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[b]Design a multi-storey building capable of withstanding an earthquake[/b]
You have to design a building which will not break apart in an earthquake. This means that
it can’t be just a rigid body as it would fracture very quickly. Therefore it needs some flexibility
to handle the moving ground. It also needs to be able to dampen the massive movements of the
ground in an earthquake so as to minimise movement of the entire building. Thus a balance
between creating a building that is too stiff or too flexible is required
Each level of the building is attached to adjacent levels by steel poles that act like massive
springs with some stiffness k. As these poles are not ideal springs, they also dampen the
oscillations caused by the earthquake. This damping is important as oscillations could become
unstable also causing the building to break apart.
Assume the earthquake causes the ground to move sinusoidally. The ground level which is
attached directly to the earth will therefore input a sinusoidal force to the rest of the building
via the steel poles.
A diagram of a building with two levels plus a ground level is shown in Fig. 2. The forces
applied to each of the levels are also shown.
Hints:
• Note that the springs cause a downward force on the Level above but an upward force on
the Level below... make sure you get your positive and negative signs right when adding
your forces in Simulink.
• Remember that there is also a weight force downwards for each level.
Constants:
• body mass = 2500kg
• Spring constant, K1 = 80000 N/m
• Damping constant, b1 = 350 Ns/m
• Force due to damping, F = b1 v, where v is the velocity.
Design requirements:
• During the earthquake, the building should not have large oscillations and the oscillations
should dissipate quickly.
5
Figure 2: The force diagram for a building with 2 levels. The steel poles can be modelled as a spring
and a dampener. An extra sinusoidal force is input into the ground level due to the earthquake.
• The earthquake could be simulated by a sinusoidal input. Think about the forces an
earthquake produces and come up with a reasonable amplitude and frequency for the
sinusoidal movement and therefore the acceleration of the ground level. HINT: It might
be easier to start with a step function (at least for initial analysis) for the force rather
than a sinusoidal input.
• The Simulink model you produce should track the position of the levels so that the
damped oscillations can be observed.
Design Hints:
6
• Consider the forces on each level separately when building the system.
F = ma = m
d2x
dt2 (1)
• The position of each of the levels can be calculated from the acceleration:
d2x
dt2 = dx
dt
= x (2)
• Try starting with the ground level only and begin to add levels when you are happy with
the results.
Optional Extras:
• Include proportional, integral, or derivative control using feedback so that the oscillations
are damped as quickly as possible.
• Different types of earthquakes... use a square wave instead of a sinusoid.
• Examine the difference between buildings with different numbers of levels.
• We’ve only considered movement of the building which is up and down. Try adding
sideways movement into the system.
[b]Design a multi-storey building capable of withstanding an earthquake[/b]
You have to design a building which will not break apart in an earthquake. This means that
it can’t be just a rigid body as it would fracture very quickly. Therefore it needs some flexibility
to handle the moving ground. It also needs to be able to dampen the massive movements of the
ground in an earthquake so as to minimise movement of the entire building. Thus a balance
between creating a building that is too stiff or too flexible is required
Each level of the building is attached to adjacent levels by steel poles that act like massive
springs with some stiffness k. As these poles are not ideal springs, they also dampen the
oscillations caused by the earthquake. This damping is important as oscillations could become
unstable also causing the building to break apart.
Assume the earthquake causes the ground to move sinusoidally. The ground level which is
attached directly to the earth will therefore input a sinusoidal force to the rest of the building
via the steel poles.
A diagram of a building with two levels plus a ground level is shown in Fig. 2. The forces
applied to each of the levels are also shown.
Hints:
• Note that the springs cause a downward force on the Level above but an upward force on
the Level below... make sure you get your positive and negative signs right when adding
your forces in Simulink.
• Remember that there is also a weight force downwards for each level.
Constants:
• body mass = 2500kg
• Spring constant, K1 = 80000 N/m
• Damping constant, b1 = 350 Ns/m
• Force due to damping, F = b1 v, where v is the velocity.
Design requirements:
• During the earthquake, the building should not have large oscillations and the oscillations
should dissipate quickly.
5
Figure 2: The force diagram for a building with 2 levels. The steel poles can be modelled as a spring
and a dampener. An extra sinusoidal force is input into the ground level due to the earthquake.
• The earthquake could be simulated by a sinusoidal input. Think about the forces an
earthquake produces and come up with a reasonable amplitude and frequency for the
sinusoidal movement and therefore the acceleration of the ground level. HINT: It might
be easier to start with a step function (at least for initial analysis) for the force rather
than a sinusoidal input.
• The Simulink model you produce should track the position of the levels so that the
damped oscillations can be observed.
Design Hints:
6
• Consider the forces on each level separately when building the system.
F = ma = m
d2x
dt2 (1)
• The position of each of the levels can be calculated from the acceleration:
d2x
dt2 = dx
dt
= x (2)
• Try starting with the ground level only and begin to add levels when you are happy with
the results.
Optional Extras:
• Include proportional, integral, or derivative control using feedback so that the oscillations
are damped as quickly as possible.
• Different types of earthquakes... use a square wave instead of a sinusoid.
• Examine the difference between buildings with different numbers of levels.
• We’ve only considered movement of the building which is up and down. Try adding
sideways movement into the system.