Civil Engineering Reference
In-Depth Information
Under very high magnitude and very infrequent earthquakes for
It should be noted that these rules of thumb have a high
degree of inaccuracy (± 50%) since the dynamic behaviour
of real structures is so variable. It should also be noted that
for example the second method shown above will generally
give lower values than would be derived from a 3D struc-
tural analysis of a structure and some codes limit the use
of 'too high' a period to a proportion of a 'code derived'
value, so that the engineer does not suffer from 'sharp pen-
cil' syndrome.
Some key aspects of seismic loads are as follows:
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the structures to not collapse (i.e. failure modes which are not
'brittle' and which allow the evacuation of the structure).
The magnitude of the forces which are developed within
structures is primarily governed by the peak ground accelera-
tion (PGA) designed for - the PGA is derived by a statistical
analysis of earthquakes and the attenuation of the associated
ground motions for the location under consideration, plus an
allowance for local soil effects (classically the example of the
Mexico City earthquake where many structures are located
on deep clay layers, which amplifi ed the earthquake induced
ground accelerations experienced by the buildings affected).
The commonly used measure of risk is a 'rock' PGA with a
10% probability of exceedance in 50 years, which corresponds
to a 475 year 'return period' and maps of 'seismic hazard' are
typically prepared on that basis. For the 475 year return period
locations can be consider to fall into different 'categories' as
follows:
a.
Ductility - a basic principle used in most seismic de-
sign codes is that buildings are designed for 'equivalent
forces' - effectively scaled inertial forces. This allows for
dissipation of energy through structural and non-structural
mechanisms (for example, the formation of 'plastic hinges'
in a reinforced concrete beam).
b.
Capacity Design - another basic principle, which is to
design a structure with elements sized and detailed to
'force' a ductile, rather than 'non-ductile' failure mech-
anism - the classic example being the 'strong column -
weak beam' approach, where in a moment resisting frame
the strength of the column is set relative to the beam so
that a plastic hinge will always form in the beam rather
than in the column (and hence avoidance of a collapse
mechanism).
PGA approximately 0.075 g - Low seismic risk - use of 'equiva-
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lent static methods'.
PGA of approximately 0.15 to 0.20 g - Intermediate seismic risk -
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detailing and some limits on design.
PGA of 0.3 to 0.4 g - High seismic risk - requires consideration
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of dynamic analysis procedures, special detailing, limits of 'types'
of lateral load resisting systems and in general particular attention
from the conceptual level.
c .
Design Philosophy - The general approach when design-
ing for high seismic loads is to develop a clear lateral load
resisting system, which preferably should be symmetrical
on plan and with the centre of stiffness aligned with the
centre of mass (to reduce potentially problematic torsional
effects) and to avoid sudden changes in stiffness or strength
vertically (particularly soft or weak storeys in multi-storey
buildings.
Typically it would be acceptable for engineers without a back-
ground in seismic design to undertake designs in areas of
low seismic risk and with advice/support to carry out design
in areas of intermediate seismic risk. It would be considered
unadvisable for engineers who have not been appropriately
trained and who do not have suffi cient experience, to design
structures within an area of high seismic risk. The possibility
of errors within the concept, let alone within the detailing, is
suffi cient to make recourse to an 'expert' advisable.
The natural frequency, or more frequently the fundamental
period (i.e. the inverse of the natural frequency), of a structure
is typically signifi cant. This is the period which corresponds
to the 'fi rst mode' dynamic response, which can be thought
of as a 'half sine wave' - this gives a linear acceleration with
height (i.e. the 'inverted triangle') of forces typically assumed
by engineers designing for 'seismic loads'.
Rules of thumb for estimation of building period:
Generally seismic design codes assume that base shear is
determined by a formula such as:
V =
CIW
RT
C = Coeffi cient based on the PGA (peak ground acceleration) and
soil conditions
I = Importance factor
R = Load reduction (ductility) factor
T = period - it should be noted that codes generally contain approaches
for approximating periods for different structures or else more
sophisticated numeric analysis techniques can be used - such as
modal analyses of 3D FE models; codes often contain 'limits',
recognising that any analysis, no matter how apparently precise,
is in fact by nature relatively inaccurate
W = seismic weight
For example, for a 10-storey offi ce building, with a reinforced
concrete shear wall system the period might be 1 second and
T = 0.56
√(EI/mL
4
) - where m is the equivalent distributed mass,
E is the composite Young's modulus and I the second moment of
inertia, with L being the height of the 'cantilever'.
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T = C
t
(h
n
)
3/4
- where C
t
is a coeffi cient that varies depending upon
the type of lateral load resisting system and h
n
is the overall height
of the building.
T = n/10 - where n is the 'number of storeys'.
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