Help Page for the JavaPowered Simulation for Nonlinear MultiStory Buildings 

Table of Contents 




Welcome to the help page of the JavaPowered Simulation for Nonlinear MultiStory Buildings.
It is common to design structures to behave nonlinearly under extreme load conditions, e.g. earthquakes and hurricanes. Therefore, it is important to instruct students or practitioners to better understand the effect of nonlinear behavior of buildings. This nonlinear dynamic analysis virtual laboratory (VL) has been developed for his purpose.
In this VL, users are given wide flexibility to perform dynamic analysis. Users can choose the number of stories, as well as select the floor mass, stiffness, and damping coefficients for each story. Four models, are provided to portray the behavior of the structure. These modes are: (a) linear stiffness and linear viscous damping; (b) linear stiffness and nonlinear powerlaw damping; (c) hysteretic stiffness using the BoucWen model and linear viscous damping; and (d) hysteretic bilinear stiffness and linear viscous damping. The same type of model is employed for all columns, but the parameters defining this model can be varied for each story. Sinusoidal and four historical earthquake excitations can be chosen for conducting the dynamic analysis.
This document offers a description of how to operate and use the JavaPowered Simulation for Nonlinear MultiStory Building, a picture of which is shown below, and also the technical background of this simulation. A number of "homework" problems (or exercises) are suggested and references are provided.
Response Frame Response Frame Control Panel Response Frame Response Frame
Figure 1. JavaPowered Simulation Applet
As shown in Figure 1, there are four response frames on the left of the user interface. On the right, there is a control panel for conducting structural analysis and changing parameters. There is also an animation panel which provides the animated response through a virtual building model. This panel is shown in Figure 2. The control panel and animation panel are interchanged with each other by clicking the “Show Virtual Model” or “Show Control Panel” button located at the lower corner of their panels. A description of each of these components is given below. Control Panel Located on the far right of the simulator, this panel is used to enter specific data for the structure and excitation. This panel also contains buttons to do calculation and animation and the button which links to this help page. Structure Parameters
Structure Models


Figure 2. Animation Panel




Figure 3. Mass Input Frame 
analysis results can be displayed. The default is to display the structural behavior
described by linear model.
Response and Excitation
Action Buttons
Animation Panel The animation frame, interchangeable with the control panel, shows the behavior of the multistory building under the specified excitation. Buildings, described using Linear Model, Nonlinear Damping Model, BoucWen Model and Bilinear Model, can be animated by the appropriate selection in the left choice of this frame. The user can also choose to animate absolute or relative motion of the structure:

Response Frames
There are four response frames on the left of the simulator. The functions of these four response frames are identical, except that the top left frame can also display the earthquake excitation. There is a selection button at the lower right corner of each frame. For the top left frame, this selection button brings up a dialogue box (shown in Figure 4) for user to select the earthquake excitation or response to display. For the other three response frames, the selection button brings up a similar dialogue box for a response selection only. Peak response information such as the maximum value of each response, peak reduction (= maximum peak of each case / maximum peak of Linear Model case * 100 (%)) is displayed in the bottom of this frame. On the top left of the simulator, the response frame can show current excitation signal, either in displacement or acceleration. Five historical excitation records are available for simulation:


Figure 4. Earthquake/Response Selection Frame 
Tokachioki (Hachinohe) Earthquake: Northsouth component recorded at Hachinohe City during the Tokachioki earthquake of May 16, 1968. The magnitude is 7.9 and the maximum ground acceleration is 0.2294g.
Northridge Earthquake: Northsouth component recorded at Sylmar County Hospital parking lot in Sylmar, California, during the Northridge, California earthquake of Jan. 17, 1994. The magnitude is 6.8 and the maximum ground acceleration is 0.8428 g.
Hyogoken Nanbu (Kobe) Earthquake: Northsouth component recorded at Kobe Japanese Meteorological Agency (JMA) station during the Hyogoken Nanbu (Kobe) earthquake of Jan. 17, 1995. The magnitude is 7.2 and the maximum ground acceleration is 0.8337g.
Definition of the Primary Parameters
N: total number of stories.
: mass of the ith floor.
: elastic stiffness of the ith floor.
: damping coefficient of the ith floor.
Mathematical Model
The equation of motion for a singlestory building (N = 1) is
The equations of motion for a multistory building (N > 1) are
The equation of motion for a singlestory building (N = 1) is
The equations of motion for a multistory building (N > 1) are
The equation of motion for a singlestory building (N = 1) is
The equations of motion for a multistory building (N > 1) are
In the above equations, the restoring force is defined as
in which is the solution of the following equation
, , , and are the shape parameters for the hysteresis loops. These parameters are defined here as
The equation of motion for a singlestory building (N = 1) is
The equations of motion for a multistory building (N > 1) are
In the above equations, the restoring force is defined as
and for i > 1
where and ; and are displacements relative to the the center of the hysteresis loop.Figure. 6 Illustration of Displacement and
Other Definitions
Spring Force: force related to stiffness only.Damping Force: force related to damping only.
Shear Force: summation of the shear and damping force.
For an 8story building, change the mass, stiffness and damping coefficients to achieve approximately a 1.0 Hz first natural frequency and 2% first damping ratio.
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Berg GV (1989): Elements of Structural Dynamics. Prentice Hall.
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The support of the National Science Foundation (ECL9701471) through the Multidisciplinary Center for Earthquake Engineering Research (MCEER) is gratefully acknowledged.