Help Page for the Java-Powered Simulation for Earthquake Engineering


Table of Contents

 

Page created by Sung-Han Sim
Last updated on 1/1/2008


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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

Animation Panel

Plot Panel

 

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

  • Area: El Centro area is selected for this simulator. The design spectrum and all historical earthquake records are obtained in this area.

  • Site Class: Classification of a site based on the types of soils as defined in Table 1. (The default is D.)

  • 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.

  • Site Coefficients: Fa and Fv are determined by the site class, Ss, and S1 as shown in Table 2 and 3.

  • Damping Ratio: Viscous damping ratio. 5% damping ratio is used.

  • 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.

  • 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

  • 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.

  • Damping: Viscous damping ratio of the SDOF system. (The default value is 0.05.)

  • Min. Period: Lower bound in which the response spectra is calculated. (The default value is 0 second.)

  • Max. Period: Upper bound in which the response spectra is calculated. (The default value is 3.0 seconds.)

  • 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.)

  • Ductility: Maximum displacement divided by the yield displacement. (The default values are 2.0 and 3.0)

  • 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)

Technical Backgrounds

Mathematical Model

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

Force Reduction Factor

The force reduction factor is defined as

where

= 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.

Homework


References


Acknowledgements

The support of the National Science Foundation through the Multidisciplinary Center for Earthquake Engineering Research (MCEER) is gratefully acknowledged.


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