Dynamics Flashcards
What happens to tanks during an earthquake?
The soil may liquefy if it does, the tanks can FLOAT OUT OF THE GROUND.
How is the equation G = (3-e)^2/(1+e) * (p’)^0.5 applied?
p’ is taken below the structure (and so includes the structure’s bearing pressure).
p’ = 1 + 2Ko/3 sigma’v
e is the voids ratio
A bridge has mass moment of inertia I and natural frequency omega. What is its stiffness?
Meq = \int{I * sin(x)^2}
Keq = omega^2 MeqName 3 elements of blast resistant design
Stand Off
Redundancy
Appropriate Glazing
What is admittance?
H(omega)
Where is ground displacement on a tripartite graph?
k->0 T->inf
Where is ground acc’n on a tripartite graph?
k->inf T->0
What is the column shear?
=12EI/h^3 * (u1-u2)
If there are multiple modes, need (u1-u2)*=sqrt(sum( {u1-u2}^2 ) )
What happens in partial liquefaction?
p’ lowers, so G falls, resonance may get worse.
In what kinds of soil can liquefaction occur?
Loose, saturated sands.
What is the displacemene of mode u_i in an earthquake?
= \Gamma_i * S_d * u_i
\Gamma_i is modal participation factor
S_d(\omega_i) is the displacement on the tripartite of T_i
Don’t forget u_i (the mode shape itself!) e.g. if u_i = 2 on the top floor, the top floor displacement is 2 * ug* gamma
How is the soil natural frequency calculated?
Imagine a sinusoid to bedrock. The wavelength is 4h. The speed is vs.
f = vs / 4h
How is the ductility factor defined?
\mu = u_f / u_y
u_f is failure
u_y is yield
What is eccentric bracing?
In a K-brace, the two diagonals don’t quite meet. This eccentricity allows a plastic hinge to form.
What does eccentric bracing allow?
A plastic hinge can form, dissipating energy without buckling.
Why is concentric bracing bad?
Members will buckle as the building sways one way then the other. As a result, there is no ductility.
What do helical strakes achieve?
They prevent vortices synchronising up a structure.
What is galloping?
On eg a hexagonal shape, the seperation points move when the structure sways because the apparent wind direction changes. This causes self-reinforcing swaying
What are the scaling laws for blast?
z* = z/(w^1/3)
t* = t/(w^1/3)
i* = i/(w^1/3)
i is the impulse = \int{P}dt
What is the damping ratio of a welded steel building?
1%
What is the damping ratio of a masonry building?
10%
What is SRSS?
Square Root Sum of Squares.
Name 5 solutions to liquefaction.
Air Sparging Bio-Cementation in-situ Densification improved drainage lower water table
How is concrete designed in seismic zones?
Require ductility, so ensure under-reinforced, lots of shear reinforcement.
Lots of reinforcement lapping and anchorage
Why is timber suited to seismic zones?
Nails provide ductility.
What is R_aa(\tau) for \tau = 0?
Raa(0) = 1/T * \int{a(t)*a(t) dt} = \sigma_a ^ 2
Why is spectral analysis not valid for soils?
Soils are non-linear, so we can’t just superpose spectral results.
What are flutter derivatives?
Flutter is controlled by two coupled differential equations:
m \ddot{h} + c \dot{h} + k h = c1 h + c2 \dot{h} + c3 alpha + c4 \dot{alpha}
I \ddot{alpha} + c \dot{alpha} + k alpha = c5 h + c6 \dot{h} + c7 alpha + c8 \dot{alpha}
c1 - c8 are flutter derivatives.
What is flutter?
Coupled vertical and torsional motions of flat plate-like structures.
How are flutter derivatives calculated?
By the scanlan method:
c1 - c8 are measured in a wind tunnel by applying a particular wind speed, and harmonic motions are applied (ie f is also chosen). c1 - c8 are found by measuring pressures.
Note that c1 - c8 are for a particular wind speed and frequency.
When do the flutter equations hold?
They hold true at the point of instability. We are therefore interested in the wind speed at which they hold true.
m \ddot{h} + c \dot{h} + k h = c1 h + c2 \dot{h} + c3 alpha + c4 \dot{alpha}
I \ddot{alpha} + c \dot{alpha} + k alpha = c5 h + c6 \dot{h} + c7 alpha + c8 \dot{alpha}
How can the flutter equations be simplified?
Sometimes, can set h = 0 and look at a purely torsional flutter:
I \ddot{alpha} + c \dot{alpha} + k alpha = c7 alpha + c8 \dot{alpha}
Flutter occurs when c8 > c and so there’s negative damping
Glazing options include:
Annealed, toughened, polycarbonate, laminated, and…
anti-shatter film ; curtains
Glazing options include:
Annealed, toughened, anti-shatter film, curtains, and…
polycarbonate, laminated
Discuss benefits of polycarbonate glass.
V good for blast resistance, but scratches easily and degrades in UV.
Discuss benefits of laminated glass.
2 + sheets of glass with interlayer. The interlayer can undergo large plastic strains.
Why is toughened glass better than annealed glass?
It breaks into smaller fractions.
In wind engineering, unsteady velocities lead to a static force and a fluctuating force. What is this fluctuating force?
Say U(t) = u + d(t)
u is constant.
F(t) = 1/2 rho Cd A ( U(t) )^2
= f + rho Cd A u * d(t)
How are spatial decorrelations accounted for in wind engineering?
Consider the area average of the forcing term. Then have two terms:
Sxx(omega) = mechanical admittance * aerodynamic admittance * Suu(omega)
Aerodynamic admittance <1 -> Sxx(omega) reduced due to area effects. Happens when length scale of fluctuations similar to length scale of building ( sqrt{A} )
A cantilever of length L has a lumped mass at the top. Modelling it as a third order polynomial, what is a sensible mode shape?
The mode shape needs to be compatible with B.C.s, which are u(0) = u’(0) = 0
and u’‘(L) = 0 due to no B.M.
u’’‘(L) =/= 0 because shear force is needed to move the lumped mass.
