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Performance Based Seismic Design is an Effective Tool for Evaluation of an
Existing Concrete Structures using Nonlinear Dynamic Time-History Analysis
Prepared by:
Prof. Dr. Ibrahim M. Metwally
Concrete Structures Research Institute, Housing & Building Research Centre,
P.O. Box 1770 Cairo, Egypt [email protected]
COURSE CONTENT
Introduction
This course is about Performance Based Seismic Design is an Effective Tool for
Evaluation of an Existing Concrete Structures using Nonlinear Dynamic TimeHistory
Analysis
This course is very useful for researchers, under graduate, post-graduate students, professional
engineers, academics, PhD holder in structural engineering field. This course learns the engineers
how to find the capacity and performance evaluation of existing reinforced concrete structurers
easily.
Learning Objectives
At the conclusion of this course, the student will be able to evaluate the performance and capacity
of reinforced concrete structures and will
Be able to provide engineers with a capability to evaluate the structural safety of
existing concrete buildings
Be able to provide engineers with a capability to design buildings that have predictable
and reliable performance in earthquakes
Be able to perform the nonlinear dynamic analysis of concrete buildings
Be able to define which parts must be retrofitted after nonlinear analysis
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The Aim of Performance-Based Seismic Design
The main objective of performance-based seismic design process is to evaluate how a building is
likely to perform under potential hazards. In performance-based design, identifying and assessing
the performance capability of a building is an integral part of the entire design process.
Performance-based design begins with the selection of design criteria stated in the form of one or
more performance objectives. Each performance objective is a statement of the acceptable risk of
incurring specific levels of damage. The consequential losses that occur as a result of the damage
at a specified level of seismic hazards are calculated. Losses can be associated with structural
damage, non-structural damage, or both. They can be expressed in the form of casualties, direct
economic costs, and downtime (time out of service), resulting from damage. In performance-based
design, identifying and assessing the performance capability of a building is an integral part of the
design process which guides the many design decisions that must be incorporated. Fig. 1 shows a
flowchart which presents the key steps in the performance-based design process. It is an iterative
process that begins with the selection of performance objectives, followed by the development of
a preliminary design, an assessment as to whether or not the design meets the performance
objectives and finally redesign and reassessment, if required, until the desired performance level
is achieved
Fig.1 : Performance based design flow diagram
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METHODS OF ANALYSIS
Lateral force analysis (linear)
Modal response spectrum analysis (linear)
Non-linear static (pushover) analysis
Non-linear time history dynamic analysis
Fig. 2 : Methods of Analysis
NOTE:
In Redesign (Assessment of existing buildings):
Elastic analysis methods currently in use (for new buildings) have a reliability under specific
conditions to make sure new buildings to be met.
In most cases, these conditions are not met in the old buildings (Nonlinear ones are needed).
Why Nonlinear Dynamic Time History Analysis and Not Pushover One?
Because of that the pushover analysis is a static analysis it cannot take into account the effects of
dynamic characteristics of the buildings as energy content, duration and frequency content of an
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accelerogramme while nonlinear dynamic (time history) analysis perform a dynamic analysis of
structure under input accelerograme and then the effect of those parameters will be taken into
account leading to more accurate assessment. It is widely recognized that nonlinear dynamic
Analysis constitutes the most accurate way for simulating response of structures subjected to strong
levels of seismic excitation.
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Inelastic Nonlinear Time History Analysis
Some buildings may be too complex to rely on the nonlinear static procedure. Those cases may
require time history analysis of the nonlinear behavior of the structure during analysis for a
particular example of earthquake. The kinds of the buildings that may require this specialized
analysis are highly irregular or complicated.
This method is performed using time histories prepared according to the actual ground motions
recorded. The requirements for the mathematical model for time history analysis are identical to
those developed for response spectrum analysis. The damping matrix associated with the
mathematical model shall reflect the damping inherent in the structure deformation levels less than
the yield deformation.
Nonlinear dynamic analysis commonly referred to as “Inelastic Nonlinear Time History Analysis”
shall be used to determine the reliable displacement capacities of a structure or frame as it reaches
its limits of structural stability.
Time History Analysis sometimes called Response History Analysis or Transient Dynamic
Analysis, involves a time-step-by-time-step evaluation of building response. It is used to determine
the dynamic response of a structure to arbitrary loading using the accelerogram (variation of
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ground acceleration with time recorded at a point on ground during an earthquake) as base motion
input.
For an earthquake time analysis, the set of applied forces changes continuously as the ground
acceleration changes. If the building is being damaged then the stiffness continuously changes as
well. The response is calculated at each time step, typically every 1/100th of a second or less. At
each step the loads are changed, and the stiffness also changed if necessary. For a typical building
this may require solving a set of several thousand simultaneous equations up to 3000 times. This
is where computer speed becomes essential.
Need for Time History Analysis
Time history analysis is applicable to both linear elastic and nonlinear inelastic response analysis
of buildings.
• Elastic linear time history analysis is required when the results of response spectrum
analysis indicate that the computed story drift or roof displacement exceed the allowable
values, or when special conditions exist.
• An inelastic nonlinear time history analysis may be necessary when the results of a elastic
linear time history analysis show that the structure could suffer significant damage during a major earthquake.
Often the elastic linear analysis underestimate certain behaviors, particularly relating to
the higher mode of vibration which will result to a high base shear. The calculated forces
will be significantly greater than the section capacity over a large region and are repeated
several times during the earthquake excitation. Hence, severe cracking of the concrete,
joint slippage, and yielding of reinforcements can be expected. Under these conditions, the
dynamic behavior of the structure is drastically different from the linear response, and a
valid estimate of the damage is possible only if a true nonlinear performance is
incorporated in the analysis. Therefore, nonlinear time history analysis is used to justify a
structural design of a structure.
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Difficulties in Time History Analysis
There are several difficulties in time history analysis:
• First, it is not known whether the selected accelerogram is appropriate to use.
• Second, errors in assumed damping and other quantities can be cumulative when large
number of modes are involved.
Code Requirements
Because time history analysis is sensitive to modeling and ground motion assumptions, Uniform
Building Code (UBC) require a minimum of three time history components that shall be scaled
from selected strong earthquake motions recorded at or near the site; or strong earthquake motions
recorded at other sites with similar geological, topographic and seismotectonic characteristics, and
use the maximum response of the parameter of interest for design. The purpose is to ensure
adequate coverage of the difficulty.
If seven or more pairs are selected and scaled, then the average value of the response parameter of
interest may be used for design.
When appropriate recorded ground-motion time history pairs are not available, appropriate simulated ground-motion time history pairs may be used to make up the total number required. Synthetic accelerograms should be based on probabilistic methods.
There are some available software as SeismoMatch , SeismoArtif and EZ-FRISK, they can be used to predict where earthquakes will occur, what their characteristics will be, and what will be the ground motions generated. They can perform spectral matching. Spectral matching makes
adjustments to an input accelerogram so that its response spectrum matches a target response spectrum.
The word pairs, means that the instrumentation that recorded the earthquake accelerations captured
the two horizontal components of ground motion and one vertical component of ground motion
simultaneously (e.g., the earthquake records of 1940 El Centro Site 270 degrees, 1940 El Centro
Site 180 degrees, and 1940 El Centro Site vertical).
Although most of commercial design software as, Staad Pro., ETABS, SAP2000, etc…, can
apply acceleration records along the three axes of the model simultaneously, the procedure to date has not applied vertical acceleration concurrent with the horizontal acceleration. Therefore, a
pair of two horizontal components of the earthquake record are applied simultaneously to the
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computer model history load case. The orientation of the applied loads is then varied to determine the worst-case direction for design (since UBC does not provide guidance as to the
orientation of the earthquake along the principal axes of the building).
The response of the building is calculated by means of digital computer for each of the ground
motions, and the final design of the building shall be made so that the structure is safe in the event
that any of the ground motions were to occur.
Response of Buildings to Design Earthquakes
For each of the design earthquakes, the time history response of the high-rise building is calculated
by means of digital computer. The customary procedure is to calculate the six to ten lowest modes
of vibration, that is, their natural periods of vibration and their mode shapes. The time history of
each mode of vibration to the ground motion is then calculated. The summation of responses of all
the modes of vibration then give the building response. The maximum response of the parameter
of interest of the building when using commercial available software as ETABS, Sap 2000, Stadd
pro or Robot Structural must be scanned to determine the maximum inter-floor shear force at the
various story heights during the earthquake, the maximum overturning moments at the various
story heights, the maximum displacements of the floors, and the maximum acceleration at each
floor.
[But in SeismStruct, Combinations and Envelopes task allows you to set up groups of analyses,
and to use enveloping or averaging to get limit state usage (Demand/Capacity) ratios for nonlinear
performance assessment].
The foregoing quantities such as building lateral deflection, inter-story drift, shear force,
overturning moments, and acceleration at each floor are determined using ETABS or MIDAS Gen
for each of the design earthquakes and the appropriate design of the building is then made. These
are illustrated on the next five slides.
Bases for Selecting the Efficient Software
Due to faster solver system and fiber based concept among all software’s SeismoStruct software
is chosen to perform Nonlinear Dynamic Analysis. SeismoStruct is finite element package capable
of predicting the large displacement behavior of space frames and 3D buildings under static or
dynamic loading, taking into account both geometric nonlinearities and material inelasticity and is
capable to consider the whole plasticity along the concrete member length & depth giving a reliable
and accurate nonlinear analysis rather than other ones which dependent on the concentrated
plasticity modeling as Robot Structural, Sap 2000, Staad pro. & Etabs.
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To perform nonlinear time history analysis, ground motions directly applied to the model, it needs a suitable ground motions. Selecting ground motions should be accurate in nonlinear time history
analysis. An incremental iterative algorithm with the employment of NewtonRaphson procedures is used to obtain the solution. The dynamic time-history analysis is computed by direct integration of the equations of motion with the Newmark scheme.
Performance Criteria
Performance evaluation is carried out in terms of displacement profile and drift limit from
performance criteria mentioned in ATC-40 and FEMA-356.
EXAMPLE – Full Assessment of Seven -Story RC Concrete Structure
Description, Material Properties & Modeling
This example describes the modelling of a full-scale, six-story, three-dimensional RC building, which was designed for gravity loads only. It has a plan and vertical irregularity as shown in Fig. 3, 4 &5. The presence of structural irregularities has an adverse effect on the seismic response of the structure.
• Columns geometrical dimensions and longitudinal reinforcement inadequate to satisfy the
biaxial bending and axial load demand.
• Weak column-strong beam condition led to the formation of the plastic hinges in the
columns
• The lack of stirrups on joints, the poor local detailing and the insufficient columns
confinement have increased the risk of brittle and local failure mechanisms
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Fig. 3- Plan view for floors 1 and 2
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Fig. 4- Plan view for floors 3,4,5 and 6
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Fig. 5- 3D view
The structure consists of 12 RC columns with 600 × 600 mm cross section and longitudinal
reinforcement 12 Ø 20. & the stirrups for both columns and beams are 5 Ø 10/m. All connected
beams have the same geometry (400 × 750 mm). The geometry and reinforcement of the column
and beams are shown in Fig. 6 and 7 respectively.
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Fig. 6- Geometry and reinforcement of the RC column (SiesmoStruct)
Fig. 7- Geometry and reinforcement of the RC beams (SiesmoStruct)
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The Mander et al. concrete model is employed for defining the nonlinear behavior of concrete
material with the following parameters:
The properties of the used concrete (fc = 20 MPa) in SesimoStruct are as follows: :
The properties of the used steel reinforcement(fy = 444.4 MPa) in SesimoStruct are as follows:
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Analysis
The used analysis is nonlinear dynamic time history analysis which needs also a time history of
acceleration of all the possible earthquakes that can occur in the site. To assessment the seismic
capacity of the building and to do performance based seismic analysis. The building will exposed
to 3-directional time history ground motion at supporting nodes simultaneously (Fig.8).
Fig. 8 – FE Model of the building subjected to 3-directional time history ground motions at
supporting nodes (SeismoStruct)
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Performance Criteria
According to ACT-40(Table 1); under the 3-directional time history ground motion, the building is considered structurally acceptable and stable, because it lies in immediate occupancy(IO) range. Also, according to Table 2[Ghobarah], the inter-story drift limit of the upper node which has highest displacement (42.8 mm see to Fig. 9) is 0.13 % which refers to slight damage.
Fig. 9- Maximum lateral displacement in X- direction due to 3-directional time history ground
motion
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Table 1 - Deformation Limits (ACT 40)
Inter-Story
Drift Limit
Performance Level
Immediate
Occupancy(IO)
Damage Control Life Safety
(LS)
Structural Stability
or (CP)
Max.
Total Drift
0.01 × h 0.01- 0.02 × h 0.02 × h (0.33×Vi /Pi)× h
Max.
Inelastic Drift
0.005 × h 0.005-0.015 × h no limit no limit
Notes for ACT-40: o Once the running the nonlinear dynamic time history analysis, the overall
performance of the structure can be checked to see whether it matches the required
performance level, based on inter-story drift limits specified in ATC40, which are
– 0.01×h for immediate occupancy (IO),
– 0.01- 0.02× h for damage control
– 0.02× h for life safety(LS), and
– (0.33 × Vi / Pi) × h or (0.33 × base shear ∕ building weight ) × h for structural
stability or Collapse Prevention (CP)
Where, h = height of the building
Vi = the total calculated lateral force in story i
Pi =the total gravity load (DL+LL) at story i
– The performance level is based on the importance and function of the building. For
example, hospitals and emergency services buildings are expected to meet a
performance level of IO.
– For structural stability, the max. total drift limit is not very restrictive, many
engineers would find this level of drift unacceptably high, especially for an older
building with questionable details. Lower limits may be appropriate in many cases.
Table 2 - Limit-state drift ratio limits for bare RC moment resisting frames according to Ghobarah
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Ɵmax : maximum inter-story drift
Inter-story drift = [lateral displacement (at a certain node) of story (i) - lateral displacement
of story (i-1)] / height of floor
Retrofitting Works Design
After nonlinear dynamic time history analysis of the existing building, the failed RC columns by
diagonal shear cracking which appears in a brown color (Fig. 10) must be retrofitted. SeismoStruct contains in retrofitting module, different FRP wrapped types, in this model, Sika FRP sheets wrap (Sika Wrap230C )will use to retrofit the failed RC columns. Technical data and
properties of the used FRP sheets as shown in Fig. 11.
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Fig. 10- Brown color indicating to serious diagonal shear cracks
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Fig. 11- Technical Data of Sika Wrap230C ( Sesimostruct)
SeismoStruct can retrofitted the failed RC elements by FRP sheets. Fig. 12 shows that the retrofitted model can sustain the applied loads from 3-directional time history ground motions
without any damage.
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Fig. 12- Retrofitted Model
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References
1. ATC. Seismic evaluation and retrofit of concrete buildings—volume 1 (ATC-40). Report
No. SSC 96- 01. Redwood City (CA): Applied Technology Council; 1996.
2. FEMA356 (2000), NERPH Recommended Provisions for Seismic Regulations for New
Building, Seismic Safety Council for the Federal Emergency Management Agency,
Washington, D.C.
3. Ghobarah A. On drift limits associated with different damage levels. In: International
workshop on performance-based seismic design, June 28–July 1, 2004.
4. Mander, J.B., Priestley, M.J.N, and Park, R. "Theoretical stress-strain model for confined
concrete," Journal of Structural Engineering, American Society of Civil Engineers,
Vol.114, No. 8, 1988, pp. 1804-1825.
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