EDUSOFT PACKAGE FOR STRUCTURAL ENGINEERING

Web-based Educational Material using JAVA for Structural Dynamics

C. G. Panagiotopoulos

, G. D. Manolis

and A. Athanatopoulou

Department of Continuum Mechanics, University of Seville, Camino de los Descubrimientos, Seville, Spain

Department of Civil Engineering, Aristotle University, Panepistimioupolis, Thessaloniki, Greece

Keywords:

Structural Dynamics, Web-based Applications, Single Degree-of-freedom Systems, Multiple Degree-of-

freedom Systems, Modal Analysis, Time History Analysis, Earthquake Spectra, Multi-story Buildings.

Abstract:

In this work, we present the construction of an integrated, web-based software package offering structural dy-

namics analysis capabilities for use by both undergraduate and graduate students in civil engineering programs

who specialize in earthquake engineering. The software package is built on a Java platform and comprises ﬁve

modulus, focusing on the analysis of single and multiple degree-of freedom systems, modal analysis of 2D

and 3D frames, and earthquake spectra construction.

1 INTRODUCTION

Greece is the most earthquake-prone country in the

EU, so infrastructure built must conform in terms of

structural design to the European code EC8 (CEN,

2004). To this end, Civil Engineering departments in

Greece have been offering courses in structural dy-

namics and earthquake engineering (Chopra, 2007)

since the 1980’s. Two difﬁculties are encountered

here: (i) students must have a good structural analysis

background from past semesters and (ii) any mean-

ingful examples that must be worked out carry a large

volume of computation, often necessitating the use of

ﬁnite element packages that turns out to be cumber-

some because the structure has to be modelled a pri-

ori.

In this work, we develop versatile, easy to use ed-

ucational tools for solving problems in structural dy-

namics. The web turns out to be the preferred way

of access by setting up a dedicated electronic address

as http://edusoft.civil.auth.gr, “edusoft” being an um-

brella address containing a number of application pro-

grams. Access to “edusoft” is free, unlimited and

applications are open-source under the GPL license,

which obviates the need to register users and at the

same time precludes unauthorized external use. Un-

der code numbers TE1800 and TE 2400 for the Dy-

namics of Structures I and II courses, we have the ﬁve

modules (“jesdof”, “espec”, “jframe”, “jsisma” and

“jTframe”) described herein. Once accessed, the en-

vironment is interactive and good quality graphs as

as well as real time animation of the response are

produced. We note that a Java runtime environment

(JRE) has to be activated in the receiving computer

for the programs to function (Gosling et al., 2005),

and the language of application is Greek.

It should be mentioned here that development

of educational packages on various types of elec-

tronic platforms is an ongoing activity. As exam-

ples, we mention diverse work ranging from that of

(Katsanos et al., 2011) on seismic design of rein-

forced concrete buildings based on the Matlab plat-

form for professional engineers and that of (Sobha-

ninejad et al., 2011) on integrated earthquake simula-

tion comprising hazard quantiﬁcation, disaster quan-

tiﬁcation and post-earthquake recovery for use by

government agencies and planners.

Finally, two object-oriented, open source software

frameworks that create both parallel and serial ﬁnite

element computer applications for structural response

to dynamic loads such as earthquakes are OpenSees

(http://nees.org) and Nemesis (http://www.nemesis-

project.org) projects. These platforms are written in

C++ and utilize Fortran numerical libraries as well

as interpreted/scripting languages (i.e., Tcl, Pyhton,

etc.). However, the scale of computation and model-

ing details are vastly higher compared to our work,

and requires from the user competence in dynamic

structural analysis.

299

G. Panagiotopoulos C., D. Manolis G. and Athanatopoulou A..

EDUSOFT PACKAGE FOR STRUCTURAL ENGINEERING - Web-based Educational Material using JAVA for Structural Dynamics.

DOI: 10.5220/0003901402990303

In Proceedings of the 4th International Conference on Computer Supported Education (CSEDU-2012), pages 299-303

ISBN: 978-989-8565-07-5

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

2 SDOF MODULE “JESDOF”

The most fundamental concept in structural dynam-

ics is the single degree-of-freedom (SDOF) oscilla-

tor, whose understanding is crucial for students. This

was the rationale behind the development of software

module “jesdof”. More speciﬁcally, four subcate-

gories of data must be deﬁned: (a) elastic proper-

ties (stiffness), mass and energy-loss (damping); (b)

initial conditions for the displacement and velocity;

namic loading), either as an ASCII ﬁle containing dis-

crete values at equally spaced time intervals, or by a

mathematical expression; and (d) parameters associ-

ated with the time integration algorithm used to nu-

merically solve the governing differential equation of

the system.

The governing differential equation for dynamic

equilibrium is

m¨x(t) + c˙x(t) + kx(t) = F

f(t) (1)

where m, c, k are the mass, damper, and stiffness (in

tons, kN-sec/m and kN/m, respectively) of the struc-

tural system, while x(t) (in m) is its response to a

dynamic load of magnitude F

(in kN) and dimen-

sionless time variation f(t). Note that overdots de-

note derivatives with respect to time t. Furthermore,

the natural frequency and fundamental period of the

SDOF system are ω

= k/m, T = 2/ω

(in rad/sec and

sec, resp.). It is standard practice to deﬁne a dimen-

sionless damping ratio ζ = c/2mω

in lieu of damper

values. Finally, the closed form solution of the SDOF

is given by Duhamel’s integral as

x(t) = x

cos(ω

t) + ( ˙x

/ω

)sin(ω

t) +

f(t)sin



(t − τ)



dτ (2)

where x

, ˙x

are initial displacement and velocity of

the system, while x

= F

/k is its equivalent static

displacement. For ground accelerations ¨x

(t), the

forcing function becomes F(t) = −m¨x

(t) and the

SDOF kinematics are understood to be relative to the

ground motion. Solution is accomplished through nu-

merical integration of Eq. 2 using the Newmark beta

algorithm, with the time interval of interest subdi-

vided into N increments of size equal to or less than

T/10. The structural response is given in a simple

text area. Finally, the user may visualize the motion

of the system in the graph area of the GUI by select-

ing as abscissa and ordinate variables in combination:

time, external force, displacement, velocity and accel-

eration.

3 RESPONSE SPECTRA “ESPEC”

This application produces elastic response spectra

from ground motion recordings, deﬁned as the plot

of maximum response (for either kinematic or force

variables) versus frequency (or period) of all possi-

ble SDOF systems under a speciﬁc type of external

force (usually a seismically-induced ground motion).

More speciﬁcally, response spectra are parametric in

terms of damping (e.g., ζ = 0− 10%) and are com-

puted from Duhamel’s integral of Eq. 2 by varying

the natural period of an SDOF system so as to sweep

an acceptable range that corresponds to real struc-

tures, i.e., 0 ≤ T ≤ 3.0 (in sec). Following computa-

tion, the results may be presented as absolute pseudo-

acceleration, relative pseudo-velocity or relative dis-

placement related as

= ωS

= ω

(3)

The above an exact relation for a damping ratio of

zero and approximate otherwise. Module “espec” uti-

lizes the Newmark-beta numerical integration algo-

rithm for integrating the equation of motion in time.

4 3-STORY FRAME “JFRAME”

Application module “jframe” does modal analysis of

a simple three story plane frame that translates into a

three DOF system, whose properties are user deﬁned

as the elastic and inertial characteristics plus the ge-

ometrical conﬁguration. Upon entering the input pa-

rameters, this program module computes and presents

in simple text area the following fundamental data:

stiffness matrix, mass matrix, period and frequency

associated with each eigenmode, the components for

each eigenvector, plus the participation factor, gener-

alized mass and effective mass corresponding to each

eigenmode. The underlying computation procedures

are based on the ﬁnite element method, but this does

not require any detailed knowledge from the part of

the students. Finally, there is an option to specify

an acceleration response spectrum, in which case the

program proceeds to calculate the spectral pseudo-

acceleration, relative pseudo-velocity and the relative

displacement for each eigenmode. More speciﬁcally,

the governing equation of motion for a multiple DOF

system is Eq. 1 again, except that the quantities of

interest are now matrices and vectors (of size N, the

number of independent DOF) in lieu of scalars. Of

course, the number of eigenvalues (natural frequen-

cies) and eigenvectors (corresponding modal shapes)

recovered is again N.

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5 1-STORY 3D FRAME “JSISMA”

Module “jsisma” focuses on a single story, 3D build-

ing that comprises an arbitrary number of vertical

stiffness (column) elements, whose position and me-

chanical properties are speciﬁed by the user, plus a

heavy ﬂoor slab. The column elements may be inex-

tensional or may have zero resistance to torsion. The

ﬂoor slab is considered to act as a rigid diaphragm

in the horizontal plane. There are also two options

concerning its out-of-plane rigidity, namely ﬂexible

or rigid. The set of output parameters computed by

this module are stiffness and mass matrices, the co-

ordinates of elastic centre and the inertial radius, the

period, frequency and coordinates of each eigenvec-

tor, and the coordinates of modal poles. The difﬁ-

culty with space frames is the correct deﬁnition of

their stiffness and masses, once the dominant mode

of deformation motion has been deﬁned.

6 PLANAR FRAME “JTFRAME”

Application module “jTframe” examines a three story

plane frame with base isolation which translates into a

four DOF system, whose properties are user deﬁned:

elastic and inertial characteristics plus the geometrical

conﬁguration. This module computes and presents in

simple text area the following fundamental data: stiff-

ness matrix, mass matrix, period and frequency asso-

ciated with each eigenmode, the components for each

eigenvector, plus the participation factor, generalized

mass and effective mass corresponding to each eigen-

mode. Next, there is an option to specify an acceler-

ation response spectrum, in which case the program

proceeds to calculate the spectral response for each

eigenmode. Up to this point, module “jTframe” is

similar to module “jframe”, except for the fact that

the user may deﬁne a variable number of stories and

incorporate base isolation. Next, the user may deﬁne

time-dependent loads at each story level, either as an-

alytical functions of time or from an external ASCII

ﬁle. Also, the transient loading may be given in terms

of a base acceleration ﬁle. After specifying the dis-

crete time step and the total time of duration, the tran-

sient response of the frame is computed and results

are presented through use of a GUI application. In

here, the animation option has been utilized and the

frame motion is shown in real time, in parallel with a

conventional plot for time history at a speciﬁed point

on the structure. These last plots allow the user to

deﬁne parameters for the two axes chosen from the

set of time, displacement, velocity, acceleration, and

external load at each story level.

7 NUMERICAL EXAMPLES

In this section some illustrative examples using mod-

ules of EDUSOFT follow to show the use of educa-

tional packages.

7.1 Computation of SDOF Response

In here, we will use application module “jesdof” to il-

lustrate the use of these web-based educational pack-

ages. More speciﬁcally, the input parameters re-

quested by this module are (i) stiffness, mass and

damping ratio of the SDOF system, (ii) initial con-

ditions, (iii) description of the external force (analyt-

ical function of time or from an external ASCII ﬁle),

and (iv) integration parameters for Duhamel’s integral

(default values are recommended). Output is (i) nat-

ural period and (ii) graphical representation of the re-

sponse (displacement, velocity, acceleration) as func-

tions of time. For an SDOF system with properties

m = 10 tons, k = 200 kN/m, ζ = 5%

under a unit harmonic load of the type

f(t) = sin(1.1ω

t), 0 ≤ t ≤ 10sec

and zero initial conditions, a sample output screen is

given in Figure 1 for the displacement time history.

For the same system with initial conditions

= 0.001m, v

= 0.01m/sec

the computed phase space projection on the

displacement-velocity plane is plotted in Figure 2.

Similar examples can be worked out for various types

of loading functions in combination with the initial

conditions.

Figure 1: Module “jesdof” screen depicting the SDOF dis-

placement time response x(t) (in m) for an external har-

monic loading.

7.2 Transient Response of a Planar

Frame

The structure here is understood to be a simple, ﬁxed

base, single-bay, three-story frame. What is required

EDUSOFTPACKAGEFORSTRUCTURALENGINEERING-Web-basedEducationalMaterialusingJAVAfor

StructuralDynamics

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Figure 2: GUI from module “jesdof” depicting an SDOF

computed response to initial conditions as a phase space

projection in terms of displacement versus velocity.

as input is (i) lateral dimension and story heights

(in m), (ii) story masses (in tons), (iii) cross-section

lateral stiffness of the columns (in kN/m) and their

modulus of elasticity (in kN/m

) (beams are assumed

rigid), and (iv) the input response spectrum (either

from use of “espec” or from an external ASCII ﬁle).

Output comprises (i) graphical representation of the

frame’s modal shapes and associated natural frequen-

cies, (ii) generalized mass values and participation

factors, and (iii) the resulting spectral displacements,

velocities and accelerations for each mode of the

structure. Figure 3 depicts the input dialog for a three-

story frame and in Figure 4 we present the respec-

tive input dialog for the forces. Finally, output re-

garding this example is given in reference to module

“jTframe” in Figure 5 .

Figure 3: Module “jTframe” input dialog box deﬁning

the geometrical and material properties of the three-story

frame.

8 CONCLUSIONS

Regarding actual use of the present educational pack-

age for structural dynamics analysis, we conclude that

the teaching experience accumulated during the ﬁrst

two years of use in actual classroom environment has

been most positive. Three modulus (“jesdof”, “es-

Figure 4: Module “jTframe” input dialog box deﬁning the

external time-dependent loads, the total time interval of in-

terest plus the time step, followed by output of modal infor-

mation.

Figure 5: Module “jTframe” screen depicting a time history

animation of the three-story frame motion plus its displace-

ment response as deﬁned by the user; the green box marks

current state information.

pec”, “jframe”) were taught to 4th year undergradu-

ates after the ﬁrst ﬁve weeks of instruction, in groups

of 35 students, for a two hour period in a computer

laboratory. These sessions were preceded by lec-

tures summarizing basic structural dynamics concepts

and the relevant material was accessible through the

electronic address http//:blackboard.lib.auth.gr. They

were then followed up by two more lectures on the

semester project, for which the students could utilize

the tools available to help complete it. Course eval-

uation results indicated a favourable reception of this

type of classroom activity by the students involved.

ACKNOWLEDGEMENTS

The EPEAEK II project entitled “Upgrading Civil

Engineering Studies at AUTH”, 2007-2009, is ac-

knowledged.

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REFERENCES

CEN (2004). Eurocode 8. design provisions of structures for

earthquake resistance. part 1: General rules, seismic

actions and rules for buildings. European Committee

for Standardization, Brussels, Belgium.

Chopra, A. (2007). Dynamics of Structures: Theory and Ap-

plications to Earthquake Engineering. Prentice-Hall,

Upper Saddle River, New Jersey.

Gosling, J., Joy, B., Steele, G., and Bracha, G. (2005). The

Java Language Speciﬁcation Third Edition. Addison-

Wesley, third edition edition.

Katsanos, E., Taskari, O., and Sextos, A. (2011). A matlab-

based educational tool for seismic design of ﬂexibly

supported r/c buildings. Computer Applications in En-

gineering Education, DOI 10.1002/cae.20568.

Sobhaninejad, G., Hori, M., and Kabeyasawa, T. (2011).

Enhancing integrated earthquake simulation with high

performance computing. Advances in Engineering

Software, 42:286–292.

APPENDIX

In terms of programming, a minimum prerequisite for

a modern educational-type development is use of the

graphical user interface (GUI). Another aspect to be

considered is the “open source” policy for software.

The philosophy behind this type of policy arises nat-

urally in an academic environment, where free shar-

ing of information is crucial for the development and

dissemination of technology in the context of both re-

search and education. Furthermore, we opt to use here

the Java Web Start technology instead of the Java Ap-

plet technology that is common in the majority of ap-

plications.

Finally, we mention here the extensibility of such

applications, in order to be modiﬁed in several lan-

guages, using the internationalization feature of Java.

It is also relatively straightforward to include more

advanced topics, as for example non-linear response

in the case of “jframe” or “jTframe”, that would be of

considerable interest in postgraduate study courses in

advanced structural dynamics.

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StructuralDynamics

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