ProDRiS - DICA - Politecnico di Milano

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ProDRiS - DICA - Politecnico di Milano
POLITECNICO DI MILANO
Dipartimento di Ingegneria Civile e Ambientale
Department of Civil and Environmental Engineering
Sezione ProDRiS
Progettazione, Diagnostica e Riabilitazione Strutturale
Structural Design, Diagnostics and Rehabilitation
ProDRiS – Faculty Staff
1 PO
– Professors (4);
2 PA
– Associate Profs (2);
2
3 RI
– Assistant Profs (6)
+ 10 Research Fellows
Fabio Biondini 2
Matteo Bruggi 3
Giuliana Cardani 3
Paola Condoleo 3
Dario Coronelli 3
Elsa Garavaglia 2
Maurizio Lualdi 3
Pier Giorgio Malerba 1
Gianpaolo Rosati 1
Alberto Taliercio 1
Cristina Tedeschi 3
Luigi Zanzi 1
Scientific Coordinator
Sezione ProDRiS
ProDRiS – Research Areas
3
Theory and Methods of Structural Design
• Structural Analysis
• Structural Reliability
• Structural Optimization
• Life-Cycle Design
Survey, Inspection, Monitoring and Structural Diagnostics
• Built Heritage
• Non Destructive Testing (NDT)
• Geophysical Prospections
Design of New Structures and Rehabilitation of Existing Structures
• Materials and Structures
• Bridges and Buildings
• Maintenance and Safety of Existing Structures
• Fastenings and Connections
Sezione ProDRiS
ProDRiS – Research Areas
4
Theory and Methods of Structural Design
• Structural Analysis
• Structural Reliability
• Structural Optimization
• Life-Cycle Design
Survey, Inspection, Monitoring and Structural Diagnostics
• Built Heritage
• Non Destructive Testing (NDT)
• Geophysical Prospections
Design of New Structures and Rehabilitation of Existing Structures
• Materials and Structures
• Bridges and Buildings
• Maintenance and Safety of Existing Structures
• Fastenings and Connections
Sezione ProDRiS
Theory and Methods of Structural Design
5
Time-evolution of damage in historical buildings
2008: ‘numerical
collapse’
AD
1591
1691
1900
1800
Creep-induced damage in Pavia belltower (†1989):
numerical prediction
Sezione ProDRiS
Prediction of crack evolution in
San Vitale Basilica via XFEM
Theory and Methods of Structural Design
6
Prediction of the macroscopic mechanical properties of brickwork
Deformed unit cell under normal stress (a) or shear (b)
unit cell
(a)
Macroscopic Young’s and shear moduli
vs joint thickness
Sezione ProDRiS
(b)
Macroscopic creep curves under
normal stress and shear
Theory and Methods of Structural Design
7
Topology optimization applied to thermal insulation
Optimized block sections for different
out-of-plane compliances
Typical
commercial
masonry blocks
heat flux
Influence of shear keys
on optimal design
Sezione ProDRiS
Gain in thermal transmittance:
Indented blocks
Smooth blocks
Theory and Methods of Structural Design
8
Finite element analysis of no-tension structures
Formulation of an energy-based method
to distribute and orientate an ad hoc
orthotropic material that behaves as a
compression-only medium
Investigation on the behavior of
masonry structures in terms of both
stresses and displacements:
- at the serviceability limit state (SLS)
- at incipient collapse (US)
Principal stresses at SLS (p=0)
Deformed shape, expected collapse mechanism and principal stresses at US
Sezione ProDRiS
Theory and Methods of Structural Design
9
Optimal fiber-reinforcement of existing structures
Formulation of an optimization method to distribute and
orientate an available amount of unidirectional fiberreinforcement (FRP) such that in-plane stresses are
feasible with a Tsai-Wu strength criterion governing the
underlying anisotropic layer.
Plain/reinforced concrete and brickwork can be dealt with
Optimal distribution and orientation of FRP strips for an architrave subject to horizontal loads
Sezione ProDRiS
Theory and Methods of Structural Design
Topology optimization including displacement and stress constraints
Optimal design of truss-like structures for minimum
weight subject to displacement and stress constraints,
including non-symmetric behavior of the material in
tension and compression (Drucker-Prager)
Optimal design and relevant D-P stress maps for three
optimization strategies with s=2/3: a) displacementconstrained, b) stress-constrained, c) displacementand stress- constrained
Sezione ProDRiS
10
Theory and Methods of Structural Design
11
Topology optimization of micro-structured media under dynamic loads
Optimal design for maximum
dynamic stiffness of Cosserat media,
investigating the effect of the
microstructure on the achieved
optimal layout
Deep cantilever
with two masses
A new material model to penalize stiffness and mass on
the design unknowns without numerical instabilities
Transition from truss-like to beam-like layouts, for increased values of the characteristic
length of the material
Sezione ProDRiS
Theory and Methods of Structural Design
12
Structural Optimization and Conceptual Design
Adaptive Evolutionary Process
Static Evolutionary Process
Sezione ProDRiS
Theory and Methods of Structural Design
13
Optimal Strut-and-Tie Models for Concrete Structures
φ6/225
2φ10
(0)
Linear Elastic (p0)
Cracked (p1)
SezioneNonlinear
ProDRiS
Nonlinear Cracked (p2>p1)
Nonlinear Cracked (p3>p2)
Nonlinear Cracked (p4=pu)
Theory and Methods of Structural Design
14
Form finding and structural optimization
Form finding in cable nets. Application of the Force Density Method
A bridge with two set of cables in two inclined planes
Optimal solution for a large cable roof (displacement scale factor =20%)
CABLE STRUCTURES
• Form finding;
• Internal mechanisms and prestressing distribution evaluation;
• Structural optimization (genetic algorithms);
• Applications: cable roofs, cable domes, cable beams,
footbridges with new forms.
Internal mechanism in a Geiger dome
Sezione ProDRiS
Theory and Methods of Structural Design
15
Nonlinear and Limit Analysis of Concrete Structures
Nonlinear Analysis
Limit Analysis
Fan
Semifan
Harp
Type
λ
pu1 = g+λq
[kN/m]
Nonlinear
Analysis
pu2
[kN/m]
Fan
9.14
429
300
0.70
Semifan
8.41
403
300
0.74
Harp
5.97
315
220
0.70
Limit Analysis
Sezione ProDRiS
Effectiveness
Factor
cracked concrete
concrete at failure (εc ≈ εcu)
pu2 / pu1
Effectiveness Factor (system level)
ν c = 0.5 +
1.25
fc
= 0.71
Theory and Methods of Structural Design
16
Markovian approach in reliability assessment and maintenance planning
P∆(ijt t)0 =
[ Fij (t0 + ∆t ) − Fij (t0 ) ]
pij
µ (t , k ) = (1 − δ (t , k ) ) ⋅
s
∑ [ 1 − Fik (t0 )] pik
Rk (t ) − S k (t )
Rk (t )
k =1
Conditional probability
different states.
of
transition
through
Condition index as suitable life-cycle
indicator for the selective maintenance.
Selective maintenance scenarios
1.0E-03
1.0
0.9
Condition index µ
P(m,0j)∆t|t0=1yr
8.0E-04
6.0E-04
4.0E-04
2.0E-04
d
0.8
0.7
0.6
0.5
0.4
µ =0.40
0.3
0.2
0.0E+00
0
5
10
15
20
25
30
35
40
45
50
8
6
0.1
0
10
20
30
Time [years]
instant of maintenance
1.20
1.10
n
Cq
q =1
(1 + v) q
Cm = ∑
n
t
m
= ∑ C0 q
q =1
C q = C f + ∑ δ k ⋅ Vk ⋅ cqk
k =1
Total cost Cm=C2, of the scenario (2)
normalized to the cost C1 of the
scenario (1). Cq is the sum of initial
cost C0 and replacement cost C(1,m), of
the scenario (2) normalized to the cost
C1 of the scenario (1), for different
values α of the fixed cost of
maintenance Cf =α C0.
Normalized cost c
Cost analysis applied to different scenarios
1.00
0.90
0.80
(1)
(2)
(2)
(2)
(2)
(2)
(2)
0.70
0.60
0.50
0.00
0.02
0.04
0.06
Discount rate n
Sezione ProDRiS
0.08
a =0.00
a =0.05
a =0.10
a =0.15
a =0.20
a =0.25
0.10
9
10
40
50
Theory and Methods of Structural Design
Life-Cycle Assessment and Design of Bridges and Structures
www.ialcce.org | www.iabmas.org
www.iabmas-italy.it
Certosa Cable-Stayed Bridge
0.150
Yielding Moment my
0.140
0.130
0.120
Damaged Structure
0.110
Rehabilitated Structure
0.100
0.090
0
Sezione ProDRiS
10
20
30
Time [year]
40
50
Theory and Methods of Structural Design
18
Structural Robustness and Seismic Resilience of Bridges and Structures
Exposure
Scenario
Life-Cycle Seismic Performance of a RC Bridge exposed to Corrosion
a g (t )
ag0
Time-variant Functionality!
Time-variant Resilience under Seismic
and Environmental Hazards
ROBUSTNESS
Q(t ) =
R=
Sezione ProDRiS
1
t h − t0
∫
th
t0
Q(t )dt
ProDRiS – Research Areas
19
Theory and Methods of Structural Design
• Structural Analysis
• Structural Reliability
• Structural Optimization
• Life-Cycle Design
Survey, Inspection, Monitoring and Structural Diagnostics
• Built Heritage
• Non Destructive Testing (NDT)
• Geophysical Prospections
Design of New Structures and Rehabilitation of Existing Structures
• Materials and Structures
• Bridges and Buildings
• Maintenance and Safety of Existing Structures
• Fastenings and Connections
Sezione ProDRiS
Survey, Inspection, Monitoring and Structural Diagnostics
Non-destructive testing: high resolution radar applications
Objective: development of NDT technologies for Cultural Heritage diagnostics
Example of ultra-high frequency radar survey in
small spaces between decorations and frescoes on
the counterfacade of S.Andrea Basilica in Mantova:
3D radar maps from dual-polarized data detect a
vertical metal anchor embedded in the masonry. It is
part of a tie-rod system connecting the counterfacade and the facade of the church.
Example of radar tomography:
horizontal section of a masonry pillar.
The radar map demonstrates that the
pillar perimeter consists of regular
stone blocks while the inner core
consists of irregular and poorly
cemented stone and brick material.
attenuation map high
low
Sezione ProDRiS
20
Survey, Inspection, Monitoring and Structural Diagnostics
21
Non-destructive testing: high resolution radar applications
Objective: development of radar technique for quality assessment of quarried stone blocks
Example of 3D radar reconstruction of
a defect in a marble block. The defect
consists of a clay inclusion that was
visible on the top surface of the block.
The radar result shows the size and
the 3D shape of the clay inclusion.
Sezione ProDRiS
Example of high frequency 3D
radar survey to map ultra-thin
cracks and discontinuities in a
marble block.
Survey, Inspection, Monitoring and Structural Diagnostics
22
Non-destructive testing: high resolution radar applications
Objective: development of radar technique for Quality Control of reinforced concrete
Example of 3D radar reconstruction
of the reinforcement net in a
concrete slab.
Analysis of radar data in perpendicular and parallel
polarization vs. reinforcement diameter: the ratio of
energy scattered in orthogonal polarizations shows
a behaviour consistent with the radar cross-section
theory. A dual-polarized antenna is a promising
tool for non-invasive assessment of rebar diameter.
Sezione ProDRiS
Survey, Inspection, Monitoring and Structural Diagnostics
23
Geophysical Prospections: Civil Protection applications
Objective: monitoring unstable rockslopes with microseismic sensor networks
Principle of microseismic monitoring
with a wireless sensor network.
Sezione ProDRiS
Example of a microseismic event detected by 5
three-component geophones installed on the
unstable rockslope of Mt. San Martino (Lecco).
Survey, Inspection, Monitoring and Structural Diagnostics
24
Geophysical Prospections: Civil Protection applications
Objective: development of technologies for search and rescue actions
Testing a new prototype of microseismic
equipment for detection and localization
of survivors trapped in building debris.
Sezione ProDRiS
Example of microseismic noise generated by a survivor
and detected by the prototype equipment in the training
field of the Search and Rescue team of VVF in Pisa.
Survey, Inspection, Monitoring and Structural Diagnostics
25
Vault of Sala dei Mappamondi - Royal Academy of Sciences TORINO
Geometrical survey and inspections for determination of the thickness of the vault
Mortar sampling for laboratory analyses
Sezione ProDRiS
Survey, Inspection, Monitoring and Structural Diagnostics
Vault of Sala dei Mappamondi - Royal Academy of Sciences TORINO
Thermographic investigations
Passive thermography was used
to identify
the shape of the timber structure
hidden inside the mortar layers.
Active thermography was useful
to detect
the
presence
of
detachments
between the frescoed surface layer
of the vault and its internal structure,
and to evaluate the crack pattern
that may be observed at the intrados
of the vault.
Stratigraphic surveys,
mortar sampling and
optical observations.
Sezione ProDRiS
26
Survey, Inspection, Monitoring and Structural Diagnostics
27
Repair of masonries by injection of grouts
The sample have been injected, in controlled condition of 20°C and 75% RH, using a injector and a pipe connected with a hole at the base
of a plexiglas cylinder, so to prevent any pressure loss. The same procedure was used for the prisms
Prisms and cylinders
were cut into slices
and the filled cracks
were observed.
Images
show
a
penetration
and
adhesion of the grout
to the crack surface
Sezione ProDRiS
Survey, Inspection, Monitoring and Structural Diagnostics
28
Durability of masonry repaired by CFRP textiles
Salt crystallization tests on brick masonry reinforced by CFRP textiles RILEM TC 243 MSC
Sample S2a_p1
220 200 180 160 140 120 100
80
60
40
20
0
2
4
8
10
mm
12
Damage measuring device: a) lasers profilometer, b) scheme of the measurement.
Moisture and Temperature Influence on FRP Masonry Bonding
The proposed artificial ageing was carried out as
follows (at 60% RH):
a: +20 to +70°C in 1 h (0.8°C/min)
b: 3 hours at 70°C
c: +70°C to -10°C in 1:30 h (1.0°C/min)
d: 3 hours at -10°C
e: -10°C to +70°C in 1:30 h (1.0°C/min)
Analysis at stereomicroscope showing two types
of rupture:
a) presence of a border below the fibre at the
limit of the impregnated layer;
b) b) detachment of the border with failure in the
brick
Sezione ProDRiS
S1_P1
S1_P2
S1_P3
S2a_P1
S3a_P3
S3a_P2
4.0
Loss (%)
mm
5.0
6
3.0
2.0
1.0
0.0
1
2
3
4
Cycle
5
6
7
Survey, Inspection, Monitoring and Structural Diagnostics
29
Fragility curves approach for long term behavior and durability assessment
εv(x103)
10
K
W
Ec S B
Q
M
In
0
Laboratory data
collection for long
behavior assessment
W
-10
Ec
εh(x103)
-20
In
Q
B
-30
-40
M
S
K
0
200000
400000
600000
800000
time [sec]
[mm]
0
50
100
150
200
0
MA T0
Cycle I
Cycle II
Cycle III
Cycle IV
Cycle V
Cycle VI
Cycle VII
5
A
15
[mm]
10
20
25
Laboratory data
collection for durability
assessment
30
F− (c)
1

C
0.9
1.5
1.0
1.5
−

 =2.5

 =1.5
0.8
L(c*, )
2.0
i(%)
2.0
i(%)
2.5
L(c*, )
2.5

 =2.0
0.7

0.6
 =3.0
0.5
0.4
1.0
0.3
0.5
0.5
0.0
0.0
0
1
2
3
4
5
6
Cycles
Sezione ProDRiS
7
0.2
0.1
0
1
2
3
4
Cycles
5
6
7
0
0
2
4
6
8
10
12
c (cycles)
14
16
18
20
Survey, Inspection, Monitoring and Structural Diagnostics
Durability of the bond between FRP/TRM and masonry substrates
30
[RILEM Tc CSM and
RELUIS 2014]
Influence of aggressive environmental conditions (moisture, temperature and
soluble salts presence) on the bond between FRP/TRM and masonry
substrates. Experimental tests (pull-off test) have been carried out on site on
full-scale models made in brickwork and lime-stonework at 3 different heights.
Sezione ProDRiS
Theory and Methods of Structural Design
31
Built heritage: structural survey
The bell tower of Arcisate
Location of the
investigations and
summary of the
results obtained
Survey of the external
crack pattern
Location of the internal and
external profiles on the masonry
sections.
Magnification of the geometry
variation:
the profiles that were not surveyed
are plotted with dashed lines.
Sezione ProDRiS
Scheme used to interpret
the displacement.
Survey, Inspection, Monitoring and Structural Diagnostics
32
Built heritage: structural survey
Static behaviour of a double curvature brickwork vault
Rigid body motion
of the grid of I
beams: the grid has
undergone a
rotation
Intrados of the vault
Crack pattern of the vault intrados
Hanging system: thin metal elements
bolted to the beam web
Hanging system: flat metal strips wrapped
below the beam flange
Rigid body motion
(in red) and profiles
as measured during
the geometrical
survey (in blue)
Cracks are more concentrated on the vault
portion with greater curvature, especially
where the vault perimeter is not confined
by the hallway
The direction of diagonal cracks
correspond to that of the buttress walls
A long crack going
E-W is probably due to tensile stress,
according to the I iron beam profiles
described later
Sezione ProDRiS
Load-induced displacements (magnified 10 times):
symmetrical shapes characteristic of continuous beams,
with a rather “flat” center portion
Larger vertical displacement probably due to tensile stress
Survey, Inspection, Monitoring and Structural Diagnostics
33
Investigation and diagnosis of the built patrimony of historic centres in seismic areas
A methodology for the study of vulnerability at large scale:
1. Definition of the building and masonry typology
2. Crack pattern and structural damage survey
3. Use of an abacus and interpretation of the crack pattern
4. Material characterization: laboratory and on site tests (a minimal investigation program is suggested)
5. Seismic vulnerability analysis
6. Choice and analytical assessment of the improvement techniques
Isolated building
Crack pattern survey also adopting axonometric
representations and volumetric stratigraphical analysis, in order
to single out their typical failure mechanisms, also in presence
of modern or traditional retrofitting techniques.
A
A'
Row building
UI 197
Survey
template
UI 198
UI 199
Complex buildings
2.3 - SCHEMA DEI CINEMATISMI E STATO DI DANNO (anno 2001) DELL'EDIFICIO U.M.I. 10
1
1
2
2
3
2
4
0
1
5m
3
PROSPETTO SUD
1
5
0
1
3
5m
PROSPETTO NORD
1 Danno: lesioni diffuse in corrispondeza delle teste delle
travi di copertura.
1 Meccanismo: martellamento degli elementi di copertura
per spinta fuori piano.
2 Danno: lieve spanciamento della parete con lesioni
pressocchè verticali in corrispondenza degli elementi di
differente rigidezza.
2 Meccanismo: spinta fuori dal piano della parete sud a
causa della particolare conformazione della pianta, della
disomogeneità del tessuto murario, e della spinta delle
travi del solaio.
3 Danno: lesione verticale in corrispondenza dell'attacco
dei due edifici.
3 Meccanismo: risposte differenziate all'azione sismica
degli edifici adiacenti; nel punto di collegamento, che è la
zona più debole, si presenta una concentrazione di sforzi
di trazione che porta alla rottura del collegamento stesso.
4 Danno: lesione nel maschio snello
4 Meccanismo: schiacciamento dell'elemento snello per
forze nel piano della parete.
5 Danno: lesione in prossimità dell'angolata
5 Meccanismo: distacco tra i muri d'ambito per interazione
di forze agenti sulle pareti ortogonali.
Sezione ProDRiS
Application of simply kinematics
models to describe the mechanical
behaviour
Survey, Inspection, Monitoring and Structural Diagnostics
Historic masonry quality evaluation with NDT and MDT
34
[RELUIS 2014]
A necessary methodology for the quality evaluation of historic load-bearing
STONE masonry with visual inspection and using the test results based on
Non-Destructive Techniques.
With the help of an optical system, the double
flat-jack test is able to show in real time the
distribution of the forces in the irregular
masonry specimen, showing stones rotation
and where tensile stress is higher and so
cracks are forming. Other complementary ND
tests have to be evaluated to understand the
intrinsic “ductility” of that poor masonry.
1.20
2 000
1 900
SU-PM-J1D
6
LVDT 1
1 800
LVDT 2
LVDT 4
Sforzo [N/mm2]
LVDT 5
2
0.80
5 4 3
4
1
LVDT 3
2
1 700
7
3
1 600
1 500
1 400
1
1 300
1 200
1 100
1 000
Pietra 6-4
900
3
0.40
800
Pietra 3-7
700
pietra 5-2
600
Stato di
sforzo locale
500
400
300
0.00
εv
εl
2
5
200
100
0
-2.00
-1.00
0.00
1.00
2.00
Deformazione [µm/mm]
Sezione ProDRiS
0
200
400
600
800
1000
1200
1400
1600
Survey, Inspection, Monitoring and Structural Diagnostics
35
Building Information Modelling BIM applied to Built Heritage [PRIN 2013-15]
Evaluation of the use of BIM for the design and the documentation of built heritage in
the restoration process. The interoperability among BIM (Revit or ArchiCad) and
structural analysis software is evaluated, as well as the documentation of the crack
pattern, the improvement of the calculation model with the introduction of the crack
pattern and the creation of a control system of NDT data and monitoring tests results.
BIM as a crack pattern documentation
and crack pattern exported in Abaqus
Export/import procedure results of two simple testing models with different format.
Sezione ProDRiS
Example of virtual sensor placed on the
model and its records
ProDRiS – Research Areas
36
Theory and Methods of Structural Design
• Structural Analysis
• Structural Reliability
• Structural Optimization
• Life-Cycle Design
Survey, Inspection, Monitoring and Structural Diagnostics
• Built Heritage
• Non Destructive Testing (NDT)
• Geophysical Prospections
Design of New Structures and Rehabilitation of Existing Structures
• Materials and Structures
• Bridges and Buildings
• Maintenance and Safety of Existing Structures
• Fastenings and Connections
Sezione ProDRiS
Design of New Structures and Rehabilitation of Existing Structures 37
Advanced Cement-Based Materials
40
45SE28-1
45SE28-2
45SE28-3
σ (MPa)
30
20
10
0
0
2
4
ε %o
6
8
Compressive behavior of Self-Compacting Concrete
210
150
105
Ø24
Ø16
48
32
72
SCC
UNBONDED
LENGTH
24
16
UNBONDED
LENGTH
24
8 16
Ø8
SCC
UNBONDED
LENGTH
SCC
Effect of size in the bond behavior of Self-Compacting Concrete
Thermal degradation of fiber reinforced extruded materials
Structural behavior of Self-Compacting Concrete Filled Tubes
Sezione ProDRiS
10
Design of New Structures and Rehabilitation of Existing Structures 38
Post-installed fastenings for use in concrete
Simulated seismic crack movement conditions
τ = τ (Δ𝑇𝑇,Δ𝑡𝑡, 𝑇𝑇𝑚𝑚𝑚𝑚𝑚𝑚 , 𝑡𝑡)
13
12
11
10
9
fb,test (N/mm²)
8
fb,test
7
6
T11
fb,m=a.θ-b
5
4
t1
3
2
1
θmax
θk
0
0
θ50
min
100
150
200
250
300
350
Temperature (°C)
Fire resistance of post-installed rebars: decay of bond strength
as a function of temperature and exposure time
Sezione ProDRiS
Post-installed fastenings under seismic action
Design of New Structures and Rehabilitation of Existing Structures 39
Structural and non-structural use of glass
Mechanical behaviour of point fixing devices: experimental and numerical analyses
Flexural and lateral torsional buckling experimental
investigation of glass beams
Sezione ProDRiS
Influence of ambient condition on viscous behaviour of
laminated glass
Design of New Structures and Rehabilitation of Existing Structures 40
Wood connections with three-dimensional nailing plates
Behavior under monotonic
and cyclic loading
Three dimensional nailing plates for structural use
in wood connections: angle brackets, joist hangers,
post bases, hold downs
Behaviour of dowel-type
fasteners
Joist Hangers: experimental investigation
Sezione ProDRiS
Angle Brackets: experimental investigation and
enhancement in analytical model
Design of New Structures and Rehabilitation of Existing Structures 41
Seismic Design and Retrofitting of Precast Structures
2001-2003 ECOLEADER
ELSA/JRC, Ispra
Sezione ProDRiS
2003-2006 GROWTH
2009-2012 SAFECAST
2012-2015
SAFECLADDING
Design of New Structures and Rehabilitation of Existing Structures 42
Natural Hazards vs decision-making processes in buildings life-cycle management
Network diagram explaining potential connection between Structural Design
Function and vulnerability parameters.
Poisson Energy Theory
Prof. Imagawa, Denk Univbersity, Tokyo, Japan
 Natural conditions
 Social environments
Fy {M x ; S y ; Lz ; J n ; Cα ; Dβ ; Eγ } ≥ 
Required performances

 Past and present designs
This theory establishes an interdependent connection between the main
features that define a building and its performance under external loading
conditions.
Development of
a new cognitive function: relation between the main
parameters that define an optimal intervention strategy (structural performance,
sustainability, funds).
Safety optimisation

 Building heritagepreservation

Human life safeguard
 Material resourcesoptimisation
GSM { Pxy ; S z ; Fα } ≥ 
Environmental preservation

Energy efficiency

Cost optimisation

 Funds management andrationalisation
Sezione ProDRiS
Design of New Structures and Rehabilitation of Existing Structures 43
Testing, Modelling and Design of R/C slabs
Testing and modelling of voided slabs
Punching
Tests
LPMSC
Politecnico
di Milano
Nonlinear analysis of flat slabs
for gravity and lateral actions
Pushover
and
Nonlinear
Time History
Analysis of
Flat slab
floors
NLFE
Modelling
(Abaqus)
Voided
Slabs
(Daliform)
Sezione ProDRiS
Grid model
(Coronelli, 2010)
Design of New Structures and Rehabilitation of Existing Structures 44
Analysis and monitoring of the Duomo di Milano
Limit Analysis of the cathedral of Milan
FE modelling of foundation soil
and settlement monitoring
3D FE analyses
NLFE
Modelling
(Abaqus)
 Study of the
geometry and loads
 Structural models
 Limit analysis
Monitoring
(Veneranda Fabbrica del Duomo)
Sezione ProDRiS
Design of New Structures and Rehabilitation of Existing Structures 45
Residual bearing capacity of riveted steel ties deformed by the swelling of interstitial rust
ν = 0,5
Pressure/displacement relationships for an axial force ν=N/Nyelding=0,5: (a) cosinusoidal pressure profile; (b) sinusoidal pressure
profiles; (c) F.E. solution
without
section reduction due to the rivet hole; (d) F.E. solution with section reduction due to rivet hole .
Sezione
ProDRiS
Design of New Structures and Rehabilitation of Existing Structures 46
Integral Bridges – An Integral Bridge for A380 Transit
The West Bridge under construction.
Cross section of the West Bridge. Relative
proportions among bridge, aircraft and railway.
Displacement fields for different positions of the aircraft.
Sezione ProDRiS
Deformed configurations for the
heaviest loading conditions.

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