# Structural Dynamics and Earthquake Engineering

## Transcription

Structural Dynamics and Earthquake Engineering
```Structural Dynamics and Earthquake
Engineering

Course 10
Design of buildings for seismic action (2)
http://www.ct.upt.ro/users/AurelStratan/
Combination of the effects of the components of
the seismic action
 Seismic action has components along three orthogonal
axes:
– 2 horizontal components
– 1 vertical components
Vrance a, 04.03.1977, INCERC (B), NS
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-1.95
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Vrancea, 04.03.1977,
timp, sINCERC (B), EW
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1.62
acceleratie, m/s 2
 Peak values of ag for
horizontal motion are NOT
recorded at the same time instant
 Peak values of response are NOT
recorded at the same time instant
acceleratie, m/s 2
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timp, s
1
Combination of the effects of the components of
the seismic action
 Simultaneous action of two orthogonal horizontal
components (lateral force or spectral analysis):
– Seismic response is evaluated separately for each direction of
seismic action
– Peak value of response from the simultaneous action of two
horizontal components is obtained by the SRSS combination of
directional response:
2
2
EEd  EEdx
 EEdy
 Alternative method for combination
of components of seismic actions
Combination of the effects of the components of
the seismic action
 When vertical component
is considered as well:
2
2
2
EEd  EEdx
 EEdy
 EEdz


2
Vertical component
 Vertical component of seismic action shall be considered
when vertical peak ground acceleration agv0.25g, and the
structure has one of the following characteristics:
–
–
–
–
–
has horizontal elements spanning over 20 m
has cantilever elements with a length over 5 m
has prestressed horizontal elements
has columns supported on beams
is base-isolated
Conceptual design of buildings
 Seismic response of structures subject to considerable
uncertainties:
– characteristics of future seismic motions
– diff. between structural models and real structural behaviour
• elastic model  inelastic response
• static analysis dynamic behaviour
• …
 Conceptual design of buildings located in seismic areas
is necessary, in order to provide an adequate seismic
response:
–
–
–
–
–
–
structural simplicity
uniformity, symmetry and redundancy
bi-directional strength and stiffness
torsional resistance and stiffness
diafragmatic behaviour at storey levels
3
Structural simplicity
 Simple, compact, symmetric structures
 Modelling, analysis, design, detailing and construction of
structures subjected to smaller uncertainties
Uniformity, symmetry and redundancy
 Structures should be as regular as possible, with a
uniform plan layout, allowing for a short and direct
transmission of inertia forces to lateral resisting system
 Redundancy: failure of a single member does not imply
failure of the whole structure
4
Bi-directional strength and stiffness
 Gravity - force resisting systems
 Lateral - force resisting systems
sistem de preluare a fortelor gravitationale
sistem de preluare
a fortelor laterale
 Seismic motion has components on both horizontal
directions
 Structures should have similar strength and stiffness
along two main directions
Torsional resistance and stiffness
 Seismic forces  centre of mass (CM)
 Resisting forces  centre of rigidity (CR)
 Torsionally flexible systems  large forces and
deformations in perimetral elements
lateral-force
resisting system
lateral-force
resisting system
gravity-force
resisting system
gravity-force
resisting system
 Conclusion (1): lateral force resisting systems are more
efficient away from the centre of rigidity
5
Torsional resistance and stiffness
 Seismic forces  centre of mass (CM)
 Resisting forces  centre of rigidity (CR)
 Eccentricity  torsion  increased displ. and forces
2x
2x
D2y
Fx
CR=CM
Fx
CM
CR
e0y
D1y
Y
D1x
D1x
X
 Conclusion (2): lateral force resisting systems should be
located as symmetrical as possible
Storey diaphragms
 Behaviour of floors as rigid diaphragms
– Collect and transmit forces to lateral-force resisting systems
– Lateral-force resisting systems work together
– Especially relevant in case of complex and non-uniform layouts of
lateral-force-resisting systems, or combination of such systems
of different stiffness
F
F
6
Foundations
 Design and construction of the foundations and of the
connection to the superstructure shall ensure that the
whole building is subjected to a uniform seismic
excitation
 Recommendations:
– discrete number of structural walls, of different width and
stiffness
box-type or cellular foundation
– individual foundation elements
foundation slab or tie-beams between these elements
Criteria for structural regularity
 Structural regularity:
– plan
– elevation
 Regularity of a structure affects:
– structural model, 2D or 3D
– analysis method, lateral force method or modal response
spectrum analysis
– value of the behaviour factor q, that need to be reduced for
structures irregular in elevation
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Criteria for regularity in plan
 A symmetrical distribution of stiffness and mass
 Compact plan configuration, close to a convex polygonal
shape (set-backs of max 10% from floor area)
 Rigid diaphragms at storey levels
 At each level, in each principal direction of the structure,
the eccentricity shall satisfy:
eox  0,30 rx
eoy  0,30 ry
eox , eoy - the distance between the centre of stiffness and
the centre of mass, measured in the direction normal to
the direction of analysis considered
rx, ry – the square root of the ratio of the torsional
stiffness to the lateral stiffness in each direction
Criteria for regularity in elevation
 Lateral-force resisting systems shall run without
interruption from their foundations to the top of the
building
 Mass and lateral stiffness shall be constant or reduce
 In framed buildings the ratio of the actual storey
resistance to the resistance required by the analysis
should not vary disproportionately between adjacent
storeys
 Stiffness: reductions are no larger than 30% with respect
 Strength: reductions are no larger than 20% with respect
 Mass: is not larger than 50% of the mass of adjacent
storeys
8
Criteria for regularity in elevation
 Restrictions on setbacks
Consequences of structural regularity on analysis
and design
Regularity
Allowed simplification
Behaviour factor (q)
Plan
Elevation
Model
Linear-elastic analysis
YES
YES
Planar
* Lateral force
Reference value
YES
NO
Planar
Modal
Reduced value (by 20%)
NO
YES
Spatial
Modal
Reference value
NO
NO
Spatial
Modal
Reduced value (by 20%)
 *Only if building height is less than 30 m and fundamental
period of vibration T1 < 1.50 s
 Plan irregularity: large torsional eccentricities  3D
models
 Vertical irregularities: significant contribution of higher
modes of vibration 
– modal response spectrum analysis
– reduced values of behaviour factor
9
Structural model
 The model of the building shall adequately represent the
distribution of stiffness and mass
 Floors that cannot be modelled as infinitely rigid in-plane
 translational masses (only) can be considered lumped
in nodes
 Floors that can be modelled as infinitely rigid in-plane 
storey masses can be lumped at the centre of mass of
each storey:
M M  m
x
– 2 translational components
– 1 rotational components
y

i
M zz   mi d i2
myi
mi
mxi
di
My
Y
Mx
CM
Mzz
X
Accidental torsional effects
 Uncertainties associated to distribution of storey masses
and/or spatial variation of ground motion
 Accidental eccentricity e1i = 0.05 Li
 Spatial structural model: M 1i  e1i Fi
±e1x
Y
Fx
CM
±e1y
Ly
CM
X
Fy
Lx
10
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