corso di dottorato in ottimizzazione strutturale: applicazione mensola strallata - bontempi
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Franco Bontempi
Ordinario di Tecnca delle Costruzioni
Facolta’ di Ingegneria Civile e Industriale
Sapienza Universita’ di Roma
Introduzione alla
OTTIMIZZAZIONE STRUTTURALE:
APPLICAZIONE AD UNA
MENSOLA STRALLATA
2
Ottimizzazione Strutturale
franco.bontempi@uniroma1.it
3
Object of the course
• Introduction of basic and advanced ideas
and aspects of structural design without to
much stress on the analytical apparatus
but with some insigth on the computational
techniques.
Ottimizzazione Strutturale
franco.bontempi@uniroma1.it
4
General Scheduling
• 1st Day:
Basic definitions of structure, requirements,
values, optimization, …;
• 2nd Day:
Advanced specific case of structural optimization
(service / ultimate / extreme scenarios);
• 3rd Day:
Advanced concepts (structural systems,
advanced criteria, tools of design)
EVOLUTION OF THE DESIGN
OF A CABLE-STAYED BRACKET
THE OBJECT
An innovative device for
precast/prestressed beam support
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CONNECTION REGIONS
• Presence of high stress levels;
• Diffusive field of stress - so-called D-regions;
• Geometrical complexity, related to the position and interference of different structural parts converging there;
• Requirements of minimum space usage, essentially due to architectural appearance;
• Necessity to guarantee a substantial good structural behavior - strength, ductility, and robustness;
• Demand from constructability point of view.
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BASIS OF DESIGN (1)
• simplicity:
the structural configuration of the connection must be made by very regular and flat parts, by which
– the stress state has the most possible uniformity;
– there are no stress concentrations;
– the load transfer is obtained by the most straight path;
– it is possible to develop a complete integration between steel parts and concrete mass, with an
accurate structural anchorage.
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BASIS OF DESIGN (2)
• dependability:
the structural configuration must be have
– suitable functional performance characteristics
(Serviceability Limit States, SLS),
– appropriate strength capacity
(Ultimate Limit States, ULS),
– capacity to support accidental situations, without
showing disproportionate consequences when
triggered by limited damage
(Structural Robustness).
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CONCEPTUAL DESIGN
Definition and optimization
of the structural configuration
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STRUCTURAL SCHEME
Versione iniziale
Versione finale
beam SX beam DX
column
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LOAD SCHEMES
Reinforcement
Bars
Vsd
Reinforcement
Bars
Vsd
Reinforcement
Bars
Vsd
Reinforcement
Bars
Vsd
SYM ASYM
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FIRST ANALYSIS (A):
two dimensional geometry
co
lum
n
a
Vsd
Vsd
a/2
Vsd*=Vsd/2
Vsd* =Vsd/2
co
lum
n
a
Vsd
Vsd
co
lum
n
a
Vsd
Vsd
a/2
Vsd*=Vsd/2
Vsd* =Vsd/2
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• the steel parts, the longitudinal bars and the
stirrups are represented by bars working both
in tension and in compression, while concrete
parts are lumped into bars with no tension
behavior;
• one model a segment of concrete column
sufficient to extinguish the diffusive effects
connected with this D-region, i.e. until a B-
region is reached, governed by the so-called
Bernoulli stress regime;
FIRST ANALYSIS (B):
mechanical modeling by S&T
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Strut & Tie Models
Reinforcement
Bars
Vsd
Reinforcement
Bars
Vsd
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Reinforcement
Bars
Vsd
Reinforcement
Bars
Vsd
Strut & Tie Results
stirrups longitudinal bars
concretesteel bracket
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Hybrid models
Reinforcement
Bars
Vsd
Reinforcement
Bars
Vsd
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Global responseEnd of external bracket displacement
-8,00
-7,00
-6,00
-5,00
-4,00
-3,00
-2,00
-1,00
0,00
0 500 1000 1500 2000
Load [KN]
Uy
[m
m]
Vsd=600 KN - th=8mm
Vsd=850 KN - th=10mm
Vsd=1050 KN - th=12mm
Vsd=1500 KN - th=18mm
Y
X
End of external bracket displacement
-8,00
-7,00
-6,00
-5,00
-4,00
-3,00
-2,00
-1,00
0,00
0 500 1000 1500 2000
Load [KN]
Uy
[m
m]
Vsd=600 KN - th=8mm
Vsd=850 KN - th=10mm
Vsd=1050 KN - th=12mm
Vsd=1500 KN - th=18mm
Y
X
Y
X
Y
X
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Local response
>290
<-290
>290
<-290
>290
<-290
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EVOLUTION OF THE FORM (1)
600.0
250.0
15.0
60.2
70.0
145.0
56°
66°
50°
378.5
188.0
320.1ww
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EVOLUTION OF THE FORM (2)
600.0
369.4
55°
66°
50°
224.4
15.0
60.0
70.0
145.0
280.0
399.4
126.0
100.8
195.0
230.7
188.0
69.7
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EVOLUTION OF THE FORM (3)
Versione iniziale
Versione finale
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Results for
concrete core and steel frame
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Results for
steel bottom frame and attacment
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CONCLUSIONS• The evolution of the design of a bracket component,
supported by a cable-stayed system, is presented.
• This apparently simple element conceals a rather complex structural geometry, developed to be suitable both for strength requirements and constructability. The so devised solution can assure:– Manufacturing of precast elements without exterior parts;
– Minimal size of the bracket and completely hidden insertion in the supported beams;
– Compliance with different standards.
• The evolution of the leading concepts and of the geometry of this element is explained together with the numerical analysis obtained both by synthetic models, like strut & tie, and by full non linear finite element models.
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Stro N
GERwww.stronger2012.com
52
54
INDEX PART 1
Basis of the Problem
Strut & Tie Modeling
Finite Element Analysis by
Substrucuring Technique and S&T
Improvement Strategies
Models and Programs Validation
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INDEX PART 2
Thickness Improvement
Shaping
Results for Shaping Type B
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Vsd [kN] thickNess (th) [mm]
600 8
850 10
1050 12
1500 18
SCENARIOUS
Lateral
Plate
Original Optimized Shaped
Weight (kg) 9,6 9,1 9,9
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STRUCTURAL RESPONSE (I)
Upper edge displacement
0,00
0,05
0,10
0,15
0,20
0,25
0,30
0,35
0,40
0,45
0 500 1000 1500 2000
Load [KN]
Ux
[m
m]
Vsd=600 KN - th=8mm
Vsd=850 KN - th=10mm
Vsd=1050 KN - th=12mm
Vsd=1500 KN - th=18mm
Y
X
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Y
X
Centre of Diaphram
0,0
50,0
100,0
150,0
200,0
250,0
0 500 1000 1500 2000
Load [KN]
Str
es
s_
x [
MP
a]
Vsd=600 KN - th=8mm
Vsd=850 KN - th=10mm
Vsd=1050 KN - th=12mm
Vsd=1500 KN - th=18mm
Centre of Diaphram
0,00%
0,02%
0,04%
0,06%
0,08%
0,10%
0,12%
0 500 1000 1500 2000
Load [KN]
To
tal S
tra
in_
x
Vsd=600 KN - th=8mm
Vsd=850 KN - th=10mm
Vsd=1050 KN - th=12mm
Vsd=1500 KN - th=18mm
Centre of Diaphram
0,0
50,0
100,0
150,0
200,0
250,0
0,00% 0,02% 0,04% 0,06% 0,08% 0,10% 0,12%
Total Strain_x
Str
ess_x [
MP
a]
Vsd=600 KN - th=8mm
Vsd=850 KN - th=10mm
Vsd=1050 KN - th=12mm
Vsd=1500 KN - th=18mm
STRUCTURAL RESPONSE (II)w
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End of external bracket displacement
-8,00
-7,00
-6,00
-5,00
-4,00
-3,00
-2,00
-1,00
0,00
0 500 1000 1500 2000
Load [KN]
Uy
[m
m]
Vsd=600 KN - th=8mm
Vsd=850 KN - th=10mm
Vsd=1050 KN - th=12mm
Vsd=1500 KN - th=18mm
Y
X
STRUCTURAL RESPONSE (III)w
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ALTERNATIVE GEOMETRIC
CONFIGURATIONS
TIPO B
1
2 3450°
31°
288.8
83.2
69.0
30.0
TYPE B
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Vsd = 600 kN SYM th = 8 mm
cap element stress / e-plastic analysis
>290
<-290
>290
<-290
von MISES
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Vsd = 600 kN ASYM th = 8 mm
cap element stress / e-plastic analysis
>290
<-290
von MISES
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Vsd = 850 kN SYM th = 10 mm
cap element stress / e-plastic analysis
>290
<-290
von MISES
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Vsd = 850 kN ASYM th = 10 mm
cap element stress / e-plastic analysis
>290
<-290
von MISES
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Vsd = 1050 kN SYM th = 12 mm
cap element stress / e-plastic analysis
>290
<-290
von MISES
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Vsd = 1050 kN ASYM th = 12 mm
cap element stress / e-plastic analysis
>290
<-290
von MISES
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Vsd = 1500 kN SYM th = 18 mm
cap element stress / e-plastic analysis
>290
<-290
von MISES
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Vsd = 1500 kN ASYM th = 18 mm
cap element stress / e-plastic analysis
>290
<-290
von MISES
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PART 1Framework
of the structural problem
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DESIGN CRITERIA
• SIMPLICITY:
1. the load path from the loading appliction points to
the main internal region of the structural element
must be the simplest and the quitest; it means that
– the stress flow should be regular;
– stress concentrations should be avoided;
– the loading transfer should prefer direct
placement;
– integration between steel parts and concrete
must be accurate and anchorage truthful;
• DEPENDABILITY;
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PERFORMANCE CRITERIA (i)
• Ultimate Limit State:
1. strength verified by partial safety factors
disequations; there are admitted yielded
parts of the bracket and damaged portions
of the concrete in the structural element;
– the strength capacity will be verified by non
linear analysis, starting from unloaded to
collapse loading;
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PERFORMANCE CRITERIA (ii)
• Serviceability Limit State:
1. the structural behavior should be elastic-
linear until an adequate loading level
(usually, the ultimate loading level / 1.5);
– in particular, steel parts must not be yielded
anywhere and the concrete must experience
a low stress level;
2. the displacements of the bracket for service
loading must be limited;
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PERFORMANCE CRITERIA (iii)
• Structural Robustness:
1. the connection device failure should develop
after major failure of the structural elemnt at
which the connection device is inserted;
2. the connection device must be able to
support the failure of one of the external ties,
i.e. each tie and directly connected parts
must be able anyway to support the double
of the service limit loading;
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tie-rod
frame
tie shield
tie junction
closure plate
C junction
bottom rib
external plate
external bracket
rigid block
adjacent concrete
STRUCTURAL PARTSw
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LOADING SYSTEMS:
SYM. vs ASYM.
Reinforcement
Bars
Vsd
Reinforcement
Bars
Vsd
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-1000
-800
-600
-400
-200
0
200
400
600
800
1000
-2000 0 2000 4000 6000 8000 10000
N
M
SYM
ASYM
M [kNm]
compressionN [kN]
tension
stirrups
longitudinal
bars
As=5 ø 22
As’=5 ø 22
ø 8/2b 9 cm
COLUMN REINFORCEMENT DESIGN
Reinforcement
ACTION N [kN] M [kNm]
SYM 2100 0
ASYM 1050 462
50 cm
60 cm
79
STRUCTURAL MODELING (i)
• A slice of half column is considered
(plane stress assumption)
co
lum
n
a
Vsd
Vsd
a/2
Vsd*=Vsd/2
Vsd* =Vsd/2
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STRUCTURAL MODELING (model #1)
Strut & Tie modeling of the stayed bracket
STEP #1 STEP #2
STEP #3 STEP #4
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STRUCTURAL MODELING (model #2)
Alternative S&T modeling of the stayed bracket
STEP #1
STEP #3 STEP #4
STEP #2
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STRUCTURAL MODELING (model #3)
Alternative S&T modeling of the stayed bracket
STEP #1
STEP #3 STEP #4
STEP #2
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STRUCTURAL MODELING
OF CONCRETE PART (I):
trusswork discretization
ablslAA
absaAA
basbAA
ba
ba
ba
dd
yy
xx
2
2
2
2
2
83
2
383
2
383
2
,
,
,
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4321,,, uuuu
VIVIVIIIIIINNNNNN ,,,,,
ax
yu
x
by
yv
y
abxv
yu yx
bl
aNNNNN
VIVIII
x
al
bNNNNN
VIVIVIII
y
lNNN VIV
xy
xyyx NNN ,,
STRUCTURAL MODELING
OF CONCRETE PART (II):
stress representation
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LOADING SYSTEMS: SYM.
Reinforcment
Bars
Vsd
C + SteelCSteel
VsdVsd
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LOADING SYSTEMS: ASYM.
Reinforcment
BarsC + SteelCSteel
Vsd Vsdww
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Model S&T #1
Results for SYM
loading system
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Vsd = 1050 kN – cap element stress
• max tension = 389,7 MPa
• min compression = -232,5 MPa• tension = 582,7 MPa
90
Vsd = 1050 kN – reinforcement bar stress
• max tension = 96,3 MPa
• min compression = -59,1 MPa
stirrups longitudinal
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Vsd = 1050 kN – concrete stress
• max tension = 0 MPa
• min compression = -17,7 MPa
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Model S&T #1
Results for ASYM
loading system
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Vsd = 1050 kN – cap element stress
• max tension = 228,1 MPa
• min compression = -424,3 MPa• tension = 582,7 MPa
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Vsd = 1050 kN – reinforcement bar stress
stirrups longitudinal
• max tension = 280,9 MPa
• min compression = -125,4 MPa
95
Vsd = 1050 kN – concrete stress
• max tension = 0 MPa
• min compression = -25,1 MPa
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Model S&T #2
Results for SYM
loading system
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Vsd = 1050 kN – cap element stress
• max tension = 422,1 MPa
• min compression = -295,7 MPa• tension = 582,7 MPa
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Vsd = 1050 kN – reinforcement bar stress
stirrups longitudinal
• max tension = 143,9 MPa
• min compression = -49,4 MPa
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Vsd = 1050 kN – concrete stress
• max tension = 0 MPa
• min compression = -19,8 MPa
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Model S&T #2
Results for ASYM
loading system
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Vsd = 1050 kN – cap element stress
• max tension = 631,8 MPa
• min compression = -718,7 MPa• tension = 582,7 MPa
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Vsd = 1050 kN – reinforcement bar stress
• max tension = 331,3 MPa
• min compression = -115,5 MPa
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Vsd = 1050 kN – concrete stress
• max tension = 0 MPa
• min compression = -23,1 MPa
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Model S&T #3
Results for SYM
loading system
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Vsd = 1050 kN – cap element stress
• max tension = 380,1 MPa
• min compression = -303,7 MPa• tension = 582,7 MPa
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Vsd = 1050 kN – reinforcement bar stress
stirrups longitudinal
• max tension = 120 MPa
• min compression = -83,6 MPa
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Vsd = 1050 kN – concrete stress
• max tension = 0 MPa
• min compression = -28,8 MPa
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Sinthesis of the Results for
S&T Models
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SUMMARY OF RESULTS (SYM) Vsd = 1050 kN
SYM Vsd= 1050 kN Limit
Model 1 2 3 Design
SMAXBIEL [N/mm^2] 582,71 582,71 582,71 580
TENSION [kN] 696,1 696,1 696,1
SMAXTEL [N/mm^2] 389,75 422,02 380,1 290
TENSION [kN] 423,2 458,3 412,8
SMINTEL [N/mm^2] -232,46 -295,7 -303,68 -290
SMAXSTAF [N/mm^2] 96,3 143,86 120,02 374
SMINSTAF [N/mm^2] -0,02 29,99 -24,88 -374
SMAXLONG [N/mm^2] -52,93 -36,34 -48,85 374
SMINLONG [N/mm^2] -59,16 -49,41 -83,6 -374
SMAXCLS [N/mm^2] 0 0 0 1,5
SMINCLS [N/mm^2] -17,72 -19,84 -28,8 -28
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SUMMARY OF RESULTS (ASYM) Vsd = 1050 kN
ASYM Vsd= 1050 kN Limit
Model 1 2 Design
SMAXBIEL [N/mm^2] 582,71 582,71 580
TENSIONE [kN] 696,1 696,1
SMAXTEL [N/mm^2] 228,09 631,84 290
TENSION [kN] 305,18 341,2
SMINTEL [N/mm^2] -424,31 -718,65 -290
SMAXSTAF [N/mm^2] 164,65 297,32 374
SMINSTAF [N/mm^2] 1,75 0 -374
SMAXLONG [N/mm^2] 280,92 331,34 374
SMINLONG [N/mm^2] -125,4 -115,55 -374
SMAXCLS [N/mm^2] 0 0 1,5
SMINCLS [N/mm^2] -25,08 -23,11 -28
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Legenda
Output Descrizione Valore di
Design
[N/mm^2]
SMAXBIEL tensione massima negli elementi rappresentanti i tiranti 580
SMAXTEL tensione massima negli elementi rappresentanti il telaio 290
SMINTEL tensione minima negli elementi rappresentanti il telaio -290
SMAXSTAF tensione massima negli elementi rappresentanti le armature lente
secondarie del pilastro
374
SMINSTAF tensione massima negativa negli elementi rappresentanti le armature lente
secondarie del pilastro
- 374
SMAXLONG tensione massima negli elementi rappresentanti le armature lente
principali del pilastro
374
SMINLONG tensione massima negativa negli elementi rappresentanti le armature lente
principali del pilastro
- 374
SMAXCA tensione massima negli elementi rappresentanti il calcestruzzo 1,5
SMINCA tensione massima negativa negli elementi rappresentanti il calcestruzzo -28
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FINITE ELEMENT
ANALYSIS BY
SUBSTRUCTING
TECHNIQUE AND S&T
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RIGID
LINKS
BEAM ELEMENTS
STRUCTURAL MODELING: LINKSw
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Reinforcement
Vsd Vsd
C + SteelCSteel
Vsd
SYMMETRIC CONFIGURATION
118
Vsd = 1050 kN – cap element stress:
elastic analysis (stress X)
>290
<-290
119
Vsd = 1050 kN – cap element stress:
elastic analysis (stress Y)
>290
<-290
120
>290
<-290
Vsd = 1050 kN – cap element stress:
elastic analysis (Von Mises) (I)w
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Vsd = 1050 kN – cap element stress:
elastic analysis (Von Mises) (II)
>580
<-580
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Vsd = 1050 kN – reinforcement bar stress
stirrups longitudinal
• max tension = 96,6 MPa
• min compression = -61,3 MPa
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concrete
• max tension = 0 MPa
• min compression = -18,2 MPa
• tension = 582,7 MPa
Vsd = 1050 kN – ties and concrete stressw
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SUMMARY OF RESULTS (SYM) Vsd= 1050 kN
SIMM Vsd= 1050 kN Limit
Model 1 substruct Design
SMAXBIEL [N/mm^2] 582,71 582,72 580
TENSION [kN] 696,1 696,1
SMAXTEL
(SMTEL_x)[N/mm^2] 389,75 653,2 290
TENSION [kN] 423,2 388,07
only “substructured” SMTEL_y [N/mm^2] 291,5 290
only “model 1” SMINTEL [N/mm^2] -232,46 -290
only “substructured” SmTEL_x [N/mm^2] -530,4 -290
only “substructured” SmTEL_y [N/mm^2] -641,62 -290
SMAXSTAF [N/mm^2] 96,3 90,32 374
SMINSTAF [N/mm^2] -0,02 -6,93 - 374
SMAXLONG [N/mm^2] -52,93 -55,52 374
SMINLONG [N/mm^2] -59,16 -61,29 - 374
SMAXCLS [N/mm^2] 0 0 1,5
SMINCLS [N/mm^2] -17,72 -18,21 -28
Linear elastic Steel
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ELASTIC- PLASTIC MATERIAL LAW
WITH VON MISES CRITERION
62519.4
]N/mm[ 10000
max
2
max
00138.0
]N/mm[ 290 2
y
y
][N/mm 210000 2
0 E
*100/1 01 EE
x10^(-3)
E0
E1
y
ymax
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>290
<-290
Vsd = 1050 kN – cap element stress:
e-plastic analysis (stress X)w
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>290
<-290
Vsd = 1050 kN – cap element stress:
e-plastic analysis (stress Y)w
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.fra
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129
>290
<-290
Vsd = 1050 kN – cap element stress:
e-plastic analysis (Von Mises) (I)w
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>580
<-580
Vsd = 1050 kN – cap element stress:
e-plastic analysis (Von Mises) (II)w
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Vsd = 1050 kN – cap element strain:
e-plastic analysis (Von Mises strain) w
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132
Vsd = 1050 kN – reinforcement bar stress
• max tension = 132 MPa
• min compression = -54,9 MPa
stirrups longitudinal
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Vsd = 1050 kN – ties and concrete stress
concrete
• max tension = 0 MPa
• min compression = -19,8 MPa• tension = 582,7 MPa
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SUMMARY OF RESULTS (SYM) Vsd= 1050 kN
SIMM Vsd= 1050 kN Limit
Model elastic e-plastic Design
SMAXBIEL [N/mm^2] 582,72 582,72 580
TENSION [kN] 696,1 696,1
SMTEL_x [N/mm^2] 653,2 560 290
TENSION [kN] 388,07 371,09
SMTEL_y [N/mm^2] 291,5 324,26 290
SmTEL_x [N/mm^2] -530,4 -515,65 -290
SmTEL_y [N/mm^2] -641,62 -632,07 -290
SMAXSTAF [N/mm^2] 90,32 122,93 374
SMINSTAF [N/mm^2] -6,93 15,55 - 374
SMAXLONG [N/mm^2] -55,52 -42,81 374
SMINLONG [N/mm^2] -61,29 -54,89 - 374
SMAXCLS [N/mm^2] 0 0 1,5
SMINCLS [N/mm^2] -18,21 -19,77 -28
elastic steel
e-plastic steel
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-25
-20
-15
-10
-5
0
0 200 400 600 800 1000 1200
Load
Uy
Load application
Structural response (1)w
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0,00
2,00
4,00
6,00
8,00
10,00
12,00
14,00
0 200 400 600 800 1000 1200Load
Ux
Spigolo alto
Structural response (2)w
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0,000
0,001
0,001
0,002
0,002
0,003
0 200 400 600 800 1000 1200
Load
Ela
sti
c S
train
_x
Centre of Diaphram
-0,010
0,000
0,010
0,020
0,030
0,040
0,050
0,060
0 200 400 600 800 1000 1200
Load
Pla
sti
c S
tra
in_
x
Centre of Diaphram
0,000
0,010
0,020
0,030
0,040
0,050
0,060
0 200 400 600 800 1000 1200
Load
To
tal S
tra
in_
x
Centre of Diaphram
Structural response (3)w
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0
50
100
150
200
250
300
350
400
450
0,0000 0,0100 0,0200 0,0300 0,0400 0,0500 0,0600
Total Strain_x
Str
ess_x
Centre of Diaphram
0
50
100
150
200
250
300
350
400
450
0 200 400 600 800 1000 1200
Load
Str
es
s_
x
Centre of Diaphram
0,000
0,010
0,020
0,030
0,040
0,050
0,060
0 200 400 600 800 1000 1200
Load
To
tal S
train
_x
Centre of Diaphram
Structural response (4)w
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C + SteelCSteel
Vsd
ASYMMETRIC CONFIGURATION
Reinforcement Bars
Vsd
e-plastic steel
140
Vsd = 1050 kN – cap element stress
e-plastic analysis (stress X)
>290
<-290
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Vsd = 1050 kN – cap element stress
e-plastic analysis (stress Y)
>290
<-290
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>290
<-290
Vsd = 1050 kN – cap element stress
e-plastic analysis (Von Mises) (I)w
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Vsd = 1050 kN – cap element stress
e-plastic analysis (Von Mises) (II)
>580
<-580
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Vsd = 1050 kN – reinforcement bar stress
• max tension = 348,9 MPa
• min compression = -116,1 MPa
stirrups longitudinal
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145
• max tension = 0 MPa
• min compression = -23,5 MPa
• tension = 582,7 MPa
Vsd = 1050 kN – ties and concrete stress
concrete
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COMMENTS• The actual configuration of the Stayed Bracket
seems to be not able in sustaining adequately the load of Vsd=1050 kN both in symmetric and asymmetric load scenarios.
• In general, the frame stresses are greater than the yielding values, also if they are less than the failure values.
• The amplitude of the yielded zone suggest to adopt strategies to improve the stayed bracket performances:
Strategy 1: improve the frame thickNess
Strategy 2: improve the frame size
Strategy 3: downloading
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Reinforcement
Vsd Vsd
C + SteelCSteel
Vsd
SYMMETRIC CONFIGURATIONw
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.fra
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149
th0
Strategy 1: improve the frame thickNess
Actual Improved
th1
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150
Vsd = 1050 kN – cap element stress
e-plastic analysis (stress X)
>290
<-290
Strategy 1: improve the frame thickNess
Actual thickNess
th = 6 mm
Improved thickNess
th = 10 mm
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151
Vsd = 1050 kN – cap element stress
e-plastic analysis (stress Y)
Strategy 1: improve the frame thickNess
>290
<-290
Actual thickNess
th = 6 mm
Improved thickNess
th = 10 mm
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Vsd = 1050 kN – cap element stress
e-plastic analysis (Von Mises) (I)
>290
<-290
Actual thickNess
th = 6 mm
Strategy 1: improve the frame thickNess
Improved thickNess
th = 10 mm
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>580
<-580
Vsd = 1050 kN – cap element stress
e-plastic analysis (Von Mises) (II)
Actual thickNess
th = 6 mm
Strategy 1: improve the frame thickNess
Improved thickNess
th = 10 mm
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Vsd = 1050 kN – cap element strain – e-
plastic analysis (Von Mises strain)
Strategy 1: improve the frame thickNess
Actual thickNess
th = 6 mm
Improved thickNess
th = 10 mm
155
Vsd = 1050 kN – cap element strain
e-plastic analysis (Von Mises strain) Improved thickNess
th = 10 mm
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>580
<-580
Vsd = 1050 kN – cap element stress
e-plastic analysis (Von Mises)
th = 10mm
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Vsd = 1050 kN – cap element stress
e-plastic analysis (Von Mises)
>290
<-290
th = 10mm
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h0 h1
Strategy 2: improve the frame size
Actual Improved
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159
Vsd = 1050 kN – cap element stress
e-plastic analysis (stress X)
>290
<-290
Strategy 2: improve the frame size
Actual size
h = 145 mm
Improved size
h = 200 mm
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Vsd = 1050 kN – cap element stress
e-plastic analysis (stress Y)
>290
<-290
Strategy 2: improve the frame size
Actual size
h = 145 mm
Improved size
h = 200 mm
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Vsd = 1050 kN – cap element stress
e-plastic analysis (Von Mises) (I)
>290
<-290
Strategy 2: improve the frame size
Actual size
h = 145 mm
Improved size
h = 200 mm
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>580
<-580
Vsd = 1050 kN – cap element stress
e-plastic analysis (Von Mises) (II)
Strategy 2: improve the frame size
Actual size
h = 145 mm
Improved size
h = 200 mm
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163Reinforcement
Vsd Vsd
C + SteelCSteel
Vsd
SYMMETRIC CONFIGURATION
Vsd = 850
kN
thickNess:
th = 6 mm
Strategy 3: downloading
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Vsd = 850/1050 kN – cap element stress
e-plastic analysis (Von Mises)
Vsd = 850 kN Vsd = 1050 kN
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Vsd = 850/1050 kN – cap element stress
e-plastic analysis (Von Mises)
Vsd = 850 kN
386 N/mm^2MAX in questa
zona
Vsd = 1050 kN
560 N/mm^2
166
Vsd = 850/1050 kN – cap element strain –
e-plastic analysis (Von Mises)
Vsd = 850 kN Vsd = 1050 kNLa scala è
diversa
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SYM_Vsd = 850 kN
Stress e-plastic analysis (Von Mises) Strain e-plastic analysis (Von Mises)
th = 10 mmw
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COMPARISON BETWEEN TWO F.E.
PROGRAMSw
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>290
<-290
Vsd = 1050 kN – cap element stress
e-plastic analysis (stress X)
>290
<-290
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Vsd = 1050 kN – cap element stress
e-plastic analysis (stress Y)
>290
<-290
>290
<-290
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>290
<-290>290
<-290
Vsd = 1050 kN – cap element stress
e-plastic analysis (Von Mises) (I)w
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.fra
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173
>580
<-580
Vsd = 1050 kN – cap element stress
e-plastic analysis (Von Mises) (II)
>580
<-580
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Upper edge displacement
0,00
2,00
4,00
6,00
8,00
10,00
12,00
14,00
0 200 400 600 800 1000 1200
Load [KN]
Ux
[m
m]
ANSYS STRAUSY
X
STRUCTURAL RESPONSE COMPARISON (I)w
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175
Centre of Diaphram
0,0
50,0
100,0
150,0
200,0
250,0
300,0
350,0
400,0
450,0
0 200 400 600 800 1000 1200
Load [KN]
Str
ess_x [
MP
a]
ANSYS STRAUS
Y
X
Centre of Diaphram
0,00%
1,00%
2,00%
3,00%
4,00%
5,00%
6,00%
0 200 400 600 800 1000 1200
Load [KN]
To
tal S
tra
in_
x
ANSYS STRAUS
Centre of Diaphram
0,0
50,0
100,0
150,0
200,0
250,0
300,0
350,0
400,0
450,0
0,00% 1,00% 2,00% 3,00% 4,00% 5,00% 6,00%
Total Strain_x
Str
es
s_
x [
MP
a]
ANSYS STRAUS
STRUCTURAL RESPONSE COMPARISON (II)w
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End of external bracket displacement
-25,00
-20,00
-15,00
-10,00
-5,00
0,00
0 200 400 600 800 1000 1200
Load [KN]
Uy [
mm
]
ANSYS STRAUS
STRUCTURAL RESPONSE COMPARISON (III)w
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.fra
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on
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PART 2Solutions
for the structural problem
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179
Vsd [kN] thickNess (th) [mm]
600 8
850 10
1050 12
1500 18
SCENARIOSw
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th0
Strategy 1: improve the frame thickNess
Actual Improved
th
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Reinforcement
Vsd Vsd
C + SteelCSteel
Vsd
SYMMETRIC CONFIGURATIONe-plastic Steel
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>290
<-290
Vsd = 600 kN SYM th = 8 mm
cap element stress / e-plastic analysis
>290
<-290STRESS Y
STRESS X
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>580
<-580
Vsd = 600 kN SYM th = 8 mm
cap element stress / e-plastic analysis
>290
<-290
von MISES I
von MISES II
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C + SteelCSteel
Vsd
ASYMMETRIC CONFIGURATION
Reinforcement Bars
Vsd
e-plastic Steel
ww
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>290
<-290
Vsd = 600 kN ASYM th = 8 mm
cap element stress / e-plastic analysis
STRESS Y>290
<-290
STRESS X
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>580
<-580
Vsd = 600 kN ASYM th = 8 mm
cap element stress / e-plastic analysis
>290
<-290
von MISES I
von MISES II
189
Reinforcement
Vsd Vsd
C + SteelCSteel
Vsd
SYMMETRIC CONFIGURATIONe-plastic Steel
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>290
<-290
Vsd = 850 kN SYM th = 10 mm
cap element stress / e-plastic analysis
>290
<-290STRESS Y
STRESS X
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>580
<-580
Vsd = 850 kN SYM th = 10 mm
cap element stress / e-plastic analysis
>290
<-290
von MISES I
von MISES II
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C + SteelCSteel
Vsd
ASYMMETRIC CONFIGURATION
Reinforcement Bars
Vsd
e-plastic Steel
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>290
<-290
Vsd = 850 kN ASYM th = 10 mm
cap element stress / e-plastic analysis
STRESS Y>290
<-290
STRESS X
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>580
<-580
Vsd = 850 kN ASYM th = 10 mm
cap element stress / e-plastic analysis
>290
<-290
von MISES I
von MISES II
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Reinforcement
Vsd Vsd
C + SteelCSteel
Vsd
SYMMETRIC CONFIGURATIONe-plastic Steel
ww
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>290
<-290
Vsd = 1050 kN SYM th = 12 mm
cap element stress / e-plastic analysis
>290
<-290STRESS Y
STRESS X
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>580
<-580
Vsd = 1050 kN SYM th = 12 mm
cap element stress / e-plastic analysis
>290
<-290
von MISES I
von MISES II
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C + SteelCSteel
Vsd
ASYMMETRIC CONFIGURATION
Reinforcement Bars
Vsd
e-plastic Steel
ww
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200
>290
<-290
Vsd = 1050 kN ASYM th = 12 mm
cap element stress / e-plastic analysis
STRESS Y>290
<-290
STRESS X
201
>580
<-580
Vsd = 1050 kN ASYM th = 12 mm
cap element stress / e-plastic analysis
>290
<-290
von MISES I
von MISES II
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203
Reinforcement
Vsd Vsd
C + SteelCSteel
Vsd
SYMMETRIC CONFIGURATIONe-plastic Steel
204
>290
<-290
Vsd = 1500 kN SYM th = 18 mm
cap element stress / e-plastic analysis
>290
<-290STRESS Y
STRESS X
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>580
<-580
Vsd = 1500 kN SYM th = 18 mm
cap element stress / e-plastic analysis
>290
<-290
von MISES I
von MISES II
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C + SteelCSteel
Vsd
ASYMMETRIC CONFIGURATION
Reinforcement Bars
Vsd
e-plastic Steel
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>290
<-290
Vsd = 1500 kN ASYM th = 18 mm
cap element stress / e-plastic analysis
STRESS Y>290
<-290
STRESS X
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>580
<-580
Vsd = 1500 kN ASYM th = 18 mm
cap element stress / e-plastic analysis
>290
<-290
von MISES I
von MISES II
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Summary for Proposed ThickNess:
von Mises stress / SYM / e-plastic analysis
>290
<-290
Vsd=1050 kN
th=12 mm
Vsd=1500 kN
th=18 mm
Vsd=600 kN
th=8 mm
Vsd=850 kN
th=10 mm
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Y
X
Upper edge displacement
0,00
0,05
0,10
0,15
0,20
0,25
0,30
0,35
0,40
0,45
0 500 1000 1500 2000
Load [KN]
Ux
[m
m]
Vsd=600 KN - th=8mm
Vsd=850 KN - th=10mm
Vsd=1050 KN - th=12mm
Vsd=1500 KN - th=18mm
STRUCTURAL RESPONSE (I)w
ww
.fra
nc
ob
on
tem
pi.o
rg
211
Y
X
Centre of Diaphram
0,0
50,0
100,0
150,0
200,0
250,0
0 500 1000 1500 2000
Load [KN]
Str
es
s_
x [
MP
a]
Vsd=600 KN - th=8mm
Vsd=850 KN - th=10mm
Vsd=1050 KN - th=12mm
Vsd=1500 KN - th=18mm
Centre of Diaphram
0,00%
0,02%
0,04%
0,06%
0,08%
0,10%
0,12%
0 500 1000 1500 2000
Load [KN]
To
tal S
tra
in_
x
Vsd=600 KN - th=8mm
Vsd=850 KN - th=10mm
Vsd=1050 KN - th=12mm
Vsd=1500 KN - th=18mm
Centre of Diaphram
0,0
50,0
100,0
150,0
200,0
250,0
0,00% 0,02% 0,04% 0,06% 0,08% 0,10% 0,12%
Total Strain_x
Str
ess_x [
MP
a]
Vsd=600 KN - th=8mm
Vsd=850 KN - th=10mm
Vsd=1050 KN - th=12mm
Vsd=1500 KN - th=18mm
STRUCTURAL RESPONSE (II)w
ww
.fra
nc
ob
on
tem
pi.o
rg
212
End of external bracket displacement
-8,00
-7,00
-6,00
-5,00
-4,00
-3,00
-2,00
-1,00
0,00
0 500 1000 1500 2000
Load [KN]
Uy
[m
m]
Vsd=600 KN - th=8mm
Vsd=850 KN - th=10mm
Vsd=1050 KN - th=12mm
Vsd=1500 KN - th=18mm
Y
X
STRUCTURAL RESPONSE (III)w
ww
.fra
nc
ob
on
tem
pi.o
rg
214
30.0
69.0
83.2
288.8
TIPO C
1
195.0
25.2
31°50° 432
ALTERNATIVE CONFIGURATIONS
TIPO A
31°50° 432
1
30.0
90.0
83.2
288.8
TIPO B
1
2 3450°
31°
288.8
83.2
69.0
30.0
ACTUAL
TYPE B TYPE C
TYPE AACTUAL
ww
w.f
ran
co
bo
nte
mp
i.o
rg
215
Vsd = 1050 kN SYM th = 12 mm
cap element stress / e-plastic analysis
>290
<-290
von MISES
Actual
Tipo ATYPE A
ww
w.f
ran
co
bo
nte
mp
i.o
rg
216
Vsd = 1050 kN SYM th = 12 mm
cap element stress / e-plastic analysis
>290
<-290
von MISES
Actual
Tipo BTYPE B
ww
w.f
ran
co
bo
nte
mp
i.o
rg
217
Vsd = 1050 kN SYM th = 12 mm
cap element stress / e-plastic analysis
>290
<-290
von MISES
Actual
Tipo CTYPE C
ww
w.f
ran
co
bo
nte
mp
i.o
rg
219
ALTERNATIVE GEOMETRIC
CONFIGURATIONS
TIPO B
1
2 3450°
31°
288.8
83.2
69.0
30.0
TYPE B
ww
w.f
ran
co
bo
nte
mp
i.o
rg
221
>290
<-290
Vsd = 600 kN SYM th = 8 mm
cap element stress / e-plastic analysis
>290
<-290STRESS Y
STRESS X
ww
w.f
ran
co
bo
nte
mp
i.o
rg
222
>580
<-580
Vsd = 600 kN SYM th = 8 mm
cap element stress / e-plastic analysis
>290
<-290
von MISES I
von MISES II
ww
w.f
ran
co
bo
nte
mp
i.o
rg
223
Vsd = 600 kN SYM th = 8 mm
cap element stress / e-plastic analysis
>290
<-290
>290
<-290
von MISES
ww
w.f
ran
co
bo
nte
mp
i.o
rg
224
>290
<-290
Vsd = 600 kN ASYM th = 8 mm
cap element stress / e-plastic analysis
STRESS Y>290
<-290
STRESS X
ww
w.f
ran
co
bo
nte
mp
i.o
rg
225
Vsd = 600 kN ASYM th = 8 mm
cap element stress / e-plastic analysis
>290
<-290
von MISES
ww
w.f
ran
co
bo
nte
mp
i.o
rg
227
>290
<-290
Vsd = 850 kN SYM th = 10 mm
cap element stress / e-plastic analysis
>290
<-290STRESS Y
STRESS X
ww
w.f
ran
co
bo
nte
mp
i.o
rg
228
Vsd = 850 kN SYM th = 10 mm
cap element stress / e-plastic analysis
>290
<-290
von MISES
ww
w.f
ran
co
bo
nte
mp
i.o
rg
229
>290
<-290
Vsd = 850 kN ASYM th = 10 mm
cap element stress / e-plastic analysis
STRESS Y>290
<-290
STRESS X
ww
w.f
ran
co
bo
nte
mp
i.o
rg
230
Vsd = 850 kN ASYM th = 10 mm
cap element stress / e-plastic analysis
>290
<-290
von MISES
ww
w.f
ran
co
bo
nte
mp
i.o
rg
232
>290
<-290
Vsd = 1050 kN SYM th = 12 mm
cap element stress / e-plastic analysis
>290
<-290STRESS Y
STRESS X
ww
w.f
ran
co
bo
nte
mp
i.o
rg
233
Vsd = 1050 kN SYM th = 12 mm
cap element stress / e-plastic analysis
>290
<-290
von MISES
ww
w.f
ran
co
bo
nte
mp
i.o
rg
234
>290
<-290
Vsd = 1050 kN ASYM th = 12 mm
cap element stress / e-plastic analysis
STRESS Y>290
<-290
STRESS X
ww
w.f
ran
co
bo
nte
mp
i.o
rg
235
Vsd = 1050 kN ASYM th = 12 mm
cap element stress / e-plastic analysis
>290
<-290
von MISES
ww
w.f
ran
co
bo
nte
mp
i.o
rg
237
>290
<-290
Vsd = 1500 kN SYM th = 18 mm
cap element stress / e-plastic analysis
>290
<-290STRESS Y
STRESS X
ww
w.f
ran
co
bo
nte
mp
i.o
rg
238
Vsd = 1500 kN SYM th = 18 mm
cap element stress / e-plastic analysis
>290
<-290
von MISES
ww
w.f
ran
co
bo
nte
mp
i.o
rg
239
>290
<-290
Vsd = 1500 kN ASYM th = 18 mm
cap element stress / e-plastic analysis
STRESS Y>290
<-290
STRESS X
ww
w.f
ran
co
bo
nte
mp
i.o
rg
240
Vsd = 1500 kN ASYM th = 18 mm
cap element stress / e-plastic analysis
>290
<-290
von MISES
ww
w.f
ran
co
bo
nte
mp
i.o
rg
th = 12 mm
Vsd = 1050*1,33 kN = 1396 kN
ww
w.f
ran
co
bo
nte
mp
i.o
rg
243
>290
<-290
Vsd = 1050*1,33= 1396,5 kN SYM th = 12 mm
cap element stress / e-plastic analysis
>290
<-290STRESS Y
STRESS X
ww
w.f
ran
co
bo
nte
mp
i.o
rg
244
>290
<-290
von MISES I
Vsd = 1050*1,33= 1396,5 kN SYM th = 12 mm
cap element stress / e-plastic analysis
>580
<-580
von MISES II
ww
w.f
ran
co
bo
nte
mp
i.o
rg
B3D
246
ANALISI E VERIFICHE STRUTTURALI
DELLE CONFIGURAZIONI
per Vsd = 1050 Kn
IN PRESENZA DI PLUVIALE / A 2 VIE
ISOTROPADicembre 2007
ww
w.f
ran
co
bo
nte
mp
i.o
rg
INFLUENZA DELLA
PRESENZA DEL PLUVIALE
Vsd = 1050 Kn
ww
w.f
ran
co
bo
nte
mp
i.o
rg
250
Definizione del modello (3)
253
Stato di sforzo nel conglomerato (1)
Sforzi verticali
ww
w.f
ran
co
bo
nte
mp
i.o
rg
254
Stato di sforzo nel conglomerato (2)
Sforzi verticali
ww
w.f
ran
co
bo
nte
mp
i.o
rg
255
Stato di sforzo nel conglomerato (3)
Sforzi verticali
ww
w.f
ran
co
bo
nte
mp
i.o
rg
256
Stato di sforzo nel conglomerato (4)
Sforzi verticali
ww
w.f
ran
co
bo
nte
mp
i.o
rg
257
Stato di sforzo nel conglomerato (5)
Sforzi verticali
ww
w.f
ran
co
bo
nte
mp
i.o
rg
258
Stato di sforzo nel conglomerato (6)w
ww
.fra
nc
ob
on
tem
pi.o
rg
259
Stato di sforzo nel conglomerato (7)w
ww
.fra
nc
ob
on
tem
pi.o
rg
260
Stato di sforzo nel conglomerato (8)w
ww
.fra
nc
ob
on
tem
pi.o
rg
261
Stato di sforzo nel conglomerato (9)w
ww
.fra
nc
ob
on
tem
pi.o
rg
262
Stato di sforzo nel conglomerato (10)w
ww
.fra
nc
ob
on
tem
pi.o
rg
263
Stato di sforzo nel conglomerato (11!)
Von Mises !
ww
w.f
ran
co
bo
nte
mp
i.o
rg
264
Stato di sforzo nel conglomerato (12!)
Von Mises !
ww
w.f
ran
co
bo
nte
mp
i.o
rg
265
Stato di sforzo nei piatti verticali (1)w
ww
.fra
nc
ob
on
tem
pi.o
rg
266
Stato di sforzo nei piatti verticali (2)w
ww
.fra
nc
ob
on
tem
pi.o
rg
267
Stato di sforzo nei piatti verticali (3)w
ww
.fra
nc
ob
on
tem
pi.o
rg
268
Stato di sforzo nei piatti di chiusuraw
ww
.fra
nc
ob
on
tem
pi.o
rg
CONFIGURAZIONE A 2 VIE
ISOTROPA
Vsd = 1050 Kn
ww
w.f
ran
co
bo
nte
mp
i.o
rg
277
Discretizzazione singolo piatto verticalew
ww
.fra
nc
ob
on
tem
pi.o
rg
279
Stato di sforzo nel conglomerato (1)
Sforzi verticali
ww
w.f
ran
co
bo
nte
mp
i.o
rg
280
Stato di sforzo nel conglomerato (2)
Sforzi verticali
ww
w.f
ran
co
bo
nte
mp
i.o
rg
281
Stato di sforzo nel conglomerato (3)
Sforzi verticali
ww
w.f
ran
co
bo
nte
mp
i.o
rg
282
Stato di sforzo nel conglomerato (4)
Sforzi verticali
ww
w.f
ran
co
bo
nte
mp
i.o
rg
283
Stato di sforzo nel conglomerato (5)
Sforzi verticali
ww
w.f
ran
co
bo
nte
mp
i.o
rg
284
Stato di sforzo nel conglomerato (6)
Sforzi verticali
ww
w.f
ran
co
bo
nte
mp
i.o
rg
285
Stato di sforzo nel conglomerato (7)
Sforzi verticali
ww
w.f
ran
co
bo
nte
mp
i.o
rg
286
Stato di sforzo nel conglomerato (8)
Sforzi verticali
ww
w.f
ran
co
bo
nte
mp
i.o
rg
287
Stato di sforzo nel conglomerato (9)w
ww
.fra
nc
ob
on
tem
pi.o
rg
288
Stato di sforzo nel conglomerato (10)w
ww
.fra
nc
ob
on
tem
pi.o
rg
289
Stato di sforzo nel conglomerato (11)w
ww
.fra
nc
ob
on
tem
pi.o
rg
290
Stato di sforzo nel conglomerato (12)w
ww
.fra
nc
ob
on
tem
pi.o
rg
291
Stato di sforzo nel conglomerato (13)w
ww
.fra
nc
ob
on
tem
pi.o
rg
292
Stato di sforzo nel conglomerato (14)w
ww
.fra
nc
ob
on
tem
pi.o
rg
293
Stato di sforzo nel conglomerato (15)w
ww
.fra
nc
ob
on
tem
pi.o
rg
294
Stato di sforzo nel conglomerato (16)w
ww
.fra
nc
ob
on
tem
pi.o
rg
295
Stato di sforzo nel conglomerato (17)w
ww
.fra
nc
ob
on
tem
pi.o
rg
296
Stato di sforzo nel conglomerato (18!)
Von Mises !
ww
w.f
ran
co
bo
nte
mp
i.o
rg
297
Stato di sforzo nel conglomerato (19!)
Von Mises !
ww
w.f
ran
co
bo
nte
mp
i.o
rg
298
Stato di sforzo piatti verticali (1)w
ww
.fra
nc
ob
on
tem
pi.o
rg
299
Stato di sforzo piatti verticali (2)w
ww
.fra
nc
ob
on
tem
pi.o
rg
300
Stato di sforzo piatti verticali (3)w
ww
.fra
nc
ob
on
tem
pi.o
rg
301
Stato di sforzo piatti verticali (4)w
ww
.fra
nc
ob
on
tem
pi.o
rg
302
Stato di sforzo piatti verticali (5)w
ww
.fra
nc
ob
on
tem
pi.o
rg
303
Stato di sforzo nei piatti di chiusuraw
ww
.fra
nc
ob
on
tem
pi.o
rg
Stro N
GERwww.stronger2012.com
305
307
ANALISI E VERIFICHE STRUTTURALI
DELLA MENSOLA DI APPOGGIO
per Vsd = 1050 kNMaggio 2008
ww
w.f
ran
co
bo
nte
mp
i.o
rg
311
MODELS OF EXTERNAL PARTw
ww
.fra
nc
ob
on
tem
pi.o
rg
vertical
longitudinal
transversal
CONFIGURAZIONI
Configurazione iniziale e
rinforzata
ww
w.f
ran
co
bo
nte
mp
i.o
rg
326
Mensola senza rinforzo:
vista superiore
ww
w.f
ran
co
bo
nte
mp
i.o
rg
327
Mensola con rinforzo:
vista superiore
ww
w.f
ran
co
bo
nte
mp
i.o
rg
328
Mensola senza rinforzo:
vista inferiore
ww
w.f
ran
co
bo
nte
mp
i.o
rg
329
Mensola con rinforzo:
vista inferiore
ww
w.f
ran
co
bo
nte
mp
i.o
rg
330
Mensola senza rinforzo:
vista di lato
ww
w.f
ran
co
bo
nte
mp
i.o
rg
331
Mensola con rinforzo:
vista di lato
ww
w.f
ran
co
bo
nte
mp
i.o
rg
332
Mensola senza rinforzo:
vista di fronte
ww
w.f
ran
co
bo
nte
mp
i.o
rg
333
Mensola con rinforzo:
vista di fronte
ww
w.f
ran
co
bo
nte
mp
i.o
rg
ANALISI NON LINEARE
Analisi elasto-plastica con
elementi di contatto della
configurazione iniziale
ww
w.f
ran
co
bo
nte
mp
i.o
rg
CONFIGURAZIONE FINALE
Verifiche in campo elasto plastico e
vincoli monolateri sul profilato a C
ww
w.f
ran
co
bo
nte
mp
i.o
rg
Caratteristiche complessive:
• Azione verticale mensola: Vd=1050 kN;
• Acciaio mensola: Fe510 – S355;
• Tiranti: 2 Ø 42 classe 10.9 (M42);
• Bulloni ritegno: 2 Ø 16 classe 10.9 (M16):
resist. taglio Vrd,tot = 2x70 = 140 kN;
resist. trazione Nrd,tot = 2x99 = 180 kN;
• Peso mensola fusa: 15.7 kg.
345
ww
w.f
ran
co
bo
nte
mp
i.o
rg
MF01-1 AD 00 modb NOFLEX
Carico:
Verticale 1050 kN
ww
w.f
ran
co
bo
nte
mp
i.o
rg
MF01-1 AD 00 modc NOFLEX
Carico:
Verticale 1050 kN
Longitudinale 250 kN
ww
w.f
ran
co
bo
nte
mp
i.o
rg
MF01-1 AD 00 modd NOFLEX
Carico:
Verticale 1050 kN
Trasversale 250 kN
ww
w.f
ran
co
bo
nte
mp
i.o
rg
MF01-1 AD 00 mode NOFLEX
Carico:
Verticale 1050 kN
Trasversale 175 kN
Longitudinale 175 kN
ww
w.f
ran
co
bo
nte
mp
i.o
rg
SLU(Fz,Fx,Fy)=(1050,175,175) [kN]
393
MF01-1 AD 00 modf NOFLEX
Carico:
Verticale 1050 kN
Longitudinale 500 kN
ww
w.f
ran
co
bo
nte
mp
i.o
rg
SLE (Fz,Fx,Fy)=(1050,500,0) [kN]
403
417
Pesi soluzioni
fattore
correttivo
utilizzo
SNODO TIRANTE ACCIAIO 39NiCrMo3 bonificato 668 PR/02 1.4 2 2.8 1.9 5.3
AGGANCIO MENSOLA - - PR/15 - 1 0.1 1.0 0.1
PIATTO 115x8 l40 S355JR - Fe510B 355 0.3 1 0.3 1.0 0.3
BARRA POSTERIORE MENSOLA S355JR - Fe510B 355 PR/14 5.5 1 5.5 1.0 5.5
NERVATURA MENSOLA S355JR - Fe510B 355 PR/13 1.2 4 4.8 1.0 4.8
PIATTO MENSOLA S355JR - Fe510B 355 PR/12 3.8 1 3.8 1.0 3.8
PESO COMPLESSIVO 17.3 1.1 19.8
SOLUZIONE FUSA INIZIALE
PESO COMPLESSIVO S355JR - Fe510B 14.3 1.0 14.3
CON RINFORZO
PESO COMPLESSIVO S355JR - Fe510B 16.0 1.0 16.0
SOLUZIONE COMPOSTA materiale tasso di lavoro (Mpa) codice peso (kg) # peso (kg) - peso (kg)
ww
w.f
ran
co
bo
nte
mp
i.o
rg
418
Stro N
GERwww.stronger2012.com
419
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