Presentation poster for final year's individual project

1. Seismic protection using variable stiffness
-Part 2-
Neofytos Theodorou (MEng Civil Engineering)
University of Salford. School of Computing, Science, and Engineering
Introduction
Figure 1: The arrangements of the two models
May 2015
Fixed base model
Non linear arrangement Linear arrangement
Through testing under sinusoidal
ground displacements as well as
earthquakes it is proven that the use
of a non linear spring is able to
reduce forces moments and
accelerations when compared to an
identical linear spring structural
arrangement. The elastic properties
of both spring types have been
proven. The structure returns back to
its original position after the seismic
event has stopped hence protecting
the yield point. This thesis has also
provided a good datum in terms of
calibrating the correct value of non
linear stiffness needed for any
structure in order to achieve seismic
protection.
Conclusion
Dowrick, D. J. (2003). Earthquake risk
reduction. Chichester: Wiley.
Kobori, T., Takahashi, M., Nasu, T.,
Niwa, N. and Ogasawara, K. (1993).
Seismic response controlled structure with
Active Variable Stiffness
system. Earthquake Engng. Struct. Dyn.,
22(11), pp.925-941.
Nagarajaiah, S., Pasala, D., Reinhorn,
A., Constantinou, M., Sarlis, A. and
Taylor, D. (2013). Adaptive Negative
Stiffness: A New Structural Modification
Approach for Seismic Protection. AMR,
639-640, pp.54-66.
References
Directorate of Civil Engineering
Abstract
The purpose of this dissertation is to
examine in depth and review seismic
protection using techniques with
variable stiffnesses. The main aim is to
achieve reduction from seismic forces
on the structure to avoid permanent
deformation, the main technique used is
with the non linear stiffness properties
of springs. During the process two
models are designed in a software called
ANSYS to represent two storey
buildings, each model has two
arrangements the one with linear springs
to serve as haunches and the second
with non linear type springs to serve as
haunches. The first model has a fixed
base while on the second the base
connections are pinned. The two models
undertake same testing procedures in
order to check their reactions under
sinusoids and earthquakes. The two
arrangements of the two models are
compared in terms of final maximum
values of displacement, accelerations,
internal forces and bending moments
The two arrangements are also tested in
their elasticity properties and if they are
able to bring the structure back to
equilibrium once the seismic event is
over. At the end efficiency factors from
the reductions obtained from the non
linear spring are presented for each
model. comments analyzing all the
results follow
To test different numerical models
designed as two storey structures with
different base fixity conditions
To test different types of springs
which serve as haunches
To test whether or not the use of non
linear spring is able to reduce forces
moments and accelerations on the
structure which is subjected to
sinusoids and earthquakes.
To test the elastic properties of both
spring types and if they are able to
bring the global structure back to
equilibrium when an earthquake stops
To examine the efficiency from the
use of a non linear spring against the
linear by dividing their corresponding
values
Aims & Objectives
Efficiency factors
The use of a non linear spring in any
model has proven that has high
reduction efficiency in all
parameters. The reduction is obvious
when the sinusoids have ground
frequency same as the natural
frequency of the model. In addition
more swaying causes more non
linear spring deformation. This
mainly happens on the pinned
structure. An earthquake produces
less forces and moments therefore
reduction is smaller. No difference is
observed at displacements and
accelerations due to the variety of
frequencies observed in the
earthquake’s spectra.
Figures 8 and 9 show how the
structure returns to its original
position after the seismic event has
stopped. The non linear spring has
proven that is elastic in all its phases.
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0 5 10 15 20 25
Displacement(m)
Time (s)
Top storey top left node
Top storey top left
node
Elastic properties
Earthquakes have always been a
major problem for the society due
to the enormous damages that
they usually produce. The target
is to achieve building a structure
which is able to reduce all forces
and moments to be resisted.
(Dowrick, D. J., 2003). These
resisting forces and moments are
affected by the global stiffness of
the structure. Changes in stiffness
can be obtained by substituting
specific elements which provide
stability such as bracing, beams
and supports. The only efficient
solution to this problem is the
introduction of devices with
variable stiffness properties
mainly achieved by using springs
which can change stiffness as
they deform. Having a device
with these properties means that
there will be alterations on the
structure’s stiffness when an
earthquake strikes the building in
order to protect it in addition they
create a pseudo yield point which
is far lower therefore the actual
yield point of the structure.
Exceeding the pseudo yield point
is not an issue because the spring
can deform and return to its
original position once the force
applied to it is removed. Also it
does not oppose motion therefore
it absorbs forces, produced from
the earthquake, as it deforms. In
this thesis springs with linear and
non linear properties are used as
haunches to simulate stiff points
of the structure. Testing under
sinusoids and earthquakes will
prove if the use of a non linear
spring which changes stiffness as
it deforms is able to reduce
forces, moments and
accelerations when compared to a
linear spring testing.
Models preparation in ANSYS
Define linear and non linear
stiffness by using the continuous
modal analysis method
Hit the same natural frequency
between the two arrangements.
Set parameters for the time
history (damping, time steps,
ground frequency and
acceleration
Methodology
0
0.05
0.1
0.15
0.2
0.25
0.3
0 1 2 3 4
Displacements(m)
Frequency (Hz)
Spectra displacement
Non linear Model
displacements
Linear springs model
0
10
20
30
40
50
60
0 1 2 3 4
Accelerationm/s2
Frequency (Hz)
Spectra acceleration
Linear springs model
Non linear springs
model
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 1 2 3 4
force(N)
Frequency (Hz)
Spectra Force
Linear springs model
Non linear springs
model
Figure 2: Linear and non linear spring
stiffness
Sample of results –Fixed base model
Figure 3: Sinusoidal spectra displacement
Figure 4: Sinusoidal spectra acceleration
Figure 5: Sinusoidal spectra Forces
Figure 8 and 9: Non linear and linear
arrangement structure –Original position
Earthquakes
0
200
400
600
800
1000
1200
1400
1600
0 5 10 15 20 25
force(N)
Ground displacements (x default) (m)
Spectra Force
Linear springs model
Non linear springs
model
Figure 6: Earthquake spectra force
0
100
200
300
400
500
600
700
0 5 10 15 20 25
Moments(Nm)
Ground displacements (x default) (m)
Spectra moments
Linear springs model
Non linear springs
model
Figure 7: Earthquake spectra Moment
Reduction on the maximum values
produced on the non linear spring
arrangement as the earthquake increases.
No significant difference is observed at
displacements and accelerations due to the
variety of frequency contained in the
earthquake’s spectra.
-500
0
500
1000
1500
2000
2500
-0.01 0 0.01 0.02 0.03 0.04
Force(N)
Displacement (m)
Linear and non linear spring's stiffness
plotted together
Linear spring's stiffness
Non linear spring's
stiffness
-2.00E-01
-1.50E-01
-1.00E-01
-5.00E-02
0.00E+00
5.00E-02
1.00E-01
1.50E-01
2.00E-01
2.50E-01
0 5 10 15 20 25
Displacements(m)
Time (s)
Top storey top right node
Linear
Significant difference on the non linear
spring arrangement at resonance
conditions.
Sinusoids