Transcript Imperial College London

Robustness assessment for multiple
column loss scenarios
M. Pereira and B. A. Izzuddin
Department of Civil and Environmental Engineering
Robustness assessment framework
Robustness Assessment
Damage Scenarios
Single Damage Scenario
Multiple Damage Scenarios
Sudden single column loss
Sudden single column loss
Sudden two adjacent column loss
Column loss scenario – Main Stages
(i) Nonlinear static response of the damaged structure under gravity
loading
(ii) Simplified dynamic assessment to establish the maximum dynamic
response under column loss scenarios
(iii)Ductility assessment of the connections/structure
Dynamic response of a SDOF system – Point Load
Mu + K u = P
-
=
Dynamic response of a SDOF system – UDL
M u + K u = wL
-
=
Dynamic response of a MDOF system – UDL
-
=
Pseudo-static response of a MDOF system
N
Un   
k 1
ud ,n ,k
0
Pk dus , k
N
N
k 1
k 1
Wn   Pn, k ud , n, k  n  P0, k ud , n, k
N
Wn  U k , n  n 

ud , n , k
0
k 1
Pk dus , k
N
P
k 1
u
0, k d , n , k
Simplified Dynamic Assessment – Case Study
Floor system
Service Load
Edge: 406UB38 (Floor), 305UB28 (Roof)
Internal: 305UB25 (Floor), 152UB16 (Roof)
Transverse: 356UC153 (Floor), 254UC107 (Roof)
Floor Dead Load: 4.2 kN/m2 (factored 1)
Floor Live Load: 5.0 kN/m2 (factored 0.25)
Edge Floor (Facade) Dead Load: 8.3 kN/m
Roof Loads : ½ of Floor Loads
Individual beam level – Longitudinal edge beam
Rigid Column
Flexible Column
Longitudinal edge beam - Rigid Column
2 Point Load
Uniformly Distributed Load
• Accurate
Slight overestimation
approximation
as of
expected
the dynamic
in the response
static analysis
for both
more
loading
visiblecases
for 2
point load (concentrated masses)
• High frequencies excitation for uniformly distributed mass case
Longitudinal edge beam - Flexible Column
Uniformly Distributed Load
• Slight
Good approximation
overestimationof
inthe
thedynamic
static analysis
response for a case with variable
deformation mode during loading
• High frequencies excitation
Individual floor level
Detailed Floor Grillage Model
Simplified Floor Grillage Model
Compatibility between members
assuming a governing mode
N
u
and
W
n
 U k , n  n 
 
k 1
N
d ,n ,k
0
 P
k 1
Pk dus , k
u
0, k d , n , k
Individual floor
(Pseudo)
(Pseudo) Static
Static vs.
Detailed
Dynamic
vs.
Simplified
Detailed Model
Models
• Accurate
Vertical
Betterapproximation
Good
approximation
displacement
approximation
of
of
point
floor
structural
of the
ofvertical
zero
dynamic
response
system
support
response
acceleration
from
reaction from
(maximumbeams
assembling
individual
static
individual
displacement)
(rigidbeams
columns)
with
corresponds
vertical
rigid columns,
reaction
to point
rather
profiles
of exact
than
•vertical
flexible
Dominant
reaction
columns
trapezoidal
prediction
mode
as of
expected
deformation for floor
system
• Use
Under/overestimation
of longitudinal edge
of vertical
beam forsupport
governing
reaction
member
is and
•observed
imposed
Additional
compatibility
for rotational
total down/upwards
restraint
in remaining
given
acceleration
floor
by transverse
members beams
torsional stiffness
Conclusions
•
Successful extension of the multi-level simplified dynamic
assessment to structures subjected to two adjacent columns loss
• Dominant trapezoidal mode observed even for asymmetric
load/structural configuration
• Consideration of reaction transmitted to surrounding structure for
alternate load path assessment (including column resistance /
connection shear failure)
• Further studies on effect of high frequency excitation in
instantaneous system failure
Conclusions
Comparing the dynamic and pseudo-static responses:
• Validity of the assumption of zero kinetic energy at maximum
dynamic displacement for MDOF system;
• Conservative assumption of the inertial forces distribution for
determination of dynamic vertical support reaction.
Comparing detailed and simplified assembly models responses:
• Simplified models are feasible for structures exhibiting constant
deformation mode during loading.
Multiple floors level
Detailed Multiple Floors Model
Simplified Multiple Floor Model
Compatibility between members
assuming a governing mode
and
N
ud , n , k
Pk dus , k


0
W n  U k ,n  n  k 1N
 P0,k ud ,n,k
k 1
Multiple floors
(Pseudo)
(Pseudo) Static
Static vs.
Detailed
Dynamic
vs.
Simplified
Detailed Model
Models
• Accurate
Vertical
Good approximation
Satisfactory
displacement
approximation
approximation
of
point
structural
of the
of floor
zero
dynamic
response
system
vertical
response
acceleration
either
support
using
(maximum
detailed
reaction
floors
from
static
individual
assembly
displacement)
beams
or starting
(rigid
corresponds
from
columns)
individual
to point
vertical
beams
of exact
• Dominant
vertical
assembly.
reaction
reaction
profiles
trapezoidal
prediction
taking into
mode
as
account
of
expected
deformation
moderatefor
load
multiple
floor system between floors
redistribution
• Equally
Under/overestimation
satisfactory approximation
of vertical support
using reaction
either 1stisFloor or
observed
Roof
longitudinal
for total down/upwards
edge beams as governing
acceleration
members