M.E. thesis Push over analysis
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ABSTRACT Earthquakes present a threat to public safety and welfare in a significant portion everywhere. Recent earthquakes in many parts of the world have demonstrated the vulnerability of existing reinforced concrete structures to moderate and strong ground motions. There are many existing buildings which have been designed according to earlier codes. In these codes, either design for seismic loads was not a requirement or design was for lower levels of seismic forces. Many existing buildings do not meet the seismic strength requirements of present day earthquake codes due to structural inadequacies. Structures adequately designed for usual loads like dead loads, live loads, wind loads, etc are not necessarily safe for earthquake forces. For normal loads, the structure remains within elastic range of the material during service stage. It is neither practical nor economically viable to design structures to remain within elastic limits during earthquakes. The evaluation based on nonlinear static by pushover analysis is necessary to check the adequacy of existing building. The objective of the present study is to evaluate the adequacy of seismic effect by means of Pushover analysis using SAP 2000 and retrofit the building for the deficiency found in the analysis. The building considered for analysis is an existing multistory (G+11)designed for earlier code of IS 456- 1964 without considering earthquake effect. The building is modeled as 3-D and slab as Diaphragm and earthquake load for zone III is adopted to check the adequacy. In Pushover analysis, most of the hinges were formed in the two rows of lower levels of bottom most storey in PUSHOVER-X and all the rows of bottom most storey in PUSHOVER-Y are occurred. Hence the Ground floor column has to be strengthened to withstand the earthquake forces for Zone III for the building located at Chennai. The performance point was obtained in the zone III for the pushover analysis along X and Y direction are enclosed in the report for evaluation. The inter storey drift as obtained in the analysis and permissible were compared. Therefore, the building was found to be inadequate for design earthquake in Ground storey needs
to be retrofitted by
using FRB composites
strengthening methods to suit the site requirement.
or any other suitable
CHAPTER 1 INTRODUCTION 1.1
GENERAL Recent earthquakes in India and in different parts of the world occurred, resulting losses, especially human lives, have highlighted the structural inadequacy of buildings to carry seismic loads. There is an urgent need for assessment of existing buildings in terms of seismic resistance. No one can predict where and when earthquake will appear and what intensity they will strike the ground motion. Many existing buildings are designed according to earlier
codes. In these codes, either design for seismic loads was not a
requirement or design was for lower levels of seismic forces. Structures adequately designed for usual loads like dead loads, live loads, wind loads, etc are not necessarily safe for earthquake forces. For normal loads, the structure remains within elastic range of the material during service stage. It is neither practical nor economically viable to design structures to remain within
elastic limits during earthquakes. As per IS1893 (part 1)- 2002
‘Criteria for Earthquake Resistant Design of Structures’ is to ensure that structures possess
at least a minimum strength to withstand minor
earthquakes which occur frequently, without damage; resist moderate earthquakes without significant structural damage though some nonstructural damage may occur; and aims that structures withstand major earthquakes without collapse. One of the major challenges that faced by structural engineers is to determine the
seismic capacity of an existing
building and to rehabilitate these buildings to upgrade their seismic capacity if needed. Significant amount of research have been reported towards the mitigation of seismic
conventional design and construction procedure, proposing careful detailing of structural systems and improving many new materials and energy devices conductive to the dissipation of energy imparted to the structure during seismic excitation. 1
Many existing multi-storey buildings in earthquake prone regions of India are vulnerable to severe damage under earthquakes. These buildings do not meet the requirements of seismic design. The buildings, which appeared to be strong enough, were crumbled like houses of cards during Bhuj earthquake. The following are the reasons for retrofitting an existing building:(i)
The building was not designed as per the codes.
Subsequent revision of codes and design practice.
Subsequent upgrading of the seismic zone.
Deterioration of strength due to aging of the building.
Modification of the building.
Change in use of the building.
Wrong construction practices and
Lack of knowledge for earthquake resistant design. It is uneconomical to demolish these buildings and rebuild them as per the prescribed codes. Therefore studying seismic response to evaluate the existing buildings for their seismic performance using
analysis (Nonlinear static analysis) and retrofit it if there is any deficiency in the design/ strength requirement for survival during earthquake forces. As the world move toward the implementation of Performance Based Engineering philosophies in seismic design of civil structures, new seismic design provisions will require structural engineers to perform nonlinear analysis of the structures they are designing. Nonlinear static analysis, or pushover analysis, has been developed over the past twenty years and has become the preferred analysis procedure for design and seismic performance evaluation purposes as the procedure is relatively simple and considers post-elastic behavior. However,
simplifications that some amount of variation is always expected to exist in seismic demand prediction of pushover analysis. Although, in literature, pushover analysis has been shown to capture essential structural response characteristics under seismic action, the accuracy and the reliability of pushover analysis in predicting global and 2
local seismic demands for all structures have been a subject of discussion and improved pushover procedures have been proposed to over come certain limitations of traditional pushover procedures. However,
demanding and conceptually complex that use of such procedures are impractical in engineering profession and codes. As traditional pushover analysis is widely used for design and seismic performance evaluation purposes, its limitations, weaknesses and the accuracy of its predictions in routine application should be identified by studying the factors affecting the
pushover predictions. In other words,
the applicability of pushover analysis in predicting seismic should be investigated
for low, mid and high-rise structures by
identifying certain issues such as modeling nonlinear member behavior, computational scheme of the procedure, variations in the predictions of various lateral load patterns utilized in traditional pushover analysis, efficiency of invariant lateral load patterns in representing higher mode effects and accurate estimation of target displacement at which seismic demand prediction of pushover procedure is performed. 1.2
NEED FOR NON LINEAR ANALYSIS For seismic performance evaluation, a structural analysis of the mathematical model of the structure is required to determine force and displacement demands in various components of the structure. Several analysis methods, both elastic and inelastic, are available to predict the seismic performance of the structures. Most of the codes including Indian codes are based on linear analysis and limit state/ultimate design procedure .The earthquake codes calculated for a linear structure is reduced by a reduction factor based on available ductility ratio and over strength in the structure. It has been found in the fast earthquakes that this criterion is generally adequate for the normal type of structures. In respect of structures with some irregularity or structures required to satisfy a particular performance 3
level, this criterion is not sufficient and a nonlinear analysis of the building is required. The most basic nonlinear analysis procedure is the complete nonlinear time history analysis. However, this method has difficulty in selection of design time history, as the codes give design response spectrum and not the design time history. Further this method is considered to be too complex and impractical for general users. FEMA 273 and ATC 40 present some simplified nonlinear analysis method, which can be used easily, and provide valuable insight in to the behavior of the structure during earthquake. The pushover method uses intersection of capacity (pushover) curve and the reduced response spectrum to determine maximum displacement. Hence this method is used for analysis purpose to evaluate the performance of the existing building using SAP 2000. 1.3
DESCRIPTION OF PUSHOVER ANALYSIS Pushover analysis is a technique by which a computer model of the building is subjected to a lateral load of a certain shape (i.e., parabolic, inverted triangular or uniform). The intensity of the lateral load is slowly increased and applied to the structure, in the presence of full gravity dead, until a predetermined level of roof displacement is approached. The magnitude of lateral loads at floor levels do not affect the response of the structure in displacement-controlled pushover analysis, but the ratio in which they are applied at each floor level alters response of the structures. Pushover analysis is an efficient way to analyse the behavior of the structure, highlighting the sequence of member cracking and yielding as the base shear value increases. This can be used for the evaluation of the performance of the structure and the locations with inelastic deformation. The primary use of pushover analysis is to obtain a measure of over strength and to obtain a sense of the general capacity of the structure to sustain inelastic deformation. Push-over analysis can provide a significant insight into the weak links in seismic performance of 4
a structure. A serious of iterations are usually required during which, the structural deficiencies observed in one iteration, are rectified and followed by another. This iterative analysis and design process continues until the design satisfies a pre-established performances criteria. The performance
criteria for pushover analysis is generally
established as the desired state of the building given a roof-top or spectral displacement amplitude. The loads acting on the structure are contributed from slabs, beams, columns, walls, ceiling finishes. They are calculated by conventional methods according to IS 456-2000 and are applied as gravity loads along with live loads as per IS 875(Part II) in the model created. The lateral loads and their vertical distribution on each floor level are determined as per IS 1893-2002. These loads are then applied in “PUSH-Analysis case” during the analysis. Pushover analysis can be performed as force-controlled or displacement controlled. In force-controlled pushover procedure, full load combination is applied as specified, i.e, force-controlled procedure should be used when the load is known (such as gravity loading). Also, in forcecontrolled pushover procedure some numerical problems that affect the accuracy of results occur since target displacement may be associated with a very small positive or even a negative lateral stiffness because of the development of mechanisms and P-delta effects. Generally, pushover analysis is performed as displacement-controlled proposed by Allahabadi to overcome these problems. In displacementcontrolled procedure, specified drifts are sought (as in seismic loading) where the magnitude of applied load is not known in advance. The magnitude of load combination is increased or decreased as necessary until the control displacement reaches a specified value. Generally, roof displacement at the center of mass of structure is chosen as the control displacement.
The internal forces and deformations computed at the
target displacement are used as estimates of inelastic strength and deformation demands that have to be compared with available capacities for a performance check. 5
Structures are expected to deform inelastically when subjected to severe earthquakes, so seismic performance evaluation of structures should be conducted considering post-elastic behavior. Therefore, a nonlinear analysis procedure must be used for evaluation purpose as post-elastic behavior can not be determined directly by an elastic analysis. Moreover, maximum inelastic displacement demand of structures should be determined to adequately estimate the seismically induced demands on structures that exhibit inelastic behaviour. Various simplified nonlinear analysis procedures and approximate methods to estimate maximum inelastic displacement demand of structures are proposed in literature. The widely used simplified nonlinear analysis procedure, pushover analysis, has also been an attractive subject of study. 1.4
PAST STUDIES OF NONLINEAR ANALYSIS Rosenblieth and Herera (1964) proposed a procedure in which the maximum deformation of inelastic SDOF system is estimated as the maximum deformation of a linear elastic SDOF system with lower lateral stiffness (higher period of vibration, Teq) and higher damping coefficient (ζ.eq) than those of inelastic system.
Gulkan and Sozen (1974) noted that most of the time the displacement would be
significantly smaller than the maximum response under
earthquake loading. Gulkan and Sozen developed an empirical equation for equivalent damping ratio using secant stiffness. Only 2D models of stuctures in
plan and elevation can be analysed by the
procedure. Iwan and Kowalsky (1980) developed empirical equations to define the period shift and equivalent viscous damping ratio to estimate maximum displacement demand of inelastic SDOF system from its linear representation. Fajfar and Fischinger (1987)
proposed the N2 method as a simple
nonlinear procedure for seismic damage analysis of reinforced concrete buildings. 6
Kunnath et al (1990) developed an analytical modeling scheme to assess the damageability of reinforced concrete buildings experiencing inelastic behaviour under earthquake loads. Jain and Mir (1991) presented the inelastic response of six-storey reinforced concrete frames. These frames were subjected to the ElCentro earthquake. It was shown that the ductility requirements in columns were quite high and they were unsafe. Vasseva (1994) carried out a seismic analysis of frames taking into account the geometrical non-linearities. Considerable displacement appeared in the columns on the first storeys when geometric nonlinearities were taken into account. Soroushian et al (1998) developed an empirical hysteretic model for masonry shear walls using the results of cyclic tests performed on thirty seven single -storey walls. Dymiotis et al (1999) studied the seismic reliability of reinforced concrete frames with uncertain drift and member capacity. A statistical description of the critical inter-storey drift was derived using existing experimental results mainly from shaking tables of small scale bare frames. Elnashai (2001) analyzed the dynamic response of structure using static pushover analysis. The significance of pushover analysis as an alternative to inelastic dynamic analysis in seismic design and assessment were discussed. 1.5.
USE OF PUSHOVER RESULTS Pushover analysis has been the preferred method for seismic performance evaluation of structures by the major rehabilitation guidelines and codes because it is conceptually and computationally simple. Pushover 7
analysis allows tracing the sequence of yielding and failure on member and structural level as well as the progress of overall capacity curve of the structure. The expectation from pushover analysis is to estimate critical response parameters imposed on structural system and its components as close as possible to those predicted by nonlinear dynamic analysis. Pushover analysis provide information on many response
not be obtained from an elastic static or elastic dynamic analysis. These are •
estimates of inter-storey drifts and its distribution along the height
determination of force demands on brittle members, such as axial force demands on columns, moment demands on beam-column connections
determination of deformation demands for ductile members
Identification of location of weak points in the structure (or potential failure modes)
consequences of strength deterioration of individual members on the behavior of structural system
identification of strength discontinuities in plan or elevation that will lead to changes in dynamic characteristics in the inelastic range
verification of the completeness and adequacy of load path Pushover analysis also expose design weaknesses that may remain hidden in an elastic analysis. These are story mechanisms, excessive deformation demands, strength irregularities and overloads on potentially brittle members. Although pushover analysis has advantages over elastic analysis procedures,
predictions and limitations of current
pushover procedures must be
identified. The estimate of target displacement, selection of lateral load patterns and identification of failure mechanisms due to higher modes of vibration are important issues that affect the accuracy of pushover results.
Target displacement is the global displacement expected in a design earthquake. The roof displacement at mass center of the structure is used as target displacement. The accurate estimation of target displacement associated with specific performance objective
accuracy of seismic demand predictions of pushover analysis. In pushover analysis, the target displacement for a multi degree of freedom (MDOF) system is usually estimated as the displacement demand for the corresponding equivalent single degree of freedom (SDOF) system. The basic properties of an equivalent
are obtained by using a shape vector which represents the deflected shape of the MDOF system. However, in pushover analysis, generally an invariant lateral load pattern is used that the distribution of inertia forces is assumed to be constant during earthquake and the deformed configuration of structure under the action of invariant lateral load pattern is expected to be similar to that experienced in design earthquake. As the response of structure, thus the capacity curve is very sensitive to the choice of lateral load distribution , selection of lateral load pattern is more critical than the accurate estimation of target displacement. The lateral load patterns used in pushover analysis are proportional to product of story mass and displacement associated with a shape vector at the story under consideration. Commonly used lateral force patterns are uniform, elastic first mode, "code" distributions and a single concentrated horizontal force at the top of structure. Multi-modal load pattern derived from Square Root of Sum of Squares (SRSS) story shears is also used to consider at least elastic higher mode effects for long period structures. These loading patterns usually favor certain deformation modes that are triggered by the load pattern and miss others that are initiated and propagated by the ground motion and inelastic dynamic response characteristics of the structure . Moreover, invariant lateral load patterns could not predict potential failure modes due to middle or upper story mechanisms caused by higher mode effects. Invariant load patterns can
9 provide adequate predictions if the structural response is not severely affected by higher modes and the structure has only a single load yielding mechanism that can be captured by an invariant load pattern. FEMA-273 recommends utilising at least two fixed load patterns that form upper and lower bounds for inertia force distributions to predict likely variations on overall structural behavior and local demands. The first pattern should be uniform load distribution and the other should be "code" profile or multi-modal load pattern. The 'Code' lateral load pattern is allowed if more than 75% of the total mass participates in the fundamental load. The invariant load patterns can not account for the redistribution of inertia forces due to progressive yielding and resulting changes in dynamic properties of the structure. Also, fixed load patterns have limited capability to predict higher mode effects in post-elastic range. These limitations have led many researchers to propose adaptive load patterns which consider the changes in inertia forces with the level of inelasticity. The underlying approach of this technique is to redistribute the lateral load shape with the extent of inelastic deformations. Although some improved predictions have been obtained from adaptive load patterns , they make pushover analysis computationally demanding and conceptually complicated. The scale of improvement has been a subject of discussion that simple invariant load patterns are widely preferred at the expense of accuracy. Whether lateral loading is invariant or adaptive, it is applied to the structure statically that a static loading can not represent inelastic dynamic response with a large degree of accuracy. The above discussion on target displacement and lateral load pattern reveals that pushover analysis assumes that response of structure can be related to that of an equivalent SDOF system. In other words, the response is controlled by fundamental mode which remains constant throughout the response history without considering progressive yielding. Although this assumption is incorrect, some researchers obtained satisfactory local and global pushover predictions on low to mid-rise structures in which response is dominated by fundamental mode and inelasticity is distributed throughout the height of the structure .
LIMITATIONS OF PUSHOVER ANALYSIS It must be emphasized that the pushover analysis is approximate in nature and is based on static loading. As such
it cannot represent dynamic
phenomena with a large degree of accuracy. It may not detect some important deformation modes that may occur in a structure subjected to severe earthquakes, and it may exaggerate others. Inelastic dynamic response may differ significantly from predictions based on invariant or adaptive static load patterns, particularly if higher mode effects become important. Limitations are imposed also by the load pattern choices. Whatever load pattern is chosen, it is likely to favor certain deformation modes that are triggered by the load pattern and miss others that are initiated and propagated by the ground motion and inelastic dynamic response characteristics of the structure. The simplest example is a structure with a weak top story. Any invariant load pattern will lead to a concentration of inelastic deformations in the top story and may never initiate inelastic deformations in any of the other stories. Thus, good judgment needs to be employed in selecting load patterns and in interpreting the results obtained from selected load patterns. 1.7 RETROFIT METHODS The purpose of seismic retrofitting a building is to enhance the structural capacities (lateral strength, lateral stiffness, ductility, stability and integrity) so that the building can withstand the design level of earthquake. After analysis, a decision on
whether or not to retrofit an unsafe building
depends on many factors. Lifeline buildings must necessarily be retrofitted, in view of their extreme importance otherwise, they may meet the tragic fate of the Bhuj District Hospital Complex. Important buildings should also be retrofitted. If the seismic strength of an existing building (or structural component) is only 33% of that required by the current standard for a new building, the risk involved is as high as about 20 times that of the new building. If the strength is two-thirds that required by current standard, the risk reduced to 3 times the standard risk ; this level of risk is generally
11 considered as the limit of acceptable risk. Hence, it is recommended that seismic retrofit be necessarily undertaken when the strength of an existing building drops 70% of the capacity required by the current standard. RCC Columns are the key elements of concrete structures designed to resist vertical as well as lateral loads. Majority of the structures that were built in India during 20th century are seismically deficient. Seismic retrofit of these older structures, particularly columns has been an important issue.
CHAPTER 2 AIM AND SCOPE OF THE PRESENT INVESTIGATION 2.1
AIM AND OBJECTIVE OF STUDY
The aim of the present study is to check the adequacy of seismic effect an existing multistory RCC building during earthquake by Pushover analysis. The study focuses on the following for detailed evaluation. 1)
To check the adequacy of existing building for present seismic condition as per IS: 1893-2002 by Pushover analysis using SAP 2000.
To find whether building is capable to withstand seismic load for present conditions and to determine the maximum critical load at which building will fail. and what load building will be failed.
To suggest suitable retrofit measure at affordable cost.
2.2 NEED FOR
(i) The existing building is designed for gravity load of Dead load, Live load and Lateral load of Wind load based on Working Stress method using old code IS:456- 1964 without considering the seismic loads. (ii) It is a aged building used for Public purpose. (year of construction 1976). (iii) It is high rise massive structure, hence attract higher seismic forces.
CHAPTER 3 ANALYSIS OF EXISTING MULTISTOREY RCC BUILDING AND RETROFIT 3.1
INTRODUCTION Earthquakes produce the most severe loading on structures. Code of Practice
for earthquake engineering has been designed with aim that human lives are protected, damage is limited and service structures repair operational. Earthquake causes shaking of the ground. So, a building resting on the latter will experience motion at its base. The earthquake resistant structure must include a complete seismic and gravity force resisting system capable of providing adequate strength, stiffness and energy dissipation capacity to withstand the seismic ground motion within the prescribed limits of deformation and strength demand. Earthquake ground motion causes shaking of the structures leading to inertia forces. The ground motion is quite random in magnitude and direction. At any instant the ground motion can be resolved into horizontal and vertical components. Since the existing structure is designed against gravity loads and lateral load of wind loads, structure need to be designed and checked to resist horizontal components of the inertia forces. 3.2
DESCRIPTION OF STRUCTURE
(i) Building Frame System
: RC OMRF
: Office purpose
(iii) Built in the year
(iv) Seismic Zone
: III (Chennai)
(v)No. of Storey
: Multiple Piles
(vii) Materials used
: M15 & Fe415
(viii) Plan Dimension
: 33.0m x 16.6m
(ix) Height of Building
: 40.8 m
(x) Soil type assumed
: Type II (Medium soil)
Fig 3.1 Structural Plan
Fig 3.2 RCC Details of Beams
Fig 3.3 RCC Details of Columns
3.3 SEISMIC LOAD CALCULATION To ensure safety of building of structure under earthquake IS:1893 -2002 is used to calculate total design lateral force of design seismic base shear (V B) along X and Y direction shall be calculated.
Gravity loads At Floor levels Dead load Self weight 0.12 Floor finishes 0.05 Partition wall Weight Live load (Office Purpose)
kN/m 9.00 ²
At Roof level Self weight 0.12 Weathering course Live load (Roof with access)
5.25 Component Weight Beam Weight at each floor level
Column Weight at each floor level
Wall Weight at each floor
Parapet wall weight Slab Floor area
kN/m 6.75 ²
0.48 165.00 0.18 87
584 90 684 KN
377 598 977 KN
684 371 1055 KN
slab load at roof level slab load at floor level Equivalent load at roof level Equivalent load at each floor level No. of Storeys Total Seismic weight of building = (4970+6551x11)=
394 4969.95 4970
3834.60 684.00 12
0 6550.60 6551
Seismic load calculation - with brick infill loads Equivalent Static load Method is adopted as per IS 1893 2002 Seismic base shear
Z I Sa 2 R g
Response Reduction factor R
Force along width direction - X direction Seismic base shear
Ah Height of the Building h
Z I Sa 2 R g 40.8
Width of the building d
For RC frame building with brick infill
0.09 x h / √d 0.64
For Medium soil site & T = 0.64 Sa/g
Ah 0.057 Force along width direction - Y direction Response Reduction factor R 3
Height of the Building h
Width of the building d
For RC frame building with brick infill
0.09 x h / √d 0.901
For medium soil site & T = 0.901 Sa/g =
LATERAL FORCE ON NODAL POINTS
level 12 11 10 9 8 7 6 5 4 3 2 1
hi 2 4970 6551 6551 6551 6551 6551 6551 6551 6551 6551 6551 6551 77031
40.8 37.4 34 30.6 27.2 23.8 20.4 17.0 13.6 10.2 6.8 3.40
8.273 9.163 7.573 6.134 4.847 3.711 2.726 1.893 1.212 0.682 0.303 0.076 ∑46.592
Wi (KN) X
0.178 0.197 0.163 0.132 0.104 0.080 0.059 0.041 0.026 0.015 0.007 0.002
776 859.6 710.4 575.4 454.6 348.1 255.7 177.6 113.7 63.9 28.4 7.10
in Force/Node Y 551.2 610.5 504.5 408.7 322.9 247.2 181.6 126.1 80.7 45.4 20.2 5.0
(KN) X 70.55 78.14 64.58 52.31 41.33 31.64 23.25 16.14 10.33 5.81 2.58 0.65
Y 183.73 203.47 168.17 136.22 107.63 82.41 60.54 42.04 26.91 15.14 6.73 1.68
Fig3.4 Dead Load along X direction
Fig3.5 Dead Load along Y direction
Fig3.6 Live Load
Fig3.7 Seismic load along Y direction
Fig3.8 Seismic load along X direction
Pushover analysis is a static non-linear procedure in which the magnitude of the lateral forces are incrementally increased, maintaining the predefined distribution pattern along the height of the building. With the increase in magnitude of the loads, weak links and failure of the building are found. Pushover analysis can determine the behaviour of a building including the ultimate load and the maximum inelastic deflection. Local non-linear effects are modeled and the structure is pushed
until a collapse mechanism developed. At
each step, the base shear and the roof displacement can be plotted to generate the pushover curve. It gives an idea of the maximum base shear that the structure is capable of resisting. For regular buildings, it can also give a rough idea about the global stiffness of the building. Instead of plotting the base shear versus roof displacement, the base acceleration can be plotted with the roof displacement (Capacity spectrum). The spectral acceleration and spectral displacement, as calculated from the linear elastic response spectrum for a certain damping (initial damping 5%) is plotted in the acceleration displacement response spectrum (ADRS) format. The locus of the demand points in the ADRS plot is referred to as the demand spectrum. The demand spectrum corresponds to the inelastic deformation of the building. The seismic performance of a building can be evaluated in terms of pushover curve, performance point, displacement ductility, plastic hinge formation etc. The base shear Vs roof displacement curve is obtained from the pushover analysis from which the maximum base shear capacity of structure can be obtained, The curve is transformed into capacity spectrum by SAP 2000 as per ATC 40 and demand or response spectrum is also determined for the structure depending upon the seismic zone, soil conditions and required building performance level. The ‘performance point’ is point where the capacity curve crosses the demand curve. The intersection of demand and capacity spectrum at 5% damping gives the performance point of the structure analysed. If the performance point exists and the damage state at this point is acceptable, the structure satisfies the target performance level. At the performance point, the resulting responses of the building should be checked using certain acceptability criteria. It must be emphasized that the pushover analysis is approximately in nature and is based on the statically applied load. It estimates an envelope curve 26
of the behaviour under the dynamic load. 3.4.1 ASSUMPTIONS (1) Seismic Zone III is considered as the building is located at Chennai. (2) As the building is constructed very long back, the age factor in the analysis is not considered. (3) Building considered to be noncompliant with IS 13920:1993 (R=3). (4) As the foundation rest with multiple pile with pile cap, Fixity is considered at pile cap. Soil-structure interaction neglected. (5) Elevator walls not considered as lateral load resisting elements. 3.4.2 METHODOLOGY OF PUSHOVER ANALYSIS The following sub sections provide procedure for determining capacity, demand and Performance using capacity spectrum method. 3.4.3 STRUCTURAL MODELLING A computer model was created and non linear analysis was performed using SAP 2000.
For the analysis, 3-D modeling of the existing building reinforced
concrete frame was developed. The beams and columns were modeled as frame elements considering the flexural properties to be assigned to beams and columns were cross sectional
dimensions, material properties, etc. The stiffness for
columns and beams were taken as 0.7E I g, 0.5EIg according for the cracking in the members and the contribution of flanges in the beams. The beam-column joints were modeled by giving end offsets at the joints. This is intended to get the bending moments at the face of the beams and columns . A rigid zone factor of one was taken to entire rigid connection of the components. Floor slabs were assumed to act as diaphragms, which ensure integral action of all the vertical lateral load-resisting elements. The weight of the slab was distributed as triangular and trapezoidal load for two way slab
distributed load for one way slab to the surrounding beams as per IS:456-2000. The brick infill load was assigned on the beams. The seismic mass at each floor was calculated and applied at front nodes at each direction as nodal forces. The effect of soil-structure interaction was ignored in the analysis. The ends of the columns are assumed to be fixed at the bottom.
PUSHOVER ANALYSIS The lateral force distribution along the height of the building according to
IS:1893-2002 was used in the pushover analysis. Pushover analyses were performed independently in the two orthogonal X and Y directions using SAP 2000. The target displacement at the roof of the building was taken as 0.004 times building height to comply with Clause 7.11.1 of IS:1893-2002. Beams and columns were modeled with concentrated plastic hinges at the column and beam faces respectively. Beams have moment (M3) hinges, whereas columns have axial load and biaxial moment (PMM) hinges. Geometric non-linearity of the structure was considered in the lateral pushover analyses. The results of pushover analysis both in X and Y direction are depicted in the figures shown. The Green color indicates pushover curve, the red color indicates demand curve and the yellow color indicates damping curve. The intersection of pushover and demand curve shows the performance point. If the performance point is reached in both the direction, the building will be seismic resistant and there is no need to retrofit. There are three pushover cases for the evaluation of buildings. Gravity push is used to apply gravity load. Push X is the lateral push in X direction starting at the end of gravity push. Push Y is the lateral push in Y direction starting at the end of gravity push. The pushover analysis was conducted for the frame considering P-Δ effect. The pushover analysis involves application of monotonically increase lateral deformation patterns and monitoring inelastic behaviour within the structure. The relationship of base shear and roof displacement (capacity curve) and 5% damped elastic design response spectrum (demand curve) of the model was established. The capacity and demand curves converted into a spectral displacement and spectral acceleration format to obtain the performance. The performance point is the intersection point of the capacity and the demand curves. The output of the capacity curve gives the coordinates of the pushover curve and summarizes the number of inches in each state. The coordinates of capacity curve and demand curve were transform into spectral acceleration versus spectral displacement coordinates. The curve slotted in this format are called as capacity spectrum and demand spectrum respectively. Applied Technology Council(ATC – 40) provides three different procedures(procedures A,B and C) to 28
establish the earthquake – induced deformation demands in this study, procedure B was adopted. The number of hinges formed in the beams and columns at the performance point (or at the point of termination of the pushover analysis) and their performance levels can be used to study the vulnerability of the building. The vulnerability can be quantified using the concept of ‘vulnerability index’.
Fig3.9 Isometric View of model
Fig3.10 Slab Modeling (Diaphragm)
Fig3.11 Beam Column Joint (End length offset)
Fig 3.12 Deformed Shape (PUSH-X)
Fig 3.13 DEFORMATION (PUSH-X)
Fig 3.14 HINGE FORMATION (PUSH-X)
Fig 3.15 Hinge Formation (PUSH-Y)
Fig3.16 Capacity Curve (PUSH-Y)
Fig3.17 Capacity Curve (PUSH-X) 37
Fig3.18 Base Vs Displacement Curve (PUSH-X)
Fig3.19 Base Vs Displacement Curve (PUSH-Y) 38
CHAPTER 4 RESULTS AND DISCUSSION 4.1 INTRODUCTION A Twelve- storeyed Reinforced concrete 3-D space frame of an existing building was taken as a case study for evaluating the adequacy of seismic effect by PUSHOVER analysis using SAP 2000. The frame was subjected to specified seismic forces for Zone III as per IS: 1893 (Part 1)-2002 in addition to Gravity loads with P-Δ effect. The various results of the building on Pushover curve, Displacements Vs Storey Drifts, Location of Hinges formed are indicated in the above figures shown. 4.2
The Pushover curves for the building in
X direction and Y direction of the
model are indicated in the Figures 3.18 and 3.19 shown. These curves depict the global behaviour of the model in terms of its stiffness and ductility. The stiffness and ductility ratios of the frame along Y direction is 1.20 times greater than that along X direction. 4.3 CAPACITY SPECTRUM, DEMAND SPECTRUM AND PERFORMANCE POINT The demand and capacity spectra for the lateral push along the two orthogonal direction for the Zone III are shown in Figures 3.16 and 3.17 . Performance point was obtained for the model in Zone III along both the directions. The pushover analysis indicates the performance in X direction is stronger than performance in Y direction. 4.4 DISPLACEMENTS AND STOREY DRIFTS The displacements at ultimate load are plotted in Figures 3.16 and 3.17. The inter-storey drifts corresponding to the displacements profiles are shown in Figures 3.20 and 3.21. It can be seen that the inter-storey drift at the lower floor levels is more than the permissible limit of 0.4%. 4.5 LOCATION OF HINGES The location of hinges formed in the building model during earthquake forces along both the directions are shown in figures 3.12 and 3.15. The hinges are formed in the lower most storey in first two rows of column in X direction and three rows of lower most columns in Y direction. 39
From the result it is observed that maximum base shear was 4036 KN which is about 20% of seismic weight of frame and the maximum displacement corresponding to this base shear is 0.53m. The frame is pushed to a maximum displacement of 4% of its height. 4.7 VULNERABILITY INDEX The vulnerability indix of the building in both X and Y directions are given in the Table 4.1. It can be seen that the vulnerability index of the building is high along X and Y directions which suggests the retrofitting of the building. It can be considered that the building in lower most storey has to be strengthened so as to fulfill the requirement of safety limit of earthquake for the present zone III. 4.7 RETROFIT MEASURE As the hinges are formed in the lower most storey of columns, the size of the column or reinforcement of column has to be enhanced suitably to stiffen the columns. Retrofit may be divided into Global and local strategies. Introducing walls or braces in an open ground storey are example of global strategies. The local strategies include jacketing of columns and beams by concrete or steel and use of carbon fibre sheet and fibre reinforced polymer wraps. Since only strengthening is required in Ground storey,
CHAPTER 5 SUMMARY AND CONCLUSION 5.1 SUMMARY The seismic behaviour of an existing multistory RCC building was investigated for Zone III as per latest IS Codal provision and Pushover analysis using SAP 2000. The following parameters are observed: •
Capacity Spectrum, Demand Spectrum and Performance Point
Displacement Vs Storey Drifts
Location of Hinges
Inter Storey drift
Based on the results obtained from the software, the following conclusions are made: 5.2 CONCLUSION The shear capacity of the frame is observed to be little higher than the demand in the zone III. The pushover curves in X direction and Y direction gives the performance of the structure. The inter-storey
drift at the lower floor levels exceed permissible code limit of
0.4%. The inter-storey drift profile of the frame illustrates the soft-storey mechanism which is undesirable in the seismic regions. The hinges are concentrated at the lower most floor level of columns in both X and Y direction Pushover cases which demonstrates the inadequacy of some of the columns in the ground storey. The vulnerability
index of the frame is high and therefore, the frame is found to
be unsafe for the design earthquakes. When a column is subjected to earthquake loading, its energy absorption capacity is the main concern rather than its load carrying capacity. Even though various alternatives are available, it is preferable to use FRB composites because they possess high strength to weight ratio and resistance to corrosion. 41
5.3 SCOPE FOR FUTURE STUDY Non-linear behaviour of the similar multi storey existing steel structure can be studied and compared with RCC building behaviour. It can also be suggested to compare the results of two similar software SAP 2000 and ETAB for evaluvating the seismic effect for Zone III with Zone IV for an existing multi-storey RCC building and the results are validated.
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