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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 ibrahimhbrc@gmail.com

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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