Corso di dottorato in Ottimizzazione Strutturale - applicazione a una mensola strallata - Bontempi

1Ottimizzazione Strutturale
franco.bontempi@uniroma1.it
1
Introduzione alla
OTTIMIZZAZIONE STRUTTURALE
Applicazione a una mensola strallata
Franco Bontempi
Ordinario di Tecnica delle Costruzioni
Facolta’ di Ingegneria Civile e Industriale
Sapienza Universita’ di Roma

3Ottimizzazione 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.

EVOLUTION OF THE DESIGN
OF A CABLE-STAYED BRACKET

THE OBJECT
An innovative device for
precast/prestressed beam support
www.francobontempi.org

Evolution of the design of a
cablestayed bracket
6
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.

cablestayed bracket
7
REINFORCED CONCRETE
CORBELS

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STRUCTURAL STEEL CORBELS

cablestayed bracket
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BEAM SUPPORT

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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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11
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).

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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16

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17

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STRUCTURAL PARTS

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19
FIRST ANALYSIS (A):
two dimensional geometry
column
a
Vsd
Vsd
a/2
Vsd*=Vsd/2
Vsd* =Vsd/2
column
a
Vsd
Vsd
column
a
Vsd
Vsd
a/2
Vsd*=Vsd/2
Vsd* =Vsd/2

cablestayed bracket
20
• 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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21
S & T Model Definition

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22
Strut & Tie Models
Reinforcement
Bars
Vsd
Reinforcement
Bars
Vsd

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23
Reinforcement
Bars
Vsd
Reinforcement
Bars
Vsd
Strut & Tie Results
stirrups longitudinal bars
concretesteel bracket

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24
Hybrid models
Reinforcement
Bars
Vsd
Reinforcement
Bars
Vsd

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25
Global response
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[mm]
Vsd=600 KN - th=8mm
Vsd=850 KN - th=10mm
Y
X
-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[mm]
Vsd=600 KN - th=8mm
Y
X
Y
X
Y
X

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26
Local response
>290
<-290
>290
<-290
>290
<-290

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27
EVOLUTION OF THE FORM (1)
600.0
250.0
15.0
60.2
70.0
145.0
56°
66°
50°
378.5
188.0
320.1

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28
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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29
Versione f

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30
CONSTRUCTABILITY (1)www.francobontempi.org

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32

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33

EXTENDED ANALYSIS
Detailed assessment

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35
THREE-DIMENSIONAL
GEOMETRY

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36
Results for
concrete core and steel frame

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37
Results for
steel bottom frame and attacment

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38
EXTERNAL PART

cablestayed bracket
39

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40

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41
MODELS OF EXTERNAL PART

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42
BASIC FORM

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43
IMPROVEMENTS

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44
ENHANCED FORM

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45
COMPRESSION ONLY CONTACT

NEXT STEP
Two way beam support

cablestayed bracket
47
TWO WAY SUPPORT (1)

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48
TWO WAY SUPPORT (2)

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49
ENHANCHED 2WAY SUPPORT

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50
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.

Str
o N
GER
www.stronger2012.com
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51

STRUCTURAL ANALSYS AND ASSESSMENT
OF
THE STAYED BRACKET
by B.S. ITALIA / Gruppo STYL-COMP
Report April 2007
Dr.-Ing. Franco Bontempi, Ph.D., P.E.,
Professor of Structural Analysis and Design,
School of Engineering, Department of Structural and Geotechnical Engineering,
UNIVERSITY OF ROME "LA SAPIENZA", Via Eudossiana 18 - 00184 Rome (ITALY)
tel. +39-06-44585.265,.750, fax. +39-06-4884852 - franco.bontempi@uniroma1.it
Postgraduate School of Reinforced Concrete Structures "F.lli Pesenti"
Department of Structural Engineering,
POLYTECHNIC OF MILAN, Piazza L. da Vinci 32 - 20133 Milan (ITALY)
tel. +39-02-2399.4375,.4203, fax. +39-02-2399.4220
mobile: +39-339-3956300 - franco.bontempi@francobontempi.org

FB - April 2007 STAYED BRACKET 53
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

INDEX PART 2
ThickNess Improvement
Shaping
Results for Shaping Type B

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

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[mm]
Vsd=600 KN - th=8mm
Y
X

Y
X
Centre of Diaphram
0,0
50,0
100,0
150,0
200,0
250,0
0 500 1000 1500 2000
Load [KN]
Stress_x[MPa]
Vsd=600 KN - th=8mm
Centre of Diaphram
0,00%
0,02%
0,04%
0,06%
0,08%
0,10%
0,12%
0 500 1000 1500 2000
Load [KN]
TotalStrain_x
Vsd=600 KN - th=8mm
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
Stress_x[MPa]
Vsd=600 KN - th=8mm
STRUCTURAL RESPONSE (II)

-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[mm]
Vsd=600 KN - th=8mm
Y
X
STRUCTURAL RESPONSE (III)

ALTERNATIVE GEOMETRIC
CONFIGURATIONS
TIPO B
1
2 3
450°
31°
288.8
83.2
69.0
30.0
TYPE B

Vsd = 600 kN SYM th = 8 mm
cap element stress / e-plastic analysis
>290
<-290
>290
<-290
von MISES

Vsd = 600 kN ASYM th = 8 mm
>290
<-290
von MISES

>290
<-290
von MISES

PART 1
Framework
of the structural problem

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;

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;

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;

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;

tie-rod
frame
tie shield
tie junction
closure plate
C junction
bottom rib
external plate
external bracket
rigid block
adjacent concrete
STRUCTURAL PARTS

LOADING SYSTEMS:
SYM. vs ASYM.
Reinforcement
Bars
Vsd
Reinforcement
Bars
Vsd

-1000
-800
-600
-400
-200
0
200
400
600
800
1000
-2000 0 2000 4000 6000 8000 10000
N
M
SYM
ASYM
M [kNm]
compression
N [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

STRUCTURAL MODELING (i)
• A slice of half column is considered
(plane stress assumption)
column
a
Vsd
Vsd
a/2
Vsd*=Vsd/2
Vsd* =Vsd/2

STRUCTURAL MODELING (model #1)
Strut & Tie modeling of the stayed bracket
STEP #1 STEP #2
STEP #3 STEP #4

Alternative S&T modeling of the stayed bracket
STEP #1
STEP #3 STEP #4
STEP #2

STRUCTURAL MODELING
OF CONCRETE PART (I):
trusswork discretization
ab
lslAA
a
bsaAA
b
asbAA
ba
ba
ba
dd
yy
xx
2
2
2
2
2
8
3
2
3
8
3
2
3
8
3
2
,
,
,









































4321
,,, uuuu
VIVIVIIIIII
NNNNNN ,,,,,
a
x
y
ux
 


b
y
y
vy
 


abx
v
y
u yx
 




b
l
aNNNN
N
VIVIII
x











a
l
bNNNN
N
VIVIVIII
y











l
NNN VIV
xy

xyyx NNN ,,
STRUCTURAL MODELING
OF CONCRETE PART (II):
stress representation

LOADING SYSTEMS: SYM.
Reinforcment
Bars
Vsd
C + SteelCSteel
VsdVsd

LOADING SYSTEMS: ASYM.
Reinforcment
Bars
C + SteelCSteel
Vsd Vsd

Model S&T #1
Results for SYM
loading system

Vsd = 1050 kN – cap element stress
• max tension = 389,7 MPa
• min compression = -232,5 MPa
• tension = 582,7 MPa

Vsd = 1050 kN – reinforcement bar stress
stirrups longitudinal

Vsd = 1050 kN – concrete stress
• max tension = 0 MPa

Model S&T #1
Results for ASYM
loading system

Model S&T #2
Results for SYM
loading system

• min compression = -295,7 MPa• tension = 582,7 MPa

Model S&T #2
Results for ASYM
loading system

Model S&T #3
Results for SYM
loading system

Sinthesis of the Results for
S&T Models

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

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

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

FINITE ELEMENT
ANALYSIS BY
SUBSTRUCTING
TECHNIQUE AND S&T

STRUCTURAL MODELING
Reinforcement

STRUCTURAL MODELING: CAP

RIGID
LINKS
BEAM ELEMENTS
STRUCTURAL MODELING: LINKS

Reinforcement
Vsd Vsd
C + SteelCSteel
Vsd
SYMMETRIC CONFIGURATION

Vsd = 1050 kN – cap element stress:
elastic analysis (stress X)
>290
<-290

elastic analysis (stress Y)
>290
<-290

>290
<-290
elastic analysis (Von Mises) (I)

elastic analysis (Von Mises) (II)
>580
<-580

concrete
Vsd = 1050 kN – ties and concrete stress

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
SMINCLS [N/mm^2] -17,72 -18,21 -28
Linear elastic Steel

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/mm210000 2
0 E
*100/1 01 EE 


x10^(-3)
E0
E1
y
y
max

>290
<-290
e-plastic analysis (stress X)

>290
<-290
e-plastic analysis (stress Y)

>290
<-290
e-plastic analysis (Von Mises) (I)

>580
<-580
e-plastic analysis (Von Mises) (II)

Vsd = 1050 kN – cap element strain:
e-plastic analysis (Von Mises strain)

concrete

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
SMINCLS [N/mm^2] -18,21 -19,77 -28
elastic steel
e-plastic steel

-25
-20
-15
-10
-5
0
0 200 400 600 800 1000 1200
Load
Uy
Load application
Structural response (1)

0,00
2,00
4,00
6,00
8,00
10,00
12,00
14,00
0 200 400 600 800 1000 1200
Load
Ux
Spigolo alto

0,000
0,001
0,001
0,002
0,002
0,003
0 200 400 600 800 1000 1200
Load
ElasticStrain_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
PlasticStrain_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
TotalStrain_x
Centre of Diaphram

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
Stress_x
Centre of Diaphram
0
50
100
150
200
250
300
350
400
450
0 200 400 600 800 1000 1200
Load
Stress_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
TotalStrain_x
Centre of Diaphram

C + SteelCSteel
Vsd
ASYMMETRIC CONFIGURATION
Reinforcement Bars
Vsd
e-plastic steel

>290
<-290

>580
<-580

concrete

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

Reinforcement
Vsd Vsd
C + SteelCSteel
Vsd

th0
Actual Improved
th1

>290
<-290
Actual thickNess
th = 6 mm
Improved thickNess
th = 10 mm

>580
<-580
Actual thickNess
th = 6 mm
Improved thickNess
th = 10 mm

Vsd = 1050 kN – cap element strain – e-
plastic analysis (Von Mises strain)
Actual thickNess
th = 6 mm
Improved thickNess
th = 10 mm

Vsd = 1050 kN – cap element strain
e-plastic analysis (Von Mises strain)
Improved thickNess
th = 10 mm

>580
<-580
e-plastic analysis (Von Mises)
th = 10mm

>290
<-290
th = 10mm

h0 h1
Actual Improved

>290
<-290
Actual size
h = 145 mm
Improved size
h = 200 mm

>580
<-580
Actual size
h = 145 mm
Improved size
h = 200 mm

FB - April 2007 STAYED BRACKET 162Reinforcement
Vsd Vsd
C + SteelCSteel
Vsd
Vsd = 850
kN
thickNess:
th = 6 mm
Strategy 3: downloading

Vsd = 850/1050 kN – cap element stress
Vsd = 850 kN Vsd = 1050 kN

Vsd = 850/1050 kN – cap element stress
Vsd = 850 kN
386 N/mm^2MAX in questa
zona
Vsd = 1050 kN
560 N/mm^2

Vsd = 850/1050 kN – cap element strain –
Vsd = 850 kN Vsd = 1050 kNLa scala è
diversa

SYM_Vsd = 850 kN
Stress e-plastic analysis (Von Mises) Strain e-plastic analysis (Von Mises)
th = 10 mm

COMPARISON BETWEEN TWO F.E.
PROGRAMS

>290
<-290
>290
<-290

>580
<-580
>580
<-580

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[mm]
ANSYS STRAUS
Y
X
STRUCTURAL RESPONSE COMPARISON (I)

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]
Stress_x[MPa]
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]
TotalStrain_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
Stress_x[MPa]
ANSYS STRAUS
STRUCTURAL RESPONSE COMPARISON (II)

-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)

PART 2
Solutions
for the structural problem

Vsd [kN] thickNess (th) [mm]
600 8
850 10
1050 12
1500 18
SCENARIOUS

th0
Actual Improved
th

Reinforcement
Vsd Vsd
C + SteelCSteel
Vsd
e-plastic Steel

>290
<-290
>290
<-290
STRESS Y
STRESS X

>580
<-580
>290
<-290
von MISES I
von MISES II

C + SteelCSteel
Vsd
Reinforcement Bars
Vsd
e-plastic Steel

>290
<-290
STRESS Y
>290
<-290
STRESS X

>580
<-580
>290
<-290
von MISES I
von MISES II

Reinforcement
Vsd Vsd
C + SteelCSteel
Vsd
e-plastic Steel

>290
<-290
>290
<-290
STRESS Y
STRESS X

>580
<-580
>290
<-290
von MISES I
von MISES II

C + SteelCSteel
Vsd
Reinforcement Bars
Vsd
e-plastic Steel

>290
<-290
STRESS Y
>290
<-290
STRESS X

>580
<-580
>290
<-290
von MISES I
von MISES II

Reinforcement
Vsd Vsd
C + SteelCSteel
Vsd
e-plastic Steel

>290
<-290
>290
<-290
STRESS Y
STRESS X

>580
<-580
>290
<-290
von MISES I
von MISES II

C + SteelCSteel
Vsd
Reinforcement Bars
Vsd
e-plastic Steel

>290
<-290
STRESS Y
>290
<-290
STRESS X

>580
<-580
>290
<-290
von MISES I
von MISES II

Reinforcement
Vsd Vsd
C + SteelCSteel
Vsd
e-plastic Steel

>290
<-290
>290
<-290
STRESS Y
STRESS X

>580
<-580
>290
<-290
von MISES I
von MISES II

C + SteelCSteel
Vsd
Reinforcement Bars
Vsd
e-plastic Steel

>290
<-290
STRESS Y
>290
<-290
STRESS X

>580
<-580
>290
<-290
von MISES I
von MISES II

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

Y
X
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[mm]
Vsd=600 KN - th=8mm
STRUCTURAL RESPONSE (I)

Y
X
Centre of Diaphram
0,0
50,0
100,0
150,0
200,0
250,0
0 500 1000 1500 2000
Load [KN]
Stress_x[MPa]
Vsd=600 KN - th=8mm
Centre of Diaphram
0,00%
0,02%
0,04%
0,06%
0,08%
0,10%
0,12%
0 500 1000 1500 2000
Load [KN]
TotalStrain_x
Vsd=600 KN - th=8mm
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
Stress_x[MPa]
Vsd=600 KN - th=8mm
STRUCTURAL RESPONSE (II)

-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[mm]
Vsd=600 KN - th=8mm
Y
X
STRUCTURAL RESPONSE (III)

30.0
69.0
83.2
288.8
TIPO C
1
195.0
25.2
31°
50° 4
32
ALTERNATIVE CONFIGURATIONS
TIPO A
31°
50° 4
32
1
30.0
90.0
83.2
288.8
TIPO B
1
2 3
450°
31°
288.8
83.2
69.0
30.0
ACTUAL
TYPE B TYPE C
TYPE AACTUAL

>290
<-290
von MISES
Actual
Tipo A
TYPE A

>290
<-290
von MISES
Actual
Tipo B
TYPE B

>290
<-290
von MISES
Actual
Tipo C
TYPE C

ALTERNATIVE GEOMETRIC
CONFIGURATIONS
TIPO B
1
2 3
450°
31°
288.8
83.2
69.0
30.0
TYPE B

>290
<-290
>290
<-290
STRESS Y
STRESS X

>580
<-580
>290
<-290
von MISES I
von MISES II

>290
<-290
>290
<-290
von MISES

>290
<-290
STRESS Y
>290
<-290
STRESS X

>290
<-290
von MISES

>290
<-290
>290
<-290
STRESS Y
STRESS X

>290
<-290
von MISES

>290
<-290
STRESS Y
>290
<-290
STRESS X

>290
<-290
von MISES

>290
<-290
>290
<-290
STRESS Y
STRESS X

>290
<-290
von MISES

>290
<-290
STRESS Y
>290
<-290
STRESS X

>290
<-290
von MISES

>290
<-290
>290
<-290
STRESS Y
STRESS X

>290
<-290
von MISES

>290
<-290
STRESS Y
>290
<-290
STRESS X

>290
<-290
von MISES

RESULTS FOR
STRUCTURAL
ROBUSTNESS

th = 12 mm
Vsd = 1050*1,33 kN = 1396 kN

>290
<-290
Vsd = 1050*1,33= 1396,5 kN SYM th = 12 mm
>290
<-290
STRESS Y
STRESS X

>290
<-290
von MISES I
Vsd = 1050*1,33= 1396,5 kN SYM th = 12 mm
>580
<-580
von MISES II

Str
o N
GER
cablestayed bracket
244

245
ANALISI E VERIFICHE STRUTTURALI
DELLE CONFIGURAZIONI
per Vsd = 1050 Kn
IN PRESENZA DI PLUVIALE / A 2 VIE
ISOTROPA
Dicembre 2007

INFLUENZA DELLA
PRESENZA DEL PLUVIALE
Vsd = 1050 Kn
246

247
Definizione del modello (1)

248

249

250

251

252
Stato di sforzo nel conglomerato (1)
Sforzi verticali

253
Sforzi verticali

254
Sforzi verticali

255
Sforzi verticali

256
Sforzi verticali

257

258

259

260

261

262
Stato di sforzo nel conglomerato (11!)
Von Mises !

263
Von Mises !

264
Stato di sforzo nei piatti verticali (1)

265

266

267
Stato di sforzo nei piatti di chiusura

268
Stato di sforzo negli attacchi a C

CONFIGURAZIONE A 2 VIE
ISOTROPA
Vsd = 1050 Kn
269

270

271

272

273

274
Discretizzazione conglomerato

275
Discretizzazione piatti verticali

276
Discretizzazione singolo piatto verticale

277
Discretizzazione piatti chiusura

278
Sforzi verticali

279
Sforzi verticali

280
Sforzi verticali

281
Sforzi verticali

282
Sforzi verticali

283
Sforzi verticali

284
Sforzi verticali

285
Sforzi verticali

286

287

288

289

290

291

292

293

294

295
Von Mises !

296
Von Mises !

297
Stato di sforzo piatti verticali (1)

298

299

300

301

302
Stato di sforzo nei piatti di chiusura

303
Stato di sforzo attacchi a C

Str
o N
GER
cablestayed bracket
304

305
ANALISI E VERIFICHE STRUTTURALI
DELLA MENSOLA DI APPOGGIO
per Vsd = 1050 kN
Maggio 2008

cablestayed bracket
306
EXTERNAL PART

cablestayed bracket
307

cablestayed bracket
308

cablestayed bracket
309
MODELS OF EXTERNAL PART
vertical
longitudinal
transversal

CONFIGURAZIONI
Configurazione iniziale e
rinforzata
310

311
Mensola senza rinforzo

312
Mensola con rinforzo

313
Rinforzo

314

315

316
Rinforzo

317

318

319
Rinforzo

320
Deformabilità senza rinforzo

321
Deformabilità con rinforzo

322

323

324
Mensola senza rinforzo:
vista superiore

325
Mensola con rinforzo:
vista superiore

326
vista inferiore

327
vista inferiore

328
vista di lato

329
vista di lato

330
vista di fronte

331
vista di fronte

ANALISI NON LINEARE
Analisi elasto-plastica con
elementi di contatto della
configurazione iniziale
332

333
Moltiplicatore = 0.60

334

335

336

337

338

339

340

341

CONFIGURAZIONE FINALE
Verifiche in campo elasto plastico e
vincoli monolateri sul profilato a C
342

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.
343

MF01-1 AD 00 modb NOFLEX
Carico:
Verticale 1050 kN
344

SLE (Fz,Fx,Fy)=(1050,0,0) [kN]
345

SLU (Fz,Fx,Fy)=(1050,0,0) [kN]
346

SLE (Fz,Fx,Fy)=(1050,0,0) [kN]
347

SLU (Fz,Fx,Fy)=(1050,0,0) [kN]
348

SLE (Fz,Fx,Fy)=(1050,0,0) [kN]
349

SLU (Fz,Fx,Fy)=(1050,0,0) [kN]
350

SLE (Fz,Fx,Fy)=(1050,0,0) [kN]
351

SLU (Fz,Fx,Fy)=(1050,0,0) [kN]
352

MF01-1 AD 00 modc NOFLEX
Carico:
Verticale 1050 kN
Longitudinale 250 kN
353

SLE (Fz,Fx,Fy)=(1050,250,0) [kN]
354

SLU (Fz,Fx,Fy)=(1050,250,0) [kN]
355

SLE (Fz,Fx,Fy)=(1050,250,0) [kN]
356

SLU (Fz,Fx,Fy)=(1050,250,0) [kN]
357

SLE (Fz,Fx,Fy)=(1050,250,0) [kN]
358

SLU (Fz,Fx,Fy)=(1050,250,0) [kN]
359

SLE (Fz,Fx,Fy)=(1050,250,0) [kN]
360

SLU (Fz,Fx,Fy)=(1050,250,0) [kN]
361

SLE (Fz,Fx,Fy)=(1050,250,0) [kN]
362

SLU (Fz,Fx,Fy)=(1050,250,0) [kN]
363

SLE (Fz,Fx,Fy)=(1050,250,0) [kN]
364

SLU (Fz,Fx,Fy)=(1050,250,0) [kN]
365

SLE (Fz,Fx,Fy)=(1050,250,0) [kN]
366

SLU (Fz,Fx,Fy)=(1050,250,0) [kN]
367

MF01-1 AD 00 modd NOFLEX
Carico:
Verticale 1050 kN
Trasversale 250 kN
368

SLE (Fz,Fx,Fy)=(1050,0,250) [kN]
369

SLU (Fz,Fx,Fy)=(1050,0,250) [kN]
370

SLE (Fz,Fx,Fy)=(1050,0,250) [kN]
371

SLU (Fz,Fx,Fy)=(1050,0,250) [kN]
372

SLE (Fz,Fx,Fy)=(1050,0,250) [kN]
373

SLU (Fz,Fx,Fy)=(1050,0,250) [kN]
374

SLE (Fz,Fx,Fy)=(1050,0,250) [kN]
375

SLU (Fz,Fx,Fy)=(1050,0,250) [kN]
376

SLE (Fz,Fx,Fy)=(1050,0,250) [kN]
377

SLU (Fz,Fx,Fy)=(1050,0,250) [kN]
378

SLE (Fz,Fx,Fy)=(1050,0,250) [kN]
379

SLU (Fz,Fx,Fy)=(1050,0,250) [kN]
380

SLE (Fz,Fx,Fy)=(1050,0,250) [kN]
381

SLU (Fz,Fx,Fy)=(1050,0,250) [kN]
382

MF01-1 AD 00 mode NOFLEX
Carico:
Verticale 1050 kN
Trasversale 175 kN
383

SLE(Fz,Fx,Fy)=(1050,175,175) [kN]
384

SLU(Fz,Fx,Fy)=(1050,175,175) [kN]
385

SLE(Fz,Fx,Fy)=(1050,175,175) [kN]
386

SLU(Fz,Fx,Fy)=(1050,175,175) [kN]
387

SLE(Fz,Fx,Fy)=(1050,175,175) [kN]
388

SLU(Fz,Fx,Fy)=(1050,175,175) [kN]
389

SLE(Fz,Fx,Fy)=(1050,175,175) [kN]
390

SLU(Fz,Fx,Fy)=(1050,175,175) [kN]
391

SLE(Fz,Fx,Fy)=(1050,175,175) [kN]
392

SLU(Fz,Fx,Fy)=(1050,175,175) [kN]
393

SLE(Fz,Fx,Fy)=(1050,175,175) [kN]
394

SLU(Fz,Fx,Fy)=(1050,175,175) [kN]
395

SLE(Fz,Fx,Fy)=(1050,175,175) [kN]
396

SLU(Fz,Fx,Fy)=(1050,175,175) [kN]
397

SLE(Fz,Fx,Fy)=(1050,175,175) [kN]
398

SLU(Fz,Fx,Fy)=(1050,175,175) [kN]
399

MF01-1 AD 00 modf NOFLEX
Carico:
Verticale 1050 kN
400

SLE (Fz,Fx,Fy)=(1050,500,0) [kN]
401

SLU (Fz,Fx,Fy)=(1050,500,0) [kN]
402

SLE (Fz,Fx,Fy)=(1050,500,0) [kN]
403

SLU (Fz,Fx,Fy)=(1050,500,0) [kN]
404

SLE (Fz,Fx,Fy)=(1050,500,0) [kN]
405

SLU (Fz,Fx,Fy)=(1050,500,0) [kN]
406

SLE (Fz,Fx,Fy)=(1050,500,0) [kN]
407

SLU (Fz,Fx,Fy)=(1050,500,0) [kN]
408

SLE (Fz,Fx,Fy)=(1050,500,0) [kN]
409

SLU (Fz,Fx,Fy)=(1050,500,0) [kN]
410

SLE (Fz,Fx,Fy)=(1050,500,0) [kN]
411

SLU (Fz,Fx,Fy)=(1050,500,0) [kN]
412

SLE (Fz,Fx,Fy)=(1050,500,0) [kN]
413

SLU (Fz,Fx,Fy)=(1050,500,0) [kN]
414

415
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)

Str
o N
GER
cablestayed bracket
416

Corso di dottorato in Ottimizzazione Strutturale - applicazione a una mensola strallata - Bontempi

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