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Help Page for
the Java-Powered Simulation for Earthquake Engineering |
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Introduction
Welcome to the help page of the Java-Powered Simulation
for Earthquake Engineering.
This Virtual Laboratory (VL) illustrates three
important concepts in Earthquake Engineering; response spectrum analysis of
high-rise buildings, design spectrum, and force reduction factor. The user
interface of the VL consists of the three tabs in which those concepts are
shown. The purpose of each tab is as follows.
1. Response spectrum analysis in high-rise buildings
In the first tab, users are allowed to compare
the responses obtained using the time history and response spectrum analyses
in a high-rise building. Although only the first few modes are considered
in the structural design, contribution from the higher modes is not ignorable
especially in the high-rise buildings. Users can selected the number of modes
to be considered, and verify the effect on the structural responses by comparing
the shear force distributions calculated from the time history and response
spectrum analyses. The VL utilizes a multi-story shear
building model as a test bed modeled using the Timoshenko beam theory, and
provides essential parameters for the structure, time history and response
spectrum analyses.
2. Comparison of design and response spectra
The second tab compares a design spectrum of
a specific area with response spectra calculated from the historical earthquake
records in the same area. Users can verify the design spectrum is in most
cases greater than the response spectra.
3. Force reduction factor
In the third tab, users can plot the force
reduction factor which varies with the natural period but is normally assumed
as a constant. This VL is focused on ductility among a number of factors that
affect the force reduction factor. Hysteretic bilinear stiffness model is
used to depict nonlinearity of the structure with the ductility selected by
users.
The VL provides useful buttons which can be found
at the bottom of the control panel in each tab. The user can save all data
by clicking the Save Data button. In addition, the VL displays an animation
based on the building response, which gives users a better understanding of
dynamic analysis.
This document offers a description of how to operate and use
the Java-Powered Simulation for Earthquake Engineering as well some technical
background. Homework problems (or exercises) are also suggested and references
are provided.
How to Use the Virtual
Laboratory
As shown in Figure 1,2, and 3 the program
interface consists of the three tabs, response spectrum analysis of high-rise
building, design spectrum, and force reduction factor. Each tab consists of
control panel, animation panel (only for the first tab), and plot panel.
Response Spectrum Analysis of High-rise
Building
In this tab shown in Figure 1, response spectrum analysis
is conducted for a high-rise building to verify the effect of the higher
modes. Users can compare the shear force distributions obtained from the
response spectrum and time history analyses in the plot panel. The parameters
necessary for the analyses are provided on the control panel, located
on the right of the simulator. Animation of the building can be seen in
the animation panel.
| Plot panel |
Animation panel |
Control panel |
|
| Plot panel |
Animation panel |
Control panel |
Figure
1. User interface (Response spectrum analysis of high-rise building)
Control Panel
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Number of floors: total number of floors. (The default
value is 40.)
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Modal Damping Ratio: viscous damping ratio of all
modes. (The default value is 0.03.)
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Material and Section: Young's modulus, shear modulus,
mass density, sectional area, and moment of inertia can be specified.
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Pseudo Acceleration: natural frequencies and pseudo
acceleration associated with structural parameters. These values will
be updated automatically if structural parameters are changed.
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Select mode: The user-specified modes will be considered
in the response spectrum analysis. (The default values are 1 and 2.)
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Modal Combination: modal combination rule that is used
in the response spectrum analysis. (The default is SRSS.)
-
Select Ground Motion: Earthquake record that is used
to excite the structure. (The default is El Centro.)
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Number of Modes: total number of the lower modes that
is used in the time history analysis.
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Absolute Motion displays the response
of the structure from an inertial reference frame. Thus, the ground
is seen moving.
-
Relative Motion displays the response
of the structure from a reference frame attached to the ground.
Plot Panel
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y(t): time history of the ground excitation and the
corresponding measured responses
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x-y: response vs. response plot
Comparison of Design and Response
Spectra
The design spectrum is derived as the envelope of response
spectra from a large number of possible earthquakes. Thus, the response
spectra from the site specific natural records shall be less conservative
than the design spectrum in the area as can be found in the plot panel
in Figure 2. This is not an issue of smoothing but the basis of the spectra
in the code. The design spectrum is calculated based on the International
Building Code (IBC) 2006.
| Plot panel |
Control panel |
|
| Plot panel |
Control panel |
Figure
2. User interface (Comparison of design and response spectra)
Control Panel
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Area: El Centro area is selected for this simulator.
The design spectrum and all historical earthquake records are obtained
in this area.
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Site Class: Classification of a site based on the
types of soils as defined in Table 1. (The default is D.)
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Spectral Accelerations: Ss and
S1 are the mapped spectral accelerations for
short and 1 second periods, respectively. Ss
of 1.5 and S1 of 0.6 are for El Centro area.
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Site Coefficients: Fa and Fv
are determined by the site class, Ss, and S1
as shown in Table 2 and 3.
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Damping Ratio: Viscous damping ratio. 5% damping
ratio is used.
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Site Specific Ground Motions: Site specific historical
records used to obtain response spectra. By clicking the button,
a dialogue window will pop up in which users can select the ground
motions.
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Damping Ratio: Viscous damping ratio of the single
degree of freedom (SDOF) model. The same damping ratio of 5% is
used.
Table 1. Site class and soil profile.
(See Table 1613.5.2 in IBC 2006 for more information.)
Site Class |
Soil Profile Name |
A |
Hard rock |
B |
Rock |
C |
Very dense soil and soft rock |
D |
Stiff soil profile |
E |
Soft soil profile |
Table 2. Values of site coefficient Fa.
(See Table 1613.5.3(1) in IBC 2006 for more information.)
Site Class |
Mapped Spectral
Response Acceleration at Short Period |
Ss≤0.25 |
Ss=0.50 |
Ss=0.75 |
Ss=1.00 |
Ss≥1.25 |
A |
0.8 |
0.8 |
0.8 |
0.8 |
0.8 |
B |
1.0 |
1.0 |
1.0 |
1.0 |
1.0 |
C |
1.2 |
1.2 |
1.1 |
1.0 |
1.0 |
D |
1.6 |
1.4 |
1.2 |
1.1 |
1.0 |
E |
2.5 |
1.7 |
1.2 |
0.9 |
0.9 |
Table 3. Values of site coefficient Fv.
(See Table 1613.5.3(2) in IBC 2006 for more information.)
Site Class |
Mapped Spectral
Response Acceleration at 1-Second Period |
S1≤0.1 |
S1=0.2 |
S1=0.3 |
S1=0.4 |
S1≥0.5 |
A |
0.8 |
0.8 |
0.8 |
0.8 |
0.8 |
B |
1.0 |
1.0 |
1.0 |
1.0 |
1.0 |
C |
1.7 |
1.6 |
1.5 |
1.4 |
1.3 |
D |
2.4 |
2.0 |
1.8 |
1.6 |
1.5 |
E |
3.5 |
3.2 |
2.8 |
2.4 |
2.4 |
Plot Panel
The design and response spectra are shown in this
panel. The figures are automatically updated whenever users change
the parameters in the control panel.
Force
Reduction Factor
The force reduction factor in earthquake engineering can
be determined by blah blah, including strength reduction, ductility. In
this VL, only ductility is considered and other factors are assumed as
unity. To calculate the force reduction factor, linear and nonlinear dynamic
analyses of a SDOF system with different ductility values that can be
selected by users. By dividing the elastic response spectrum by the inelastic,
the force reduction factor is obtained and shown in Figure 3.
| Plot panel |
Control panel |
|
| Plot panel |
Control panel |
Figure 3. User interface (Force Reduction
Factor)
Plot Panel
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Earthquake: This drop-down menu allows users to select
a ground excitation among four historical earthquake records. The
default is the N-S component of the 1940 El Centro earthquake.
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Damping: Viscous damping ratio of the SDOF system.
(The default value is 0.05.)
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Min. Period: Lower bound in which the response spectra
is calculated. (The default value is 0 second.)
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Max. Period: Upper bound in which the response spectra
is calculated. (The default value is 3.0 seconds.)
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Period Step: Increment in the period axis of the response
spectra. Too small value might result in a long computation time when
users click the "Update Spectra" button down in the control
panel. (The default value is 0.05 second.)
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Ductility: Maximum displacement divided by the yield
displacement. (The default values are 2.0 and 3.0)
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Post yield Stiffness Ratio: Post yield stiffness divided
by the initial stiffness. (The default value is 0.0 which means perfect
plastic.)
Save
Figures and Data
The VL supports two saving options, one for figures and
the other for data. Figures shown on the response plot panels can be saved
by clicking any figure except the virtual building. Figures are saved as
PNG format. Users are also able to save all data by clicking the "Save
Data" button on the bottom of the control panel. (Response spectrum
analysis of high-rise building only)
The bilinear stiffness model
used in this simulator is found here.
Timosheno
Beam Theory
The coupled equations for the deflection y and
the bending slope φ can be written as
(Timoshenko 1955)
where
E = elastic modulus
G = shear modulus
I = moment of inertia
k = numerical shape factor for cross section
A = cross sectional area
γ = weight per unit volume
Let
where 
and L is the length of beam. The boundary conditions for this problem are
Then, the solution for Y(x) and Ψ(x) is as follows.
if 
if 
where
The force reduction factor is defined as
= elastic
response spectral ordinate
= inelastic
response spectral ordinate
Although there are other factors that contribute the reduction
factor such as the strength and redundancy factors, herein only ductility
is taken into account.
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Conduct the following experiment in the first tab. Use
the default damping ratio, material and sectional properties, ground excitation,
and the number of modes in the linear dynamic analysis.
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Plot and compare the shear force distributions from
the time history and response spectrum analyses for a 50-story building
with the modes from 1 to 2 in the response spectrum analysis. Use the
modes from 1 to 5 to see the shear force distributions.
-
Repeat the above example for a 5-story building. What
conclusion can be drawn?
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Observe the design and response spectra changing the site
class.
-
Plot the force reduction factor for the ductility values
of 2.0, 3.0 and 4.0 when the ground motion is Kobe earthquake.
-
Newman A (1996): Special Edition Using Java.
Que Cooperation, Indianapolis, IN.
-
Bruce Eckel (2003): Thinking in Java. Prentice
Hall.
-
Craig RR and Kurdila AJ, Fundamentals of Structural
Dynamics, John Wiley & Sons.
-
Press WH, Flannery BP, Teukolsky SA, Vetterling
WT (1987): Numerical Recipes: The Art of Scientific Computing.
Cambridge University Press.
-
Elnashai AS and Sarno LD (2005), Introduction to earthquake
structural engineering, CEE572 Lecture Note, University of Illinois
at Urbana-Champaign.
-
Timoshenko SP (1955), Vibration problems in engineering,
third edition, D. Van Nostrand Company, Inc., New York, N. Y., pp.329-331.
-
Huang TC (1961), The effect of rotatory inertia and of shear
deformation on the frequency and normal mode equations of uniform beams
with simple end conditions, Journal of Applied Mechanics, pp579-584.
Acknowledgements
The support of the
National Science Foundation through the Multidisciplinary Center for Earthquake
Engineering Research (MCEER) is gratefully acknowledged.
