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

1Ottimizzazione Strutturale

[email protected]

1

Introduzione alla

OTTIMIZZAZIONE STRUTTURALEApplicazione a una mensola strallata

Franco Bontempi

Ordinario di Tecnica delle Costruzioni

Facolta’ di Ingegneria Civile e Industriale

Sapienza Universita’ di Roma

2

2015

3Ottimizzazione Strutturale

[email protected]

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

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http://www.francobontempi.org/

Evolution of the design of a

cablestayed bracket

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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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REINFORCED CONCRETE

CORBELS

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STRUCTURAL STEEL CORBELSw

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BEAM SUPPORTw

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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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cablestayed bracket

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STRUCTURAL PARTSw

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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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S & T Model Definitionw

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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



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




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

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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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Versione iniziale

Versione finale

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CONSTRUCTABILITY (1)w

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cablestayed bracket

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EXTENDED ANALYSIS

Detailed assessment

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THREE-DIMENSIONAL

GEOMETRY

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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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EXTERNAL PARTw

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MODELS OF EXTERNAL PARTw

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BASIC FORMw

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IMPROVEMENTSw

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ENHANCED FORMw

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COMPRESSION ONLY CONTACTw

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NEXT STEP

Two way beam support

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TWO WAY SUPPORT (1)w

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TWO WAY SUPPORT (2)w

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ENHANCHED 2WAY SUPPORTw

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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


cablestayed bracket

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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 - [email protected]

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 - [email protected]

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

PART 0Synthesis


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

[m

m]

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]

Str

es

s_

x [

MP

a]

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]

To

tal S

tra

in_

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

Str

ess_x [

MP

a]

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

[m

m]

Vsd=600 KN - th=8mm




Y

X

STRUCTURAL RESPONSE (III)


ALTERNATIVE GEOMETRIC

CONFIGURATIONS

TIPO B

1

2 3450°

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 1Framework

of the structural problem

BASIS OF THE

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]

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


STRUCTURAL MODELING (i)

• A slice of half column is considered

(plane stress assumption)

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lum

n

a

Vsd

Vsd

a/2

Vsd*=Vsd/2

Vsd* =Vsd/2

STRUT & TIE

MODELING


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

ablslAA

absaAA

basbAA

ba

ba

ba

dd

yy

xx

2

2

2

2

2

83

2

383

2

383

2

,

,

,


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


LOADING SYSTEMS: SYM.

Reinforcment

Bars

Vsd

C + SteelCSteel

VsdVsd


LOADING SYSTEMS: ASYM.

Reinforcment

BarsC + 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


• min compression = -59,1 MPa

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

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

ELASTIC MODELS


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



• tension = 582,7 MPa

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

ELASTO-PLASTIC MODELS


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


>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 1200Load

Ux

Spigolo alto



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



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



C + SteelCSteel

Vsd

ASYMMETRIC CONFIGURATION

Reinforcement Bars

Vsd

e-plastic steel




>290

<-290




>580

<-580




• tension = 582,7 MPa


concrete

IMPROVEMENT

STRATEGIES


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





>290

<-290

Actual thickNess

th = 6 mm

Improved thickNess

th = 10 mm




>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

MODELS

& PROGRAMS

VALIDATIONS


COMPARISON BETWEEN TWO F.E.

PROGRAMS


>290

<-290



>290

<-290




>290

<-290

>290

<-290


>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

[m

m]

ANSYS STRAUSY

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]

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)



-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 2Solutions

for the structural problem

THICkNESS

IMPROVEMENT


Vsd [kN] thickNess (th) [mm]

600 8

850 10

1050 12

1500 18

SCENARIOUS


th0


Actual Improved

th

th= 8 mm

Vsd = 600 kN


Reinforcement

Vsd Vsd

C + SteelCSteel

Vsd

SYMMETRIC CONFIGURATIONe-plastic Steel


>290

<-290



>290

<-290STRESS 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

th= 10 mm

Vsd = 850 kN


Reinforcement

Vsd Vsd

C + SteelCSteel

Vsd



>290

<-290



>290

<-290STRESS 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

th = 12 mm

Vsd = 1050 kN


Reinforcement

Vsd Vsd

C + SteelCSteel

Vsd



>290

<-290



>290

<-290STRESS 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

th = 18 mm

Vsd = 1500 kN


Reinforcement

Vsd Vsd

C + SteelCSteel

Vsd



>290

<-290



>290

<-290STRESS 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

[m

m]

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]

Str

es

s_

x [

MP

a]

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]

To

tal S

tra

in_

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

Str

ess_x [

MP

a]

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

[m

m]

Vsd=600 KN - th=8mm




Y

X

STRUCTURAL RESPONSE (III)

SHAPING


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




>290

<-290

von MISES

Actual

Tipo ATYPE A




>290

<-290

von MISES

Actual

Tipo BTYPE B




>290

<-290

von MISES

Actual

Tipo CTYPE C

RESULTS FOR

SHAPING

TYPE B


ALTERNATIVE GEOMETRIC

CONFIGURATIONS

TIPO B

1

2 3450°

31°

288.8

83.2

69.0

30.0

TYPE B

th = 8 mm

Vsd =600 kN


>290

<-290



>290

<-290STRESS 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

th = 10 mm

Vsd = 850 kN


>290

<-290



>290

<-290STRESS Y

STRESS X




>290

<-290

von MISES


>290

<-290



STRESS Y>290

<-290

STRESS X




>290

<-290

von MISES

th= 12 mm

Vsd = 1050 kN


>290

<-290



>290

<-290STRESS Y

STRESS X




>290

<-290

von MISES


>290

<-290



STRESS Y>290

<-290

STRESS X




>290

<-290

von MISES

th = 18 mm

Vsd = 1500 kN


>290

<-290



>290

<-290STRESS 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

<-290STRESS Y

STRESS X


>290

<-290

von MISES I

Vsd = 1050*1,33= 1396,5 kN SYM th = 12 mm


>580

<-580

von MISES II

Stro N



cablestayed bracket

244

245

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

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

Stro N



cablestayed bracket

304

305

ANALISI E VERIFICHE STRUTTURALI

DELLA MENSOLA DI APPOGGIO

per Vsd = 1050 kNMaggio 2008

ww

w.f

ran

co

bo

nte

mp

i.o

rg



cablestayed bracket

306

EXTERNAL PARTw

ww

.fra

nc

ob

on

tem

pi.o

rg



cablestayed bracket

307

ww

w.f

ran

co

bo

nte

mp

i.o

rg



cablestayed bracket

308

ww

w.f

ran

co

bo

nte

mp

i.o

rg



cablestayed bracket

309

MODELS OF EXTERNAL PARTw

ww

.fra

nc

ob

on

tem

pi.o

rg

vertical

longitudinal

transversal


CONFIGURAZIONI

Configurazione iniziale e

rinforzata

310

ww

w.f

ran

co

bo

nte

mp

i.o

rg


311

Mensola senza rinforzow

ww

.fra

nc

ob

on

tem

pi.o

rg


312

Mensola con rinforzow

ww

.fra

nc

ob

on

tem

pi.o

rg


313

Rinforzow

ww

.fra

nc

ob

on

tem

pi.o

rg


314


ww

.fra

nc

ob

on

tem

pi.o

rg


315


ww

.fra

nc

ob

on

tem

pi.o

rg


316

Rinforzow

ww

.fra

nc

ob

on

tem

pi.o

rg


317


ww

.fra

nc

ob

on

tem

pi.o

rg


318


ww

.fra

nc

ob

on

tem

pi.o

rg


319

Rinforzow

ww

.fra

nc

ob

on

tem

pi.o

rg


320

Deformabilità senza rinforzow

ww

.fra

nc

ob

on

tem

pi.o

rg


321

Deformabilità con rinforzow

ww

.fra

nc

ob

on

tem

pi.o

rg


322


ww

.fra

nc

ob

on

tem

pi.o

rg


323


ww

.fra

nc

ob

on

tem

pi.o

rg


324

Mensola senza rinforzo:

vista superiore

ww

w.f

ran

co

bo

nte

mp

i.o

rg


325

Mensola con rinforzo:

vista superiore

ww

w.f

ran

co

bo

nte

mp

i.o

rg


326


vista inferiore

ww

w.f

ran

co

bo

nte

mp

i.o

rg


327


vista inferiore

ww

w.f

ran

co

bo

nte

mp

i.o

rg


328


vista di lato

ww

w.f

ran

co

bo

nte

mp

i.o

rg


329


vista di lato

ww

w.f

ran

co

bo

nte

mp

i.o

rg


330


vista di fronte

ww

w.f

ran

co

bo

nte

mp

i.o

rg


331


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

332

ww

w.f

ran

co

bo

nte

mp

i.o

rg


333

Moltiplicatore = 0.60w

ww

.fra

nc

ob

on

tem

pi.o

rg


334


ww

.fra

nc

ob

on

tem

pi.o

rg


335


ww

.fra

nc

ob

on

tem

pi.o

rg


336


ww

.fra

nc

ob

on

tem

pi.o

rg


337


ww

.fra

nc

ob

on

tem

pi.o

rg


338


ww

.fra

nc

ob

on

tem

pi.o

rg


339


ww

.fra

nc

ob

on

tem

pi.o

rg


340


ww

.fra

nc

ob

on

tem

pi.o

rg


341


ww

.fra

nc

ob

on

tem

pi.o

rg


CONFIGURAZIONE FINALE

Verifiche in campo elasto plastico e

vincoli monolateri sul profilato a C

342

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.

343

ww

w.f

ran

co

bo

nte

mp

i.o

rg


MF01-1 AD 00 modb NOFLEX

Carico:

Verticale 1050 kN

344

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

345

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

346

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

347

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

348

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

349

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

350

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

351

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

352

ww

w.f

ran

co

bo

nte

mp

i.o

rg


MF01-1 AD 00 modc NOFLEX

Carico:

Verticale 1050 kN

Longitudinale 250 kN

353

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

354

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

355

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

356

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

357

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

358

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

359

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

360

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

361

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

362

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

363

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

364

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

365

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

366

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

367

ww

w.f

ran

co

bo

nte

mp

i.o

rg


MF01-1 AD 00 modd NOFLEX

Carico:

Verticale 1050 kN

Trasversale 250 kN

368

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

369

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

370

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

371

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

372

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

373

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

374

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

375

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

376

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

377

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

378

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

379

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

380

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

381

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

382

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 kN383

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

384

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

385

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

386

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

387

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

388

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

389

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

390

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

391

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

392

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

393

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

394

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

395

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

396

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

397

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

398

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

399

ww

w.f

ran

co

bo

nte

mp

i.o

rg


MF01-1 AD 00 modf NOFLEX

Carico:

Verticale 1050 kN

Longitudinale 500 kN

400

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

401

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

402

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

403

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

404

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

405

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

406

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

407

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

408

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

409

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

410

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

411

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

412

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

413

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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

414

ww

w.f

ran

co

bo

nte

mp

i.o

rg


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)

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Stro N



cablestayed bracket

416

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

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