Civil Engineering Reference
In-Depth Information
Several types of energy dissipation devices can provide hysteretic, friction and viscous damping; these
are cost-effective for seismic retrofi tting of structures (e.g. Di Sarno and Elnashai, 2005). The latter
devices are also being increasingly used for new structures because of their ability to considerably
reduce storey displacements, accelerations and shears (Soong and Spencer, 2002 ).
Structural damping is a measure of energy dissipation in a vibrating system that results in bringing
the structure back to a quiescent state. It is associated with absorption of seismic energy in structural
components. It also accounts for material viscosity and friction at connections and supports. In structural
components, the energy imparted by earthquakes is dissipated mainly through hysteretic damping
characterized by action-deformation loops. Such loops express action- deformation relationships of
materials, sections, members, connections or systems under alternating loads. For hysteretic damping,
the dissipation varies with the level of displacement, but it is constant with the velocity. The amount
and mechanisms of material hysteretic damping vary signifi cantly depending on whether the material
is brittle, such as concrete and masonry, or ductile, e.g. metals. For RC energy dissipation is due to
opening and closing of cracks but the material remains held together by the steel. In masonry, there is
also sliding along the cracks; hence the hysteretic damping of masonry is lower than that of RC.
Whereas hysteretic damping is complex and cannot be expressed in simple forms, it is almost always
represented in dynamic analysis as equivalent viscous damping, which is proportional to the velocity.
This form of damping conveniently allocates a parameter to the velocity term in the dynamic equilib-
rium equations that matches the mass and stiffness terms associated with acceleration and displacement,
respectively.
Friction or Coulomb damping results from interfacial mechanisms between members and connections
of a structural system, and between structural and non-structural components such as infi lls and parti-
tions. It is independent of velocity and displacement; its values signifi cantly depend on the material
and type of construction. For example, in steel structures, the contribution of friction damping in bolted
connections is higher than welded connections. In infi lled masonry walls, friction damping is generated
when cracks open and close. In other materials, e.g. for concrete and masonry, this type of damping
cannot be relied upon because of the degradation of stiffness and strength under cyclic load
reversals.
Values of hysteretic damping
ξ
m
for common materials of construction are outlined in Table 2.6 .
These are expressed as ratios of the critical damping. It is observed that
ξ
m
increases with the amplitude
of action or deformation. The values in Table 2.6 are, however, approximate estimates of damping for
different construction materials.
For relatively small values of damping, e.g. less than 10- 15%, hysteretic, viscous and friction
damping can be conveniently expressed by 'equivalent viscous damping'
c
eq
as follows (Jennings,
1968 ):
Table 2.6
Hysteretic damping for different construction materials (
after
Bachmann
et al
., 1995 ).
Material
Damping,
ξ
m
(%)
Reinforced concrete
Small amplitudes (un - cracked)
0.7 - 1.0
Medium amplitudes (fully cracked)
1.0 - 4.0
High amplitudes (fully cracked) but no yielding of reinforcement
5.0 - 8.0
Pre - stressed concrete (un - cracked)
0.4 - 0.7
Partially stressed concrete (slightly cracked)
0.8 - 1.2
Composite
0.2 - 0.3
Steel
0.1 - 0.2
