Seismic Evaluation of Reinforced Concrete Structures

Seismic Evaluation of Reinforced Concrete StructuresABSTRACT

Occurrences of recent earthquakes in India and in different parts of the world and the 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. Most of the existing buildings, which do not fulfill the current seismic requirements, may suffer extensive damage or even collapse if shaken by a severe ground motion. The aim of evaluation is to assess the seismic capacity of earthquake vulnerable buildings or earth quake damaged buildings for future use. The evaluation may also prove helpful for degree of intervention required in seismically deficient structures.

INTRODUCTIONThe Buildings, which appeared to be strong enough, may crumble like houses of cards during earthquake and deficiencies may be exposed. Experience gain from the recent earthquake of Bhuj, 2001 demonstrates that the most of buildings collapsed were found deficient to meet out the requirements of the present day codes. In last decade, four devastating earthquakes of world have been occurred in India, and low to mild intensities

earthquakes are shaking our land frequently. Due to wrong construction practices and ignorance for earthquake resistant design of buildings in our country, most of the existing

buildings are vulnerable to future earthquakes. it is imperative to seismically evaluate the existing building with the present day knowledge to avoid the major destruction in the future earthquakes. The Buildings found to be seismically deficient should be retrofitted/strengthened. Evaluation of building is required at a two stages (1) Before the retrofitting, to identify the weakness of the building to be strengthened, and (2) After the retrofitting, to estimate the adequacy and effectiveness of retrofit. Evaluation is complex process, which has to take not only the design of building but also the deterioration of the material and damage cause to the building, if any. The difficulties faced in the seismic evaluation of the building are threefold. There is no reliable method to estimate the in-situ strength of the material in components of the building. Analytical method to model the behavior of the building during earthquake is either unreliable or too complex to handle with the generally available tools. The third difficulty is the un-availability of reliable estimate of earthquake parameters, to which the buildings expected to be subjected during its residual life.Evaluation criteriaThe consequence of evaluation of any building should be quantitatively evaluated for its effectiveness from the viewpoints of strength, stiffness & ductility.

1. Strength/capacity:

The essence of virtually all seismic evaluation procedures is a comparison between some measures of Demand that earthquake take place on a structure to measure of the Capacity of the building to resist. Traditional design procedures characterize demand and capacity as forces. Base shear (Total Horizontal force at the lowest level of the building) is a normal parameter i.e. used for the purpose. It involves calculation of base shear demand that would be generated by given earthquake, or intensity of ground motion, and compare this to the base shear capacity of the building. The capacity of the building is an estimate of base shear that would be acceptable. If the building subjected to a force equal to its base shear capacity, some deformation and yielding might occur in some structural elements, but the building would not collapse or reach undesirable level of damage. If the demand generated by the earthquake is less than the capacity than the design is deemed acceptable. More sophisticated works needs to compare the seismic demand of every structure elements with its capacity i.e. demand capacity ratios. 2. Stiffness:

The first formal seismic design procedure recognized that the earthquake acceleration would generate forces proportional to the weight of building. Over the years, empirical knowledge about the behaviour of real structures in earthquakes and theoretical understanding of structural dynamics advanced. The basic procedure modified to reflect the demand generated by the earthquake acceleration also a function of stiffness of the structure. It helps to recognize the inherently better behavior of some building over the others.

To get minimum damage and less psychological fear in the mind of peoples during the earthquake. IS 1893: 2002 permits maximum inter-story drifts as 0.004 times the story height. Inter-story drifts always depend upon the stiffness of the respective storey (IS 1893-2002). Again the abrupt changes in the stiffness along the load paths may lead to high stress concentration at some load transfer points and may create local crushing. Hence stiffness always plays vital roles and considered as an important criteria in the seismic evaluation of the building.3. Ductility:

Earthquake motion often induces forces large enough to cause inelastic deformations in the structure. If the structure is brittle, sudden failure could occur. However ,if the structure is to made to behave to ductile, sudden failure to sustain the earthquake effects better with some deflection larger than the yield deflection by absorption of energy. The capacity of structure to resist seismic demand is a property known as ductility. It is the ability to deform to beyond initial yielding without failing abruptly. This property is a critical component of structural integrity and required as an essential element for safety from sudden collapse during severe shocks.Methods for the evaluation of existing buildingsThe aim of these methods is to direct the evaluating engineer to identify the weak links in the structure that could precipitate the structural or component failure.

The methodologies available so far for the evaluation of existing buildings can be broadly divided into two categories.1. Qualitative Methods

2. Analytical Methods

1. Qualitative Methods:

These are based on the background information available of the building and its construction site. It requires some or few documents like architectural and structural drawings, past performance of similar buildings, under severe earthquakes, visual inspection report, some non-destructive test results. The methods under this category are Field Evaluation Method, Rapid Visual Screening Method, ATC-14 Methodology etc. The qualitative evaluation of a structure is conducted by a visual examination of the structure along with some testing of materials.2. Analytical Methods:

These methods are based on the considerations of the capacity and ductility of buildings on the basis of available drawings. The methods in this considerations Capacity/Demand (C/D) method, Screening method, Pushover analysis, Nonlinear inelastic analysis etc. It is often seen that the drawings of buildings are generally not available due to one or more reasons. Moreover, the evaluation of the capacity and ductility of a building is also a cumbersome task, which is difficult for a field engineer and may not be practical in the present Indian scenario. It is important to underline that the methods of evaluation procedure should be very simple and immediate based on synthetic information that can prove suitable for risk evaluation on large populations. Therefore, qualitative evaluation of the buildings is generally being carried out.

Components of seismic evaluation methodologyThe evaluation of any building requires a wide knowledge about the structures, cause and nature of damage in structures and its components, material strength etc.

The proposed methodology is divided into three components.1. Condition assessment

2. Visual inspection/Field evaluation

3. Non-Destructive Evaluation1.Condition Assessment for EvaluationThe aim of condition assessment of the structure us the collection of information about the structure and its past performance characteristics to similar type of structure during past earthquakes ant the qualitative evaluation of structure for decision making purpose.

Data Collection/Information Gathering:Collection of the data is an important portion for the seismic evaluation of the existing building. The information required for the evaluated building can be divided as follows Building data

Architectural, structural and construction drawings

Vulnerability parameters : no.of storeys, year of construction and total floor area

Specifications , soil reports, and design calculations

Seismicity of the site

Construction data: Identifications of gravity load resisting system Identification of lateral load resisting system

Maintenance, addition, alteration, or modifications in structures

Field surveys of the structures existing conditions

Structural data:

Materials

Structural concept; Vertical and horizontal irregularities, Torsional eccentricity, pounding, Short column and others

Detailing concept : Ductile detailing, special confining reinforcement

Foundations

Non-Structural elements

Past performance data:

Past performance of similar type of structure during the earthquake provides considerable amount of information for the building, which is under evaluation process. Following are the areas of concern, which are responsible for poor performance of buildings during earth quake.Material concerns:

Low grade concrete Deterioration in concrete and reinforcement

High cement sand ratio

Corrosion in reinforcement

Use of recycled steel as reinforcement

Spalling of concrete by the corrosion of embedded reinforcing bars

Corrosion related to insufficient concrete cover

Poor concrete placement and porous concrete

Structural concerns: The relatively low stiffness of the frames-excessive inter storey drifts, damage to non structural items. Pounding-column distress, possibly local collapse

Unsymmetrical building(U,T,L,V) in plan-torsional effects and concentration of damage at the junctures

Unsymmetrical buildings in elevation- abrupt change in lateral resistance

Vertical strength discontinuities-concrete damage in the soft storeys

Short column

Detailing concerns: Large tie spacing in columns lack of confinement if concrete core- Shear failures

Insufficient column lengths-concrete to spall

Locations of inadequate splices-Brittle shear failures

Insufficient column strength for full moment hinge capacity-brattle shear failure

Lack of continuous beam reinforcement-Hinge reformation during load reversals Inadequate reinforcing of beam column joints or location of beam bar splices at columns-joint failures

Improper bent up of longitudinal reinforcing in beams as shear reinforcement- shear failure during load reversals

Foundation dowels that are insufficient to develop the capacity of columns steel above-local column distress

Seismic evaluation data:It provides a general idea about the building performance during an earthquake. The criteria of evaluation of building will depend on the following

Material evaluation: Building height > 3 storeys, minimum grade of concrete M20, desirable M30 to M40 particularly in columns of low stories.

Maximum grade of steel will be Fe415 due to adequate ductility.

No significant deterioration in reinforcement

No evidence of corrosion or spalling of concrete

Structural components: Evaluation of column shear strength and drift

Evaluation of plan irregularities Evaluation of vertical irregularities

Evaluation of discontinuous load paths

Beam-column joints

Pounding Interaction between frame and infill

Structural detailing:Flexure members

Limitation of sectional dimensions

On minimum and maximum flexural reinforcement

Restriction of lap splices

Development length requirements

Shear reinforcement requirements

Columns

Limitations of sectional dimensions

Longitudinal reinforcement requirements

Transverse reinforcement Special confining requirementsFoundation

Column steel dowelled into the foundation

Non-Structural components

Cornices, parapet, and appendages are anchored

Exterior cladding and veneer are well anchored

2.Field Evaluation / Visual Inspection Method

It is an integral part of the evaluation and is the most widely used form of Non-Destructive Evaluation.

Procedure for visual inspection method :Description

Perform a walk through inspection to become familiar with the structure

Gather background documents and information on the design, construction, operation, and maintenance of the structure.

Plan the complete investigation

Perform detailed visual investigation and type of damage, cracks spalls and delaminations, buckling or fracture of reinforcement, estimating driftEquipments

Optical magnifier allows a detailed view of local areas of distress

Stereomicroscope allows a 3D view of surface

Fiber scopes and bore scopes

Tape

Flash light

Crack comparator

Pencil, sketch board, camera

Execution

To identify the location of vertical structural elements like columns or walls

To sketch the elevation with sufficient details

To take photographs of the cracks

Observation of the non-structural elements

Limitations

Only surface damages can be visualized No identification of inner damage

Identification of seismic damage in building componentsPossible damage in building components generally observed after earthquakes are as follows

Seismic evaluation of reinforced concrete columns:Damage is mainly due to lack of confinement, large tie spacing, insufficient splice length ,in adequate splicing at the same section, poor concrete quality, less than full height masonry infill partitions.

The most common modes of failure are as follows.

Mode 1:

Formation of plastic hinge at the base of ground level columns

Mechanism:

The column, when subjected to seismic motion, its concrete begins to disintegrate and the load carried by concrete shifts to longitudinal reinforcement of the column. This additional load causes buckling of longitudinal reinforcement. As a result the column shortens and looses its ability to carry even the gravity load.Reasons: Insufficient confinement lengths and improper confinement in plastic hinge due to smaller number of ties.

Design Consideration:

Consideration is to be paid on plastic hinge length or length of confinement.

Mode 2: Diagonal Shear cracking in mid span of columns

Mechanism:

In old buildings column failures were more frequent since the strength of the beams in such constructions was kept higher then that of the columns. This mode of failure brings the loss of axial load carrying capacity of the column. As the axial capacity diminishes the gravity load carried by the columns transferred to the neighboring elements resulting massive redistribution of forces.

Reason:Wide spacing of transverse reinforcement

Mode 3:

Shear and splice failure of longitudinal reinforcement

Mechanism:

Splices of column longitudinal reinforcement in older buildings were commonly designed for compression only with relatively light transverse reinforcement enclosing the lap. Under earthquake motion, the longitudinal reinforcement may be subjected to significant tensile stresses, which requires lap lengths for tension substantially exceeding those for compression. As a result slip occurs along the splice length with spalling of concrete.

Reasons:

Deficient lap splice length of column longitudinal reinforcement with lightly spaced transverse reinforcement.

Design consideration:

Lap splices should be provided only in the center half of the member length and it should be proportionate to tension splice. Spacing of transverse reinforcement as per IS:13929-1993

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Mode 4: Shear failures in captive columns and Short columnsMechanism: A reduction in clear height of captive or short columns increases the lateral stiffness. Therefore these columns are subjected to larger shear force during the earthquake. If these columns , reinforced with conventional longitudinal and transverse reinforcement, and subjected to relatively high axial loading fail by splitting of concrete along their diagonals, if the axial loading is low, the most probable mode of failure is by shear sliding along full depth cracks at the member ends.Reason: Large shear stresses, when the structure is subjected to lateral forces are not accounted for in the standard frame design procedure.Design consideration:

The best solution for captive column or short column is to avoid the situation otherwise use separation gap in between the non-structural element and the vertical structural element with appropriate measures.

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Seismic Evaluation of Reinforced Concrete Beams

Only a few examples exist in which buildings have exhibited plastic hinges in the beam. The probable regions of hinging area are at and near their interactions with supporting columns. An exception may be where a heavy concentrated load is carried at some intermediate point on the span. The causes of hinging are lack of confinement of concrete core .The shear flexure mode of failure is most commonly observed during the earthquake.

Mode 5: Shear-Flexure failure

Mechanism: Two types of plastic hinges may form in the beams of multi-storied framed construction depending upon the span of beams. In case of short beams or where gravity load supported by the beam is low , plastic hinges are formed at the column ends and damage occurs in the form of opening of a crack at the end of beam otherwise there is a formation of plastic hinge at and near end region of beam in the form of diagonal shear cracking.Reason: Lack of longitudinal compressive reinforcement, infrequent transverse reinforcement in plastic hinge zone, bad anchorage of bottom reinforcement into the support , bottom steel termination at face of the column.

Design consideration:

The beams should not be too stiff with respect to adjacent columns so that plastic hinging will occur in beam rather than column. To ensure that the plastic hinge zones in beams have adequate ductility.Seismic Evaluation of Reinforced Concrete Beam-Column jointsBeam-column joints are critical element in frame structures and are subjected to high shear and bond slip deformations under earthquake loading .The common causes for the failure of beam-column joints are c/s properties of joint region, amount and distribution of column vertical steel, inadequate or absence of reinforcement in beam-column joint, absence of confinement of hoop reinforcement, inappropriate location of bar splices in columns.

Mode 6:Shear failure in Beam-Column joint

Mechanism:The most common failures observed in exterior joints are due to either high shear or bond due to severe earthquakes. Plastic hinges are formed in the beams at the column faces. As a result cracks develop in the overall beam depth. In the interior joint, the beam reinforcement at both the column faces undergoes different stress conditions because of opposite sights of seismic bending moments results in failure if joint core.Reason: Inadequate anchorage of flexural steel in beams , lack of transverse reinforcement.

Design consideration:

Reliable anchorage of beam reinforcement in the joints

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Seismic Evaluation of Reinforced Concrete SlabsGenerally slabs on beams performed well during earthquakes and are not dangerous but cracks in slab creates serious aesthetic and functional problem. It reduces strength , stiffness and energy dissipation capacity of building for future earthquake. In flat slab construction punching shear is the primary cause of failure.

Mode 7: Shear cracking in slabs

Mechanism: Damage to slabs often occurs due to irregularities such as large openings at concentration of earthquake forces widely spaced shear walls, at the staircase flight landings.

Reason: Existing micro cracks which widen due to shaking, differential settlement.Design consideration:

Use secondary reinforcement in the bottom of the slab.

Avoid the use of flat slab in high seismic zones.

Seismic Evaluation of Reinforced Concrete Shear wallsMode 8:

Four types of failure modes are generally observed

1. Diagonal tension-compression failure in the form of cross-shaped shear cracking.

2. Sliding shear failure cracking at the interface of new and old cracking.

3. Flexure and compression in bottom end region of wall.

4. Diagonal tension in the X shaped cracking in coupling beams

Mechanism:Shear walls are subjected to shear and flexure deformations based on slenderness ratio. Therefore damage in shear walls may generally occurs due to inadequate shear and flexure capacity of wall.

Reason:

Flexural/boundary compression failure Flexure/diagonal tension

Sliding shear

Coupling beams

Construction joint

Design consideration:

Concrete Shear walls must have boundary elements or columns thicker than walls, which will carry vertical load after shear failure if wall.

A proper connection between wall vs. diaphragm as well as wall vs. foundation to complete the load path.

Proper bonding at the construction joint in the form of shear friction reinforcement

Provision of diagonal steel in the coupling beam.

Seismic Evaluation of Reinforced Concrete Infill walls

Infill panels in Reinforced concrete frames are the cause of unequal distribution of lateral forces in the different frames of the buildings, producing vertical and horizontal irregularities etc.

Mode 9:Shear failure of Masonry infill

Mechanism: Frames with infill possess much more lateral stiffness than the bare frame, and hence initially attracts most of the lateral forces during an earthquake. Being brittle the infill starts disintegrate as soon as its strength is reached.

Reason: Infill causes asymmetry of load application, resulting in increased torsional forces and changes in the distribution of shear forces between lateral load resisting system.

Design consideration:

Two strategies are possible either complete separation between infill walls and frame by providing separation joint so that two systems do not interact or complete anchorage between frame and infill to act as an integral unit.

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Seismic Evaluation of Reinforced Concrete ParapetsUn-reinforced concrete parapets with large height to thickness ratio and not improper anchoring to the roof diaphragm may also constitute a hazard, the hazard posed by a parapet increases in direct proportion to its height above building base.

Mode 10:Brittle flexure out of plane failure

Mechanism:Parapet walls are acceleration sensitive in the out of plane direction resulting in topple.

Reason: Not properly braced

Design consideration:

Analyzed for acceleration forces and braced and connected with roof diaphragm.

Non-Destructive TestingVisual inspection has the obvious limitation that only visible surfaces can be inspected. Internal defects go unnoticed and no quantitative information is obtained about the properties of concrete. For this reason a visual inspection is usually supplemented by NDT methods.Rebound Hammer/Swiss Hammer:The rebound hammer is the most widely used non-destructive device for quick surveys to assess the quality of concrete. Used for testing the concrete based upon the rebound principal strength of in-place concrete.

Limitations:

Not give a precise value of compressive strength

Sensitive to the quality of concrete; Corbonation increases the rebound number.

More reproducible results from formed surface rather then finished surface. Surface moisture and roughness also effect the reading

Not take more than one reading at the spot

Penetration Resistance Method-Winster probe test:Used to determine the quality and compressive strength of in-situ concrete .It is based on the depth of penetration of probes into concrete by means of powder-actuated driver. This provides a measure of hardness or penetration resistance of the material that can be related to its strength.

Limitations:

Both probe penetration and rebound hammer test provides means of estimating the relative quality of concrete not absolute value of strength of concrete.

Probe test may be cause of minor cracks in concrete.

Rebar locator/Convert meter:It is used to determine quantity, location, size and condition of reinforcing steel in concrete. These devices are based on the interaction between reinforcing bars and low frequency electromagnetic fields.Limitations:

Difficult to interpret at heavy congestion of reinforcement

Embedded metals sometimes effect the reading.

Ultrasonic pulse velocity:

It is used to determine the elastic constants and the density. By conducting tests at various points on a structure, lower quality concrete quality can be identified by its lower pulse velocity. Pulse-Velocity measurements can detect the presence of voids or discontinuities within a wall.

Limitations:

An increase of moisture content increases the velocity.

The pulse may propagate through the bars and result in an apparent pulse velocity which is higher than that propagating through concrete. Presence of voids and cracks increases the length of travel path and result in an longer travel time.

Impact Echo:

It is a method for detecting discontinuities within the thickness of wall.

Limitations:

Accuracy mainly depends on the skill of engineer.

The size, type, sensitivity and natural frequency of the transducer also affect the results.

Spectral analysis of surface waves:

To assess the thickness and elastic stiffness of material, size and location of discontinuities within the wall such as voids, large cracks.

Limitations:

Interpretation of results is complex.

Mainly used on slabs

Penetrating Radar:It is used to detect the location of reinforcing bars, cracks, voids or other material discontinuities.

Limitations:

Mainly used for detecting sub-surface condition of slab

Not useful for detecting the small differences in materials

Closely spaced bars make difficult to detect features below the layer of steel.Method to perform simplified nonlinear analysis (Pushover Analysis):

Two key elements of a performance based design procedure are demand and capacity. Demand is a representation of the earthquake ground motion. Capacity is a representation of the structures ability to resist the seismic demand. The structure must have the capacity to resist the demand of the earthquake such that the performance of the structure is compatible with the objectives of the design. Simplified non-linear analysis procedures using pushover methods such as the capacity spectrum requires determination of three primary elements: Capacity, demand and performance. Each of these elements is briefly discussed as:

Capacity: The overall capacity of a structure depends on the strength and deformation capacities of the individual components of the structure. A Pushover analysis procedure uses a series of sequential elastic analysis, superimposed to approximate a forcedisplacement capacity diagram of the overall structure. The mathematical model of the structure is modified to account for reduced resistance of yielding components. A lateral force distribution is again applied untill a predetermined limit is reached. Pushover capacity curves approximate how structure behaves after exceeding the elastic limits.

Demand (Displacement): Ground motions during an earthquake produce complex horizontal displacement patterns in structure that may vary with time. Tracking this motion at every time step to determine structural design requirements is judged impractical. For nonlinear method it is easier and more direct to use a set of lateral displacement as a design condition for a given structure and ground motion, the displacement is an estimate of the maximum expected response of the building during ground motion.

Performance: Once a capacity curve and demand displacement are defined, a performance check can be done. A performance verifies that structural & non-structural components are not damaged beyond the acceptable limits of performance objectives for the forces and displacement implied by the displacement demand.

Evaluation based upon Elastic Approach:As mentioned in ATC-40, both elastic and in-elastic methods are available for the analysis of existing concrete buildings. Seismic Evaluation can be performed by Elastic procedures using DCRs (Demand-Capacity Ratios): The work carried out by (Bhardwaj, 2002) is based on elastic approach. This is a linear elastic analysis, which involves the following three stages, namely:

Input data stage:i) Study of site soil conditions.

ii) Measurement of actual geometry of buildings and its component.

iii) In-situ NDT to estimate to actual strength of concrete in the building components.

iv) Test to estimate actual strength of steel reinforcement bars in the building components

and the extent of corrosion, to carefully estimate their available diameters.

Analysis stage:

v) Preparation of 3 D model of building frame using measure geometry & material

properties.

vi) Estimation of design later force on building using IS 1893:2002 for the given design

response spectra.

vii) Application of design lateral force on 3D building model to determine stress

resultants (i.e. axial forces, shear forces, bending moments etc.), in the frame members

and determination of inter-story drifts.

viii) Determination of RC member capacities with actual cross-sectional geometry and

material properties as per IS 456:2000/IS 13920:1993 and DCR of RC members at

critical locations.

ix) Identification of deficient member or deficiency in lateral stiffness of the building if

any.

Retrofit and verification stage:

x) Identification of suitable retrofitting techniques to rectify the deficiencies.

xi) Estimation of the new member sizes along with the addl. Reinforcement required,

and/or the new members requires.

xii) Reanalysis of buildings to confirm the adequacy with then proposed retrofit

techniques.

xiii) If strength and stiffness requirement are satisfied than the propose retrofits scheme

may be adopted, else other more appropriate retrofits scheme may be identified.ATC-40 PROCEDURE FOR SEISMIC EVALUATION

This following is the step-by-step procedure prescribed in ATC-40 for the development of Capacity Curve.

Step-by-Step Procedure to determine capacity:

The most convenient way to plot force displacement curve is by tracking the base shear and roof displacement. The capacity curve is generally constructed to represent the first mode response of the structure based on the assumption that the fundamental mode of vibration is the predominant response of the structure. This is generally valid for buildings with the fundamental periods of vibration upto about 1 second. For more flexible buildings with the fundamental period > 1 second, the analyst should consider addressing higher mode effects is the analysis.

1) Create a computer model of the structure following the modeling rules as per ATC-40.

2) Classify each element in the model as either primary or secondary.

3) Apply lateral storey forces to the structure in proportion to the product of the mass and

fundamental mode shape. This analysis should also include gravity loads.

[As the name implies, it is the process of pushing horizontally with a prescribed loading pattern. Incrementally untill the structure reaches a limit state. There are several levels of sophistication that may be used for the pushover analysis]

i) Simply apply a single concentrated horizontal force at the top of the structure (for one story building)

ii) Apply lateral forces to each storey in proportion to the standard code procedure without the concentrated force Ft at the top

i.e.Fx = (Wx hx / PWx hx ) x V ..(1)

iii) Apply lateral forces in proportion to the product of storey masses and first mode shape of the elastic model of the structure

i.e.Fx= (Wx x / Wx x ) x V. ..(2)

The capacity curve is generally constructed to represent the first mode response of the structure based on assumption that the fundamental mode of vibration is the predominant response of the structure.

iv) Same as level three untill first yielding. For each increment beyond yielding, adjust the forces to be consistent with changing deflected shape.

v) Similar to (iii) & (iv) above, but include the effects of the higher mode of the vibration in determining yielding in individual structural elements while plotting the capacity curve for the building in terms of first mode lateral forces and displacements. The higher mode effects may be determined by doing higher mode pushover analysis. (i.e. Loads may be progressively implied in proportion to a mode shape other than the fundamental mode shape to determine its in elastic behavior) For the higher modes the structure is being both push & pulled concurrently to maintained mode shape.

4) Calculate member forces for the required combinations of vertical and lateral load.

5) Adjust the lateral force level so that some elements (on group of elements) are stressed to with in 10% of its member strength.

6) Record the Base shear and the roof displacement. (It is also useful to record member forces & rotations because they will be needed for the performance check)

7) Revise the model using zero (or very small) stiffness for the yielding elements.

8) Apply a new increment of lateral load to the revise structure such that another element (or group of elements) yields.

[The actual forces and rotations for elements at the beginning of the increment are equal to those at the end of the previous elements. However, each application of an increment of lateral load is a separate analysis, which starts from zero initial conditions. Thus, to determine when the next elements yields, it is necessary to add the forces from the current analysis to the some of those from the previous increments]

9) At the increment of the lateral load and the corresponding increment of roof displacement to the previous total to give the accumulated values of base shear and roof displacement.

10) Repeat steps 7,8 & 9 untill the structures reaches an ultimate limit such as: instability from P-_ effects, distortions considerably beyond the desire performance level, an element reaching a lateral deformation level at which significant strength degradation begins.

Fig.3.1 Capacity CurveConversion of Capacity curve to the capacity spectrum:To use the capacity spectrum method it is necessary to convert the capacity curve, which is in terms of base shear and roof displacement to what is called a capacity spectrum, which is a representation of the capacity curve in Acceleration Displacement Response Spectra (ADRS) format i.e. (Sa vs Sd). The required equations to make the transformation are:

PF1 = {i=1 (wi i1)/g} / [ i=1 {wi ( i1)2/g}]

1 = {i=1 (wi i1)/g}2 / { i=1 (wi/g} X [ i=1 {wi ( i1)2/g}]

Sa = (V/W)/1

Sd = (_roof) / (PFiroof.1)

Where, PFi = Model participation factor for the first natural mode, 1 = Model mass coefficient for the first natural mode,Wi /g = mass assign to level i, il = amplitude of mode one at level i, N = Level N, the level which is the uppermost in the main portion of the structure.

In order to develop the capacity spectrum from the capacity curve it is necessary to do a point by point conversion to first mode spectral coordinates any point Vi,_roof on the capacity curve is converted to the corresponding point Sai ,Sdi on the capacity spectrum using the equations written above.

Fig.3.2 Capacity Spectrum Conversion

Every point on a response spectrum curve is associated with a unique spectral acceleration Sa, Spectral Velocity Sv, Spectral displacement Sd, and period T, to convert a spectrum from a standard Sa VS T format found in a building code to ADRS format it is necessary to determine the value of Sdi for each point on the curve Sai, Ti, this can be done with equations:

Sdi=(Ti2 x Sai x g) / 42 . (3)

Standard demand response spectra contain a range of constant spectral acceleration and second range of constant spectral velocity. Spectral acceleration and displacement at period Ti, are given by

Sai g = (2S) / Ti, Sdi = (Ti x Sv )/ 2 ...........(4)

Fig.3.3 Response Spectrum Conversion

Calculating performance point:

1) A First choice of point api, dpi could be the displacement obtained using the equal displacement approximation or it might be the end point of the capacity spectrum or it might be any other point chosen on the basis of engineering judgement.

2) Develop the demand spectrum as shown in figure 3.4, draw the demand spectrum on the same plot as the capacity spectrum as shown in figure 3.6

3) Referred to figure 3.8, determine if the demand spectrum intersects the capacity spectrum at point api dpi or if the displacement at which the demand spectrum intersects the capacity spectrum di is with in acceptable tolerance dpi as shown in figure 3.9.

4) If the demand spectrum does not intersects the capacity spectrum with in acceptable tolerance than select a new api dpi point.

5) If the demand spectrum intersects the capacity spectrum with in acceptable tolerance than the trial performance points api, dpi is the performance point, ap dp and the displacement dp represents the maximum structural displacement expected for the demand earthquake.

Fig.3.4 Reduced Response Spectrum

Fig.3.5 Intersection Point of Demand and Capacity Spectrums within Acceptable Tolerance.

Fig.3.6 Capacity Spectrum After Step 2

Fig.3.7 Capacity Spectrum After Step 3

Fig.3.8 Capacity Spectrum After Step 5.

Fig.3.9 Capacity Spectrum After Step 6

REFERENCES:1. Earth Resistant Design of Structures by Pankaj Agarwal, Manish Shrikhande.

2. Recent developments toward earthquake risk reduction in India by Anand S. Arya, Department of Earthquake Engineering, University of Roorkee.

3. Seismic Evaluation of Reinforced Concrete Buildings by Taranpreet Singh, Thapar institute of engineering & technology, (deemed university), Patiala 4. Seismic Evaluation and Retrofitting of Buildings and Structures N.Lakshmanan, Structural Engineering Research Centre,CSIR Campus, Taramani.5. Historical Developments And Current Status of Earthquake Engineering in India

(Proceedings of the 12th World Conference on Earthquake Engineering, Auckland, New Zealand, 2000), Sudhir K. Jain, Department of Civil Engineering, IIT Kanpur.6. On Better Engineering Preparedness: Lessons from the 1988 Bihar Earthquake Earthquake Spectra, EERI, Vol.8, No.3, 1992, Sudhir K. Jain, Department of Civil Engineering, Indian Institute of Technology Kanpur.14