric analysis of irregular structures under seismic loading reveals the effect of torsion as per Turkish Earthquake Code. For the purpose center of stiffness were changed and torsional irregularity was created. Different number of storeys was considered which were analyzed using static force procedure and dynamic force procedures. Results for both of the methods were compared and conclusion drawn. Effect of non-orthogonality was also studied by changing the orientation of the non-orthogonal walls. All these cases were studied for five different directions of earthquake. From these research results limitations in Turkish earthquake code suggested to be improve. (Semih S. Tezcan and Cenk Alhan, 2000)
The earthquake forces produced in the irregular buildings are unpredictable and can not be determine with greater accuracy thus such structures are more critically prone to earthquakes. A series of five, framed and walled structures are taken with different irregularity coefficients. This paper shows the behavior of different modules against earthquake forces and results drawn. Paper suggests more elaborative measures need to be taken by codes and standards to take over the issue of torsional irregularity. (Ozmen G and Gulay F.G. 2002)
3) Codes and Standards direct that along with the static force procedure non linear analysis are need to be performed to know the exact behavior of the structure. In this paper investigation is done by creating two different models. In first model eccentricity made only in one direction by shifting mass, whereas in second case eccentricity was produced in both directions. Near-fault zone effects were investigated alongwith far-fault results. Research work shows that displacement demand of the structures remains the same irrespective of distance from fault. The paper concludes that non linear analysis needs to be performed necessarily linear classic analysis alone are not sufficient for analysis of torsionally irregular structures. ( Emrah Erduran, February 2008)
4) To control seismic response of unsymmetrical building viscous damper are placed. With help of modal analysis effect of plan wise distribution of damping were investigated and torsional dynamic behavior were examined. For input seismic earthquake suitable performance indexes were represented by mean of norms. These norms help to distribute plan wise distribution of extra dampers with help of parametrical analysis on asymmetrical plan. Design formulas are prepared to represent the results for norms which were verified by experimentation, which is representative of seismic response of asymmetrical systems. (L. Petti , M. De Iuliis, 2008)
5) Accidental eccentricity applications provided in codes are evaluated and compared with alternative interpretations. An effect of accidental eccentricity is evaluated on the strength of different components. Flexible side elements behavior is investigated and protection measures are described to limit the forces such a comparison is made using different codes. A proposal is made with respect to codes provisions regarding accidental eccentricity, minimum value is specified laterally responding systems. Evaluation of results based on inelastic dynamic analyses indicates that all codes satisfactorily fulfill the requirements to control the response of torsionally unbalanced buildings. Similarly ductility demand and element deformation demand for all the codes are considered. This response demand has a consistence relationship with time period and geometric of the buildings. Codes requirement in design of stiff side elements are verified and found to be satisfactory. ( A.M Chandler, J.C Correnza and G.L. Hutchinson, 1995)
Torsional irregularity is defined in Building Code of Pakistan 2007 (BCP 2007) and is reproduced in Table No.2.1. and Table No. 2.2
Table 2.1 Plan Structural Irregularities
IRREGULARITY TYPE AND DEFINITION
1.Torsional irregularity – to be considered when diaphragms
are not flexible
Torsional irregularity shall be considered to exist when the maximum storey drift, computed including accidental torsion, at one end of the structure transverse to an axis is more than 1.2 times the average of the storey drifts of the two ends of the structure.
2. Re-entrant corners
Plan configurations of a structure and its lateral-force-resisting system contain re-entrant corners, where both projections of the structure beyond a re-entrant corner are greater than 15 percent of the plan dimension of the structure in the given direction.
3. Diaphragm discontinuity
Diaphragms with abrupt discontinuities or variations in stiffness, including those having cutout or open areas greater than 50 percent of the gross enclosed area of the diaphragm, or changes in effective diaphragm stiffness of more than 50 percent from one storey to the next.
4. Out-of-plane offsets
Discontinuities in a lateral force path, such as out-of-plane offsets of the vertical elements.
5. Nonparallel systems
The vertical lateral-load-resisting elements are not parallel to or symmetric about the major orthogonal axes of the lateral-force-resisting system.
Table 2.2 Vertical Structural Irregularities
IRREGULARITY TYPE AND DEFINITION
1. Stiffness irregularity – soft storey
A soft storey is one in which the lateral stiffness is less than 70 percent of that in the storey above or less than 80 percent of the average stiffness of the three storeys above.
2. Weight (mass) irregularity
Mass irregularity shall be considered to exist where the effective mass of any storey is more than 150 percent of the effective mass of an adjacent storey. A roof that is lighter than the floor below need not be considered.
3. Vertical geometric irregularity
Vertical geometric irregularity shall be considered to exist where the horizontal dimension of the lateral-force-resisting system in any storey is more than 130 percent of that in an adjacent storey. One-storey penthouses need not be considered.
4. In-plane discontinuity in vertical lateral-force-resisting element
An in-plane offset of the lateral-load-resisting elements greater than the length of
5. Discontinuity in capacity – weak storey
A weak storey is one in which the storey strength is less than 80 percent of that in the storey above. The storey strength is the total strength of all seismic-resisting elements sharing the storey shear for the direction under consideration.
2.4 CONFIGURATION REQUIREMENTS
Regular structures have no significant physical discontinuities in plan or vertical configuration or in their lateral-force-resisting systems such as the irregular features. Irregular structures have significant physical discontinuities in configuration or in their lateral-force-resisting systems. Irregular features include, but are not limited to, those described in code. All structures in Seismic Zone 1 and Occupancy Categories 4 and 5 in Seismic Zone 2 need to be evaluated only for vertical irregularities of Type 5 (Table 2.2) and horizontal irregularities of Type 1 (Table 2.1). Structures having any of the features listed in Table 2.2 shall be designated as if having a vertical irregularity. (UBC 1629.5.3)
Where no storey drift ratio under design lateral forces is greater than 1.3 times the storey drift ratio of the storey above, the structure may be deemed to not have the structural irregularities of Type 1 or 2 in Table 2.2. The storey drift ratio for the top two storeys need not be considered. (UBC 1629.5.3)
The storey drifts for this determination may be calculated neglecting torsional effects. Structures may have irregularity in plan or elevation listed in BCP 2007.
2.5 STRUCTURAL SYSTEMS
Structural systems shall be classified as one of the types listed BCP-2007 and defined under.
Bearing Wall System
A structural system without a complete vertical load-carrying space frame. Bearing walls or bracing systems provide support for all or most gravity loads. Resistance to lateral load is provided by shear walls or braced frames.
Building Frame System
A structural system with an essentially complete space frame providing support for gravity loads. Resistance to lateral load is provided by shear walls or braced frames.
Moment-Resisting Frame System
A structural system with an essentially complete space frame providing support for gravity loads. Moment-resisting frames provide resistance to lateral load primarily by flexural action of members.
A structural system with the following features comes in the category of dual system:
1. Essentially complete space frame that provides support for gravity loads.
2. Resistance to lateral load is provided by shear walls or braced frames and moment-resisting frames (SMRF, IMRF, MMRWF or steel OMRF). The moment-resisting frames shall be designed to independently resist at least 25 percent of the design base shear.
3. The two systems shall be designed to resist the total design base shear in proportion to their relative rigidities considering the interaction of the dual system at all levels.
2.6 DRIFT AND STOREY DRIFT LIMILATION
Drift or horizontal displacements of the structure shall be computed where required. For both Allowable Stress Design and Strength Design, the Maximum Inelastic Response Displacement, Î”M, of the structure caused by the Design Basis Ground Motion shall be determined in accordance with this section.
The drifts corresponding to the design seismic forces Î”S, shall be determined. To determine Î”M, these drifts shall be amplified. A static, elastic analysis of the lateral force-resisting system shall be prepared using the design seismic forces. Where Allowable Stress Design is used and where drift is being computed, the related load combinations shall be used. The resulting deformations, denoted as Î”S, shall be determined at all critical locations in the structure.
Calculated drift shall include translational and torsional deflections. The Maximum Inelastic Response Displacement, Î”M, shall be computed as follows (BCP 2007):
Î”M = 0.7 R Î”S (2.1)
Alternatively, Î”M may be computed by nonlinear time history analysis. The analysis used to determine the Maximum Inelastic Response Displacement Î”M shall consider P-Î” effects.
Storey Drift Limitation
Storey drifts shall be computed using the Maximum Inelastic Response Displacement, Î”M. Calculated storey drift using Î”M shall not exceed 0.025 times the storey height for structures having a fundamental period of less than 0.7 second. For structures having a fundamental period of 0.7 second or greater, the calculated storey drift shall not exceed 0.020 times the storey height, with exceptions of:
1. These drift limits may be exceeded when it is demonstrated that greater drift can be tolerated by both structural elements and nonstructural elements that could affect life safety. The drift used in this assessment shall be based upon the Maximum Inelastic Response Displacement, Î” M.
2. There shall be no drift limit in single-storey steel-framed structures classified as Groups B, F and S Occupancies or Group H, Occupancies. In Groups B, F and S Occupancies, the primary use shall be limited to storage, factories or workshops. Structures on which this exception is used shall not have equipment attached to the structural frame or shall have such equipment detailed to accommodate the additional drift. Walls that are laterally supported by the steel frame shall be designed to accommodate the drift.
The design lateral forces used to determine the calculated drift may disregard the limitations and may be based on the period determined, neglecting the 30 or 40 percent limitations.
2.7 SELECTION OF LATERAL-FORCE PROCEDURE
Any structure may be, and certain structures defined below shall be, designed using the dynamic lateral-force procedures. (UBC 16.8)
The simplified static lateral-force procedure may be used for the following structures of Occupancy Category 4 or 5 (UBC 1629.8.2)
1. Buildings of any occupancy (including single-family dwellings) not more than three storeys excluding basements that use light-frame construction.
2. Other buildings not more than two storeys in height excluding basements.
The static lateral force procedure may be used for the following structures: (UBC 1629.8.3)
1. All structures, regular or irregular, in Seismic Zone 1 and in Occupancy
Categories 4 and 5 in Seismic Zone 2.
2. Regular structures under 73.0 meters (240 feet) in height with lateral force resistance provided by different systems.
3. Irregular structures not more than five storeys or 20 meters (65 feet) in their height.
4. Structures having a flexible upper portion supported on a rigid lower portion where both portions of the structure considered separately can be classified as being regular, the average storey stiffness of the lower portion is at least 10 times the average storey stiffness of the upper portion and the period of the entire structure is not greater than 1.1 times the period of the upper portion considered as a separate structure fixed at the base.
Dynamic Lateral Force Procedure
The dynamic lateral-force procedure shall be used for structures, including the following: (UBC 1629.8.4)
1. Structures 73 meters (240 feet) or more in height
2. Structures having a stiffness, weight or geometric vertical irregularity of Type 1, 2 or 3 or structures having irregular features not described in code.
3. Structures over five storeys or 20 meters (65 feet) in height in Seismic Zones 3 and 4 not having the same structural system throughout their height.
4. Structures, regular or irregular, located on Soil Profile Type SF that has a period greater than 0.7 second. The analysis shall include the effects of the soils at the site . Structures with a discontinuity in capacity, vertical irregularity Type 5, shall not be over two storeys or 9 meters (30 feet) in height where the weak storey has a calculated strength of less than 65 percent of the storey above. Where the weak storey is capable of resisting a total lateral seismic force of Î©o times the design force prescribed.
Î©o = Seismic force over strength factor given in Table 16-N of UBC 97
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