Seismic loading provisions in most existing building codes focus on the minimum lateral seismic forces for which the building must be designed. Specifying the lateral forces alone is not enough to ensure that the desired level of performance will be achieved. A performance-based approach is desired in structural design where the structure is provided not only with adequate strength, but also appropriate deformability and damage tolerance for a given level of seismic hazard. Performance-based design (SEAOC, 1995) requires an accurate evaluation of performance of a structure at various stages in the design process and it requires reliable analysis of structures subjected to the design levels of loads. Although seismic design of buildings is performed based on the equivalent static loads method, current codes (NBCC, 2005) strongly recommend the use of dynamic analysis for the purpose of refinement in the design. Carrying out a detailed dynamic analysis of a structure using a number of earthquake Ground Motion Records (GMR) and constructing the performance profile of the structure in probabilistic terms, require enormous computing effort. Although the computing power of the modern computers is astounding, significant manual effort is needed in organizing the input and output data from a given analysis tool and extracting meaningful information out of the huge quantity of analysis data. It is necessary to develop simple tools to automate such analysis and extract relevant information from a large set of analysis data and this study presents a general scheme for that with the implementation to a particular analysis software, namely IDARC2D (2006), a special purpose software tool for modeling the dynamic behavior of Reinforced Concrete (RC) buildings subjected to earthquake ground motion.
Although there are a number of general purpose software packages available
for structural analysis and design, special purpose software tools are often
necessary to particular research needs. Since RC framed buildings are used in
the study, IDARC2D is used here as it is a specialized software with the capability
of analyzing earthquake damage in multistory RC buildings and has a number of
advanced analysis and modeling features which are not available in general purpose
analysis software (IDARC2D, 2006). However, IDARC2D lacks a user interface and
consequently, the input is written manually by the user to the text format and
the output is also given in text form to be read by the user. This method of
data input is cumbersome, especially if one plans to conduct dynamic analysis
involving a large number of earthquake ground motion records and multiple building
configurations and design choices. A set of interface tools have been developed
in the present study to simplify the data input and interpretation of the analysis
data. The tools presented here can be used for automating the input process
and post processing the output data to conduct a large scale simulation of earthquake
response of multi storey RC frame buildings.
To demonstrate the automation process developed here, a case study comprising a six storey RC frame building designed for Vancouver, Canada using the seismic provisions of the NBCC 2005 has been presented. The seismic performance of the building has been evaluated for a suite of eight simulated earthquake ground motion records compatible with the seismic hazard at Vancouver. To validate and compare the results obtained using IDRAC2D, the analyses have also been carried out using DRAIN2DX (Prakash et al., 1993) a well known program for inelastic dynamic analysis of two-dimensional frames. However, DRAIN2DX is more general purpose seismic response analysis software as compared to IDARC2D. Modeling RC frames using DRAIN2DX is difficult and a simplified model using the two-dimensional beam-column elements has been used here.
DESCRIPTION OF THE AUTOMATION TOOL FOR ANALYSIS AND DESIGN
As discussed earlier, a typical automation scheme for structural analysis comprises
the following three main components; pre-processor, analysis module and the
post-processor, as shown in Fig. 1. The pre-processor provides
the user interface, preferably a graphical one through which the user can define
the structural model, loads and support conditions. The pre-processing module
then validates the models and conveys necessary information to the analysis
module or engine. Once the analysis is completed, the output of that is processed
by the post-processor which is designed to present the results in desired format.
The post-processor may also be designed to process the output data from multiple
sessions of analysis, which is typical the dynamic analysis using multiple GMR
and compile the results to present the summary.
||Schematic representation of a typical scheme for analysis
In this study, this scheme has been implemented using the computer program
IDARC2D, which is an inelastic dynamic structural analysis tool used for detailed
modeling of reinforced concrete building frames. One of the important features
IDARC2D includes is automatic generation of the moment-curvature (M-Φ)
relation for beam and the axial force-moment (P-M) interaction curves for columns
given the section size and reinforcement details. It also has the option of
specifying the hysteretic behavior of the different elements of the structure.
The use of infill panels, transverse beams, shear walls, different brace types
is also another example of the many options available in this software. The
user can choose to perform time-history, push-over or quasi-static analysis
on the structure.
IDARC2D pre-processor: The pre-processor unit has been built using the Excel (Microsoft Corporation) and Visual Basic scripts. All input data are gathered in a Excel Workbook which provides appropriate forms with appropriate data labels to fill out with necessary data. The user can edit and change the editable fields and finally when the complete set of data for structural model definition, material properties, analysis options etc. are entered into the preprocessor, the user can instruct the pre-processor to prepare the IDRAC2D input files in text format by clicking on th”Write Input” button from the user interface (Fig. 2). After the input file is written, the user may run the IDARC2D program to generate the output files. The excel file contains seven worksheets where all data should be filled.
IDARC2D post-processor: Dealing with output files on the other hand
requires reading a lot of data and generating graphs for visualising the response
of the structure. This is done here using a graphical user interface developed
in MATLAB as shown in Fig. 3. The post-processing interface
developed in MATLAB scans through the output files generated by IDARC2D and
provides tools for plotting a number of response quantities. The program can
plot push-over curves, mode shapes, inter-storey drifts and time-history graphs.
||The user interface for IDRAC2D pre-processor
||The user interface for IDRAC2D post-processor
||Schematic architecture of the analysis automation system for
||P-M Interaction curve generator excel worksheet
It also organizes the output from multiple sessions of dynamic analysis with
a number of earthquake GMR into summary tables or graphs as shown in Fig.
3 (top right corner). The data processed by the post-processor can also
be presented in the Excel format.
Figure 4 shows the schematic architecture of the pre and
post processing units as described earlier. The pre-processor engine is based
on visual basic scripts or macros for manipulating an Excel workbook that gathers
the input data necessary for IDARC2D. The input form and data cells in Excel
are dynamically organized based on the type of analysis or the problem size.
Once the data is gathered through the preprocessor, the user can instruct it
to make appropriate data files in text format for IDARC2D. IDARC2D produces
a number of output text files with general information and specific structural
response, such as, storey drift, storey hysteris etc. The MATLAB based post-processor
scan through the IDARC2D output files and produces necessary graphical output
in order to visualize the analysis results, such as mode shapes, push-over curve,
time-history of displacement or drift etc.
Generating beam-column properties: Two Excel files are created specifically for designing and calculating the capacity of rectangular reinforced concrete sections subjected to simple bending. Another Excel file is designed with the aid of VB scripts to generate the Axial Load-Bending Moment (P-M) interaction curves for rectangular reinforced concrete sections with uniform reinforcement. The input to these programs are the section size, reinforcement details, materials strength and resistance factors as defined in NBCC (2005). It must be noted that these tools are not required for IDARC2D analysis as the information produced by them can be internally generated by IDARC2D based on the section size, material properties and the reinforcement details. These tools are meant to be used with DRAIN2DX which does not have the capability to generate them internally.
Figure 5 shows a screens hot of the Excel worksheet to generate
the interaction diagram. The advantage of this worksheet is that the user has
the freedom of choosing the strength reduction factors for concrete and steel.
The modulus of elasticity of concrete and steel are also specified by the user.
The sectional dimensions and reinforcement are among the input parameters as
well as position of the reinforcing steel. The stress-strain distribution of
concrete is represented by an equivalent stress block and the crushing strain
of the concrete is specified by the user. After all the data are entered, the
P-M interaction curve is generated automatically by pressing the Draw Diagram
button. First, the output data is written in another worksheet labeled Output
Data which is linked to the interaction diagram.
CASE STUDY-A SIX STOREY RC FRAME BUILDING IN VANCOUVER
The use of the pre and post processor has been demonstrated in the following
example. A six storey building in Vancouver has been designed using the NBCC
(2005) seismic provisions. The geometric details of the building are shown in
Fig. 6. The building has several 6 m bays in the N-S direction
and 3 bays in E-W direction. The E-W bays consist of two nine-meter office bays
and a central 6 m corridor bay. The storey height is 4.85 m for the first storey
and 3.65 m for all other storeys. The building is composed of a set of parallel
frames equally spaced 6 m apart. A typical intermediate frame as shown in Fig.
6 has been considered for the detailed design and analysis. The chosen cross
sections of the columns and primary beams resulting from the design are shown
in Table 1. All secondary beams are assumed to be of size
300x500 and the slab thickness is 120 mm.
Seismic provisions of NBCC 2005: The 2005 edition of NBCC allows the
use of the equivalent static load method in the structural design against earthquake
excitations. The seismic hazard is expressed in terms of a Uniform Hazard Spectrum
(UHS), which provides the maximum expected spectral acceleration Sa
of a Single-Degree-Of-Freedom (SDOF) system with 5% damping. The elastic base
shear, Ve for a building with the single-degree-of-freedom system
can be obtained by multiplying the spectral acceleration S(T) corresponding
to the fundamental period of the building, Ta with the weight of
the building, W. Considering the ductility capacity, the over-strength, the
higher mode effects and the importance of the structure the design base shear
V is given by Eq. 1:
||Accounts for higher mode effect,
||The importance factor
|Rd and Ro
||Account for ductility and overstrength, respectively.
The design base shear is distributed along the height of the building according
to provisions NBCC (2005).
||Beam and column sections
||Building layout: (a) plan and (b) elevation
Design of the building frame based on NBCC 2005: The building has been
designed to resist the effect of the equivalent lateral loads combined with
gravity loads; dead and live. The elements of the structures are designed based
on the most critical load combination. The following load combinations have
been used in the design: (a) the lateral load combination (D + 0.5L + E) and
(b) the gravity load combination (1.25D+1.5L), where D is the dead load, L is
the live load and E is the equivalent static earthquake force. The design base
shear based on the NBCC 2005 provisions is 424 kN and the ductility and overstrength
factors are 4 and 1.7, respectively. The yield stress, fy for reinforcing
steel and the 28 day concrete compressive stress, f′c are assumed
to be 400 and 30 MPa, respectively. Live load on the roof is assumed to be 2.2
kN m-2 on other floors it is 4.8 kN m-2 on the corridor
bay and 2.4 kN m2 on the other bays.
The static design however involves a few iterations until a safe and economic
cross section is reached for all elements. Since the calculation of the base
shear according to the NBCC (2005) requires the fundamental period of the structure,
which is calculated using an empirical formula, the fundamental period should
be checked against the one obtained from the modal analysis after the first
design iteration. Usually the modal analysis of the bare frame structure gives
a longer period for the fundamental mode of vibration as compared to the period
computed using the empirical formula suggested in the code. If the fundamental
period obtained from modal analysis is greater than the one obtained from the
empirical formula, according to NBCC (2005), the design base shear needs to
be revised to achieve a more realistic design load. The revision of the base
shear should be based on a period which is 50% higher than that obtained from
the empirical formula of NBCC (2005) or the one obtained from the modal analysis,
whichever is less. In this case, the code defined formula (T = 0.075(hn)3/4)
gives a period of 0.78 sec, while the modal analysis gives a value of 1.68 sec,
which is more that 1.5 times the code defined value (1.17 sec). Thus the building
needs to be redesigned for the base shear calculated using a period of 1.17
sec. The reinforcement details of the primary beams and columns are given in
Table 1. First four mode shapes of the building are shown
in Fig. 7a and the corresponding periods are 1.68, 0.54, 0.3
and 0.2 sec.
Push-over analysis: A force and displacement controlled push-over analysis
is performed to simulate the structures response to incremental lateral
loading. The push-over analysis serves as an important tool for estimating the
strength and ductility capacities of the structure. The push-over curve obtained
using the IDARC2D and DRAIN2DX are shown in Fig. 7b.
In the push-over curves as shown in Fig. 7b, the base shear
coefficient (V/W) is defined as the ratio of the base shear, V to the total
tributory weight, W for the building frame. In this case, the design base shear
coefficient is equal to 0.0733. The resulting push-over curves show that first
occurrence of hinge formation in the frame element corresponds to a base shear
coefficient of approximately 0.1 when IDARC2D is used and 0.09 when DRAIN2DX
Its clear from Fig. 7b that both programs give similar
initial response, however there is a difference between the results in the post-yielding
zone. The point where the maximum inter-storey drift reaches 2.5% (in this case
this occurs at the first storey level) is marked on both the curves.
||Analysis results: (a) Mode shapes and (b) Push-over curve
This point indicates the inter-storey drift limit in NBCC 2005 for collapse
prevention performance. The maximum value of the inter-storey drift of 2.5%
corresponds to a base shear coefficient of 0.139 and a roof drift (overall deformation)
of 1.33% when IDARC2D is used and the corresponding base shear coefficient is
0.123 and the roof drift is 1.26% when DRAIN2DX is used.
Dynamic analysis: The roof drift and inter-storey drift are important
parameters to describe the overall deformation and performance of the structure.
The roof drift or the total drift is the roof displacement expressed as a percentage
of the total height of the building, while the interstorey drift is the differential
displacement between current level to the one immediately below and expressed
as the percentage of storey height. A dynamic analysis is performed using eight
artificial ground motion records compatible with the seismic hazard at Vancouver
(Tremblay and Atkinson, 2001).
||General properties of the ground motion records
||Results: (a) Maximum inter-storey drifts and (b) Time-history
curve (Storey 1, S1)
Four of those records of long duration, while the other four records are of
short duration. The properties of these ground motions are shown in Table
2. The maximum inter-storey drifts of all floors along with the envelope
and mean values have been compiled and plotted for all eight records (Fig.
8a). The maximum inter-storey drifts also occur at the first storey level
and are equal to 2.07 and 1.46% due to the long duration and short duration
records, respectively. The time-history of the first storey produced by the
ground excitation, S1 is also plotted (Fig. 8b) to show the
displacement of this storey during the earthquake period and a few seconds later.
The total duration of the earthquake is 8.53 sec. It is clear from the time-history
graph that the response of the first floor is maximized during the excitation
period. However, after the ground motion stops, a plastic deformation of almost
0.37% (17 mm) is observed.
It should be noted that the ground floor is almost a third longer than the
rest of the floors and the ground floor columns have the same cross section
as the rest of the building columns. Increasing the ground floor column cross
sections could reduce the resulting drift to some extent. The maximum roof drift
is also calculated for all eight records and shown in Table 3.
The envelope value is found to be 0.98%, which occurs due to ground motion record
A collection of sixteen actual records are used in the nonlinear dynamic analysis.
Some of these records were selected form the seismic database of McMaster University,
Canada (Naumoski et al., 1988) and other records were selected from the
database of Pacific Earthquake Engineering Research Center (PEER, 2007). The
records were selected based on the peak spectral acceleration to peak velocity
ratio (A/V ratio) similar to the seismic motion is Vancouver, which is close
to 1. These records are scaled based on the seismic hazard spectrum for Vancouver.
The characteristics of the actual records used in the analysis before scaling
are shown in Table 4, where, A and V represent the spectral
acceleration and velocity of a GMR, respectively. As scaling affects the dynamic
response of the structure (Naumoski et al., 2004), the following two
methods of scaling are used here to identify the sensitivity of the response
to scaling: the ordinate method and the partial area method (Fig.
9). First, spectral analysis is performed for each record. The response
spectrum is then scaled to match the design spectrum of Vancouver.
The ordinate method of scaling is performed based on the fundamental period of vibration of the structure, as explained here with reference to Fig. 9a. The response spectral acceleration corresponding to the fundamental period (Sa2) is scaled to the value of the design spectral acceleration (Sa1) corresponding to the same period. In other words all data points of the record are scaled based on the factor Sa1/Sa2.
On the other hand, the partial area method of record scaling (Fig.
9b) is based on the first and second period of vibration of the structure.
The area (A2) under the response spectral acceleration curve between
1.2 times the fundamental period value and the second period value is scaled
to the corresponding area (A1) under the design spectral acceleration
curve between the same periods. All the data points of the record are scaled
based on the factor A1/A2. The response spectra of the
real GMRs scaled using the above two methods for the six-storey building is
shown in Fig. 10 and compared with the NBCC 2005 design spectrum.
Figure 11 shows the maximum inter-storey drifts of the building
frame produced by IDARC2D. The maximum Mean+SD values of the inter-storey drift
are 1.23 and 1.26% for the ordinate method and partial area method scaled records,
respectively, which occur at the first storey level. Similar values have been
produced using DRAIN2DX program as shown in Fig. 12, which
follow the same trend and orders of magnitudes for the inter-storey drift (mean+SD).
The difference in the maximum dynamic drift demand values calculated using IDARC2D
and DRAIN2DX are within 10% in all cases.
||Maximum roof drifts
||Ground Motion Records (GMR) from past earthquakes
||Methods used for scaling the ground motion records: (a) Ordinate
method, (b) Partial area method
||Comparison of the response sdpectra of scaled actual GMRs
with the NBCC 2005 spectrum: (a) Ordinate scaling and (b) Partial area scaling
||Inter-storey drift envelops using actual GMRs: (a) Ordinate
scaling and (b) Partial area scaling (IDARC2D results)
||Inter-storey drift envelops using actual GMRs: (a) Ordinate
scaling and (b) Partial area scaling (DRAIN2DX results)
The results are consistent with that using the synthesized records presented
||The article presents a pre and a post processor for the IDARC2D
computer program that is used for inelastic dynamic analysis of reinforced
concrete buildings. The tools developed herein are simple and easy to use,
so that the user can concentrate on the analysis rather than troubleshooting
the data file construction for the analysis program.
||The pre-processor has been developed using Visual Basic operated on an
Excel workbook, while the post-processor is based on the MATLAB environment.
||The pre and post processing tools developed here have been demonstrated
through a six storey RC frame building which has been designed according
to the National Building Code of Canada.
||The building is assumed to be located in Vancouver representing a high
level of seismic hazard. NBCC 2005 seismic provisions have been used in
the design. After the design phase, the building has been analyzed against
eight synthetic and sixteen real ground acceleration records corresponding
to the seismicity in Vancouver to determine its performance characteristics.
||The building is expected to resist collapse when subjected
to this level of seismic hazard and the maximum inter-storey drift value
should not exceed 2.5%. Since no inter-storey drift values exceeds 2.5%
and the structure did not collapse then the design is satisfactory.
||The IDARC2D results have been verified with that produced by DRAIN2DX.
For DRAIN2DX analysis, the RC elements have been modelled using simple beam-column
elements and to generate the properties of these elements based on the section
size and reinforcement details, a VB-Excel tool has been developed. The
results produced by IDARC2D and DRAIN2DX have been found to be comparable.
The FRDP research support provided by the Concordia University to the second author is gratefully acknowledged. The research presented here forms a part of the M.A.Sc. thesis at Concordia University by the first author under the supervision of the second author. The authors will also like to thank Mr. Wael Atassi, a graduate student at Concordia University for his valuable input.