Diapositiva 1

1
NONLINEAR ANALYSIS FOR PROGRESSIVE COLLAPSE
INVESTIGATIONS ON R.C. FRAMED STRUCTURES
ROBUSTNESS REQUIREMENT
A NON ROBUST BEHAVIOR the A.P.Murrah federal
building collapse
HANDLING WITH RISK PREVENT OR PRESUME?
(after Starossek, 2005)
PREFACE the federal building of Oklahoma city
was hit in the October 1995 by the explosion of a
bomb truck parked in front of the building
entrance. The bomb removed abruptly by brisance a
column of the first frame. In case only one
column was directly damaged, the resulting
collapse of nearly an half of the building
appears to be quite disproportionate to the
initial failure.
SAFETY
RISK

• Terrorism

• Natural disaster

• Human errors

?
Non structural measures (security, event control)
Probability
Extrinsic defenses
FEMA REPORT the investigation of the Federal
Emergency Management Agency (F.E.M.A) following
the collapse (May 1995) reported that the
building suffered a progressive collapse and
ascribed this lack of robustness of the building
to the discontinuity in the transfer girder
reinforcement (see the images below), due to the
regulations in force at the time of the
construction (70s) identifying the use of
special moment frame as possible measure for the
mitigation of the collapse.
is prevented
Invulnerability (key element
oversizing)
QUESTIONS 1) Was it progressive collapse?
(i.e. can the abrupt removal of just one
column lead to the collapse experimented by the
first frame?) 2) Could a greater reinforcement
continuity avoid the collapse?
CRITICAL EVENT
Damage
Intrinsic defenses
ROBUSTNESS
is presumed
DESCRIPTION OF THE BUILDING
ROOF GIRDER
20
28
24
8
12
16
12
10
18
26
8
14
16
20
22
24
28
6,1
6,1
6,1
6,1
6,1
6,1
6,1
6,1
6,1
6,1
G
G
TYPICAL GIRDERS
10,67
F
F
10,67
TRANSFER GIRDER
E
E
9,14
6,1
6,1
6,1
6,1
6,1
6,1
6,1
6,1
6,1
6,1
0,91m
0,91m
0,91m

• Plan dimension 60 m x 21 m

MAIN COLUMNS
COLUMN BLASTED AWAY BY THE EXPLOSION (G20)

• Main frames 3 longitudinal frames of 10 spans
  each span length 6 m

11F36
3F36
3F36
SECONDARY COLUMNS
1,52 m
1,44 m
1,52 m
1,52 m
1,44 m

• Elevation 10 floors for a total height of about
  35 m

1,30 m
DISCONTINUITY IN THE BOTTOM REINFORCEMENT OF THE
TRANSFER GIRDER
10F36

• Peculiarity 5 columns of the main frame stop at
  3 floor on a transfer girder

• Reinforcement bottom reinforcement discontinuity
  at supports in the transfer girder of 3 floor

ASSUMPTIONS AND MODELING
Nonlinear static analyses are carried out
ON
HOW

• 8 two dimensional substructures (segments of main
  girders and secondary columns next to G20 line)
• Two-dimensional frame model
• Three-dimensional building model

• Pushing load is a vertical force (directed to the
  ground) applied to the removed column joint
• Vertical displacement is monitored at the
  considered joint
• Flexure plastic hinges (lumped plasticity) are
  assigned at beam ends
• Different type of M-c diagrams are assumed for
  the hinge behaviors

RESULTS AND CONCLUSIONS

• MODELLING ASPECTS
• A full consideration of the dynamic aspects of
  the column failure would not be very useful,
  since the building without the considered column
  was not even able to sustain self and service
  weight.
• The consideration of the full 3D model of the
  building proves instead to be more significant,
  since it determines an increment of more than 50
  in the ultimate resistance of the structure with
  respect to the case in which just the 2D frame is
  considered.
• The use of full interacting axial-moment plastic
  hinges has been neglected since it proves to be
  significant only when the full geometric
  nonlinearities are also included and the
  tension-stiffening effect in the girder
  mechanisms can be considered.

• PROGRESSIVE COLLAPSE SUSCEPTIBILITY
• The building could have experimented a
  progressive collapse the presented
  investigations, by assuming the direct failure of
  just one column, shows the development of a
  mechanism that easily lead to the failure of
  adjacent columns, thus involving the major part
  of the first frame of the building in the
  collapse.
• The progressive collapse susceptibility of the
  building would not be reduced by a greater
  continuity of the reinforcement contrary to the
  original design choices, the actual standards was
  followed for the structural characterization of
  the model, that provide a continuous bottom
  reinforcement in all girders but cant help nor
  significantly reduce the building progressive
  collapse.

Luisa Giuliani Ph.D. St., Structural and
Geotechnical Engineering Department, University
of Rome La Sapienza, luisa.giuliani_at_uniroma1.it
Viviana Prisco Structural Engineer, Rome, Italy
, viviana.prisco_at_tin.it