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Help Page for the Java-Powered Simulation for Nonlinear Two-Story Buildings |
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Welcome to the help page of the Java-Powered Simulation for Nonlinear Two-Story Buildings.
It is common to design structures to behave nonlinearly under extreme load conditions, e.g. earthquakes and hurricanes. To instruct students or practitioners to better understand the effect of nonlinear behavior of buildings, our research effort has focused on the development of the nonlinear dynamic analysis virtual laboratories.
In this simulation, the structure is modeled as a two-story building. Same analytical model are used to described the behavior of each story of the structure, while different parameters are allowed for different stories. Based on different models employed, this simulator consists of four cases: (i) linear structure with each story designed as linear model; (ii) nonlinear structure with each story designed as nonlinear damping model; (iii) nonlinear structure with each story designed as hysteretic bilinear model; (iv) nonlinear structure with each story designed as hysteretic Bouc Wen model.
The user is allowed to select different model to design the structure, to change the parameters of the structure and choose different earthquake ground motions to do analysis. This simulation is intended to be used to increase understanding and provide a conceptual "feel" for various parameter changes on the performance of nonlinear structures under different excitations.
This document offers a description of how to operate and use the Java-Powered Simulation for Nonlinear Structure, 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.
Fig. 1 Java-Powered Simulation Applet
There are four components in this simulator that can be modified by the user to design the structure and to evaluate the responses: (1) Control Panel; (2) Animation Frame; (3) Excitation Frame; (4) Response Frame. These are each identified on the above picture of the simulator.
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
Excitation Parameters
Response Parameters
Animation Frame
The animation frame, located in the upper left portion of the simulation window, shows the behavior of this two story structure under the specified excitation.
Structures, designed as Linear Model, Nonlinear Damping Model, Bouc Wen 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:
Excitation Frame
Located in the top center of the simulator, the excitation frame shows current excitation signal. Five historical excitation records are available for simulation:
Response Frame
There are two response frames, which are located at the bottom left corner and bottom center of the simulator. These two identical response frames facilitate the user to investigate the responses of different stories or the same story at the same time. It can show the displacement, velocity or acceleration of each story. It also can plot the displacement (or velocity) vs. shear force (or damping force, or spring force). 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.
Definition of the Primary Parameters
(kg)
(kg) 
(KN/m) 
(KN/m) 
(KN*s/m) 
(KN*s/m) 
, post
yielding stiffness
and yielding
force 
are defined as,
where
is the yield displacement (m).
Mathematical Model
The equations of motion for the structure with linear model are
where,
is the first floor structural displacement relative to the ground (m).
is the first floor structural velocity relative to the ground (m/s).
is the first floor structural acceleration relative to the ground (m/s2).
is the second floor structural displacement relative to the ground (m).
is the second floor structural velocity relative to the ground (m/s).
is the second floor structural acceleration relative to the ground (m/s2).
is the ground acceleration (m/s2).
The equations of motion for the structure with nonlinear damping model are
where,and
are the nonlinear damping involution coefficients of the nonlinear damping model for the first and second story, respectively.
The equations of motion for the structure with hysteretic Bouc Wen model are
where the restoring forces.and
are defined as
In the above equations,and
are the solutions of the following equations,
,
,
, and
are the shape parameters for the hysteresis loops. In this case, these parameters are defined here as
The equations of motion for the structure with hysteretic bilinear model are
where the restoring forces.and
are defined as
and
whereand
;
and
are displacements relative to the center of the hysteresis loop.
Fig. 3 Illustration of Displacement
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.
The support of the National Science Foundation under Grant No. CMS 95-28083 (Dr. S.C. Liu, program director), and the support of the Multidisciplinary Center for Earthquake Engineering Research (MCEER) are gratefully acknowledged. In addition, we would like to thank Prof. Yozo Fujino of the University of Tokyo for his help in securing the Kobe and Hachinohe earthquake records.
