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Franco BontempiProfessore Ordinario di Tecnica delle Costruzioni
Facolta’ di Ingegneria Civile e IndustrialeSapienza Universita’ di Roma
SPECIFIC ASPECTS OF STEEL FRAMES
MODELING
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EBF
MRF CBF
Flexural
behavor
Axial
behavorMixed
Behavior
(Mainly
axial
with
flexural
localized)
LOW
STIFNESS
GOOD
DUCTILITY
GOOD
STIFNESS
LOW
DCTILITY3
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SEMI RIGID NODES
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Connection configurations and moment–rotation curves
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• Attraverso il valore di rigidezza adimensionale e conoscendo le proprietà inerziali delle travi si può ricavare il valore della rigidezza della molla rotazionale che modella il comportamento del collegamento attraverso la seguente espressione:
- E modulo di elasticità dell’acciaio;- J momento d’inerzia dell’elemento;- l lunghezza dell’elemento.
Collegamenti semi-rigidi
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JOINT DEFORMATION
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Joint panel in steel frames
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Lateral displacement of MRF
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Joint panel in the experiment
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Joint deformation approximation
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Scissor Model of Panel Joint
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Joint component
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panel
flanges
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Krawinkler Model of Panel Joint
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Comparison
Real Panel
Joint
Bbehavior
Krawinwler
Model
Scissor
Model
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l
k kEJ
Semi-Rigid + Joint Panel Deformability
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Nodes in Krawinkler Joint Model
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l
k kEJ
Semi-rigid end beam element
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AXIAL BEHAVIOR
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May be...
Not at all41
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Hysteresis of a brace under cyclic axial loading
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Effect of slenderness
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Hysteretic behavior of single-story braced frame having slender braces
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EBF
CBF
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EBF
Mixed
Behavior
(Mainly
axial
with
flex<ural
localized)
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Carico / Spostamento imposto
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Carico imposto vs. Spostamento impresso (1)
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Es. carico imposto: collaudo ponte
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Carico imposto vs. Spostamento impresso (2)
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Es. spostamento imposto:macchina di prova in laboratorio
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Typical
Component
Es.
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Lunghezza asta [ m ] I = 0.18% (C.D.M. 08) I = 0.30% I = 0.35% I = 0.40%
L asta 1-2-3 = 1.34 0.0023 0.0040 0.0047 0.0054
L asta 4 = 1.20 0.0021 0.0036 0.0042 0.0048
L asta 5 = 2.43 0.0042 0.0073 0.0085 0.0097
Le imperfezioni delle
diagonali sono
proporzionali agli
spostamenti del primo
modo di buckling
21 43 5
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Risultato sperimentale
23/3
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Confronto sperimentale-analitico
2431
Imperfezione 0.35%
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Risultato sperimentale
25/31
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Confronto sperimentale-analitico
26/31
Pcr sp Pcr straus7
[kN (kip)] [kN (kip)]
I° punto critico 285 (64.0) 261 (58.7)
II° punto critico 257 (57.8) 255 (57.3)
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27/31
-6
-4
-2
0
2
4
6
0 1000 2000 3000 4000 5000
Storia di spostamenti
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28/31
-6
-4
-2
0
2
4
6
0 1000 2000 3000 4000 5000
Storia di spostamenti
Prima Instabilità
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29/31
-6
-4
-2
0
2
4
6
0 1000 2000 3000 4000 5000
Storia di spostamenti
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Buckling-Restrained Braced Frames (BRBF)
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Common BRB assembly
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The concept of BRB
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NUMERICAL SOLUTION
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Problema strutturale nonlineare
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Nota
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Natura iterativa
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Formulazione secante
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Schema iterativo
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Criteri di arresto
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Rappresentazione geometrica delle prime due iterazioni
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Caso di mancata convergenza della soluzione
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Formulazione tangente:Newton-Raphson (NR)
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Formulazione tangente:Newton-Raphson modificato (mNR)
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Inizializzazione
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Predictor
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Corrector
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Convergenza
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Test
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Indicatori della qualità del percorso di equilibrio.
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