Corso di dottorato in Ottimizzazione Strutturale: applicazione mensola strallata - Bontempi

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

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
www.francobontempi.org

7
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.

8
REINFORCED CONCRETE
CORBELS

9
STRUCTURAL STEEL CORBELS

10
BEAM SUPPORT

11
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.

12
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

14
STRUCTURAL SCHEME
Versione iniziale
Versione finale
beam SX beam DX
column

15
LOAD SCHEMES
Reinforcement
Bars
Vsd
Reinforcement
Bars
Vsd
Reinforcement
Bars
Vsd
Reinforcement
Bars
Vsd
SYM ASYM

19
STRUCTURAL PARTS

20
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

21
• 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

22
S & T Model Definition

23
Strut & Tie Models
Reinforcement
Bars
Vsd
Reinforcement
Bars
Vsd

24
Reinforcement
Bars
Vsd
Reinforcement
Bars
Vsd
Strut & Tie Results
stirrups longitudinal bars
concretesteel bracket

25
Hybrid models
Reinforcement
Bars
Vsd
Reinforcement
Bars
Vsd

26
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

27
Local response
>290
<-290
>290
<-290
>290
<-290

28
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

29
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

30
Versione f

31
CONSTRUCTABILITY (1)www.francobontempi.org

32

33

34

EXTENDED ANALYSIS
Detailed assessment

36
THREE-DIMENSIONAL
GEOMETRY

37
Results for
concrete core and steel frame

38
Results for
steel bottom frame and attacment

39
EXTERNAL PART

42
MODELS OF EXTERNAL PART

43
BASIC FORM

44
IMPROVEMENTS

45
ENHANCED FORM

46
COMPRESSION ONLY CONTACT

NEXT STEP
Two way beam support

48
TWO WAY SUPPORT (1)

49
TWO WAY SUPPORT (2)

50
ENHANCHED 2WAY SUPPORT

51
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
52

ADETTAGLI BASE

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

55
INDEX PART 2
Thickness Improvement
Shaping
Results for Shaping Type B

PART 0
Synthesis

57
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

58
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

59
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)www.francobontempi.org

60
-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)www.francobontempi.org

61
ALTERNATIVE GEOMETRIC
CONFIGURATIONS
TIPO B
1
2 3
450°
31°
288.8
83.2
69.0
30.0
TYPE B

62
Vsd = 600 kN SYM th = 8 mm
cap element stress / e-plastic analysis
>290
<-290
>290
<-290
von MISES

63
Vsd = 600 kN ASYM th = 8 mm
>290
<-290
von MISES

64
>290
<-290
von MISES

65
>290
<-290
von MISES

66
>290
<-290
von MISES

67
>290
<-290
von MISES

68
>290
<-290
von MISES

69
>290
<-290
von MISES

PART 1
Framework
of the structural problem

BASIS OF THE
PROBLEM

72
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;

73
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;

74
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;

75
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;

76
tie-rod
frame
tie shield
tie junction
closure plate
C junction
bottom rib
external plate
external bracket
rigid block
adjacent concrete
STRUCTURAL PARTSwww.francobontempi.org

77
LOADING SYSTEMS:
SYM. vs ASYM.
Reinforcement
Bars
Vsd
Reinforcement
Bars
Vsd

78
-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

79
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

STRUT & TIE
MODELING

81
STRUCTURAL MODELING (model #1)
Strut & Tie modeling of the stayed bracket
STEP #1 STEP #2
STEP #3 STEP #4

82
Alternative S&T modeling of the stayed bracket
STEP #1
STEP #3 STEP #4
STEP #2

83
Alternative S&T modeling of the stayed bracket
STEP #1
STEP #3 STEP #4
STEP #2

84
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
,
,
,









































85
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

86
LOADING SYSTEMS: SYM.
Reinforcment
Bars
Vsd
C + SteelCSteel
VsdVsd

87
LOADING SYSTEMS: ASYM.
Reinforcment
Bars
C + SteelCSteel
Vsd Vsd

Model S&T #1
Results for SYM
loading system

89
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
stirrups longitudinal

91
Vsd = 1050 kN – concrete stress
• max tension = 0 MPa

Model S&T #1
Results for ASYM
loading system

93

94

95

Model S&T #2
Results for SYM
loading system

97
• min compression = -295,7 MPa• tension = 582,7 MPa

98

99

Model S&T #2
Results for ASYM
loading system

101

102

103

Model S&T #3
Results for SYM
loading system

105

106

107

Sinthesis of the Results for
S&T Models

109
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

110
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

111
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

113
STRUCTURAL MODELING
Reinforcement

114
STRUCTURAL MODELING: CAPwww.francobontempi.org

115
RIGID
LINKS
BEAM ELEMENTS
STRUCTURAL MODELING: LINKSwww.francobontempi.org

ELASTIC MODELS

117
Reinforcement
Vsd Vsd
C + SteelCSteel
Vsd
SYMMETRIC CONFIGURATION

118
Vsd = 1050 kN – cap element stress:
elastic analysis (stress X)
>290
<-290

119
elastic analysis (stress Y)
>290
<-290

120
>290
<-290
elastic analysis (Von Mises) (I)

121
elastic analysis (Von Mises) (II)
>580
<-580

122

123
concrete
Vsd = 1050 kN – ties and concrete stresswww.francobontempi.org

124
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

ELASTO-PLASTIC MODELS

126
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

127
>290
<-290
e-plastic analysis (stress X)

128
>290
<-290
e-plastic analysis (stress Y)

129
>290
<-290
e-plastic analysis (Von Mises) (I)

130
>580
<-580
e-plastic analysis (Von Mises) (II)

131
Vsd = 1050 kN – cap element strain:
e-plastic analysis (Von Mises strain)

132

133
Vsd = 1050 kN – ties and concrete stress
concrete

134
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

135
-25
-20
-15
-10
-5
0
0 200 400 600 800 1000 1200
Load
Uy
Load application
Structural response (1)www.francobontempi.org

136
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

137
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

138
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
Structural response (4)

139
C + SteelCSteel
Vsd
ASYMMETRIC CONFIGURATION
Reinforcement Bars
Vsd
e-plastic steel

140
>290
<-290

141
>290
<-290

142
>290
<-290

143
>580
<-580

144

145
Vsd = 1050 kN – ties and concrete stress
concrete

IMPROVEMENT
STRATEGIES

147
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

148
Reinforcement
Vsd Vsd
C + SteelCSteel
Vsd
SYMMETRIC CONFIGURATIONwww.francobontempi.org

149
th0
Actual Improved
th1

150
>290
<-290
Actual thickNess
th = 6 mm
Improved thickNess
th = 10 mm

151
>290
<-290
Actual thickNess
th = 6 mm
Improved thickNess
th = 10 mm

152
>290
<-290
Actual thickNess
th = 6 mm
Improved thickNess
th = 10 mm

153
>580
<-580
Actual thickNess
th = 6 mm
Improved thickNess
th = 10 mm

154
Vsd = 1050 kN – cap element strain – e-
plastic analysis (Von Mises strain)
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

156
>580
<-580
e-plastic analysis (Von Mises)
th = 10mm

157
>290
<-290
th = 10mm

158
h0 h1
Actual Improved

159
>290
<-290
Actual size
h = 145 mm
Improved size
h = 200 mm

160
>290
<-290
Actual size
h = 145 mm
Improved size
h = 200 mm

161
>290
<-290
Actual size
h = 145 mm
Improved size
h = 200 mm

162
>580
<-580
Actual size
h = 145 mm
Improved size
h = 200 mm

163Reinforcement
Vsd Vsd
C + SteelCSteel
Vsd
Vsd = 850
kN
thickNess:
th = 6 mm
Strategy 3: downloading

164
Vsd = 850/1050 kN – cap element stress
Vsd = 850 kN Vsd = 1050 kN

165
Vsd = 850/1050 kN – cap element stress
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 –
Vsd = 850 kN Vsd = 1050 kNLa scala è
diversa

167
SYM_Vsd = 850 kN
Stress e-plastic analysis (Von Mises) Strain e-plastic analysis (Von Mises)
th = 10 mmwww.francobontempi.org

MODELS
& PROGRAMS
VALIDATIONS

169
COMPARISON BETWEEN TWO F.E.
PROGRAMS

170
>290
<-290
>290
<-290

171
>290
<-290
>290
<-290

172
>290
<-290
>290
<-290

173
>580
<-580
>580
<-580

174
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)

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]
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)www.francobontempi.org

176
-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

THICKNESS
IMPROVEMENT

179
Vsd [kN] thickNess (th) [mm]
600 8
850 10
1050 12
1500 18
SCENARIOS

180
th0
Actual Improved
th

th= 8 mm
Vsd = 600 kN

182
Reinforcement
Vsd Vsd
C + SteelCSteel
Vsd
e-plastic Steel

183
>290
<-290
>290
<-290
STRESS Y
STRESS X

184
>580
<-580
>290
<-290
von MISES I
von MISES II

185
C + SteelCSteel
Vsd
Reinforcement Bars
Vsd
e-plastic Steel

186
>290
<-290
STRESS Y
>290
<-290
STRESS X

187
>580
<-580
>290
<-290
von MISES I
von MISES II

th= 10 mm
Vsd = 850 kN

189
Reinforcement
Vsd Vsd
C + SteelCSteel
Vsd
e-plastic Steel

190
>290
<-290
>290
<-290
STRESS Y
STRESS X

191
>580
<-580
>290
<-290
von MISES I
von MISES II

192
C + SteelCSteel
Vsd
Reinforcement Bars
Vsd
e-plastic Steel

193
>290
<-290
STRESS Y
>290
<-290
STRESS X

194
>580
<-580
>290
<-290
von MISES I
von MISES II

th = 12 mm
Vsd = 1050 kN

196
Reinforcement
Vsd Vsd
C + SteelCSteel
Vsd
e-plastic Steel

197
>290
<-290
>290
<-290
STRESS Y
STRESS X

198
>580
<-580
>290
<-290
von MISES I
von MISES II

199
C + SteelCSteel
Vsd
Reinforcement Bars
Vsd
e-plastic Steel

200
>290
<-290
STRESS Y
>290
<-290
STRESS X

201
>580
<-580
>290
<-290
von MISES I
von MISES II

th = 18 mm
Vsd = 1500 kN

203
Reinforcement
Vsd Vsd
C + SteelCSteel
Vsd
e-plastic Steel

204
>290
<-290
>290
<-290
STRESS Y
STRESS X

205
>580
<-580
>290
<-290
von MISES I
von MISES II

206
C + SteelCSteel
Vsd
Reinforcement Bars
Vsd
e-plastic Steel

207
>290
<-290
STRESS Y
>290
<-290
STRESS X

208
>580
<-580
>290
<-290
von MISES I
von MISES II

209
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

210
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)

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]
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)www.francobontempi.org

212
-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)

SHAPING

214
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

215
>290
<-290
von MISES
Actual
Tipo A
TYPE A

216
>290
<-290
von MISES
Actual
Tipo B
TYPE B

217
>290
<-290
von MISES
Actual
Tipo C
TYPE C

RESULTS FOR
SHAPING
TYPE B

219
ALTERNATIVE GEOMETRIC
CONFIGURATIONS
TIPO B
1
2 3
450°
31°
288.8
83.2
69.0
30.0
TYPE B

th = 8 mm
Vsd =600 kN

221
>290
<-290
>290
<-290
STRESS Y
STRESS X

222
>580
<-580
>290
<-290
von MISES I
von MISES II

223
>290
<-290
>290
<-290
von MISES

224
>290
<-290
STRESS Y
>290
<-290
STRESS X

225
>290
<-290
von MISES

th = 10 mm
Vsd = 850 kN

227
>290
<-290
>290
<-290
STRESS Y
STRESS X

228
>290
<-290
von MISES

229
>290
<-290
STRESS Y
>290
<-290
STRESS X

230
>290
<-290
von MISES

th= 12 mm
Vsd = 1050 kN

232
>290
<-290
>290
<-290
STRESS Y
STRESS X

233
>290
<-290
von MISES

234
>290
<-290
STRESS Y
>290
<-290
STRESS X

235
>290
<-290
von MISES

237
>290
<-290
>290
<-290
STRESS Y
STRESS X

238
>290
<-290
von MISES

239
>290
<-290
STRESS Y
>290
<-290
STRESS X

240
>290
<-290
von MISES

RESULTS FOR
STRUCTURAL
ROBUSTNESS

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

243
>290
<-290
Vsd = 1050*1,33= 1396,5 kN SYM th = 12 mm
>290
<-290
STRESS Y
STRESS X

244
>290
<-290
von MISES I
Vsd = 1050*1,33= 1396,5 kN SYM th = 12 mm
>580
<-580
von MISES II

246
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

248
Definizione del modello (1)

249

250

251

252

253
Stato di sforzo nel conglomerato (1)
Sforzi verticali

254
Sforzi verticali

255
Sforzi verticali

256
Sforzi verticali

257
Sforzi verticali

258

259

260

261

262

263
Stato di sforzo nel conglomerato (11!)
Von Mises !

264
Von Mises !

265
Stato di sforzo nei piatti verticali (1)

266

267

268
Stato di sforzo nei piatti di chiusura

269
Stato di sforzo negli attacchi a C

CONFIGURAZIONE A 2 VIE
ISOTROPA
Vsd = 1050 Kn

271

272

273

274

275
Discretizzazione conglomerato

276
Discretizzazione piatti verticali

277
Discretizzazione singolo piatto verticale

278
Discretizzazione piatti chiusura

279
Sforzi verticali

280
Sforzi verticali

281
Sforzi verticali

282
Sforzi verticali

283
Sforzi verticali

284
Sforzi verticali

285
Sforzi verticali

286
Sforzi verticali

287

288

289

290

291

292

293

294

295

296
Von Mises !

297
Von Mises !

298
Stato di sforzo piatti verticali (1)

299

300

301

302

303
Stato di sforzo nei piatti di chiusura

304
Stato di sforzo attacchi a C

Str
o N
GER
305

CMENSOLA ESTERNA

307
ANALISI E VERIFICHE STRUTTURALI
DELLA MENSOLA DI APPOGGIO
per Vsd = 1050 kN
Maggio 2008

308
EXTERNAL PART

311
MODELS OF EXTERNAL PART
vertical
longitudinal
transversal

CONFIGURAZIONI
Configurazione iniziale e
rinforzata

313
Mensola senza rinforzo

314
Mensola con rinforzo

315
Rinforzo

316

317

318
Rinforzo

319

320

321
Rinforzo

322
Deformabilità senza rinforzo

323
Deformabilità con rinforzo

324

325

326
Mensola senza rinforzo:
vista superiore

327
Mensola con rinforzo:
vista superiore

328
vista inferiore

329
vista inferiore

330
vista di lato

331
vista di lato

332
vista di fronte

333
vista di fronte

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

335
Moltiplicatore = 0.60

336

337

338

339

340

341

342

343

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

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

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

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

SLE (Fz,Fx,Fy)=(1050,0,0) [kN]
353

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

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

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

SLE (Fz,Fx,Fy)=(1050,250,0) [kN]
368

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

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

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

SLE (Fz,Fx,Fy)=(1050,0,250) [kN]
383

SLU (Fz,Fx,Fy)=(1050,0,250) [kN]
384

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

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

SLE(Fz,Fx,Fy)=(1050,175,175) [kN]
400

SLU(Fz,Fx,Fy)=(1050,175,175) [kN]
401

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

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

SLE (Fz,Fx,Fy)=(1050,500,0) [kN]
415

SLU (Fz,Fx,Fy)=(1050,500,0) [kN]
416

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)

Str
o N
GER
419

Corso di dottorato in Ottimizzazione Strutturale: applicazione mensola strallata - Bontempi

Recomendados

Recomendados

Mais conteúdo relacionado

Destaque

Destaque (17)

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

Semelhante a Corso di dottorato in Ottimizzazione Strutturale: applicazione mensola strallata - Bontempi (20)

Mais de StroNGER2012

Mais de StroNGER2012 (20)

Último

Último (20)

Corso di dottorato in Ottimizzazione Strutturale: applicazione mensola strallata - Bontempi