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

1Ottimizzazione Strutturale

franco.bontempi@uniroma1.it

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

3Ottimizzazione Strutturale

franco.bontempi@uniroma1.it

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

Evolution of the design of a

cablestayed bracket

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

REINFORCED CONCRETE

CORBELS

cablestayed bracket

STRUCTURAL STEEL CORBELSw

cablestayed bracket

BEAM SUPPORTw

cablestayed bracket

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.

cablestayed bracket

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

cablestayed bracket

STRUCTURAL SCHEME

Versione iniziale

Versione finale

beam SX beam DX

column

cablestayed bracket

LOAD SCHEMES

Reinforcement

SYM ASYM

cablestayed bracket

STRUCTURAL PARTSw

cablestayed bracket

FIRST ANALYSIS (A):

two dimensional geometry

Vsd*=Vsd/2

Vsd* =Vsd/2

Vsd*=Vsd/2

Vsd* =Vsd/2

cablestayed bracket

• 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

cablestayed bracket

S & T Model Definitionw

cablestayed bracket

Strut & Tie Models

Reinforcement

cablestayed bracket

Reinforcement

Strut & Tie Results

stirrups longitudinal bars

concretesteel bracket

cablestayed bracket

Hybrid models

Reinforcement

cablestayed bracket

Global responseEnd of external bracket displacement

0 500 1000 1500 2000

Load [KN]

Vsd=600 KN - th=8mm

Vsd=850 KN - th=10mm

End of external bracket displacement

0 500 1000 1500 2000

Load [KN]

Vsd=600 KN - th=8mm

cablestayed bracket

Local response

cablestayed bracket

EVOLUTION OF THE FORM (1)

320.1ww

cablestayed bracket

Versione iniziale

Versione finale

cablestayed bracket

CONSTRUCTABILITY (1)w

cablestayed bracket

EXTENDED ANALYSIS

Detailed assessment

cablestayed bracket

THREE-DIMENSIONAL

GEOMETRY

cablestayed bracket

Results for

concrete core and steel frame

cablestayed bracket

Results for

steel bottom frame and attacment

cablestayed bracket

EXTERNAL PARTw

cablestayed bracket

MODELS OF EXTERNAL PARTw

cablestayed bracket

BASIC FORMw

cablestayed bracket

IMPROVEMENTSw

cablestayed bracket

ENHANCED FORMw

cablestayed bracket

COMPRESSION ONLY CONTACTw

NEXT STEP

Two way beam support

cablestayed bracket

TWO WAY SUPPORT (1)w

cablestayed bracket

TWO WAY SUPPORT (2)w

cablestayed bracket

ENHANCHED 2WAY SUPPORTw

cablestayed bracket

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.

Stro N

GERwww.stronger2012.com

cablestayed bracket

STRUCTURAL ANALSYS AND ASSESSMENT

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

PART 0Synthesis

Vsd [kN] thickNess (th) [mm]

850 10

1050 12

1500 18

SCENARIOUS

Lateral

Original Optimized Shaped

Weight (kg) 9,6 9,1 9,9

STRUCTURAL RESPONSE (I)

Upper edge displacement

0 500 1000 1500 2000

Load [KN]

Vsd=600 KN - th=8mm

Centre of Diaphram

0 500 1000 1500 2000

Load [KN]

Vsd=600 KN - th=8mm

Centre of Diaphram

0 500 1000 1500 2000

Load [KN]

Vsd=600 KN - th=8mm

Centre of Diaphram

0,00% 0,02% 0,04% 0,06% 0,08% 0,10% 0,12%

Total Strain_x

ess_x [

Vsd=600 KN - th=8mm

STRUCTURAL RESPONSE (II)

0 500 1000 1500 2000

Load [KN]

Vsd=600 KN - th=8mm

STRUCTURAL RESPONSE (III)

ALTERNATIVE GEOMETRIC

CONFIGURATIONS

TIPO B

2 3450°

TYPE B

Vsd = 600 kN SYM th = 8 mm

cap element stress / e-plastic analysis

von MISES

Vsd = 600 kN ASYM th = 8 mm

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

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

-2000 0 2000 4000 6000 8000 10000

M [kNm]

compressionN [kN]

tension

stirrups

longitudinal

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

STRUCTURAL MODELING (i)

• A slice of half column is considered

(plane stress assumption)

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

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

4321,,, uuuu

VIVIVIIIIIINNNNNN ,,,,,

aNNNNN

VIVIII

bNNNNN

VIVIVIII

lNNN VIV

xyyx NNN ,,

STRUCTURAL MODELING

OF CONCRETE PART (II):

stress representation

LOADING SYSTEMS: SYM.

Reinforcment

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

SMINSTAF tensione massima negativa negli elementi rappresentanti le armature lente

secondarie del pilastro

SMAXLONG tensione massima negli elementi rappresentanti le armature lente

principali del pilastro

SMINLONG tensione massima negativa negli elementi rappresentanti le armature lente

principali del pilastro

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

BEAM ELEMENTS

STRUCTURAL MODELING: LINKS

ELASTIC MODELS

Reinforcement

Vsd Vsd

C + SteelCSteel

SYMMETRIC CONFIGURATION

Vsd = 1050 kN – cap element stress:

elastic analysis (stress X)

elastic analysis (stress Y)

elastic analysis (Von Mises) (I)

elastic analysis (Von Mises) (II)

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

00138.0

]N/mm[ 290 2

][N/mm 210000 2

*100/1 01 EE

x10^(-3)

e-plastic analysis (stress X)

e-plastic analysis (stress Y)

e-plastic analysis (Von Mises) (I)

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

0 200 400 600 800 1000 1200

Load application

Structural response (1)

0 200 400 600 800 1000 1200Load

Spigolo alto

0 200 400 600 800 1000 1200

Centre of Diaphram

-0,010

0 200 400 600 800 1000 1200

Centre of Diaphram

0 200 400 600 800 1000 1200

Centre of Diaphram

0,0000 0,0100 0,0200 0,0300 0,0400 0,0500 0,0600

Total Strain_x

Centre of Diaphram

0 200 400 600 800 1000 1200

Centre of Diaphram

0 200 400 600 800 1000 1200

Centre of Diaphram

C + SteelCSteel

ASYMMETRIC CONFIGURATION

Reinforcement Bars

e-plastic steel

• 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

Actual Improved

Actual thickNess

th = 6 mm

Improved thickNess

th = 10 mm

Actual thickNess

th = 6 mm

Improved thickNess

th = 10 mm

Actual thickNess

th = 6 mm

Improved thickNess

th = 10 mm

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

e-plastic analysis (Von Mises)

th = 10mm

Actual Improved

Actual size

h = 145 mm

Improved size

h = 200 mm

Actual size

h = 145 mm

Improved size

h = 200 mm

Actual size

h = 145 mm

Improved size

h = 200 mm

Actual size

h = 145 mm

Improved size

h = 200 mm

FB - April 2007 STAYED BRACKET 162Reinforcement

Vsd Vsd

C + SteelCSteel

Vsd = 850

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

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

0 200 400 600 800 1000 1200

Load [KN]

ANSYS STRAUSY

STRUCTURAL RESPONSE COMPARISON (I)

Centre of Diaphram

0 200 400 600 800 1000 1200

Load [KN]

ess_x [

ANSYS STRAUS

Centre of Diaphram

0 200 400 600 800 1000 1200

Load [KN]

ANSYS STRAUS

Centre of Diaphram

0,00% 1,00% 2,00% 3,00% 4,00% 5,00% 6,00%

Total Strain_x

ANSYS STRAUS

STRUCTURAL RESPONSE COMPARISON (II)

-25,00

-20,00

-15,00

-10,00

0 200 400 600 800 1000 1200

Load [KN]

ANSYS STRAUS

STRUCTURAL RESPONSE COMPARISON (III)

PART 2Solutions

for the structural problem

THICkNESS

IMPROVEMENT

Vsd [kN] thickNess (th) [mm]

850 10

1050 12

1500 18

SCENARIOUS

Actual Improved

th= 8 mm

Vsd = 600 kN

Reinforcement

Vsd Vsd

C + SteelCSteel

SYMMETRIC CONFIGURATIONe-plastic Steel

<-290STRESS Y

STRESS X

von MISES I

von MISES II

C + SteelCSteel

Reinforcement Bars

e-plastic Steel

STRESS Y>290

STRESS X

von MISES I

von MISES II

th= 10 mm

Vsd = 850 kN

Reinforcement

Vsd Vsd

C + SteelCSteel

<-290STRESS Y

STRESS X

von MISES I

von MISES II

C + SteelCSteel

Reinforcement Bars

e-plastic Steel

STRESS Y>290

STRESS X

von MISES I

von MISES II

th = 12 mm

Vsd = 1050 kN

Reinforcement

Vsd Vsd

C + SteelCSteel

<-290STRESS Y

STRESS X

von MISES I

von MISES II

C + SteelCSteel

Reinforcement Bars

e-plastic Steel

STRESS Y>290

STRESS X

von MISES I

von MISES II

th = 18 mm

Vsd = 1500 kN

Reinforcement

Vsd Vsd

C + SteelCSteel

<-290STRESS Y

STRESS X

von MISES I

von MISES II

C + SteelCSteel

Reinforcement Bars

e-plastic Steel

STRESS Y>290

STRESS X

von MISES I

von MISES II

Summary for Proposed ThickNess:

von Mises stress / SYM / e-plastic analysis

Vsd=1050 kN

th=12 mm

Vsd=1500 kN

th=18 mm

Vsd=600 kN

th=8 mm

Vsd=850 kN

th=10 mm

0 500 1000 1500 2000

Load [KN]

Vsd=600 KN - th=8mm

STRUCTURAL RESPONSE (I)

Centre of Diaphram

0 500 1000 1500 2000

Load [KN]

Vsd=600 KN - th=8mm

Centre of Diaphram

0 500 1000 1500 2000

Load [KN]

Vsd=600 KN - th=8mm

Centre of Diaphram

0,00% 0,02% 0,04% 0,06% 0,08% 0,10% 0,12%

Total Strain_x

ess_x [

Vsd=600 KN - th=8mm

STRUCTURAL RESPONSE (II)

0 500 1000 1500 2000

Load [KN]

Vsd=600 KN - th=8mm

STRUCTURAL RESPONSE (III)

SHAPING

TIPO C

31°50° 432

ALTERNATIVE CONFIGURATIONS

TIPO A

31°50° 432

TIPO B

2 3450°

ACTUAL

TYPE B TYPE C

TYPE AACTUAL

von MISES

Actual

Tipo ATYPE A

von MISES

Actual

Tipo BTYPE B

von MISES

Actual

Tipo CTYPE C

RESULTS FOR

SHAPING

TYPE B

ALTERNATIVE GEOMETRIC

CONFIGURATIONS

TIPO B

2 3450°

TYPE B

th = 8 mm

Vsd =600 kN

<-290STRESS Y

STRESS X

von MISES I

von MISES II

von MISES

STRESS Y>290

STRESS X

von MISES

th = 10 mm

Vsd = 850 kN

<-290STRESS Y

STRESS X

von MISES

STRESS Y>290

STRESS X

von MISES

th= 12 mm

Vsd = 1050 kN

<-290STRESS Y

STRESS X

von MISES

STRESS Y>290

STRESS X

von MISES

th = 18 mm

Vsd = 1500 kN

<-290STRESS Y

STRESS X

von MISES

STRESS Y>290

STRESS X

von MISES

RESULTS FOR

STRUCTURAL

ROBUSTNESS

th = 12 mm

Vsd = 1050*1,33 kN = 1396 kN

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

<-290STRESS Y

STRESS X

von MISES I

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

von MISES II

Stro N

cablestayed bracket

ANALISI E VERIFICHE STRUTTURALI

DELLE CONFIGURAZIONI

per Vsd = 1050 Kn

IN PRESENZA DI PLUVIALE / A 2 VIE

ISOTROPADicembre 2007

INFLUENZA DELLA

PRESENZA DEL PLUVIALE

Vsd = 1050 Kn

Definizione del modello (1)

Stato di sforzo nel conglomerato (1)

Sforzi verticali

Stato di sforzo nel conglomerato (11!)

Von Mises !

Stato di sforzo nei piatti verticali (1)

Stato di sforzo nei piatti di chiusura

Stato di sforzo negli attacchi a C

CONFIGURAZIONE A 2 VIE

ISOTROPA

Vsd = 1050 Kn

Discretizzazione conglomerato

Discretizzazione piatti verticali

Discretizzazione singolo piatto verticale

Discretizzazione piatti chiusura

Sforzi verticali

Von Mises !

Stato di sforzo piatti verticali (1)

Stato di sforzo nei piatti di chiusura

Stato di sforzo attacchi a C

Stro N

cablestayed bracket

ANALISI E VERIFICHE STRUTTURALI

DELLA MENSOLA DI APPOGGIO

per Vsd = 1050 kNMaggio 2008

cablestayed bracket

EXTERNAL PARTw

cablestayed bracket

MODELS OF EXTERNAL PARTw

vertical

longitudinal

transversal

CONFIGURAZIONI

Configurazione iniziale e

rinforzata

Mensola senza rinforzow

Mensola con rinforzow

Rinforzow

Deformabilità senza rinforzow

Deformabilità con rinforzow

Mensola senza rinforzo:

vista superiore

Mensola con rinforzo:

vista superiore

vista inferiore

vista di lato

vista di fronte

ANALISI NON LINEARE

Analisi elasto-plastica con

elementi di contatto della

configurazione iniziale

Moltiplicatore = 0.60w

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.

MF01-1 AD 00 modb NOFLEX

Carico:

Verticale 1050 kN

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

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

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

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

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

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

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

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

MF01-1 AD 00 modc NOFLEX

Carico:

Verticale 1050 kN

Longitudinale 250 kN

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

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

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

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

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

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

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

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

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

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

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

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

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

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

MF01-1 AD 00 modd NOFLEX

Carico:

Verticale 1050 kN

Trasversale 250 kN

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

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

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

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

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

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

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

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

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

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

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

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

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

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

MF01-1 AD 00 mode NOFLEX

Carico:

Verticale 1050 kN

Trasversale 175 kN

Longitudinale 175 kN383

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