Renzi ordine ingegneri_firenze_printable

May 28, 20151 like492 views

lezione tenuta presso l'Ordine degli Ingegneri di Firenze,all'interno del seminario di aggiornamento professionale sulle fondazioni superficiali e profonde tenuto in data 9 marzo 2015.

Ing. Stefano Renzi
www.stefanorenzi.it
renzi.stefano@gmail.com
Fixed-Base
System

ωωωω
ω
ω
ω
ζζζζ
b
üff (t)
ü (t) 2
( ) cos ,
2 3
u D
D
I
π ω
ω ω ω
ω
= ≤
( ) 0.2 [1 cos ],
2
D
D
Iθ
π ω
ω ω ω
ω
= × − ≤
2
/1
( ) 1
2
s
u
V
I
ω
ω
λ
= Γ +
2
( / )
( ) sV d
Iθ
ω
ω
λ
= Γ
1
42
4
x x
p p
k i c m
E I
ω ω
λ
+ −
=4 4
[( / ) 4 ]
x x
p p s
k i c
E I V
ω
ω λ
+
Γ =
+
Iu ω = 0.5, ω 2/3 ω
Iθ ω = 0.2, ω > ω

θK , ζθ
xθK , ζxθ
ζζζζ
h
u
~
m
k, ζ
b
xK , ζx
üff (t)
ü (t)ü (t)
ωωωω
ωωωω
ωωωω
ββββ::::

+=
2
n
4
1
H
V
f S
n
( )
+≈+
ν−π
=+=
2
n
4
1
H
V
615.1
2
n
4
1
H
V
1
4.3
2
n
4
1
H
V
f SSLa
n

Renzi ordine ingegneri_firenze_printable

Spostamenti orizzontali
m
k
=ω
)()(
1
~
2
ωω
ω
ω
θk
kh
k
k
x
++
=
km2
c
=ξ )(
)(
~
)(
)(
~~
1
~~ 22222
ωξ
ω
ω
ωξ
ω
ω
ξ
ω
ω
ξ
ω
ω
ξ θ
θk
mh
k
m
x
x
g ++−+=
sistema
incastrato
alla base
sistema con interazione dinamica
terreno-struttura
frequenza
naturale
rapporto di
smorzamento
1. Un importante effetto dell’interazione dinamica terreno-struttura è quello di ridurre la
frequenza naturale di vibrazione del sistema terreno-struttura (il sistema è più
flessibile) ad un valore più basso di quello della struttura ipotizzata incastrata alla
base.
2. Un altro importante effetto dell’interazione dinamica terreno struttura è quello di
aumentare lo smorzamento effettivo del sistema.
0.02 0.3 0.6
1.0
1.5
2.0
1/
Exact procedure
Veletsos (1977)
h/r = 5 h/r = 3 h/r = 1
Τ
Τ
σ 0.02 0.1 1
0.00
0.25
0.50
1/
ssi
Fig . Properties of equivalent one-degree-freedom system
Exact procedure
Wolf (1985)
h/r = 5
h/r = 1
h/r = 2h/r= 0.33
σ

h
d
σ
=
1
s
h
T V
p
s
E
E
h
m
k, ζ
d
Ep Ip
Τ
Τ
0.5 1.0
1.0
1.5
2.0
2.5 Ep
/Es
= 100
1000
10000
1/ σ
0.5 1.0
0.00
0.04
0.08
0.12
1/
Ep
/Es
= 100
1000
10000
σ
Τ
Τ
0.5 1.0
1
2
3
1/
h/d = 1
5
10
σ

0.5 1.0
0.0
0.1
0.2
0.3
1/
h/d = 1
5
10
σ 0.04 0.08 0.12 0.16
0.00
0.04
0.08
0.12
( )
1
f
σ
Pile
Footing
σ)
ξ
ρ
ξ
ν
θK , ζθ
xθK , ζxθ
h
u
~
m
k, ζ
b xK , ζx
xK , ζx
xK , ζx
xK , ζx
xK , ζx
δ δ
ρ

)()(
1
~
2
ωω
ω
ω
θk
kh
k
k
x
++
=
)(
)(
~
)(
)(
~~
1
~~ 22222
ωξ
ω
ω
ωξ
ω
ω
ξ
ω
ω
ξ
ω
ω
ξ θ
θk
mh
k
m
x
x
g ++−+=
)()(
1
~
*
2
*
ωω
ω
ω
ϑk
kh
k
k
x
++
=
)(
)(
~
)(
)(
~~
1
~~ 22222
ωξ
ω
ω
ωξ
ω
ω
ξ
ω
ω
ξ
ω
ω
ξ θ
θk
mh
k
m
x
x
g ++−+=
ζζζζ
ζζζζ
ζζζζ ζζζζ

hj
m1
m2
mj
mN
•
•
•
xK , ζx
heq
meq
keq, ζeq
b
θK , ζθ
b
•
•
•
•
•
•
•
ξξξξ
ξ

xK , ζx
heq
meq
keq, ζeq
b
θK , ζθ
Seq
eq
VT
h1
=
σ
b
heq
eq
b
m
m
=µ
da S,S,T, ζ
da S
~
,S
~
,
~
,T
~
ζ

L’analisi è stata sviluppata nei
seguenti passi:
• Modellazione della torre come
un oscillatore semplice
equivalente;
• Stima dell’effetto
dell’interazione dinamica
terreno-struttura (SSI), in
termini di modifica del periodo
fondamentale di vibrazione
Frequenze fondamentali di vibrazioni in direzione N-S

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Renzi ordine ingegneri_firenze_printable

1. Ing. Stefano Renzi www.stefanorenzi.it renzi.stefano@gmail.com Fixed-Base System

2. ωωωω ω ω ω ζζζζ b üff (t) ü (t) 2 ( ) cos , 2 3 u D D I π ω ω ω ω ω = ≤ ( ) 0.2 [1 cos ], 2 D D Iθ π ω ω ω ω ω = × − ≤ 2 /1 ( ) 1 2 s u V I ω ω λ = Γ + 2 ( / ) ( ) sV d Iθ ω ω λ = Γ 1 42 4 x x p p k i c m E I ω ω λ + − =4 4 [( / ) 4 ] x x p p s k i c E I V ω ω λ + Γ = + Iu ω = 0.5, ω 2/3 ω Iθ ω = 0.2, ω > ω

3. θK , ζθ xθK , ζxθ ζζζζ h u ~ m k, ζ b xK , ζx üff (t) ü (t)ü (t) ωωωω ωωωω ωωωω ββββ::::

4. += 2 n 4 1 H V f S n ( ) +≈+ ν−π =+= 2 n 4 1 H V 615.1 2 n 4 1 H V 1 4.3 2 n 4 1 H V f SSLa n

6. Spostamenti orizzontali m k =ω )()( 1 ~ 2 ωω ω ω θk kh k k x ++ = km2 c =ξ )( )( ~ )( )( ~~ 1 ~~ 22222 ωξ ω ω ωξ ω ω ξ ω ω ξ ω ω ξ θ θk mh k m x x g ++−+= sistema incastrato alla base sistema con interazione dinamica terreno-struttura frequenza naturale rapporto di smorzamento 1. Un importante effetto dell’interazione dinamica terreno-struttura è quello di ridurre la frequenza naturale di vibrazione del sistema terreno-struttura (il sistema è più flessibile) ad un valore più basso di quello della struttura ipotizzata incastrata alla base. 2. Un altro importante effetto dell’interazione dinamica terreno struttura è quello di aumentare lo smorzamento effettivo del sistema. 0.02 0.3 0.6 1.0 1.5 2.0 1/ Exact procedure Veletsos (1977) h/r = 5 h/r = 3 h/r = 1 Τ Τ σ 0.02 0.1 1 0.00 0.25 0.50 1/ ssi Fig . Properties of equivalent one-degree-freedom system Exact procedure Wolf (1985) h/r = 5 h/r = 1 h/r = 2h/r= 0.33 σ

7. h d σ = 1 s h T V p s E E h m k, ζ d Ep Ip Τ Τ 0.5 1.0 1.0 1.5 2.0 2.5 Ep /Es = 100 1000 10000 1/ σ 0.5 1.0 0.00 0.04 0.08 0.12 1/ Ep /Es = 100 1000 10000 σ Τ Τ 0.5 1.0 1 2 3 1/ h/d = 1 5 10 σ

8. 0.5 1.0 0.0 0.1 0.2 0.3 1/ h/d = 1 5 10 σ 0.04 0.08 0.12 0.16 0.00 0.04 0.08 0.12 ( ) 1 f σ Pile Footing σ) ξ ρ ξ ν θK , ζθ xθK , ζxθ h u ~ m k, ζ b xK , ζx xK , ζx xK , ζx xK , ζx xK , ζx δ δ ρ

9. )()( 1 ~ 2 ωω ω ω θk kh k k x ++ = )( )( ~ )( )( ~~ 1 ~~ 22222 ωξ ω ω ωξ ω ω ξ ω ω ξ ω ω ξ θ θk mh k m x x g ++−+= )()( 1 ~ * 2 * ωω ω ω ϑk kh k k x ++ = )( )( ~ )( )( ~~ 1 ~~ 22222 ωξ ω ω ωξ ω ω ξ ω ω ξ ω ω ξ θ θk mh k m x x g ++−+= ζζζζ ζζζζ ζζζζ ζζζζ

11. hj m1 m2 mj mN • • • xK , ζx heq meq keq, ζeq b θK , ζθ b • • • • • • • ξξξξ ξ

12. xK , ζx heq meq keq, ζeq b θK , ζθ Seq eq VT h1 = σ b heq eq b m m =µ da S,S,T, ζ da S ~ ,S ~ , ~ ,T ~ ζ

14. L’analisi è stata sviluppata nei seguenti passi: • Modellazione della torre come un oscillatore semplice equivalente; • Stima dell’effetto dell’interazione dinamica terreno-struttura (SSI), in termini di modifica del periodo fondamentale di vibrazione Frequenze fondamentali di vibrazioni in direzione N-S

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