The New Kuip : Enfolding 24/7
"
#
$
%
&
&
'
(
)
)
*
+
&
*
,
!
)
w
The New Kuip: Enfolding 24/7
¨
¨
¡
©
¢
¢
®
¤
«
·
¨
¨
Ø
¹
f
g
h
i
j
f
k
¹
º
º
£
£
¹
¸
¹
¸
¹
Ú
¹
¸
¹
Ú
¹
¸
Þ
¸
¹
Ú
¹
è
é
¹
Ú
¹
¹
¹
j
m
y
i
r
z
e
l
h
o
f
i
v
k
p
m
h
l
i
{
q
v
q
y
h
d
w
j
e
m
f
j
g
o
h
h
m
i
m
j
l
f
i
r
k
e
j
r
d
|
}
}
~
r
r
l
v
l
e
o
o
g
l
v
q
v
o
r
~
}
g
}
h
i
v
~
m
j
}
l
e
o
c
g
l
u
¹
¹
Ú
¹
ð
»
¹
Ú
¹
Ü
Ð
m
n
j
Å
o
Î
Ñ
p
Î
î
½
h
Á
Ñ
ß
Î
á
À
Þ
¼
½
q
Õ
r
Ñ
Ã
Î
Á
Ï
¼
¾
Ñ
å
Ä
À
Å
Â
Â
À
Î
l
Ë
¾
Ï
m
Ý
»
m
j
Î
t
¯
µ
Ç
Ì
k
Â
Ñ
Ã
Ñ
å
Ï
Í
Î
Å
Â
u
v
ï
Ñ
¸
e
ä
æ
º
×
º
è
¸
ç
º
¾
Ñ
l
Å
Ã
ë
Ö
Î
»
à
Â
Ã
º
½
Å
Å
u
Æ
Ö
ã
ì
¾
Ã
´
Ý
Å
á
î
ñ
À
ß
Ï
ã
Á
Ñ
¾
à
Ñ
à
ª
Ò
Ã
à
ê
Â
¼
s
Ã
Ñ
â
Ï
Î
Ï
³
Ñ
à
½
Þ
¸
l
Á
¾
¥
Ä
¾
Ü
»
²
Û
ß
»
¸
¡
µ
Â
¾
Õ
±
Â
Ê
Î
¾
Ð
Â
·
¾
¼
°
¦
Á
Ï
Ú
À
Ï
Ê
¸
í
Î
Ô
Ù
¹
Ú
Ú
Á
º
¦
Á
Ó
Ù
¿
É
¯
¥
¾
¾
©
½
Í
¸
ª
¼
¦
¸
®
»
¹
e
l
§
¬
¸
¥
i
¹
¸
e
¦
¸
¸
d
¬
º
¶
È
¸
¨
¥
¡
¶
n
j
£
ª
x
w
Â
à
Õ
ß
Ú
ì
Å
Í
ç
¸
Ã
¾
¼
»
¼
¸
Å
Ö
Æ
¸
×
º
¸
è
c
ò
ó
ò
ô
õ
)
*
4
@
I
;
J
M
:
;
>
I
8
;
:
;
:
J
@
?
K
J
;
K
I
>
5
J
>
I
N
6
@
J
>
C
>
6
M
<
A
K
I
@
@
?
J
I
6
8
O
K
A
5
I
>
;
;
N
>
;
A
N
6
;
I
B
6
6
A
ø
ý
õ
ù
J
:
:
M
>
6
5
C
ù
J
@
I
I
:
5
@
C
J
5
N
ù
!
"
ù
û
ÿ
û
#
ÿ
û
ÿ
"
ù
ø
ÿ
ö
$
õ
û
The New Kuip: Enfolding 24/7
%
û
@
I
I
C
6
6
J
K
;
;
5
I
N
B
M
>
I
6
E
A
F
6
:
>
B
5
I
D
5
@
I
K
<
5
6
6
:
J
L
N
?
K
;
;
@
A
A
A
X
M
U
I
N
@
J
8
6
5
@
;
M
;
6
A
>
C
J
6
6
M
K
C
>
8
>
R
:
=
>
@
?
T
K
I
B
K
\
A
@
I
N
4
@
?
:
6
A
M
5
M
6
]
6
;
M
K
N
>
;
^
@
A
C
A
A
^
;
K
A
O
>
?
W
K
K
J
M
J
;
@
@
:
M
6
J
I
M
K
I
J
@
B
C
<
;
;
;
@
K
>
P
6
?
?
6
>
M
K
J
>
K
>
6
>
;
O
;
A
B
;
I
>
?
I
B
N
6
>
;
5
@
M
C
N
K
J
6
;
J
Z
J
<
C
A
K
A
;
6
K
I
>
B
6
@
B
6
M
?
B
;
6
V
X
>
?
;
C
?
@
4
C
5
;
X
J
@
6
>
6
I
I
J
K
M
;
?
4
6
A
M
L
C
6
<
K
L
@
K
>
K
>
>
K
>
Q
M
K
C
B
R
;
6
_
O
A
6
J
@
;
L
K
N
M
;
S
S
>
5
>
I
K
R
B
V
J
I
;
6
J
>
B
H
T
J
6
@
>
K
K
6
?
;
A
[
>
>
;
5
6
K
G
<
M
;
N
J
F
5
6
;
>
E
N
8
@
I
I
C
:
6
6
>
6
M
A
;
N
@
I
O
>
I
6
I
@
K
V
K
5
N
G
L
I
@
5
@
;
6
:
`
A
>
B
;
?
I
6
@
>
B
I
T
5
I
K
?
I
A
@
A
J
5
?
6
K
:
6
L
J
M
J
K
;
6
I
;
5
K
8
;
a
I
C
6
6
K
>
>
b
T
L
<
I
6
M
I
J
K
A
A
6
6
R
J
@
B
;
5
N
6
>
I
>
>
;
M
C
f
@
;
@
M
<
J
B
8
A
R
<
I
;
:
L
5
R
K
6
?
8
M
I
K
5
6
M
@
A
I
B
;
T
;
I
5
M
@
I
6
>
J
M
;
>
;
?
K
M
d
R
@
I
>
L
I
K
6
N
K
K
K
I
K
>
L
B
?
8
V
B
@
@
;
K
@
M
A
^
?
?
K
K
;
6
@
8
6
A
:
8
M
6
J
A
O
6
>
P
C
6
A
6
>
I
@
L
J
;
K
?
8
6
B
5
@
T
<
>
M
6
P
6
J
>
O
@
N
J
B
B
>
>
;
@
C
U
K
:
K
6
;
M
M
6
5
J
J
A
5
J
>
B
P
;
;
6
B
`
<
M
K
C
P
>
M
;
L
ü
û
D
6
Y
?
;
K
K
B
@
@
V
;
õ
ö
C
6
>
A
I
N
M
6
ø
ö
I
5
L
@
5
I
M
6
6
K
;
B
>
I
;
L
6
C
<
M
@
>
;
O
A
C
@
T
A
N
>
6
K
@
<
K
N
M
@
;
K
>
J
5
8
;
N
6
M
B
6
P
6
M
6
I
@
J
M
K
6
B
V
B
`
O
N
;
K
>
T
5
I
L
6
P
B
6
>
6
K
6
6
K
M
M
;
>
;
?
C
T
>
;
M
L
:
I
>
K
C
@
M
I
?
J
A
;
<
:
^
5
6
I
I
6
N
U
@
O
M
>
<
@
:
@
J
M
6
6
:
M
K
@
C
6
B
?
J
K
I
B
5
O
I
K
J
6
6
;
A
;
B
M
M
I
;
L
M
I
T
:
6
K
K
B
B
>
;
:
B
L
;
>
K
V
M
>
O
I
^
>
M
5
J
B
M
@
I
T
;
6
T
;
8
K
5
>
K
õ
B
J
A
J
B
K
ü
ö
<
K
I
I
A
6
:
T
A
6
N
?
;
6
õ
@
:
6
I
?
N
^
?
@
B
N
@
ò
O
J
:
K
P
>
L
6
J
>
<
6
:
:
;
C
6
6
A
K
O
;
M
K
6
K
A
÷
,
C
I
K
A
?
6
>
T
J
;
J
6
@
K
ÿ
/
=
6
]
N
6
>
5
?
6
6
(
>
M
5
J
K
I
O
5
L
I
6
6
I
6
>
6
5
K
P
M
c
4
I
J
Z
M
þ
3
<
5
ø
û
L
I
K
;
E
@
B
5
6
M
B
ö
-
:
>
ý
ÿ
2
T
;
ü
ø
9
5
6
6
I
>
J
5
I
:
;
J
A
1
8
I
û
0
O
;
@
ú
/
B
K
I
ù
6
8
5
ø
.
6
B
O
-
L
]
÷
7
Y
`
,
6
6
ö
+
5
?
õ
û
B
I
6
K
I
:
>
B
>
;
I
K
5
L
I
>
L
J
K
?
B
6
;
:
U
B
>
M
N
:
;
M
6
@
K
B
I
?
A
6
:
R
>
<
M
I
M
6
I
:
K
A
?
>
6
<
@
6
J
@
6
5
:
<
6
K
5
>
6
L
<
O
J
6
J
@
<
B
6
N
J
@
J
C
K
;
6
J
>
J
K
K
B
>
I
I
6
T
;
<
C
M
L
I
6
J
T
M
I
>
<
6
K
6
J
M
;
J
@
@
<
?
@
>
C
T
@
6
8
8
M
P
;
;
6
6
I
I
B
>
I
5
I
5
I
I
M
5
@
I
5
N
6
;
@
6
K
>
N
I
@
K
J
B
6
^
>
I
e
K
K
6
6
N
M
<
d
6
6
A
I
>
I
K
N
R
I
5
6
6
:
;
>
M
I
6
5
6
V
?
6
J
6
>
I
B
;
M
N
;
<
A
;
>
6
M
K
>
B
5
@
8
I
5
6
M
6
K
J
6
;
>
I
6
C
J
K
I
6
B
;
>
I
5
6
B
6
P
6
A
@
<
S
V
ü
ø
õ
ü
ø
ý
û
ö
ô
õ
ù
&
û
ö
ö
õ
'
%
ý
û
%
ÿ
{
The New Kuip: Enfolding 24/7
®
³
¯
´
±
µ
¶
³
±
½
³
»
µ
®
´
³
Â
µ
³
½
½
µ
¹
»
¾
¹
¹
¹
°
¹
»
·
½
±
·
³
Å
µ
µ
À
®
±
À
³
´
°
µ
¯
³
¹
µ
³
°
¹
¯
À
±
°
±
°
°
°
±
²
±
³
½
³
¼
³
¯
³
´
º
´
º
µ
¯
¶
v
~
i
l
p
s
j
m
³
¼
z
o
q
t
µ
¾
½
¯
¼
l
»
³
°
·
m
p
z
u
}
u
l
h
{
È
i
n
j
q
µ
¾
»
³
®
´
k
n
l
s
l
½
º
m
q
n
q
j
m
p
o
i
v
»
³
¾
½
´
¯
·
°
¼
¯
°
²
¯
·
n
À
º
º
·
½
¯
³
½
°
³
¿
»
¹
º
¾
¯
¿
½
·
¹
±
µ
®
¯
°
µ
³
¹
»
À
¿
·
¶
µ
³
»
µ
¿
Á
±
µ
Ê
³
½
µ
µ
»
´
µ
À
¯
®
±
´
³
µ
¼
½
¾
¼
µ
»
µ
³
°
´
½
¹
´
À
À
Ä
·
³
±
µ
³
¹
¼
½
´
¾
µ
»
m
·
Ã
¹
¾
·
}
³
¹
µ
½
·
´
¾
³
Â
»
q
g
µ
¿
·
»
³
¹
·
¯
µ
µ
°
µ
¯
n
v
h
v
g
v
p
z
p
i
s
s
k
p
z
u
z
s
v
k
l
m
z
q
n
p
i
s
k
p
y
¥
´
¾
¼
¶
´
¾
·
¹
µ
¹
²
·
®
p
§
¯
º
º
Ä
½
r
n
¬
µ
²
¼
³
´
±
·
¾
¯
³
¹
±
®
À
µ
µ
«
¼
²
·
Â
ª
·
±
°
·
£
µ
À
°
À
½
»
²
Á
º
©
µ
¯
»
µ
Á
·
¯
µ
»
´
µ
°
Á
½
¥
¯
±
±
¯
¨
µ
µ
¼
¾
´
·
µ
·
½
³
¾
Á
¹
§
µ
¼
·
º
´
·
µ
®
´
²
³
´
Ê
¦
¹
±
°
³
½
³
¸
·
¾
·
Á
¤
¯
»
½
¹
¸
Å
½
º
»
¡
·
³
½
½
°
¥
¶
¾
À
³
¤
µ
¾
µ
µ
£
´
µ
´
±
Í
·
´
À
¹
Ç
³
¯
´
¾
¢
²
º
°
°
°
¡
|
{
µ
´
µ
°
Ë
µ
±
³
½
¯
¼
¯
·
¼
³
»
³
°
½
·
»
µ
º
º
¯
¯
¼
¶
º
¯
·
°
¾
µ
°
½
µ
³
·
³
®
¿
À
´
±
É
²
µ
®
½
¯
¯
±
Â
·
µ
·
°
²
µ
»
¯
·
À
´
½
µ
»
±
·
±
º
·
´
½
¾
»
¼
º
½
½
¹
·
½
·
¾
®
½
¿
³
±
³
»
±
±
®
¾
µ
·
°
À
Á
¹
¹
µ
µ
µ
±
¼
Á
µ
µ
¿
¾
µ
±
·
¯
´
¯
µ
µ
·
¯
½
³
¯
¾
¿
»
±
¹
½
»
Ä
¹
¹
´
³
Ä
À
Å
³
°
µ
µ
»
´
³
¾
³
µ
½
°
·
µ
³
»
¼
À
®
°
³
µ
¯
±
»
¾
²
´
Á
½
½
µ
µ
·
±
±
º
»
·
À
¯
º
¾
¹
·
Â
¿
µ
µ
µ
º
³
¾
Å
³
±
³
»
Æ
³
·
°
±
²
Ç
·
¼
Ä
´
¼
°
³
´
¹
µ
Æ
Ì
¾
³
½
±
À
°
³
Ï
¹
¯
µ
»
½
³
°
·
±
¶
°
³
´
³
´
µ
¾
·
±
³
µ
Ð
³
Æ
Î
µ
Á
µ
»
·
º
¿
µ
±
³
·
¼
À
µ
¹
°
²
±
¾
·
±
¾
µ
º
³
¹
°
±
³
·
½
¾
·
±
¾
¯
µ
³
µ
½
¯
¾
´
°
³
µ
¾
³
®
¯
½
»
º
¯
·
Â
µ
¾
³
Í
·
Í
±
³
°
±
·
®
¹
½
¹
¹
µ
¹
¹
¿
µ
±
½
À
³
Ò
µ
Á
½
»
®
½
³
°
·
±
½
±
À
¯
µ
Á
°
µ
¶
·
¼
³
´
µ
À
µ
¹
°
²
±
¾
·
±
¹
°
À
µ
¯
°
±
²
³
´
µ
½
¯
¾
´
°
³
µ
¾
³
®
¯
½
»
º
µ
¯
¼
·
¯
¿
½
±
¾
µ
¹
Ó
Á
°
¹
®
½
»
Ò
Ñ
½
µ
¹
³
±
Í
³
´
µ
µ
³
²
¯
°
¾
Ä
½
³
°
¼
®
·
±
±
¾
³
·
°
¼
·
°
±
±
½
³
»
µ
¯
Ä
À
°
¹
½
¾
º
°
º
³
»
°
½
Ê
±
»
½
¯
µ
Ä
Å
¹
½
®
¹
¹
º
³
µ
½
°
¾
³
±
½
¹
Ê
°
»
±
³
µ
Ä
·
µ
³
³
´
¾
Ô
µ
Ã
¶
´
·
»
µ
À
µ
¹
°
²
±
¼
¯
·
¿
³
´
µ
Á
µ
¯
Å
µ
½
¯
»
Å
¾
·
±
¾
µ
º
³
®
½
»
º
´
½
¹
µ
½
±
À
À
®
¯
°
±
²
³
´
µ
Õ
µ
±
³
Ç
µ
µ
×
à
µ
±
À
¦
µ
´
°
¯
Ö
´
³
°
¾
»
»
³
·
®
±
´
³
´
¯
¡
®
·
¹
º
Ú
á
³
µ
²
Ù
¶
®
À
°
Ø
µ
¹
¹
°
·
á
³
®
°
¹
¹
Ú
¶
å
µ
Ú
º
¼
¾
Û
°
µ
·
³
»
Ü
»
Ý
Ê
µ
¯
º
Æ
µ
À
ç
Þ
³
½
µ
ß
Ú
´
¿
Å
Û
µ
º
Æ
µ
°
æ
±
·
°
·
³
¯
Á
·
³
´
½
»
½
À
â
º
²
³
¯
®
½
À
°
°
®
·
Â
À
°
µ
¾
±
³
¼
²
¿
Ä
³
³
·
´
´
¯
µ
µ
³
´
¿
µ
µ
â
µ
Ð
·
°
¹
³
³
¼
°
¹
±
²
½
À
º
°
®
·
¹
¿
¯
º
³
·
ã
¹
¯
½
½
³
±
¹
¾
¯
¸
À
»
¿
»
®
¹
µ
½
°
³
µ
¹
¹
®
¯
³
¯
Ä
³
µ
µ
´
¯
Ä
µ
º
³
»
´
Ë
½
±
µ
·
¯
±
µ
³
µ
·
³
±
½
·
»
Á
·
½
¸
½
±
µ
³
²
°
º
·
³
±
´
»
½
¾
º
µ
»
â
µ
½
½
±
³
»
¾
Æ
·
±
·
»
²
Á
½
¯
µ
³
¯
µ
´
µ
¹
ä
½
è
·
»
¹
½
½
º
¯
°
³
¹
²
½
¹
¯
µ
°
½
»
½
¯
±
Á
µ
¯
µ
³
À
²
°
´
±
½
·
µ
³
¹
Ñ
½
»
´
µ
¶
½
Å
®
±
³
°
»
³
´
µ
¶
µ
¹
³
µ
¯
±
³
°
º
·
¼
³
´
µ
é
¯
°
µ
±
µ
±
·
·
¯
À
¹
»
½
±
À
Æ
Õ
h
h
i
j
k
l
m
n
j
m
o
i
p
q
r
n
s
l
t
u
v
w
p
q
q
n
x
y
o
p
i
y
z
j
j
n
s
s
l
ê
l
q
l
m
m
z
m
k
n
s
l
m
n
g
ì
Ã
ì
î
ï
õ
ï
ð
ò
ñ
õ
ò
ý
ó
ô
û
÷
ý
õ
ö
ò
ð
ý
õ
÷
ù
û
ò
õ
ø
ù
ý
ñ
ò
ú
ý
ì
ï
û
û
ï
ï
V
ö
ð
ü
ï
ý
ý
ò
ý
ò
ð
ù
ï
ð
ö
ò
õ
÷
û
ó
õ
ï
û
ó
ï
#
4
$
2
5
$
+
=
0
$
'
&
$
6
'
)
-
'
*
8
$
1
4
)
*
-
4
3
(
$
2
4
@
&
3
3
,
2
%
3
'
#
*
)
'
$
5
$
B
2
0
)
&
-
-
$
3
-
$
5
&
3
*
%
4
D
-
ÿ
-
ó
=
&
7
3
3
'
&
1
4
ó
'
-
$
&
4
&
-
ù
õ
-
õ
û
ü
õ
ù
ù
ÿ
ó
ÿ
ü
ý
ÿ
ò
ù
ð
ï
õ
û
ü
õ
The New Kuip: Enfolding 24/7
-
$
'
3
;
+
)
'
M
)
$
3
L
&
,
$
3
2
2
/
)
K
)
)
%
?
J
,
%
$
-
-
+
7
)
/
I
$
4
:
3
0
$
6
%
$
4
&
%
H
'
$
)
#
/
3
$
.
$
0
-
'
)
+
0
&
)
,
%
4
ÿ
õ
)
*
0
-
2
.
$
3
,
3
*
'
)
)
)
+
2
4
9
&
-
4
&
'
"
4
,
%
1
4
4
)
+
-
4
%
&
2
>
0
&
1
)
)
&
&
+
5
&
5
"
2
,
3
$
'
,
3
4
4
+
3
)
'
&
#
þ
G
"
ú
-
5
-
;
%
#
&
1
-
0
(
)
*
3
<
&
1
'
)
4
4
)
&
&
$
*
3
4
0
-
*
6
7
5
'
-
$
3
%
-
3
%
)
-
/
2
3
6
*
3
5
4
:
$
-
&
%
0
5
4
3
7
,
4
+
&
%
9
'
&
4
)
&
4
3
2
4
0
4
1
0
%
%
,
'
4
)
4
4
4
#
$
%
3
4
1
1
&
4
4
=
%
$
&
4
)
7
,
$
*
#
3
4
*
'
%
3
/
$
&
4
3
$
'
&
-
5
%
'
2
2
4
4
&
$
'
8
9
3
+
3
1
&
7
0
4
2
'
&
0
&
4
-
%
$
4
4
&
3
'
3
-
0
4
6
3
'
4
4
&
)
#
7
$
4
2
%
4
0
&
-
3
$
3
&
5
&
:
1
0
4
7
-
5
4
=
$
,
9
)
-
%
5
5
4
&
-
0
$
%
4
+
'
4
3
&
;
,
A
E
+
-
#
$
3
&
0
4
%
-
=
4
%
6
)
3
/
C
(
$
3
4
=
'
&
%
+
2
&
-
$
3
$
5
)
#
+
6
1
-
2
&
%
)
3
'
#
$
%
&
3
$
,
4
B
B
4
1
$
#
*
4
3
&
$
5
"
#
$
%
&
'
(
)
*
#
+
'
"
&
)
,
-
+
*
.
)
%
/
F
ì
ë
ü
ï
N
ï
O
P
÷
ý
ù
ò
ü
ï
Q
õ
õ
þ
õ
ý
ð
O
õ
ø
ö
ù
ï
ö
ò
ý
ù
ù
û
ò
õ
÷
þ
ù
ò
ò
ï
û
ú
õ
û
ö
R
ü
ý
ò
ï
ö
ò
÷
û
õ
ð
î
S
ï
ý
L
T
ó
M
õ
ð
ð
ï
U
!
÷
õ
û
ù
k
The New Kuip: Enfolding 24/7
³
¥
§
§
§
¥
§
¡
¥
¡
¡
¥
¬
¶
s
¦
t
¢
f
t
f
£
u
¤
¬
§
¥
¦
¡
°
¸
¬
¦
¥
¥
½
¦
¹
§
¡
§
¥
º
§
¦
»
»
¢
¡
¼
¥
¡
¬
¥
§
¥
¬
¸
¥
¡
²
§
¡
¢
¡
·
¥
¢
¢
¤
¸
¾
j
w
`
¥
¦
Y
w
c
c
[
e
¡
Y
Z
[
\
]
^
Z
]
_
Y
`
a
b
^
c
\
d
e
f
g
`
a
a
^
h
i
_
`
Y
i
j
x
j
y
c
r
q
f
§
¸
¸
¡
§
z
¥
q
[
\
{
]
r
j
a
¸
Y
¿
¸
q
¦
¯
z
^
z
®
m
¥
À
½
¡
j
a
¦
`
\
^
§
j
¬
|
`
Y
¯
b
²
Y
}
c
`
~
[
¯
¬
¬
¥
i
§
¥
_
§
°
¬
°
e
]
¥
°
¬
°
^
\
¸
c
§
¹
i
`
x
¥
\
Á
¥
¬
^
¢
p
X
j
`
¢
w
X
v
`
¢
r
q
¥
q
p
X
¥
f
^
Y
²
_
]
f
Z
`
¦
^
a
§
]
a
¥
\
¦
\
c
[
^
¡
Z
a
Y
^
¡
X
k
£
m
\
j
e
¢
o
e
¥
¥
¬
]
`
\
©
a
d
§
_
j
©
Z
]
`
c
¨
\
n
Y
f
¡
]
m
¥
a
s
§
µ
^
¬
`
b
^
§
¬
µ
¥
§
¡
§
¦
«
ª
©
¨
´
¥
±
§
¹
l
k
\
¿
^
Y
c
\
i
^
x
Y
j
^
e
`
i
^
W
Ã
Ä
Ã
Å
Æ
Ì
Æ
Ç
å
È
Ø
É
Ê
æ
Ë
ç
Ò
Ô
Ì
Ý
Í
É
Î
Ð
Ç
è
Ô
É
Ï
Ì
Ð
é
È
é
Ô
Ñ
Ã
Ò
Æ
Í
Ç
Ó
Æ
Ô
Ý
Ô
É
Ç
Æ
Ç
Í
Ì
É
Î
Ò
Ê
Æ
ê
Ê
ë
ì
Ñ
ì
Õ
í
Ö
î
ï
Ö
ð
×
ë
Ø
ñ
Ê
ï
Ù
ò
Ù
Ê
Ú
ó
Û
Ì
Ü
Ð
Ü
Ì
Ò
Ü
Ý
Ý
Ó
ô
Ð
Ì
Þ
é
Ð
ß
Ý
×
Ö
Ê
à
ó
Ö
Ó
Ô
á
É
×
Ð
Ç
Ö
à
Æ
à
õ
â
Ì
Ò
Ý
ã
ä
Ó
Ì
The New Kuip: Enfolding 24/7
ö
÷
ù
ú
û
ú
û
ü
ý
þ
ÿ
ÿ
"
"
*
#
$
%
#
$
!
&
)
$
'
"
Æ
Í
É
Ô
Ð
é
Ô
.
É
Ó
É
Ó
Æ
è
Ò
Æ
Æ
é
é
Æ
É
Ð
.
Ò
Ü
(
#
$
!
+
-
)
!
+
/
Â
é
$
é
ÿ
!
,
ÿ
Ð
Ð
é
Æ
å
Ì
Þ
Þ
Ô
é
è
Ì
é
ö
Í
Ñ
Ò
Ð
Í
é
Ó
é
Ô
É
Æ
Æ
Í
Í
É
É
Î
Ô
Ð
é
Ò
Ì
Ý
Ç
Å
Æ
Ý
Ô
è
é
Ê
÷
Ì
Ç
Ç
Æ
ø
ö
Î
Ì
Ò
ö
Ð
D
The New Kuip: Enfolding 24/7
g
h
v
g
i
w
~
x
}
}
£
¤
2
£
3
x
¤
4
5
6
3
w
§
6
8
x
¨
2
©
9
z
ª
:
~
«
;
}
~
x
5
>
w
x
y
}
|
~
}
y
w
}
w
}
x
}
}
w
9
7
:
X
}
F
L
~
6
?
Y
G
Z
2
9
5
<
~
3
6
8
C
}
~
x
{
:
=
w
~
}
|
¡
y
w
x
~
y
x
{
x
}
x
w
w
|
{
y
}
w
w
}
}
w
x
}
w
}
y
¢
z
w
~
y
;
7
5
6
H
9
C
>
F
>
1
5
D
2
7
3
:
4
7
5
<
5
6
:
7
:
3
6
9
8
2
?
7
[
?
\
]
]
1
I
^
J
_
`
J
a
K
\
L
b
?
`
M
c
M
?
N
d
O
9
P
C
P
9
2
P
<
<
e
4
9
C
>
Q
C
R
<
K
?
J
S
d
J
4
5
T
6
C
K
:
J
S
7
S
f
U
9
2
V
<
W
4
9
B
q
|
u
l
}
y
~
w
y
q
}
z
o
~
x
~
t
z
x
{
}
~
~
s
y
~
l
z
r
}
x
{
w
=
x
§
w
©
<
q
|
y
}
o
y
¬
7
y
w
y
n
y
}
~
z
p
}
x
o
{
w
w
n
x
{
¦
7
m
}
¥
~
x
m
y
y
}
w
}
|
~
|
w
w
}
y
}
~
l
{
|
y
|
k
z
}
y
1
~
y
x
y
y
j
E
D
w
{
}
w
}
~
x
}
~
x
|
{
~
x
x
x
w
y
}
}
y
x
~
y
}
{
~
y
x
|
x
~
y
}
~
w
}
~
y
y
}
}
}
x
x
}
~
~
y
z
z
w
x
~
w
y
y
}
z
~
w
y
y
}
x
w
y
}
{
y
|
}
w
y
y
x
~
w
x
}
}
}
y
y
z
|
w
~
w
}
{
x
y
}
|
x
w
x
~
z
w
|
y
y
}
|
|
w
y
x
~
}
w
~
x
w
}
{
}
}
}
{
y
x
y
~
|
}
|
}
x
x
z
~
x
y
{
}
}
}
~
w
y
x
w
~
}
|
{
x
x
x
®
?
@
9
:
:
7
A
B
8
9
2
B
C
d
C
8
6
4
O
d
C
8
6
4
A
7
9
<
<
6
6
9
9
7
7
2
2
5
5
9
9
:
:
¯
¯
5
5
7
0
7
°
°
³
´
³
µ
¶
¼
ç
è
ö
±
²
ø
è
ù
ú
ý
¸
¹
ú
º
Ô
»
Õ
ç
Â
é
ú
ÿ
·
Ç
ç
÷
ú
¶
Ó
ê
û
ü
ú
Ä
ý
÷
÷
Ö
ì
¹
¼
÷
À
×
ø
ø
ü
Á
³
ð
ý
ü
¸
Ä
ï
ü
ý
¿
×
î
ý
·
Ä
í
ÿ
ü
¾
À
þ
û
½
¹
ë
ü
ø
¼
Ì
ñ
ü
·
ò
ü
ý
½
Ã
¶
Ä
Ì
Ä
í
ø
Â
¶
ù
ü
½
¼
ú
ô
ÿ
¶
ü
º
Ù
õ
Ú
ý
²
Ü
ø
Å
Û
Ý
²
Þ
Æ
Ù
Ç
ß
º
Ý
È
à
È
º
É
á
Ê
¼
Ë
À
Ë
¼
Â
Ì
Ë
Ì
Ã
â
¼
À
×
Í
À
Î
Ì
Æ
º
²
á
±
Ã
²
Ä
¹
Ï
À
Æ
·
²
±
¶
±
ã
¼
Ð
Â
Ñ
Ì
Ã
Ò
¼
The New Kuip: Enfolding 24/7
ä
ð
ý
Á
Ú
í
ü
ý
ú
Â
ñ
ø
ü
¾
Ø
ó
ý
ù
¹
º
ï
ú
ø
¶
·
ð
¹
·
ÿ
ÿ
ù
ü
ü
ü
÷
û
ü
ú
ü
ý
ú
ÿ
÷
ÿ
ú
ø
ø
ü
ù
ü
ø
ý
ü
ý
ø
ü
ÿ
÷
û
ü
ý
ú
þ
÷
ý
ü
ÿ
ü
ø
ÿ
ü
ÿ
ù
ü
ú
ø
ú
ÿ
÷
ý
ÿ
÷
ø
ø
ø
ù
ý
ü
ÿ
÷
ø
ü
ý
ü
ù
ü
ø
ú
ÿ
ÿ
÷
ø
ú
÷
ü
Á
Â
½
Ã
Ä
¹
¶
½
¹
¾
Â
¼
·
µ
¶
Ì
Ä
Ö
×
º
å
¼
·
·
¶
æ
ä
¾
¼
Â
ä
À
(
The New Kuip: Enfolding 24/7
J
K
L
W
M
X
b
f
Y
X
n
l
^
o
f
a
^
[
h
X
d
^
Y
h
[
_
d
f
i
b
^
d
Y
h
[
g
Â&#x20AC;
d
Y
`
^
}
_
^
\
Y
[
X
^
d
f
^
X
]
e
^
h
[
Z
d
X
j
c
f
f
d
Y
`
c
d
_
\
d
Y
d
Y
^
X
^
_
`
b
;
_
*
0
#
<
+
=
f
Z
]
[
l
~
Y
f
f
'
!
`
j
Y
f
h
,
_
f
d
"
]
d
Y
b
e
_
h
d
Y
_
'
"
*
(
#
>
?
#
@
@
-
A
B
.
C
.
D
/
?
0
E
#
C
#
\
f
X
`
`
b
^
Â&#x192;
a
X
`
h
d
d
a
j
l
^
~
`
^
f
]
h
`
d
d
[
d
e
f
d
Y
f
Y
d
Y
_
d
f
Y
Â&#x2026;
Y
Z
i
d
Y
]
h
w
e
X
d
f
e
h
f
d
f
]
X
X
X
^
`
[
d
Y
j
[
^
d
X
3
4
'
4
4
H
'
"
5
6
'
/
#
.
G
.
7
'
/
.
I
8
9
:
&
Y
f
Y
j
\
h
l
X
X
h
f
`
^
d
_
[
g
[
]
d
^
l
b
f
_
[
X
k
X
d
d
e
d
e
f
]
^
d
X
\
l
Y
\
Z
d
e
Y
b
]
f
a
Y
_
_
^
]
d
f
Y
Y
Y
k
X
{
]
X
f
f
c
_
\
e
Y
d
[
_
d
d
{
f
l
f
h
p
^
j
o
j
c
^
^
`
f
f
c
d
X
[
d
_
[
]
X
f
]
^
`
X
^
e
^
[
^
\
_
^
b
j
Â
p
{
`
Z
h
_
`
f
j
a
d
[
X
f
j
\
h
f
f
Y
c
l
^
h
d
[
_
d
e
f
^
X
f
^
!
"
#
$
%
&
&
'
&
"
!
#
&
!
;
|
G
2
^
]
j
`
Y
^
j
\
e
~
f
f
]
f
f
e
d
b
X
f
X
d
[
\
e
^
f
`
j
h
d
j
[
_
]
_
]
^
_
h
]
\
Â&#x2020;
[
\
c
^
d
|
Y
[
_
f
]
]
X
[
d
~
i
Y
^
a
f
h
]
_
Y
e
d
f
f
`
Y
d
_
Â&#x160;
Y
X
b
[
`
]
f
j
Â&#x2030;
^
_
[
_
l
b
[
d
f
s
c
^
h
f
e
^
_
Y
Y
]
Â&#x2C6;
X
d
]
Â&#x2021;
d
j
c
j
`
]
f
_
Y
f
Y
e
\
Y
f
d
X
f
^
\
^
a
_
d
g
[
[
X
f
_
e
j
f
e
^
d
_
h
e
f
f
Y
p
d
c
Â&#x201E;
]
f
b
g
e
Y
|
[
[
d
]
j
^
b
d
Y
f
^
a
]
{
_
f
f
[
1
G
k
-
d
1
F
c
`
[
f
[
\
b
]
Z
c
Y
g
^
[
c
Y
\
]
^
Y
j
l
^
j
Z
[
f
j
^
f
]
f
_
f
d
e
f
d
e
X
^
e
m
d
^
X
d
c
^
d
d
f
b
{
f
\
`
_
j
e
[
_
X
g
f
X
f
_
d
Z
f
[
^
X
_
X
Y
d
[
Y
f
d
i
b
d
e
f
_
b
h
Y
d
Y
f
Z
_
_
Y
{
_
[
{
j
e
Y
`
X
c
j
f
l
f
]
\
f
X
j
[
Y
h
d
X
|
h
f
Y
j
j
i
^
Y
_
_
e
\
^
f
d
Y
d
j
d
j
]
}
^
]
^
_
|
X
^
j
Y
_
g
^
_
{
f
Z
X
c
^
Z
f
f
\
z
Y
e
f
f
y
_
]
d
X
w
Y
f
e
e
x
j
b
f
f
`
d
[
`
g
d
w
Y
c
h
_
j
Y
d
v
\
a
j
c
Y
f
[
a
]
e
e
Z
`
g
d
_
Y
d
[
]
_
e
[
u
g
X
[
X
a
r
d
b
`
^
f
f
Z
`
Q
b
t
e
V
]
l
X
[
Y
Y
s
[
`
l
_
^
c
Y
[
d
e
g
a
]
d
d
b
e
d
c
]
X
^
d
Y
f
\
f
_
e
]
^
g
o
^
Â&#x201A;
d
Y
Y
^
j
Y
a
U
|
j
_
h
]
T
r
f
d
f
]
_
]
Y
_
`
j
d
]
_
l
]
f
c
X
[
Y
`
q
\
[
_
X
R
^
j
[
h
S
_
[
f
X
l
_
d
]
_
]
[
f
Y
R
^
h
[
^
l
Q
]
^
l
f
^
P
\
b
p
h
g
[
d
o
X
O
X
_
X
]
b
Z
f
^
N
)
(
4
*
'
;
"
'
"
5
Á
Â
Õ
Ã
Â
Ë
Ô
É
Ô
Ä
Û
Å
Ó
Ä
Ã
Ó
Ï
Ù
Ó
Ä
Ë
Ï
Ä
Ç
Ï
Ë
Ë
Ë
Ð
É
Í
Ã
Â
Ã
É
É
Ì
È
É
Ö
Ï
Ù
É
Ø
Ö
Å
Ç
Í
È
É
É
Ã
Ä
È
Í
Ö
Ã
Ì
Ç
É
Í
Ä
Ç
Ì
Ç
Ó
Ù
Ä
É
¦
Ï
Ï
Ó
É
Ë
Ä
±
Ç
Ö
Ô
Ô
Ô
Ï
É
É
¥
¼
É
Ó
Ë
È
¦
Æ
Å
Ë
Ç
Ó
Ê
É
¥
Ã
Ç
Ã
Å
¥
Â
Ó
Ô
¤
Í
È
Ô
£
»
Å
Ë
Ã
¢
É
É
É
¢
º
Å
Õ
É
·
É
Í
Í
Ô
¹
Ã
Ç
Ç
¡
³
É
Ì
Ë
¸
Ñ
Ã
Ç
·
É
Ä
É
¶
Ñ
É
µ
Ô
Î
É
´
Å
Ë
Ü
É
Æ
à
Ã
Ó
Ä
Ô
Â
Ç
Ã
Ó
Ç
Ï
Ì
Å
Ä
Ó
Å
Ç
Ä
Ä
Ô
Ç
É
Ü
Ä
Ç
Å
Ç
É
Ã
É
È
Ä
Ë
Â
Ç
É
§
¨
¦
»
©
½
ª
«
¦
¬
The New Kuip: Enfolding 24/7
¾
Í
É
Ç
Å
Ô
Æ
Å
É
Ë
Ó
å
É
Ë
Ä
Æ
Å
É
Ë
Ä
Æ
Å
Ô
É
Ó
É
Ù
Ã
Ù
Ô
Ã
É
Í
Ð
Ô
Ä
Ç
È
Ä
Í
Ã
È
Í
Í
Ç
É
Â
Æ
È
É
É
Ë
Í
Å
Ç
Ç
Â
Æ
Ä
Ó
É
È
É
Å
Ã
Ã
Ì
È
Ô
Â
Í
Ó
Ð
Ç
Â
Î
Ì
Í
Å
Á
Ã
Ë
Ð
Å
Æ
Ú
Í
Ü
Ä
É
Ì
É
Í
ä
È
Ù
È
Ä
ä
Î
Ó
Ä
Ä
ã
Ä
Í
Í
Ô
Å
Â
â
Ì
Ã
Ç
Ó
á
Å
Î
Ô
Ç
Æ
ß
Î
É
Ë
Ê
Þ
Î
Ó
Ð
Å
Ý
Ö
É
Í
Í
´
Ë
Æ
Ñ
É
Ó
Ç
Ì
Ç
Ï
Å
Ã
É
Ï
Õ
Ð
Ò
Ä
Ó
Ç
³
É
Ë
Ì
Ò
Ó
Ó
Ï
Ç
È
Å
Ù
É
Ä
Ó
Ä
²
É
Ó
Ú
Õ
Ë
Ó
É
Ê
È
Ñ
Ù
Ó
É
Ç
Ä
Â
Ô
Ç
Ä
Ð
Ì
Ë
Ô
Ë
É
É
Ë
É
Â
Ã
Ó
¦
Í
Í
É
Ç
Í
Ø
Õ
Ä
Ø
É
Î
Ù
Â
Ó
Ô
Ô
Ä
Ã
Ë
É
Ù
Ë
É
Ä
Ë
Ë
É
Ó
Ø
Ã
É
Î
Õ
È
Ñ
Ç
É
Í
Ç
Ô
È
Ï
Ã
É
Î
Ó
È
Â
Ø
Ö
Í
Ç
Í
±
É
Å
Ç
Ç
±
Ì
Ã
É
Ç
Í
Ã
Å
Ä
Ë
Ù
Ò
Í
Ñ
É
Í
Ä
Ó
É
Ì
Î
Ä
Ï
Í
Ë
Í
É
°
Ã
É
Ð
Î
É
È
Ê
Å
Ë
Å
Í
Í
Å
Ô
¦
×
Ã
Í
É
É
Ç
Ä
Ô
Ï
È
Æ
Ç
Ö
É
Ì
¯
Ç
Ó
É
Ã
®
Ï
Í
Ê
Ã
Æ
Ô
Ç
Î
Å
Ó
Å
Ï
Ä
Í
É
Ä
¡
Ã
Å
Ç
Å
É
Î
Ä
Ø
Ì
Ó
È
Ì
É
Å
É
å
Ó
å
Ú
£
æ
ç
ú
è
é
Å
Ç
Ó
È
Ð
É
Ë
Ç
É
Ã
Â
È
Ó
Ô
Ã
Ô
Ã
È
É
Å
Ì
Å
î
Ã
Ç
Û
È
Ì
Ã
Õ
É
Ó
Ï
Ã
É
ò
Î
Ä
Æ
Ï
Í
Ð
Ì
É
ê
È
Ä
É
÷
Å
Ä
Ì
ò
Ç
Í
ñ
Ä
Ó
ï
ì
Ï
Ù
Ä
Ë
Å
î
í
Ì
É
Å
Æ
æ
è
Ó
Ã
Ä
ø
Ü
Ä
±
¦
¦
±
¦
ù
Í
°
Ç
Ë
È
É
Å
Å
Í
Í
Ç
Ç
Ù
Ä
Í
É
Å
Ã
Í
É
Ï
Ð
Ö
û
ü
Ó
Ô
Ý
É
á
Ë
Þ
Ä
ý
ü
Æ
â
Å
þ
Æ
á
Í
Þ
Ó
ÿ
â
Ï
Õ
Ý
Â
Ç
Þ
á
Ù
Ä
Í
Ã
Ë
Ð
É
Ä
Â
Ï
Ù
Ï
Ö
Î
É
Í
Ã
Ó
Î
Ù
Ç
Õ
Ó
Ã
Å
Ç
Ó
Ï
Ì
É
Ö
Ç
Ô
È
Ó
É
Å
Ì
Ô
Í
Õ
Ã
É
É
Ì
Î
Ã
Í
Ä
Ù
Å
É
Ì
Ä
Ë
Î
Ï
É
Ú
É
Ï
î
É
Ë
Ç
Ó
ö
Ë
Å
Ù
Ç
Ú
É
Ó
õ
Ù
Ù
Ã
î
Í
Â
Ã
É
Æ
Ä
Î
Í
Ç
Ô
Î
ê
Å
Ó
Å
Ã
ô
É
Ç
Ù
Î
ó
Ù
Ë
Ä
#
Ó
Í
Ë
"
ñ
É
É
!
Ì
Ï
È
Ô
Â
ê
É
Ç
Í
Ç
ð
Ø
Ð
É
Å
É
Ç
ê
Í
Ë
É
Ô
Ç
Ä
Ä
ï
É
Æ
È
í
Ó
Ì
Ä
É
Ó
Ç
É
Â
Ä
ì
Ã
Ë
Ç
Ë
ë
Â
Ë
Ì
Ä
Å
ê
Ô
Ï
Ç
Ó
È
Å
É
Ô
Î
Ñ
Ó
Â
Ë
Ö
Ð
È
Ã
É
Í
Ô
Ç
Ù
Ç
Í
È
Ç
É
È
É
É
Ï
×
Ç
É
Ä
Ù
Ã
Ä
Ä
Í
Ç
Ä
Ã
Å
Î
É
Ó
Ã
Ø
Ç
É
Í
Ã
Ö
Ð
Ç
È
Í
Å
É
Õ
É
Â
Í
Ä
Ï
Ô
Ð
Ä
Å
Ç
Æ
È
É
Ü
Î
Â
Î
Ã
Í
Â
Å
É
Ì
Ç
Ä
Ç
Ï
Ü
Ç
Ë
È
È
É
Ì
Ä
É
Å
Å
Æ
Ç
Ç
É
Ã
È
É
Í
Ë
Ð
Ç
È
Î
Ó
É
Ç
Ó
Ä
Ó
Ã
Ï
É
Å
Â
Ó
Ó
Ï
Ä
Ç
Ä
É
Ë
Ú
$
Ë
É
Ë
Ö
Å
É
Ã
Æ
Ö
Õ
É
Ç
Ñ
É
É
Å
Ç
È
É
Ë
Ç
Ó
Ô
Ä
Â
Ù
Ó
Å
Ô
Ä
Ç
Ë
Ë
Â
Ã
Ã
Í
Â
Å
Ô
Ä
Å
Æ
Ë
%
Ç
Í
Ì
Ï
%
Ã
É
É
Ó
Ó
Ç
Ã
É
Ó
Ç
Ì
Ì
Ã
Ó
É
Ð
Ë
Ê
&
Ì
Ë
Ä
Õ
Ä
Ù
Ï
Ä
Ä
Ç
×
Ö
É
Ô
Ó
Å
Ô
Ô
É
Ì
Ø
Í
É
Å
Ï
Å
Í
Î
É
Ù
Ì
É
Ç
Ä
Í
Å
Å
'
Ç
Ë
Ç
Í
Ì
Ã
É
Ó
Ç
É
Ù
Í
Ã
É
Ç
Ã
Ó
Ð
Ê
Ì
Ú
(
Ë
%
É
Ë
Ç
Ó
Ô
Ä
Â
Ù
Ó
Ë
Ì
Ó
Ç
Ó
Ï
Ö
Ë
Ç
Ð
Í
Ã
Â
Ã
Õ
Ó
&
Å
Ã
É
'
å
Ô
É
Ø
É
Ï
Í
Î
Ù
É
Å
Ç
Ó
Å
Ô
Ë
Í
)
Ì
*
#
!
+
Ä
Í
É
Ì
#
Í
Å
!
Í
,
Ù
Ä
-
Ì
Ã
É
Æ
É
Å
É
Ã
Ó
Ç
Ä
Í
Å
$
Ç
%
Ä
Ï
Ä
Ë
É
Ç
È
É
Ó
Ø
Ó
Ä
Ï
Ó
Õ
Ï
É
Ë
Ù
Ú
Ä
Å
Ç
È
É
Õ
Â
Ä
Ï
Ô
Ä
Å
Æ
Ç
Í
Ó
Ù
Ó
×
Ä
Ù
Â
3
±
±
¦
Ù
)
Û
Å
Ì
Ã
É
Ó
Ë
É
Ç
È
É
Ô
Ó
Ä
Ï
Ö
Â
Ë
É
Í
Ð
Ç
È
É
Õ
Â
Ä
Ï
Ô
Ä
Å
Æ
Ó
Å
Ô
Ä
Å
Ì
Ï
Â
Ô
É
Ð
Â
Ç
É
Å
Ì
Ç
Ä
Í
Å
Ë
Ä
Á
Í
Â
Ì
È
Æ
Õ
Ï
É
É
Å
Â
É
Ë
Ã
É
Ó
Ç
Í
É
Ç
Ð
Ó
Ã
Ã
Ó
Ð
É
Ê
Ó
.
Ì
&
Ë
Ô
Ù
Ó
Ó
Ö
Ç
Ì
Ë
Ó
È
Ñ
Ô
Ó
É
É
Ò
/
Ö
Å
Í
Å
å
Ù
Ó
Ç
Ì
È
Ô
Ó
'
Ö
%
Â
%
Å
Ì
Ç
Ä
Í
Å
Ë
Ã
É
Ë
Î
Í
Å
Ô
Ä
Å
Æ
Ç
Í
Ç
È
É
Ì
È
Ó
Ã
Ó
Ì
Ç
É
Ã
Í
Ð
É
Ô
Ä
Ù
Ù
É
Ô
Ä
Ó
Ì
Í
Å
Ç
É
×
Ç
0
*
#
"
Û
Å
#
Ì
"
Ã
$
É
Ó
Ë
É
Ç
È
É
Ç
È
É
Ó
É
Å
Â
Ù
Â
Ù
Õ
É
Ã
É
Ã
Í
Ð
É
Ø
É
Å
Ç
Ë
Í
Ã
Æ
Ó
Å
Ä
Ë
&
É
Ë
Î
Ú
Å
Í
Å
å
Ð
Í
Í
Ç
Õ
Ó
Ï
OUTSIDE
È
INSIDE
Ñ
IN BETWEEN
%
Ï
%
É
Ø
Û
É
Å
Å
Ì
Ã
Ç
É
'
Ë
Ó
Ë
É
Å
Õ
Í
Ð
Í
Å
å
Ë
Î
Í
Ã
Ç
É
Ø
É
Å
Ç
&
Ë
Ù
Â
Ï
Ç
Ä
Î
Â
Ã
Î
Í
Ë
É
Â
Ë
É
'
%
É
%
1
%
2
%
2
Ã
Ë
Ó
È
Í
Ã
Â
Î
Î
Ç
Ç
Ä
Ï
Ì
Í
Í
Ã
Å
Ç
Ã
Ø
Ç
È
É
É
É
Å
Ã
Ó
Ë
Ð
Ñ
Ä
Ó
Í
Ì
Ä
Ç
Å
Ä
È
Ç
Ï
Ä
Ç
Ä
Ä
É
Ø
Ù
Ó
É
Ë
Ã
Ä
Ë
Ï
Í
Í
Ä
Ì
Â
Ë
Å
Ó
É
Ó
Ç
É
Ø
Ë
Ô
É
Â
Ó
Å
Ë
Ã
Ç
Í
Ç
Ó
Ë
Ä
Â
Ì
Å
Å
Ó
Ô
Í
Å
Õ
Ï
Ä
Ê
É
Æ
Ñ
Â
Ã
Ó
Ö
Ó
Ç
Ä
Í
Å
Ë
Ç
¦
°
±
¿
À
¾
¾
I
The New Kuip: Enfolding 24/7
o
p
q
p
o
r
s
t
u
v
w
u
u
s
x
t
y
z
{
J
I
@
<
>
<
?
[
K
Q
;
D
\
L
]
7
>
:
A
8
;
H
=
B
?
:
>
;
M
C
H
C
K
:
6
I
<
7
?
8
<
9
:
A
:
?
;
?
<
8
>
;
=
D
7
<
^
D
_
`
6
`
N
a
b
O
c
O
d
P
_
Q
e
c
D
f
R
D
R
g
S
>
T
U
U
H
>
7
A
U
h
A
9
>
H
C
V
H
W
A
D
P
O
g
4
9
O
:
;
X
H
P
?
<
O
4
i
4
>
Y
7
A
5
9
Z
>
G
|
E t <h/W WZK'Z D j
k
l
> s >
m
n
l
j
k
l
h^ ;D d , zͿ
Z h^ ;t <>zͿ W> ^ ^YD dKd > ^YD hEh^ Z ^
ϭ W> z Z^ E W Z</E' W Z</E' > s > ϭ W Z</E' /Z h> d/KE ϰϬй ^ Zs/ Z W> z Z^ E , E'/E' ZKKD^ D/y h^ Z Z d /> Ϯ WZ ^^ Z WZ ^^ Z Θ D / Z^ Θ Z ^d hZ Ed^ ^WKZd^ Θ &/dE ^^ Ed Z D / > ZKKD^ &/& D d/E' ZKKD^ W Z</E' > s > Ϯ W Z</E' /Z h> d/KE ϰϬй
ϭϰϱϬ
ϭϮ͘ϱ
ϭ ϭ ϭ ϮϬ
ϭϬϬϬ ϮϬϬϬ ϮϬϬϬ ϭϴϬ
ϭϬ ϭ ϰ ϭϬ ϯϱϬ
ϵϬ ϭϬϬϬ ϭϱϬ ϭϬϬ ϭϮ͘ϱ
KE& Z E Ed Z
W Zd K& &/dE ^^ >h ^ ,KK>
ϯ D /E KE KhZ^ KE KhZ^ ,Kd > >K z </K^<^
D d , z й ^YD
й
s^
t <>z й ^YD
й
ϭϴϭϮϱ ϳϮϱϬ ϭϬϬϬ ϮϬϬϬ ϮϬϬϬ ϯϲϬϬ
ϯϯϵϳϱ
ϯϲ͘ϴϱй
Ϯϴϵϳϱ ϯϭ͘ϰϯй
ϭϱϬϬ ϵϬϬ ϭϬϬϬ ϲϬϬ ϭϬϬϬ ϰϯϳϱ ϭϳϱϬ
ϭϭϭϮϱ
ϭϮ͘Ϭϳй
ϭϭϭϮϱ ϭϮ͘Ϭϳй
ϮϭϬϴϬ ϮϮ͘ϴϲй
ϭ ϴ
ϲϬϬ ϲϬ
ϮϬϬϬϬ ϲϬϬ ϰϴϬ
ϮϭϬϴϬ
ϮϮ͘ϴϲй
ϮϬ Ϯ ϮϬ ϱ ϭ
ϱϬ ϯϱϬ ϱϬ ϲϱϬ ϴϬϬ
ϭϬϬϬ ϳϬϬ ϭϬϬϬ ϯϮϱϬ ϴϬϬ
ϲϳϱϬ
ϳ͘ϯϮй
ϯϱϬϬ
ϯ͘ϴϬй
ϭ ϯϬ ϮϬ Ϯ ϮϬ
ϴϬϬϬ ϯϬ ϱϬ ϯϱϬ ϱϬ
ϴϬϬϬ ϵϬϬ ϭϬϬϬ ϳϬϬ ϭϬϬϬ
ϭϭϲϬϬ
ϭϮ͘ϱϴй
ϮϳϬϬ
Ϯ͘ϵϯй
ϭϰϲϬ ϮϳϱϬ ϮϬ
Ϯ ϭ ϱϬ
ϮϵϮϬ ϮϳϱϬ ϭϬϬϬ
ϲϲϳϬ
ϳ͘Ϯϯй
ϯϭϬϱ
ϯ͘ϯϳй
ϮϬ
ϱϬ
ϭϬϬϬ
ϭϬϬϬ
ϭ͘Ϭϴй
ϭϬϬϬ
ϭ͘Ϭϴй
ϵϮϮϬϬ
ϵϮϮϬϬ
ϭϬϬ͘ϬϬй
ϰ s/W Ky ^ s/W >KhE' ,Kd > ZKKD^ EYh d/E' E Z ^d hZ Ed^ & E^ Ed Z ϱ hWW Z KE KhZ^ /Z h> d/KE </K^<^ s/W Ky ^ s/W >KhE' ,Kd > ZKKD^
,Kd > ZKKD^ ,Kd > >KhE' ϱϬй h^
,Kd > ZKKD^ ,Kd > >KhE'
ϲ Dh>d/Ͳh^ ' >> Z/ ^ EYh d/E' ,Kd > ZKKD^
Ϯϱй h^ ϱϬй h^
ϳ ,Kd > ZKKD^
dKd > ^YD
ϭϬϬ͘ϬϬй
ϭ͘Ϭϴй ϭ ϳ͘Ϯϯй
ϭϬϬ͘ϬϬй
ϵϬ͘ϬϬй
hWW Z KE KhZ^ ϭϮ͘ϱϴй
ϵϬ͘ϬϬй
ϴϬ͘ϬϬй
ϭ
ϴϬ͘ϬϬй ϭ͘Ϭϴй ϯ͘ϯϳй Ϯ͘ϵϯй ϯ͘ϴϬй
ϳ͘ϯϮй ϳϬ͘ϬϬй
ϳϬ͘ϬϬй ; KE KhZ^ Ϳ ϮϮ͘ϴϲй
ϲϬ͘ϬϬй
ϲϬ͘ϬϬй ; KE KhZ^ Ϳ ϮϮ͘ϴϲй
ϱϬ͘ϬϬй
ϱϬ͘ϬϬй > s >Ϯ ϭϮ͘Ϭϳй
ϰϬ͘ϬϬй
ϰϬ͘ϬϬй
ϯϬ͘ϬϬй > s > ϭ ϯϲ͘ϴϱй
ϮϬ͘ϬϬй > s > ϭ ϯϭ͘ϰϯй
ϭϬ͘ϬϬй
ϭϬ͘ϬϬй
Ϭ͘ϬϬй
Ϭ͘ϬϬй
> s >ϭ
> s >Ϯ
> s >ϯ
> s >ϰ
}
7
8
9
:
;
<
8
;
=
7
>
?
@
<
A
:
B
C
D
E
>
?
?
<
F
G
=
> s >Ϯ ϭϮ͘Ϭϳй
ϯϬ͘ϬϬй
ϮϬ͘ϬϬй
6
ϳϭϰϴϱ ϳϳ͘ϱϯй
>
7
G
H
> s >ϱ
>
;
8
9
> s >ϲ
G
>
M
> s >ϳ
~
A
> s >ϭ
T
<
<
U
G
>
M
W
=
A
<
> s >Ϯ
V
<
7
> s >ϯ
8
<
C
;
>
> s >ϰ
B
<
> s >ϱ
> s >ϲ
> s >ϳ
Z
4
5
¶
·
¸
¢
·
¹
£
º
¤
»
¼
½
¥
»
¾
¿
¦
¦
À
¾
Á
¼
Â
§
¨
©
©
ª
«
¬
¨
®
¬
¯
°
±
¦
°
²
¡
³
The New Kuip: Enfolding 24/7
Ã
LEVEL 1
¥
¦
´
µ
³
³
Ù
The New Kuip: Enfolding 24/7
Ù
Ú
Ì
Ð
Î
ë
Ì
Ï
Å
Û
Ë
ì
Ô
í
Ü
Ç
Ê
Î
Ñ
Ë
È
Ø
Í
Ò
Ï
Ê
Î
Ë
Ý
Ó
Ø
Ó
Û
Ê
Æ
Ù
Ì
Ç
Ï
È
Ì
É
Ñ
Ê
Ê
Ï
Ë
Ï
Ì
Î
È
Ë
Ô
Í
Ç
î
Ì
ï
Ô
ð
ð
Æ
ñ
Þ
ò
ß
ó
ß
ô
à
ï
Å
õ
ó
Ô
ö
á
Ô
á
÷
â
Î
ã
ä
ä
Ø
Î
Ç
Ñ
ä
ø
Ñ
É
Î
Ø
Ó
å
Ø
æ
Ñ
Ô
à
ß
÷
Ä
É
ß
Ê
Ë
ç
Ø
à
Ï
Ì
ß
Ä
ù
Ä
Î
è
Ç
Ñ
é
É
ê
Î
×
LEVEL 2
Æ
Ç
È
É
Ê
Ë
Ì
È
Ë
Í
Ç
Î
Ï
Ð
Ì
Ñ
Ê
Ò
Ó
Ô
Õ
Î
Ï
Ï
Ì
Ö
×
Í
Î
Ç
×
Ø
Ä
Å
ü
ü
ý
ÿ
þ
ÿ
!
!
ü
ÿ
ÿ
ÿ
ÿ
"
#
$
$
%
&
'
(
#
)
'
*
+
,
!
ú
+
ÿ
ú
-
ú
.
The New Kuip: Enfolding 24/7
LEVEL 3
ú
û
ÿ
þ
ÿ
!
/
ÿ
0
.
.
F
The New Kuip: Enfolding 24/7
F
G
9
=
;
Y
9
<
N
H
8
Z
A
[
I
4
7
;
>
8
5
E
:
?
<
7
;
8
J
@
E
@
H
7
3
F
9
4
<
5
9
6
>
7
7
<
8
<
9
;
5
8
A
:
4
\
9
]
A
^
^
3
_
K
`
L
a
L
b
M
]
N
c
a
A
d
O
A
O
e
P
;
Q
R
R
E
;
4
>
R
f
>
6
;
E
@
S
E
T
>
A
M
L
e
1
6
L
7
8
U
E
M
<
9
L
1
g
1
;
V
4
>
W
6
X
;
D
LEVEL 4
3
4
5
6
7
8
9
5
8
:
4
;
<
=
9
>
7
?
@
A
B
;
<
<
9
C
D
:
;
4
D
E
1
2
j
j
k
m
l
s
m
n
o
p
q
r
y
{
s
p
t
w
u
n
{
s
p
v
w
o
{
x
j
y
m
n
t
m
z
{
{
n
p
n
m
s
t
p
q
u
y
m
q
x
|
}
}
~
q
q
s
w
s
y
z
s
w
w
q
~
}
h
z
}
{
p
w
~
n
m
}
h
h
s
y
z
s
The New Kuip: Enfolding 24/7
LEVEL 5
h
i
x
y
t
z
{
p
m
t
p
u
y
s
n
l
m
{
q
s
n
n
m
u
s
y
w
´
The New Kuip: Enfolding 24/7
´
µ
§
«
©
Ç
§
ª
¼
¶
¦
È
¯
É
·
¢
¥
©
¬
¦
£
³
¨
ª
¥
©
¦
¸
®
³
®
¶
¥
¡
´
§
¢
ª
£
§
¤
¬
¥
¥
ª
¦
ª
§
©
£
¦
¯
¨
¢
Ê
§
Ë
¯
Ì
Ì
¡
Í
¹
Î
º
Ï
º
Ð
»
Ë
¼
Ñ
Ï
¯
Ò
½
¯
½
Ó
¾
©
¿
À
À
³
©
¢
¬
À
Ô
¬
¤
©
³
®
Á
³
Â
¬
¯
»
º
Ó
¤
º
¥
¦
Ã
³
»
ª
§
º
Õ
©
Ä
¢
¬
Å
¤
Æ
©
²
LEVEL 6
¡
¢
£
¤
¥
¦
§
£
¦
¨
¢
©
ª
«
§
¬
¥
®
¯
°
©
ª
ª
§
±
²
¨
©
¢
²
³
Ø
Ù
Ø
Ú
Û
á
%
/
9
-
,
(
2
%
/
!
1
'
I
-
&
(
+
/
%
+
(
/
'
$
(
$
?
!
&
)
$
/
9
(
"
%
&
0
1
(
&
(
%
/
/
"
-
&
(
+
%
!
*
+
&
/
-
$
"
D
(
-
(
)
"
G
!
"
/
-
"
'
!
&
&
-
ï
ð
"
è
á
0
0
E
9
%
?
å
ü
ñ
å
"
ò
ð
+
Ö
×
ß
(
(
(
ó
è
×
é
Þ
ô
å
Ö
Ü
×
ó
ó
Û
õ
á
ç
ö
ð
è
÷
The New Kuip: Enfolding 24/7
á
/
0
$
1
"
+
?
(
"
)
(
%
F
=
5
&
)
$
?
B
?
(
"
7
9
&
0
&
"
<
/
H
$
"
E
!
%
5
+
)
"
0
0
<
>
%
(
'
%
$
"
(
%
>
>
!
%
/
/
(
9
0
5
"
/
(
/
4
2
!
5
-
3
"
&
<
>
ç
ð
)
"
#
3
%
á
%
(
!
-
>
å
ï
"
2
!
)
-
$
&
î
ï
(
&
(
"
(
$
.
1
)
>
!
%
"
-
$
1
í
á
/
(
A
>
D
%
#
(
0
(
'
%
ì
ß
(
/
/
&
"
>
(
ì
1
1
@
>
'
ß
/
"
ë
"
"
;
"
$
%
Ö
þ
!
(
$
+
"
$
$
%
/
"
×
&
/
!
&
&
$
(
&
%
'
×
#
/
ê
,
+
!
(
"
)
/
æ
ÿ
"
0
$
ß
ÿ
(
&
C
(
"
'
"
Û
þ
!
>
ç
ý
#
D
!
+
0
7
$
$
:
%
ã
"
-
1
Þ
ß
"
$
/
/
!
/
+
*
:
â
á
1
"
Û
Ü
"
:
?
$
'
%
3
Þ
Ü
!
é
"
8
é
ð
!
%
7
'
"
&
-
&
$
+
>
"
.
&
è
Û
"
$
â
Ü
)
)
&
!
1
(
-
ç
Û
"
0
(
(
$
æ
Ø
'
(
"
Ý
é
&
1
0
(
å
ü
?
%
ä
ü
%
"
Þ
á
/
%
$
)
1
!
"
"
>
"
"
&
%
!
+
"
%
é
%
/
Ü
û
(
'
ã
å
"
)
/
â
Þ
$
$
'
á
ð
"
1
2
#
/
é
#
/
à
ç
6
0
ß
ú
&
(
+
6
&
Þ
"
'
$
Ý
ù
!
"
&
Ü
ë
/
Û
ø
E
(
7 ú
ç
é
Û
ü
Û
ü
å
å
ç
é
ð
Ü
á
ü
J
%
D
&
"
'
>
#
%
%
(
"
"
Û
â
å
ü
Q
û
ã
ç
á
Þ
é
å
ü
ù
R
ã
ð
é
ü
Û
ð
ð
R
å
S
ô
å
Þ
Û
Ü
ç
å
å
&
$
/
+
%
×
%
?
(
%
&
"
-
&
(
/
>
)
+
&
$
+
?
"
9
/
!
%
(
&
+
"
/
&
(
"
>
9
/
+
/
/
+
$
(
&
0
"
"
"
"
$
&
#
!
"
"
-
(
!
/
$
&
D
?
"
(
+
G
>
D
B
(
-
"
-
%
/
+
(
"
%
"
/
!
"
-
"
>
(
(
"
'
%
B
$
-
(
+
"
"
E
'
"
D
G
#
(
$
ç
(
!
>
%
-
D
D
"
P
å
!
8
(
+
1
1
å
E
>
ü
!
+
2
$
(
&
Û
/
%
&
1
%
ü
(
%
0
"
Û
"
"
&
é
#
(
$
>
L
"
)
0
#
%
&
&
ç
"
0
!
ú
&
+
&
-
(
-
-
D
D
"
-
/
1
D
0
2
ç
$
/
%
å
/
/
"
&
"
>
H
$
"
(
?
Ý
%
9
$
/
/
ü
1
M
0
á
"
N
D
(
#
+
Ü
(
+
0
%
0
(
/
&
>
)
ñ
0
"
/
(
1
&
Ü
D
(
!
-
Û
0
/
1
!
&
?
$
8
'
"
/
"
/
+
$
>
%
$
+
&
;
7
/
'
"
-
"
?
0
(
&
-
"
$
&
9
D
O
$
$
(
2
!
>
+
"
&
$
/
+
/
"
"
-
&
>
/
>
%
"
G
G
!
+
/
"
(
$
"
"
%
%
(
1
8
/
"
"
K
'
(
"
"
Þ
B
'
(
G
B
7
ø
Ö
7
>
2
"
%
D
(
/
(
%
$
"
/
$
#
(
&
%
/
,
"
!
"
0
$
7
0
$
/
"
G
/
'
&
E
$
(
(
-
(
%
G
(
1
/
9
$
0
$
0
+
(
D
)
$
"
'
(
"
"
"
M
D
1
/
!
(
"
/
$
"
%
"
$
ê
/
-
#
&
9
å
â
è
Û
ø
á
Þ
é
â
ð
Û
æ
â
ç
Þ
â
é
è
å
ü
é
Þ
å
Û
â
Ý
Þ
ã
ú
ç
ã
á
ð
Ü
é
Ú
ü
Û
Û
ð
ð
R
ð
é
û
ü
S
å
ß
Û
á
ð
Ü
Ü
Û
ã
á
ç
å
i
The New Kuip: Enfolding 24/7
¢
¢
«
©
¶
º
©
«
¡
¢
¤
º
¦
§
¥
l
[
V
W
]
X
«
\
g
Z
\
Y
Z
[
\
´
¥
¥
¢
§
§
§
¡
©
£
¬
¬
¢
¡
¨
©
£
ª
²
¥
£
±
¢
¢
¢
«
¤
©
¸
¶
´
¨
©
¤
¢
^
\
_
{
k
[
p
d
|
l
}
W
^
Z
a
X
[
]
h
_
b
Z
[
m
^
h
c
k
c
Z
V
i
W
\
X
_
Y
\
Z
a
Z
_
[
_
\
X
^
[
]
W
d
~
\
d
V
n
o
o
T
p
d
q
q
d
r
s
^
t
h
t
^
W
t
a
a
Y
h
^
c
u
h
v
a
T
d
o
U
o
Y
Z
[
w
h
T
_
o
U
\
U
x
^
W
y
a
Y
z
^
g
«
¶
©
¶
¢
¡
©
¦
£
¤
¢
¨
¢
¥
¢
¢
¨
Z
h
[
§
\
b
`
½
¾
W
^
h
\
¿
[
u
a
\
[
Z
Z
b
[
{
c
d
¢
h
^
_
e
a
Y
´
¤
£
¥
¨
¡
¢
§
¨
«
³
¢
^
^
_
_
Å
\
¨
·
¢
¥
©
¢
¡
§
©
§
§
¢
¬
«
§
¥
¥
·
¨
ª
¡
¥
¥
¡
¢
¢
¡
¡
¥
¥
¦
£
«
¡
¥
£
©
¨
¢
©
¦
]
W
^
^
W
g
¢
c
£
¬
¦
¹
£
¦
¡
§
©
\
Z
¢
¶
»
©
¶
¤
¬
¤
¤
¢
©
¶
©
£
¢
§
¡
£
¥
¡
£
¢
¢
¥
§
¶
¥
^
¢
©
¶
¢
§
¢
¼
¡
¢
£
¡
©
§
¸
´
¥
¡
¶
¥
«
«
^
[
Z
¥
c
a
µ
Z
_
©
g
X
¸
µ
¥
¨
[
¥
¹
¸
£
a
¢
¡
¬
©
]
^
h
¥
¢
©
¨
´
¦
c
g
Ç
¶
¡
¢
c
¢
¥
^
h
¶
Æ
t
¨
W
k
g
½
^
\
Ã
¢
¦
¶
¶
©
®
u
f
¾
£
µ
¬
u
¢
§
©
¢
¥
©
¨
¥
¦
Ä
¨
Á
\
Y
¤
§
[
¤
¥
«
¡
Ã
¥
§
¡
¡
g
¢
Â
§
©
¡
¢
¥
£
£
Á
¢
¶
¢
¢
¢
¨
À
¥
¥
¤
¡
²
\
_
¥
·
¢
§
¥
¤
©
¥
¥
[
Y
¡
¨
£
£
¥
¤
c
^
¢
¶
²
¢
¥
«
[
W
«
¡
·
¢
©
Z
c
]
¢
a
¥
¨
©
¨
¨
©
¶
g
X
¶
«
©
a
¨
©
¬
§
£
_
¢
¤
©
¤
¨
¤
¥
¨
£
«
¢
Z
¢
£
´
£
°
¢
£
¯
¤
¤
¢
¬
¥
£
¨
¬
¡
§
¢
¢
£
¡
¢
¢
©
¶
¢
¥
¢
¥
©
¥
`
\
¸
¢
¶
¢
¡
£
£
¶
¥
¢
¡
¤
ª
§
§
¨
¤
®
¬
¥
¨
¢
©
¢
¡
¤
¡
¨
©
¤
£
µ
¥
¥
«
«
£
¨
j
i
¤
_
]
h
¦
g
\
[
a
£
¶
h
X
¢
¡
c
X
¦
g
h
©
h
h
´
W
W
±
¡
Ë
^
¡
Z
c
²
c
k
¥
\
h
·
«
£
¢
¹
¨
£
c
[
¸
W
h
{
[
Y
\
\
W
\
n
_
^
[
Z
h
c
É
Z
[
Y
[
Y
\
a
\
^
h
[
Z
_
c
_
b
Z
c
{
X
^
\
u
{
^
È
X
Z
W
[
m
^
c
Z
c
\
É
[
Y
Z
\
[
Y
È
Z
h
c
É
Ê
^
[
^
È
_
\
a
[
W
]
X
[
]
W
\
_
T
U
Í
Î
Í
Ï
Ð
Ö
Ð
Ò
á
Ñ
î
Ó
Õ
ð
Ô
ï
Ü
Ö
Þ
æ
×
Ó
Ø
Ú
Ñ
ñ
Þ
Ó
Ù
Ö
Ú
ò
Ò
ò
Í
Û
Þ
Ü
Ð
×
Ñ
Ý
Ð
Þ
æ
Þ
Ó
Ñ
Ð
Ñ
×
Ö
Ó
Ø
Ü
Ô
Ô
ô
Ð
ó
õ
Û
õ
ß
ö
ø
à
÷
à
Ì
ù
á
ô
ú
Ô
ø
â
û
â
Ô
ã
ü
ä
Ö
å
Ú
å
Ö
Ü
æ
ý
å
æ
Ý
Ö
Ú
ò
ç
Ú
è
æ
Ô
Ì
à
ü
é
Ý
à
Þ
Ó
ê
Ú
Ì
Ñ
Ð
à
é
þ
é
Ö
ë
Ü
æ
ì
Ý
í
Ö
ÿ
The New Kuip: Enfolding 24/7
!
!
"
#
!
$
!
%
#
&
'
!
$
&
*
!
!
$
!
!
*
"
"
!
!
&
(
&
)
!
%
!
(
+
'
%
!
#
"
!
,
-
.
/
.
0
1
2
3
4
5
3
6
7
'
8
9
:
;
3
<
6
!
"
!
!
!
(
=
ã
Ú
Í
Ì
Ì
Û
Ü
×
Ý
Þ
Ó
Ð
×
Ó
Ø
Ü
Ö
Ñ
Ï
ò
Ü
Ð
ñ
Ö
æ
Þ
ò
Þ
ñ
Ó
æ
ò
Ø
Ô
ÿ
Ð
Þ
Ü
ò
Ö
æ
Ö
Ñ
Ö
Ñ
Ñ
Ñ
Ð
æ
æ
Ð
×
Ð
Ó
×
ÿ
Ó
Ø
Þ
Þ
Ú
ò
Ú
Ö
ò
Ü
ÿ
Ú
S
The New Kuip: Enfolding 24/7
t
u
v
u
w
x
y
z
{
|
}
y
~
|
y
S
T
F
J
H
e
F
I
Z
U
E
f
N
g
V
A
D
H
K
E
B
R
G
L
I
D
H
E
W
M
R
M
U
D
@
S
F
A
I
B
F
C
K
D
D
I
E
I
F
H
B
E
N
G
A
h
F
i
N
j
j
@
k
X
l
A
B
C
D
E
F
B
E
G
A
H
I
J
F
K
D
L
M
N
O
Y
n
>
i
Z
o
N
m
[
p
[
N
\
q
]
H
^
R
^
A
H
^
K
K
r
C
H
R
M
_
R
`
K
>
Y
N
a
q
Y
C
D
E
b
R
>
I
Y
F
a
a
s
c
H
A
?
K
C
d
H
Q
z
@
Y
m
H
I
I
F
P
Q
G
H
A
Q
R
D
F
D
F
U
A
R
U
e
A
R
A
e
F
_
D
F
F
A
Q
K
F
D
Q
K
F
E
A
_
D
H
A
M
R
e
A
F
D
M
Q
L
H
F
Q
`
F
q
`
R
G
R
E
A
C
E
b
C
]
F
P
H
K
K
E
E
>
d
d
?
ª
«
¬
¢
®
®
¢
¯
°
±
±
²
³
´
µ
°
¶
´
·
¸
¡
¡
¢
¡
¹
¢
®
£
¤
¢
¸
¥
¦
¥
º
¥
§
¢
¨
©
»
The New Kuip: Enfolding 24/7
¾
¿
ª
¾
¿
¢
®
£
¡
¢
¼
»
®
¤
¢
©
½
»
»
The New Kuip: Enfolding 24/7
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
CONTENT 3.1 Structural concept
26
26 28
3.1.1 Roof Design 3.1.2 Main Structure Design
3.2 Approximate Design of Anticlastic Prestressed Members
30
30 33 34
3.2.1 Theory and Calculations 3.2.2 Calculations for Prestressing in Cables 3.2.3 Shape of the Ring
3.3 Design of Supporting Structure
34
3.4 Preperation for Analysis in GSA
35
35 37 37 38
3.4.1 3.4.2 3.4.3 3.4.4
Input from Rhino/Grasshopper Cable properties Application of Loads Loadcases
3.5 FEM Analysis of Priliminary Design
38
38 38 39
3.5.1 Formfinding using Force Density method (Theory) 3.5.2 Non Linear static Analysis (Theory) 3.5.3 Initial Analysis for System Check
3.6 FEM Analysis of Revised Design
41
41 44 47
3.6.1 Analysis 1 3.6.2 Analysis 2 3.6.3 Analysis 3
3.7 Conclusion
Structural Design
49
25
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
The New Kuip: Enfolding 24/7
3.1 Structural Concept Including the three concepts and final design structural exploration was an integrated part of the whole design process. Many places structure defined the form of the building especially in the roof. Development of design took place on the lines of â&#x20AC;&#x2DC;Form follows Functionâ&#x20AC;&#x2122; principle so as the development of the structure. Exploration of the structure took place in two parts, 1. Roof and supporting structure 2. Main structure Considering the time span we were provided with I was able to analyse roof structure in detail and proposed basic concepts for the main structure.
3.1.1 Roof and supporting structure design The roof form was derived from the basic architectural requirements for interior space configuration, use of natural light and sustainability aspects. Architectural Requirements for the roof 1.Low height building (No white elephant) 2.Fixed roof, no retractable surface. 3.Structure should be as light and transparent as possible. 4.Integration of energy generating elements (solar panels) 5.Intimate space even for smaller functions
26
Structural Design
The New Kuip: Enfolding 24/7
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
Considering above architectural requirements we compared two type of structures , compression structure e.g. Dome and tension structure e.g. synclastic , anticlastic surfaces . In compression structure(dome) as all the structural members are in compression there will be a jungle of structural members and also height of the stadium increases which was in contradiction to architectural requirements. So I started to explore tension structures as they will be prestressed the member sizes will be smaller than compression structure. Comparison between synclastic and anticlastic tension surface â&#x20AC;&#x201C; synclastic surface creates very low height at the centre (approx 30 m) which is not desired for a football match. It is also not good for snow load and rainwater drainage. Anticlastic curve is self supporting geometry if provided with required prestressing. It is also good for snow load and rainwater drainage. So we discarded the option of synclastic surface.
Then we started to compare the basic shape of stadium seating. Seats along the longer side of the field are supposed to be visually better than the shorter side so we decided to increase no. of seats on the longer side making the bowl shape more circular than rectangular. It turned out to beneficial for the roof structure as the compression forces in the outer ring are almost equal at all the points as compared to the rectangular shape which has denser stress lines in the corners. So we decided to go ahead with the circular shape. During the exploration of the patterns of the structural grid for the roof we compared radial grid, Fibonacci curved grid and rectangular grid and we concluded with the rectangular grid as it follows the stress lines so is most efficient and uses less material.
Structural Design
27
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
The New Kuip: Enfolding 24/7
3.1.2 Main Structure (concept) –
Grid – The column grid for the main structure is derived from the car parking and circulation and dimensions of the precast concrete slab seating so there is no defined dimension for a structural bay but varies from 6.6 to 12m X 6.6m. The column grid is denser on the lower floors which don’t require large column less spaces e.g. parking, services etc. and fewer columns on the upper floors which requires large column less spaces e.g. lobbies, circulation areas etc. The roof ring is supported on a secondary ring which is integrated in the main structure, which needs to be designed as per the structural loading from the roof. The FEM calculations for the main structure has not been done because of the time limit we had.
28
Structural Design
The New Kuip: Enfolding 24/7
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
Sliding Pitch â&#x20AC;&#x201C; To slide the pitch out we need to have 100m of columless space on the ground on the eastern part of the stadium. What makes it chalanging is the live and dead load coming from the top as there are five floors of functions above that. One of the solutions which is proposed here is the double floor truss system placed 13m c/c. so that the whole two floors will act as a huge 3d truss.
Structural Design
29
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
3.2 Approximate Design of Anticlastic Prestressed Members
The New Kuip: Enfolding 24/7
In contrast to the compression structures tensile structures lack stiffness and weight. They are curvilinear geometries and built in tension (prestress). In case of anticlastic geometry two opposing curvatures balance each other. In other words the prestress in cables along one curvature stabilizes the primary load bearing action of the cable along opposite curvature. The induced tension provides stability of form. While space geometry, together with prestress, provides strength and stiffness. Since cables can resist loads only in pure tension their geometry must reflect and mirror the force flow, surface geometry is identical with force flow. The geometry (forces)must be in equilibrium so that under superimposed loads it guarantees stability and safety. Cables must have sufficient curvature and tension throughout the surface to achieve desired stiffness and strength under any loading condition. In contrast to traditional structures, where stresses result from loading, in anticlastic structures, prestresses must be specified initially so that the resulting cablenet shape can be determined.
3.2.1 Theory and calculations In anticlastic surface geometry two opposing curvatures balance each other. Under gravity loads, the main (suspended, convex, load bearing etc.) cable is prevented from moving by the secondary (concave, arched, upper bracing etc) cable, which is prestressed and pulls the suspended layer down, thus stabilizes it. The prestress force must be large enough to keep the surface in tension in any loading condition, preventing any portion of the skin or any member to slack because of compression being larger than sorted tension. In addition the magnitude of the initial tension should be high enough to provide the necessary stiffness so that the cable deflection is kept to minimum. However the amount of pretensioning not only is a function of superimposed loading but also is directly related to the roof shape and the boundary support conditions. From a structural design point of view, prestressed anticlastic surface may be organized in three main groups: 1.Saddle surface supported along exterior boundaries and possibly, in addition, supported by interior line supports. 2.Anticlastic surfaces point supported in the interior (stress concentrations) 3.Combinations. In our case we explored, investigated and analysed Saddle surface as it is only supported by the edge ring. The stress state of the cable for ideal condition of pretension only, ignoring any other influences can be derived from general membrane equation for zero external loading conditions.
30
Structural Design
The New Kuip: Enfolding 24/7
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
In our anticlastic roof structure fx = fy= 10m so we can write So tension in cables is directly proportional to square of the length. In other words longer the length more the tension. The initial tension may be induced directly to the cables or by tensioning the boundary cables using prestress equipment; the tension can also be induced by initial external overload p. Load p is helpful as a concept and can be seen as an imaginary or equivalent external load to express the prestress force. According to the membrane equation for shallow hyperbolic paraboloids under uniform vertical load action, letting w=p, the membrane/ cable net forces per unit width along each principle direction can be approximated for the assumed conditions symmetry and T=H as
Or the magnitude of the equivalent prestress load p for a surface under constant tension T is a function of the curvature. P = 2T/R With a decrease of surface curvature (or increase of radius of curvature) less prestress force is needed . Surfaces with more curvature are stiffer than the once with less curvature for the same amount of tension. We can concluded from above equations that for conditions of asymmetry, such as for different span ratios and sag ratios the membrane forces in each direction under equivalent uniform prestress load p are â&#x20AC;&#x201C;
The following relationship , important for determining the basic membrane shape, can be derived from above equation for a surface under constant tension Tx0 = Ty0 =T0
Conditions of perfect symmetry of loading, geometry and material are assumed for first preliminary design process. Not only the boundary conditions symmetrical, but also cables in each principle direction are considered identical in size and spacing so that the stiffness ratio (EA)x/(EA)y = 1. Cable sag in the range of 4% to 6% of the span generally give satisfactory results with respect to structural behaviour. In our structure the sag of cable is 10m which is 4% of the total span and crosssection of all the cables is considered as constant (EA)x=(EA)y
Structural Design
31
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
The New Kuip: Enfolding 24/7
Stiffness for the cable using (Stainless steel, austenitic, AISI 302, wrought, annealed) the elastic modules is 190 GPa and radius for the cable as 5 cm â&#x20AC;&#x201C;
Under full gravity loading, the lower hanging cable, TL are stressed to a maximum, while the arched membrane portion TT is stressed to a minimum, requiring only enough tension so that it does not slack. Hence each cable system carries an equal pretensioning force and equal share of the superimposed loading.
For first approximation purpose (under normal wind conditions where wind suction is less than snow loading), let the tensile force in stabilizing cable be equal to zero (TT=0) but not considering any safety factor. The result is a prestress force generated by an imaginary load equivalent to one half of the maximum superimposed loading p= w/2
The magnitude of the prestress force T0 is only preliminary; it has to be changed to take into account the dead to live load ratio, different cable sizes, surface flutter, rigidity of boundaries etc. Substituting T0 in above equation gives maximum tensile force per unit width.
The cable force is obtained by multiplying the unit force Tmax by the cable spacing. We may conclude that for the preliminary design of shallow cable nets, all external loads, such as snow, cladding are carried by the suspended portion of the surface, similarly to a single curvature system when the arched partition has lost its prestress and goes slack. Also notice that at least one half of the permitted tension in cables is consumed by the initial stored tension. The design of the arched cable system for light weight roof structure is derived in general, from the loading condition where maximum wint suction wu causes uplift and increases the stored prestressed tension, which is considered here equal to one half of the full gravity loading, minus the relative small effect of membrane weight. In other words, under upward loading, the maximum forces occur in the arched cables and can be approximated as w_u L^2/8f. For most cases it is conservative to consider for preliminary design purpose the cable sizes in the arched direction as equal to those in the suspended direction. We may conclude that an anticlastic surface .
Similarly, the uplift wind forces or suction forces w_u, which usually control the design of lightweight tensile cable net structures, are resisted by the arched cables or fabric strips when the suspended portion has lost its prestress and goes slack.
32
Structural Design
The New Kuip: Enfolding 24/7
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
To calculate prestressing in the cables first we need to calculate nodal load on each node. The dead weight of the roof cladding is considered 8kg/m^2 taking TEXO panels(http://www.texo.co.nz/) in reference for light weight cladding material. Self weight of 10mm dia cables is approx 61 kg/m length. Nodal load on node A will be self weight of the cables and the dead weight of the cladding material in the red box. Self weight of cables â&#x20AC;&#x201C; W1 = 61x16 =976kg = 9564.8 N Cladding load â&#x20AC;&#x201C; W2 = 8x64 = 512kg/m2 = 5056 N Total nodal load = W1+W2 = 14620.8 N There are 27 nodes for the length of 225 m cable Hence load per unit length of cable =14620.8x27/225 = 17545 N
3.2.2 Calculation for the prestressing in cables -
For analysis of the roof structure in GSA we will be using force density method for form finding so its necessary to calculate force density per unit length.
Structural Design
33
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
The New Kuip: Enfolding 24/7
3.2.3 Shape of the ring We started with the rectangular shaped flat compression ring to hold all the tension cables. The orientation of the flat beams needed to be in line with the tension forces, but during the process we realised that second moment of Inertia for each ring section is different. It was creating a lot of complications in modeling process so we decided to simplify the ring shape to circular section as second moment of Inertia for circular section is same in all directions and also this change was not affecting the architectural concept.
3.3 Design of support structure for the compression ring
Support structure for the ring was one of the crucial part of structural design as it was going to directly affect the architectural layouts and cladding design. We started with integrated support systems along with the bowl structure. This concept demanded a verticle truss structure (fig 1) simmiler to roof support structure for London 2012 velodrome building. After integrating this verticle truss in architectural model we realised it was messing around with arcitectural layouts and diameter of th roof was extending outside the site boundries So we decided to go ahead with indepndent support system simmiler to Olympic Saddle dome in Calgary in the form of angular supports along with intermidiate tie beams to prevent these columns from buckling, which finally rests on the secondary ring where roof structure meets the main structure. 34
Structural Design
The New Kuip: Enfolding 24/7
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
3.4 Preperation for Analysis in GSA 3.4.1 Input from Rhino/Grasshopper
Structural Design
35
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
The New Kuip: Enfolding 24/7
Application of GSA plugin (GeomGym) in grasshopper saved a lot of time in nodal and elemental inputs in GSA for structural analysis. Parameterization of GSA inputs in the form of material properties, section properties, sizes and constraint inputs left me only with load application in GSA. It helped in back and forth communication with Rhino model in case of some minor changes.
36
Structural Design
The New Kuip: Enfolding 24/7
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
3.4.2 Cable Properties Before Importing rhino model to GSA its important to make sure that all the elements are splitted at node junction and there are no overlapping elements. Line 3d for roof consisted of number of number of cable elements connected at nodes. In default situation all the cable elements will have same cable property. Because of which, in analysis process we might get bifurcation errors. So it was necessery to connect/ link all the cable elements to make it as cable. Cable elements are intended to be used as multinodal super elements or chains in GsRelax. These super elements can be called sliding cable elements to differentiate them from their constituent links. To define the chain or the super element, the programe looks for spacer or cable elements with the same property number and joins common nodes. So all the elements in a continious length of spacer chain or sliding cable chain must have a common property number unique to that chain. In our case we assumed that cable properties for all the cables will have same cable property, so the same cable property was applied to all the cable chains using different property number.
3.4.3 Application of Loads There are 5 different types of load used for analysis – 1.L1 – (Gravity loading) 2.L2 – (Pre stressing). As per previous calculations Prestressing of 554343.75N was given to suspended cables and 717619.2N was given to arched cables. 3.L3 – (Dead Load) Self weight of cables and dead load from cladding material resulted into 14620N of nodal load per node. (Calculation Pg 6) 4.L4 – (Snow Load). Snow load was taken as 566 N/sq.m as per NEN-EN 1991-1-3 standards, which resulted into 36224N nodal load per node. 5.L5 – (Wind Load). As the building is completely closed, there is no direct wind entering the building. So upward force is not considered and also all the horizontal wind force will be dealt by the main structure, it is not included in analysis calculations. The suction force caused by wind passing above the roof is considered and the value for it is derived from NEN-EN 1991-1-4 codes. As per NBN codes maximum wind force for Rotterdam region(Region 2) is 1.21KN/sq.m. The height of building is 55m so according to figure below there will be 1.21k/sq.m force acting on area which is 55m from west side and 0.847kN/sq.m will be acting on rest of the roof which results into nodal loads of 77440N and 50208N upward nodal loads per node.
Structural Design
37
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
The New Kuip: Enfolding 24/7
3.4.4 Loadcases – L1 – (Gravity) - used for form finding using Force density method. L1+L2 – used for form finding using normal element properties L1+L2+L3 – used for initial calculations for system check. L1+L2+L3+L4 – used for calculations in heavy snow condition L1+L2+L3+L4+L5 – used for calculations in heavy snow with heavy wind conditions
3.5 FEM Analysis Preliminary Design FEM analysis for anticlastic cable net structure was done in two analysis tasks, formfinding using force density method and non linear static analysis.
3.5.1 Form finding using Force density method (Theory) Force density form finding is a method of form finding cable networks which originated over 20 years ago in Germany. The tension in each link of the network is made proportional to its length. The resulting stiffness matrix is valid for any displacements so the method enables linear structural analysis program to form find. The form that is found is given minimum strain energy i.e. the form which minimizes the sum of the squares of the lengths of the links multiplied by the stiffness of the links. For 1D elements, the force density form finding properties set the value of force/length for succeeding bars. For this analysis only gravity loading was taken into consideration.
3.5.2 Non linear static analysis (Theory) There are several different types of non-linear analysis, but there are two different effects that need to be considered which are seen in cable net structures.
Geometric non-linearity— where the loading causes changes in the shape of the structure which must be taken into account in order to get an accurate solution. Material non-linearity— where the loading causes material to behave in a non-linear manner, typically through yielding. Different analysis options in GSA allow these effects to be accounted for in different ways. The analysis solver for all the general non-linear analysis options is called GsRelax and is based on Dynamic Relaxation. The GsRelax solver uses an iterative process similar to transient dynamic analysis with time increment. As GsRelax analysis is a static analysis, it does not use real time increment, but unit time increment and dummy masses rather than real masses. As GsRelax uses dynamic analysis to simulate static analysis, damping is also used to enable the vibration to come to rest. The results and progress of the analysis can be viewed and adjusted while the analysis is in progress. The iterative process can be tuned in the analysis wizard, and the format and frequency of reporting analysis progress adjusted.
38
Structural Design
The New Kuip: Enfolding 24/7
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
3.5.3 Initial analysis for system check After the basic form finding analysis we did non linear static analysis using GsRelax solver using only gravity loads just to check if the system works.
Structural Design
39
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
The New Kuip: Enfolding 24/7
After getting the results we realised that the ring which is supposed to work compression ring was not in entirely compression and the whole system was generating opposite axial forces and reactions in adjacent members. After investigating the problem we concluded that the problem lies in the connection between the angular column and the ring beam as the angular columns were preventing ring to compress so at some places ring was in tension resulting opposite axial forces. Solution for this problem was found in the Olympic Saddle dome in Calgary which was built on the simmiler principles. Two of the opposite column beam connection on the lowest side were pinned so that commection movement in X,Y and Z direction is restrained and all other connections were roller connections where the Z movement was restrained but X and Y movement was permitted resulting in compression behaviour of the ring. To achive this behaviour master and slave joint system was adapted for the connections adding extra nodes at respective junctions. After making necessary nodal restrain changes in model we again did non linear static analysis for system check only applying gravity load and prestressing. The ring was in complete compression and cables in pure tension but were showing snapping phenomenon. Even after increasing the prestressing the results were similar. So we concluded that the roof curvature is not enough, it need to be more curved. The sag for the cables in both directions was changed from 10m to 15m (6% of the span). After these changes further analysis was carried out.
40
Structural Design
The New Kuip: Enfolding 24/7
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
3.6 FEM Analysis of revised design 3.6.1 Analysis 1 â&#x20AC;&#x201C; (with gravity, prestressing and dead load)
Structural Design
41
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
42
The New Kuip: Enfolding 24/7
Structural Design
The New Kuip: Enfolding 24/7
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
Analysis of cable net roof under gravity, prestress and dead load gives maximum vertical nodal displacement of 1.8m but maximum translation displacement in Y direction is 4.8 m, which is not desirable. Axial forces in the beam are compression forces (17.5 x 106 max) and cables have tensile forces (2.5 x106max). maximum axial stresses in ring are 30MPa (45 MPa with safety factor) which is way below the limit of 245MPa for normal steel. The maximum combined stresses for the shorter columns are quite high (1GPa), which is not desirable.
Structural Design
43
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
The New Kuip: Enfolding 24/7
3.6.2 Analysis 2 â&#x20AC;&#x201C; (with gravity, prestressing, dead load and snow load)
44
Structural Design
The New Kuip: Enfolding 24/7
Structural Design
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
45
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
The New Kuip: Enfolding 24/7
In further analysis of roof in addition of snow load of 566 N/sq.m results into maximum vertical displacement of 3.6m and maximum translational displacement in Y direction as 6.1m both of them are not desirable from architectural and cladding point of view. Axial forces in in ring and cable donâ&#x20AC;&#x2122;t show any failure. Axial stresses are below the limit of 245MPa for normal steel.
46
Structural Design
The New Kuip: Enfolding 24/7
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
3.6.3 Analysis 3 â&#x20AC;&#x201C; (with gravity, prestressing, dead load, snow load and wind load)
Structural Design
47
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
48
The New Kuip: Enfolding 24/7
Structural Design
The New Kuip: Enfolding 24/7
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
Analysis of the roof considering all the loads performs better in terms of vertical and translational displacement, giving maximum vertical deformation and translational displacement as 0.3m and 0.35m respectively. The lesser deformation is because of the upward wind suction force acting on the cable net. Axial compression force in the rind and axial tension force in the cables are lower on the western part of the roof but ring is still in compression and cables are still in tension, so the system works fine. Axial stresses in the ring and angular columns are quite low.
3.7 Conclusion (Roof Analysis) â&#x20AC;&#x201C; Considering the results from above three analysis, we can conclude that â&#x20AC;&#x201C; 1. The system of anticlastic cable net roof structure works as compression ring and tension cables after changing the nodal conditions at ring and column junctions as master and slave joints. 2. The deformation of the tension cables in first two combination cases is unacceptable, so to make it work, either cable stiffness or prestressing in cables need to be increased. 3. Axial stresses in shorter columns is exceeding the permitted limit because of the orientation angle of the column, so either section thickness for the column need to be increased or the column inclination angle need to be reduced. Structural Design
49
The New Kuip: Enfolding 24/7
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5:
Bristogianni T. _ Calle E. _ Sakkas Panos / 4120639 _ Shitole H.
Cladding Contents 4.1 Cladding Concept
50
4.2 The Challenges of the Roof Cladding 4.3 References of the Roof Cladding 4.4 Developement of the Roof Cladding 4.5 Daylight Analysis 4.6 Detail Drawings of roof Cladding
52 54 56 58 60
4.7 The Challenges of the Facade Cladding 4.8 References and Developement of the Facade Cladding 4.9 Concept of the Facade Cladding 4.9 Facade sections 4.10 Detail Drawings of Facade Cladding
64 66 66 68 70 72
Cladding
49
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5:
Bristogianni T. _ Calle E. _ Sakkas Panos / 4120639 _ Shitole H.
The New Kuip: Enfolding 24/7
4.1.1
4.1 Cladding Concept The use of textile materials for the cladding of the Stadium was an important part of the concept that was chosen during the preliminary phase of the XXL Workshop ( 4.1.1). Textile materials like membranes, fabrics, foils or metal meshes generate innovative solutions to non standard ( 4.1.5) and temporary structures (4.1.2)and therefore could create an envelope with high levels of adaptability to complicated functional programs and to different environmental conditions ( 4.1.4) . As one of the most popular cladding for light structures, textile materials belong to a family of structures called Tensile Surface Structures. The great development in the field of composites production has created products that are not only suitable for temporary or experimental constructions but are also used to cover more and more big building projects ( 4.1.3). Their main advantages are the reduce of the weight of the structure ( textiles are lightweighted and therefore need a lightweighted structure to support them), the relative reduce of the construction budget when there is a need to cover a big surface and the great ability to realise extreme architectural shapes. The biggest disadvatage of these materials is their short life span. That is why they are mainly used for temporary structures. Nevertheless. technology has improved and their life span may rise some times to 10-15 years. In the case of the new Kuip we believe that a life span of 10-15 years creates the flexibility to accommodate new technologies in the future and may create opportunities for further development of the Stadium. 50
Cladding
The New Kuip: Enfolding 24/7
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5:
Bristogianni T. _ Calle E. _ Sakkas Panos / 4120639 _ Shitole H.
4.1.2
4.1.3
4.1.1. Sketch of the chosen concept during the preliminary phase of XXL workshop.The wrapping of the Stadium with a textile material creates new opportunities for reconfiguration and adaptation. 4.1.2 Image describing the concept of wrapping for the first pin up presentation of XXL workshop. The image is a schematical section of the Stadium proposed with a picture of the artwork:Valley Curtain (by Christo and Jeanne Claude) as background.
4.1.4
4.1.3 View of the Zenith concert Hall in Strastburg bu Massimiliano Fuksas.The use of silicone coated fiberglass membrane created a dynamic building envelope of big size and reduced budget. 4.14 Gina : the BMW prototype that uses textile to cover the body of the car. The application of textile in the movable parts of the car explore the behavior of such kind of materials in reconfigurable structures. 4.1.5 Burhnam Pavillion by Z.Hadid. It is a temporary lightweight pavillion with a non standard structure that is covered with fabric 4.1.5
Cladding
51
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5:
Bristogianni T. _ Calle E. _ Sakkas Panos / 4120639 _ Shitole H.
The New Kuip: Enfolding 24/7
4.2.1 North - South 3D section of the Stadium
4.2 The Challenges of the Roof Cladding The main challenges of the roof cladding were 1.The cover of an unusual surface ( anticlastic surface : double curvature ) with a light as possible cladding because of structural demands for a wide span lightweight roof and construction economy demands for a reduced weight of the overall structure ( 4.2.3.). 2.The exploitation of the big surface created in the roof for energy production with solar energy. The creation of an enclosed roof created the opportunity to make use of the new big surface that was created in order to produce solar energy( 4.2.4). The particular shape of the roof ( directed by the bowl of seats it covers and the architectural need for visual reduce of the Stadiumâ&#x20AC;&#x2122;s volume) divided the roof in two parts, only one of which was facing South and therefore was suitable for PV Panels( 4.2.5). 3. The creation of a roof that would completely cover the interior of the Stadium but at the same time would try to keep the lighting quality of an open air space. The full cover of the roof with PV Panels would reduce significantly the levels of daylight inside the field. Day light was of great importance for the interior of the Stadium not only because of the creation of a pleasant environment that had the most desirable qualities of an open air space but also because of the reduce of the artificially light during the daytime( the biggest disadvantage of the Stadium when compared with conventional Stadiums)
52
Cladding
The New Kuip: Enfolding 24/7
4.2.2 Roof plan
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5:
Bristogianni T. _ Calle E. _ Sakkas Panos / 4120639 _ Shitole H.
4.2.3 Roof shape:anticlastic surface
22% 78% 4.2.5 West - East section of Stadium
100%
4.2.4 Increase by 30% of the roof surface
Cladding
4.2.6 North - South section of Stadium
53
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5:
Bristogianni T. _ Calle E. _ Sakkas Panos / 4120639 _ Shitole H.
The New Kuip: Enfolding 24/7
4.3.1
4.3 References of the Roof Cladding The cable grid of the roof acted as the starting point for the adaptation of the cladding in the anticlastic surface. The size range of the grid unfortunately created 8m X 8m squares in which the cladding had to adjust. The manipulation of these zones would create a more adaptive surface to the orientation and the shape of the roof. Although folding of textile surfaces is used very often for structural reasons , in this case it would be used to create a surface better adjusted to the surroundings.
4.3.2 54
Cladding
The New Kuip: Enfolding 24/7
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5:
Bristogianni T. _ Calle E. _ Sakkas Panos / 4120639 _ Shitole H.
4.3.3
4.3.4
4.3.5
4.3.1 Preliminary sketch of the roof cladding concept. 4.3.2 Material matrix for the roof cladding: The use of flexible PV panels is very efficient way to integrate energy production in lightweiga hr structures. When combined with ETFE cushion they also let natural lighting.
4.3.6
4.3.3-4 Constructional Detail and view of the Akita Dome: a lightweight structure with textile cladding and wide span. 4.3.5-6 Atrium roofing at Palais Rothschild in Vienna.Axonometric of the roof structure thet uses ETFE as cladding and interior view. 4.3.7 Accessibility in the roof of Sony Center in Berlin. Cladding
4.3.7 55
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5:
Bristogianni T. _ Calle E. _ Sakkas Panos / 4120639 _ Shitole H.
The New Kuip: Enfolding 24/7
4.4 Developement of the Roof Cladding The demand for bigger integration in the body and the envelope building lead to the exploit of the 8m X 8m structural cable grid of the roof as the organizational grid of the roof cladding. The South orientation is the most suitable for the position of PV Panels and therefore a first division of the roof was implemented. Narrow zones were created in between the West- East cables of the roof. Through the manipulation of these zones the cladding will be able to take advantage of the direct sunlight for energy production and let indirect sunlight enter the building 56
Cladding
The New Kuip: Enfolding 24/7
Cladding
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5:
Bristogianni T. _ Calle E. _ Sakkas Panos / 4120639 _ Shitole H.
57
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5:
Bristogianni T. _ Calle E. _ Sakkas Panos / 4120639 _ Shitole H.
The New Kuip: Enfolding 24/7
4.5.1
4.5.2
4.5 Daylight Analysis The lighting quality of the interior ( 4.5.1) is most affected by the enclosing of the roof. Therefore openings were created to let indirect northern sunlight coming through. Geco and Ecotech were used to examine the ability of the roof to satisfy the standards of natural light ( 4.5.2-3-5). Also a test on direct radiation was made in order to determine a better orientation of the cladding to absorb as much as possible direct light and not get affected by self-shading ( 4.5.4) . All the above examinations were made in order to guaranty that no problems would occur and not in order to optimize the position of the cladding. 58
Cladding
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3)
The New Kuip: Enfolding 24/7
Team 5:
Bristogianni T. _ Calle E. _ Sakkas Panos / 4120639 _ Shitole H.
4.5.3
4.5.4
4.5.5 Cladding
59
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Bristogianni T. _ Calle E. _ Sakkas Panos / 4120639 _ Shitole H.
Team 5:
The New Kuip: Enfolding 24/7
4.6 Detail Drawings of roof Cladding
A1
section A-A scale:1/1000
B1
section B-B scale:1/1000
A
B
B
A
8.00
8.00
8.00
8.00
8.00
8.00
8.00
8.00
8.00
C1
section A1 scale: 1/500
60
Cladding
C2
section B1
8.00
8.00
8.00
The New Kuip: Enfolding 24/7
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) 8.00
Team 5:
8.00
8.00
8.00
8.00
8.00
Bristogianni T. _ Calle E. _ Sakkas Panos / 4120639 _ Shitole H.
C1
section A1 scale: 1/500
C2
section B1 scale:1/500
1.00
1.25
D1
3.79
D2
Cladding
elevation C2 scale: 1/50
61
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5:
Bristogianni T. _ Calle E. _ Sakkas Panos / 4120639 _ Shitole H.
The New Kuip: Enfolding 24/7
1.00
1.25
D1
D2
e
3.79
s
section C1 scale: 1/50
62
Cladding
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3)
The New Kuip: Enfolding 24/7
Bristogianni T. _ Calle E. _ Sakkas Panos / 4120639 _ Shitole H.
Team 5:
25
50
4
Custom U-Strab 3mm around cable
50
Metal cable 50mm
46
screw M10
Flat plate 180X15
27
ETFE foil
18
27
180
Silicone coated fiberglass membrane with flexible PV cells
73
70
48
Tension cable 10mm
section D1 scale: 1/5 Silicone coated fiberglass membrane ETFE foil
46
Tension cable 10mm 60 30 30
108
70
1 16
Custom U-Strab 3mm around cable
50
section D2 scale: 1/5
Cladding
63
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5:
Bristogianni T. _ Calle E. _ Sakkas Panos / 4120639 _ Shitole H.
The New Kuip: Enfolding 24/7
4.6.1
4.7 The Challenges of the Facade Cladding The main challenges of the facade cladding were generated by the fact that the facade would surround a multy functional program( 4.6.4). Therefore the facade cladding had to provide a surface that would serve each interior appropriately and at the same time would create a unifying visual effect ( 4.6.1). The cover of a complicated and diverse functional program ( retail, circulation areas, restaurants, lobbies, lounges, hotel, etc) under one unifying surface( 4.6.5) requires a cladding strategy that is adaptable to the surrounding environment ( different orientation and different urban conditions). Each space has different demands concerning the need for view or for protection from the sun ( 4.6.3) not only because of itâ&#x20AC;&#x2122;s specific program but also because of the different orientation ( 360 degrees facade). Also the outside environment ( 4.6.2) is some times attractive to view ( The Canal, the Skyline of the city, the Plaza) and some times not ( noise and pollution from the highway)
64
Cladding
The New Kuip: Enfolding 24/7
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5:
Bristogianni T. _ Calle E. _ Sakkas Panos / 4120639 _ Shitole H.
4.6.2
4.6.3
4.6.1 Riverside( North ) elevation of the Stadium. 4.6.2 Connection of the Stadium with the surrounding enviroment- main circulation paths.
4.6.4
4.6.3 Conceptual plan of the facade cladding strategy.Differnt treatment of the west-Nosth side : open view in contrast to the South side that remains covered from the unattractive highway. 4.6.4 Programatical variety and diversity in between the bowl and the facade. 4.3.7 Spreadout of the programatical diversity of the interior in relation to orientation Cladding
4.6.5 65
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5:
Bristogianni T. _ Calle E. _ Sakkas Panos / 4120639 _ Shitole H.
The New Kuip: Enfolding 24/7
4.7.1
4.7.2
4.7.3
4.7.4
4.7.5 66
4.8 References and Developement of the Facade Cladding The Zenith Concert Hall in Strasburg by Massimiliano Fuksas was a great inspiration for the cladding strategy even from the conceptual phase( 4.7.1-2). A silicone coated fiberglass membrane was chosen for the specific project. Stress resistant, fire resistant , hydrophobic and very formable the membrane was kept into place by 5 metal tubes of 50cm diameter ( 4.7.4)with average distance between them 5m and total hight of facade 26.8 m. The metal rings act as compressive elements( 4.7.3) of the facade structure. In the between distance there are cables that stretch the parts of the membrane and keep them always in tension( 4.7.5). Although the primary intension was to combine the membrane with other more rigid materials ( 4.7.8) at the end only the membrane was used to control better the size and the complexity of the project. The shape of the Stadium became an object for exploration, especially the North side of the hotel ( 4.7.7). Cladding
The New Kuip: Enfolding 24/7
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Bristogianni T. _ Calle E. _ Sakkas Panos / 4120639 _ Shitole H.
Team 5:
4.7.6
4.7.7 4.7.1 Intervantion on the image of the Zenith.With starting point the stuctural vocabulary of this building an addition of a more transparent material( ETFE foil ) could create very similar qualities to these which we seek. 4.7.2 Appart from change of material , the subtrraction of material is also a case in which a better connection to the exterior is achieved. 4.7.3 Picture during the assemply of the Zenith Facade, showing the wrapping of the rings with the membrane. 4.7.4 Section of the structure of the Zenith facade, revieling the size of the interior structure. 4.7.5 Interior view of the Zenith. 4.7.6 The Gina prototype as an inspiration for a unifying surface that has differnt gualities. 4.7.7 Developement of the Stadiums shape during the weeks. 4.7.6 Material matrix that could be used in the facade of the Stadium. Cladding
4.7.8 67
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5:
Bristogianni T. _ Calle E. _ Sakkas Panos / 4120639 _ Shitole H.
The New Kuip: Enfolding 24/7
4.9 Concept of the Facade Cladding The intention for maximum integration lead the design to try and use the floor slabs as the compressive elements that would hold the facade. Unfortunately , in order the structure to work properly the metal rings need to be longer than the tension cables. This way a useless space is created in the edge of the floor slabs . With the proper manipulation of the rings the facade was adapted to the demands of the interior. The rings run in a zone ranging from 0.9 m to 2.5m from the level of the slab. A secondary structure is generated to lift the rings to the appropriate height . This way the zone above the ring protects from the sun and the zone below opens the view to the exterior space. It is important to note that the membrane acts as a second layer of protection for the building. The lack of thermal insulation in the membrane makes the facade a cover from wind, water and overheating. 68
Cladding
The New Kuip: Enfolding 24/7
Cladding
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5:
Bristogianni T. _ Calle E. _ Sakkas Panos / 4120639 _ Shitole H.
69
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5:
Bristogianni T. _ Calle E. _ Sakkas Panos / 4120639 _ Shitole H.
The New Kuip: Enfolding 24/7
4.9 Facade sections
70
Cladding
The New Kuip: Enfolding 24/7
Cladding
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5:
Bristogianni T. _ Calle E. _ Sakkas Panos / 4120639 _ Shitole H.
71
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5:
Bristogianni T. _ Calle E. _ Sakkas Panos / 4120639 _ Shitole H.
The New Kuip: Enfolding 24/7
210
245
4.10 Detail Drawings of Facade Cladding
70
165
130
E1
E2
48
45
70
90
217
15
253
120
340
130
157
5 14
86
typical section scale: 1/50
72
Cladding
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3)
The New Kuip: Enfolding 24/7
Bristogianni T. _ Calle E. _ Sakkas Panos / 4120639 _ Shitole H.
Team 5:
Metal tube 500 X15
Custom shaped flat plate 15mm
18
Lower profile
27 15 27
Flat plate 100X15
44
Upper profile
44
screw M10
42
53
ETFE foil
section E1 scale: 1/5
Custom U-Strab 4mm around cable 46
42
35
4
Valley cable 35mm
Silicone coated fiberglass membrane
section E2 scale: 1/5
Cladding
73
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
The New Kuip: Enfolding 24/7
Digidal Design and Computation Contents 5.1. Introduction
75
5.2. Digital Design Process
75
5.2.1. Communication and Coordination
75
5.2.2. Data flow and integration of multidisciplinary design information
76
5.2.3. Parameterisation of the core model
78
5.2.4. Computational analysis as an evaluation and decision making tool:
79
Developing the Reconfigurability of the Arena
79
5.2.4.1. Research topic
79
5.2.4.2. Exploration of the space division geometry
80
5.2.4.3. Defining the shape of the structural elements
83
5.2.4.4. Study of the reconfiguration of the generating curves
86
5.2.4.5. Optimasation of the strip element
88
5.2.5. Materialisation of the design through prototype making
95
5.3. Conclusion and Reflection
96
5.4. References
97
74
Digital Design and Computation
The New Kuip: Enfolding 24/7
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
5.1. Introduction This chapter focuses on the digital design strategy developed for the coordination of a multidisciplinary team in the preliminary design stage of the “New Kuip Stadium”, the integration of the design data and the evaluation and optimisation of the proposal. It presents the key role of digital management in dealing with complex problems in a short period of time, achieving effective communication and interaction between different experts and guiding meaningful performance analyses that support the decision-making process.
5.2. Digital Design Process 5.2.1. Communication and Coordination First step, regarding the information management among the team members, was the creation of a common database. Dropbox- as currently being the most popular web-based file hosting service- was chosen for storing the shared archive. The ability of instant file synchronization and therefore updating of referenced files was the main reason that led to this decision. The structure of the archive was dynamic during the design process, to respond to the particular needs. The above indicates, for example, that folders considered to be important during the “3 Concepts Development” Stage were later deleted or merged to facilitate the navigation through the archive, while new folders were created to support the work. Once each team member started concentrating on its role, folders for each discipline were created, containing the subfolders 3D, CHARTS, DRAWINGS, IMAGES, RESEARCH, TEXTS, which were further divided in subfolders concerning each week of the program. Each discipline would save its files under the appropriate week, labeling them with the format FILE NAME_DD-MM_#, and would add new subfolders according to its specific research. The use of a common organisational filing system was crucial for quickly accessing each colleague’s work and occasional inconsistencies to the rule always delayed the data communication. Apart from each specialisation’s folder, in Dropbox also existed the following folders: 3D and DRAWINGS- that contained the core model and the referenced AutoCAD files as it will be discussed in the following section, COURSE MATERIAL, LOCATION, PRESENTATIONS, SOFTWARE and STADIUM STANDARDS. The long term “InfoBase Archive”, provided by the instructors of the Workshop, was used only for uploading the given presentations and submitting the final deliverables of the course. The created subfolders in this database were therefore: DRAWINGS, PRESENTATIONS, PROTOTYPE, and REPORT. To share information with the instructors and the other teams, regarding the progress of the design and the received feedback from the tutors, we made use of a blog page: http://g5xxl.blogspot.com .
5.1.
Screenshots from Team 5 blogspace
Digital Design and Computation
75
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
The New Kuip: Enfolding 24/7
5.2.2. Data flow and integration of multidisciplinary design information The concept of concurrent engineering can result not only to the reduction of the time needed for a project to be developed, but more importantly to a better quality of the final product, as it introduces from the very early stages of the design issues such as functionality, cost, feasibility, production, sustainability, etc. Decisions are taken guided by the feedback from each expert and possible mistakes are discovered and addressed in time. Hence, Computer Aided Design can significantly promote the integration of the different disciplines and the avoidance of clashes. According to the “Building Information Modeling” (BIM) principles, the building is firstly accurately constructed in a digital realm, before its actual construction commences. Parts of the created core model are extracted to the different experts to conduct meaningful computational analysis that predicts the building’s behavior, and simulates its performance and its life-cycle phases. The feedback from these analyses is then used to inform the core model. Various software solutions with standard databases exist in the market, promising to aid the BIM design, however, they can be limiting, sometimes, for the creativity and innovation of the project. The idea of BIM was approached in this assignment, not by using a commercial application, but by concentrating on how the flow of data and geometry between the core model and the individual 3D models could be achieved. Having as a goal a common model that could be manipulated parametrically, the Rhinoceros (Rhino) software was preferred that enabled the parameterisation of data through its plug-in Grasshopper (GH). The Worksession command was used to combine four 3D files (Architectural, Structural, Cladding, Digital) into one model. Inserted to this model, as linked blocks, were also four AutoCAD drawings produced from each discipline. All the above files were saved in the Dropbox archive, in order to be easily updated. Each expert created its own layers and named them using a prefix related to its role (ex. A_SLABS indicated a layer coming from the architect, C_ROOF_LOUVRES from the cladding expert, etc) in order for the origin of the layers to be defined in the common model. The produced model needed to be updated regularly by the digital manager so that possible clashes could be detected. Yet, the impossibility to circularly reference files in Rhino worked as a limiting factor for the design process. Each expert, while working in its specific file, could not refer to the work done by its colleagues, except if the desired files were manually inserted to its file. The chosen organisational system for the database and the fact that all produced files shared the same orientation of the design using the centre of the pitch as the (0,0,0) starting point, facilitated the exchange of information, it would have been, however, more meaningful if these references were made automatically. Still, if these matters were to be solved, another issue related to the way GH connects to the geometries set in Rhino, was working as an impediment to the automatic data update. Specifically, updating a file in Rhino literally means exchanging a previous file with its newer version. In consequence, any linkages of its geometries with GH components are lost and needed to be set again, delaying the design process. To overcome this obstacle, we intended to base the partial GH definitions on points and lines that were fixed and constant in each Rhino file, such as the basic lines of the pitch area and its centre point. This technique, while sufficient at the early design stage, proved difficult to accomplish as the complexity of the project rose. Another problem to be faced was that in order to combine in the core model the resulting design data from the parametric GH files of each team member, the data needed to lose their parametric nature (to be “baked”). A combination of all current files in one GH definition produced heavy .ghx files that performed very slowly the desired calculations and were almost impossible to handle. The common AutoCAD files on the other hand proved very useful in informing the changes realised from each expert, exactly because circular reference was possible. Moreover, the storage of these files in Dropbox enabled the notification of changes and the immediate update of the referenced files. In short, again four different files were created, each containing as a reference the files coming from the other disciplines, and the layers were similarly organised with the discipline prefixes. As mentioned before, the four AutoCAD files were inserted in the Rhino Worksession and in each separate Rhino file as linked blocks, a command that enables the update of inserted files in Rhino. To avoid possible incompatibilities between the used software, the AutoCAD drawing files were saved in AutoCAD 2000 version. 76
Digital Design and Computation
The New Kuip: Enfolding 24/7
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
In order to create a backup for the common 3D and 2D drawings, each team member was supposed to regularly save a copy of its files under its folder, in the 3D or DRAWINGS subfolder, and specifically in the appropriate week’s subfolder, using the same naming pattern as discussed before: DRAWING NAME_DD-MM_#. Despite the complications experienced in building up a core model in Rhino, the choice of the software was considered the most appropriate. A variety of plug-ins could support the individual research of each expert or convert the files to be exported in different software for further computational analysis. Hereby a synopsis of the plug-ins and software used from each discipline: Architect: • Export to SketchUp Rhino plug-in that exports Rhino files to Sketch-Up • Google SketchUp 3D modeling software • Microsoft Excel 2007 Spreadsheet application that features calculation, graphing tools, etc Structural Designer: • SSI (Smart Structural Interpreter) FOR v8.5 OASYS GSA A Rhino based plug-in that works with GH to prepare files for GSA • OASYS GSA Software package for the analysis and design of structures Cladding Expert : • Geco A Rhino based plug-in that establishes a live link between Rhino-GH and Autodesk Ecotect • Autodesk Ecotect Analysis 2011 Software for the simulation and building energy analysis • ArchCut for Rhino 4.0 A sections tool plug-in for Rhino • V-Ray for Rhino A rendering plug-in for Rhino Digital Design Manager: • Galapagos Evolutionary solver in GH • Minimal Surfaces GH add-on that generates minimal surfaces from 2 or 4 edge curves • RhinoMembrane Rhino plug-in for form-finding concerning tensile structures • Weaver Bird A Rhino base plug-in for manipulating meshes • Kangaroo Physics GH add-on that embeds physical behavior in the 3D modeling environment • StructDrawRhino (SDR) Rhino base plug-in to model structure, relax meshes, inflate meshes, etc • Microsoft Excel 2007 • Windows Movie Maker Program for making movies from photos and videos
Digital Design and Computation
77
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
The New Kuip: Enfolding 24/7
• CES EduPack Database containing material properties and process information • Active Statics Online interactive demonstrations showing the relationship between structural form and forces, by MIT • JavaView Demonstrates continuous generalized elastic curves • Wolfram Alpha Computational knowledge engine There were no problems detected regarding the file exchange of design data between the team members, as the exchange was usually made through AutoCAD (.dwg), Rhino (.3DM) and GH files (.ghx).
5.2.3. Parameterisation of the core model When starting with the development of the building in a conceptual level, it was considered important to build a parametric model that would address main aspects of the stadium and would act as a basis to all disciplines for further exploration of geometry and form. In this context, a 3D model was built in GH, using the fixed pitch geometry as a reference, which subsequently formed the basis of the core model.
5.2.
Aspects of the parametric conceptual model
In this model, the geometry of the bowl, the shape and number of the floors, the anticlastic roof, the relationship with the surroundings, the form of the green slopes and the concept of the façade were explored. Especially for the geometry of the bowl, two additional GH definitions were created to give feedback for the proper inclination of the seats- according to the FIFA regulations- the total number of seats, and the organisational grid of the stands and circulation according to Neufert’s standards. Thus, the expansion and reduction of the bowl’s volume corresponded to the application of the above regulations, which would guarantee its functionality. The parametric model proved very useful to all the team members as it encouraged form experimentations, facilitated changes and quickly resulted in a set of relationships that were to be followed along the development of the project. Parts of the model, either as baked geometries in Rhino, or as definitions in GH, were distributed to the experts as a starting point for their research. Specifically, considering the Digital Design Manager role, the individual research was focused on the reconfigurability of the arena. A baked version of the parametric core model was used for building the parametric model of the interior space.
78
Digital Design and Computation
The New Kuip: Enfolding 24/7
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
5.3. Variety of spacial configurations produced by altering the numerical sliders
5.4. Detail from the supporting GH definition that calculates the inclination of the bowl and from the parameters that were controlled in the core model
5.2.4. Computational analysis as an evaluation and decision making tool: Developing the Reconfigurability of the Arena 5.2.4.1. Research topic The research topic of the computational analysis, as formulated in accordance with the team members, addressed the reconfigurability of the arena. Main objective of this work was to materialise the design intentions for a 24-7 stadium, reinforce the main concept of enfolding spaces through the use of a lightweight flexible material, and search for optimal solutions towards the achievement of these goals. The starting point of this research was the belief that by dividing a relatively large space, as this arena of 60.000 people capacity, into smaller functional spaces, you could accomplish a more intense space usage. Previous analysis concerning the frequency with which the arena would be used for hosting local football matches (2-4 times per month), already led to the decision to keep the pitch area mainly outside the building and utilise the enclosed interior space
Digital Design and Computation
79
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
The New Kuip: Enfolding 24/7
for diverse activities. To attract, nevertheless, the community and make the building an important part of their everyday life, effort should be given in introducing essential functions that could be used in a regular daily basis. Rough estimations showed that with this strategy a 50% usage of the area of the arena (including the area of the stands) could be achieved throughout the weekdays. Therefore the interior of the bowl was used to complement the functions situated in its periphery, and answer to the needs of the community as it transformed itself into a large public space. In addition, the requirements of the clients for a stadium of 60.000 spectators resulted in an arena that would probably not be used more than 4 to 5 times per year to its full capacity, hosting either important matches or big celebrity concerts. In a regular basis, around 32.000 seats are covered during Feyenoord matches raising the issue of how the empty seats would be treated in our proposal, to avoid spaces that failed to meet the expectations and enthusiasm of the attendants of the match. The computational analysis, as it will be presented in the following sections, commenced from this statement and the necessity for reconfigurability, and worked towards its support and realisation. 5.5. Charts concerning the percentage of arena space that is expected to function during the week, if the space in reconfigured
5.2.4.2. Exploration of the space division geometry The creation of a main model in Rhino that would allow the parametric exploration of the space division geometry was the first step of this research. Having the bowl geometry, the circulation and the functional arrangement in the periphery of the bowl as constants received from the architect, an organisational pattern was created, using primary and secondary grid lines that derived from the geometry of the stands, and a set of points in the intersection of the above gridlines. Thereafter, two procedures evolved simultaneously: the defining and positioning of the spaces to be produced, and the geometrical logic of the space division. Space bubbles related the new functions to the spaces around the bowl and vaguely indicated the size and configuration of the needed spaces. Searching of ways these bubbles could be generated, the possibility of tessellating the interior using the Voronoi diagram in combination with inscribed curves was investigated, in GH. The resulting pattern created large curves at the periphery of the bowl that enclosed part of the stands as well as a potion of the pitch area, and smaller introverted spaces in the middle. Proceeding on the elevation method of these curves, the set of organisational points was projected at the horizontal plane of each floor level, to create a space grid on which 80
5.6. Organisational grid deriving from the bowl geometry 5.7. Space bubbles and proposed functions
Digital Design and Computation
The New Kuip: Enfolding 24/7
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
again the geometric pattern was applied. The various curves produced in each level were then joined through the Edge Surface command in GH. By changing the selected base-points the sculptural geometry and the limitations of this method were explored. The produced twisted textile surfaces reached the limit of the roof, from where they were supported, and established a visual continuation with the textile louvers applied at the top of the roof.
5.8.
First experiment made to divide the interior space by using a pattern based on the Voronoi diagram and inscribed interpolate curves
This short-term procedure was meant to give a quick feedback to the team of the possible formations and evoke discussions considering their feasibility, structural system, assembly technique, and demanded time for reconfiguration. The most important constrain came from the structural designer who, after processing the proposal of hanging additional weight on the roof, resulted that no load should be added on the anticlastic cable net structure, in order for the pre-tensed surface to properly function. He otherwise suggested supporting the partitions on the precast concrete bowl structure and the steel ring that could receive a large amount of additional forces. From an architectural point of view, the geometry of the spaces was evaluated, concluding that although the curves produced at the periphery created desirable spaces whose configuration could match a small amphitheatre, concert hall, or multi-sport hall, the interior divisions fragmented the space and took no advantage of the stands. This more or less defined the shape of the space bubbles that was to be sought in the next stage. In response to the structural designerâ&#x20AC;&#x2122;s feedback, a trial visualising the reconfiguration of part of the 2nd level stands area to enclose a series of 3D cinemas was produced. Principle interpolate curves were formed having as a starting point the ring and as ending point the beginning of the 2nd level stands. The controlling points of these curves were originating from the existing space grid and, once again, experimenting with the selected points resulted in a variety of possible configurations in GH. Then, â&#x20AC;&#x153;Edge Surfacesâ&#x20AC;? were produced to cover the span between the curves and create the enclosures.
Digital Design and Computation
81
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
The New Kuip: Enfolding 24/7
Combining this technique with the required shapes for the 1st level stands and pitch area, as stated from the architect, a new proposal was formed to be discussed with the structural designer and the instructors responsible for the Structural Design. The objective was to come up with a lightweight system that could create these desired curved shapes and span distances of more than 100 meters, without having intermediate supports from the ground or the roof. The short time for the reconfigurability of the space was an important factor, as well, that needed to be taken under consideration.
5.9. Proposal for the interior divisions using the feedback from the architect and the structural designer
5.10. Reconfiguration of the 2nd level stands to host 3D cinema halls
The decided system that matched the desired forms was based in a combination of inflated textile beams of circular section (the most optimal shape in this case) that would span the large distances and give form to the enclosures, and a single layer of textile membrane to be rested on top of the beams to create the covering. The airbeams could be deflated and folded back into the ground floor whereas the membrane would be rolled up and packed under the steel ring. Elaborating on the assembly and deployment of the system, we concluded that the airbeam and the covering structure should be integrated, to reach higher level of stability and to minimise the effort of reconfiguration. The basic element therefore consisted of two airbeams along the edge curves and a joining membrane on top, which once deflated it would be rolled up, with the aid of cable-suspended crane hooks that would be digitally maneuvered in the arena, borrowing the principle of the â&#x20AC;&#x153;Spycamâ&#x20AC;? camera system used in stadiums. The hooks would also work contrariwise, to help the strip element unfold without getting damaged from hitting on the seats and bring it to the pitch level, where it would be pinned. Lastly, the strips would be joined together by joining the fabric material with big plastic zippers.
5.11. Inflatable deployable mechanism 5.12. Aspect of the interior space of the stadium
When inflated, each strip could be reconfigured into different shapes: the large span condition that would reach the ground level, and the short span condition, where the end of the strip would be pinned on the beginning of the 2nd level stands. Here it must be pointed out that the 2nd smaller configuration of the strip would not always aim at the creation of functional spaces (for ex. 3D cinema) but simply focus on the coverage of the unused seats on the upper level, when a local much would take place. 82
Digital Design and Computation
The New Kuip: Enfolding 24/7
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
Having determined the logic and geometrical form of the principal element that would be used to generate the spaces, a new proposal for the shaping of the interior was produced and the distribution of the functions was reconsidered. The process showed that apart from the organisational points set on the ground level, the space grid of points was not longer necessary. In fact, the creation of interpolate curves based in a collection of points would create a curve of multiple parabolic fragments that would act as a multi-hinged arch, thus as an unstable mechanism. Hence, the curves should be produced having as reference points only their endpoints, to ensure their function as a continuous arch, pinned on its ends.
5.13. Plan showing the functions introduced in the arena during the week and 3D aspects of the reconfiguration of the interior
Nevertheless, new points of reference emerged on the ring level and the beginning of the 2nd level stands. Soon it was made clear that the ring, as being the boundary curve of an anticlastic surface, would implicate the rolling of the strips and, therefore, a secondary horizontal ring needed to be introduced, at a lower level. The update of the structural design worked in favor of the stability of the structure as the intermediate level reduced the buckling of the previously slender columns. The positioning level of the ring differed in each of the 4 wings of the stadium and was parametrically defined until more information was obtained on the height of the mechanism in its rolled configuration. All in all, the later 3D model was important for visualising the application of the strips elements in space and setting the goals that would guide the computational analysis.
5.2.4.3. Defining the shape of the structural elements The next focus of the research was the optimal curved shape the airbeams would obtain in the 1st, large span configuration. Consultation of relevant literature pointed out the parabola and the catenary curve as the most optimal formations. Although these curves have an almost similar representation, the catenary curve was selected in the end, as it would guarantee the equal distribution of stresses along the airbeam and zero bending moments in each internal section. Taking into account that the catenary curve is also the basis that generates minimal surfaces, the above choice would positively affect further stages of the design that would deal with the optimal shape of the covering membranes. To understand the behavior of the curves, the online application â&#x20AC;&#x153;Active Staticsâ&#x20AC;? provided by MIT was used. Using this tool, the relationship between form and reaction forces was established and a set of constraints was formulated to ensure that the produced curves would result to the minimum value of reaction forces. Digital Design and Computation
83
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
The New Kuip: Enfolding 24/7
As realised, the tangent at the beginning and at the end of the curve was crucially affecting the value of the reaction forces. Upon that it was decided to aim for curves that had a parallel to the ground starting tangent, which eliminated the vertical reactions and delivered only horizontal in-plane forces to the ring. The landing tangent would be ideal if it were perpendicular to the ground, creating no horizontal forces, but would also show a good performance until its inclination overcame the 26° angle difference to the perpendicular axis. After this point, the horizontal forces would surpass the vertical ones and the resultant forces would be significantly higher. In general, although the 0°-90° tangent would produce the minimum of reaction forces, it would require a longer beam length, sometimes reaching the value of 8-9 meters, adding in consequence to the total load to be carried and the amount of used material. The 26° range was therefore important in finding a compromising solution that would satisfy both requirements.
5.14. Difference between catenary and parabolic curve
In the GH environment a variety of different curves was considered, either to form the catenary curve or to work with simplified approximations that could more easily provide control of the parameters of the desired curves. The Catenary Curve command in GH was the only command that could regulate beforehand the length of the curve, apart from the starting and ending point. However it could not include the starting and ending tangents as inserted parameters. The Bezier Span command (the Quadratic Bézier Curve is a parabolic segment) could include the tangents in the starting parameters but could not control the length. Therefore, an attempt was made to control all the above parameters by using parabolic curves- that are based on simpler equations, as an approximation of the catenary curve. When using a symmetric parabolic curve, the equations could be easily applied to Function components in GH and regulate the curve. The resulting shapes, however, were not the desired. Asymmetrical parabolas were approaching the wanted configuration but were connected to much complicated equations, difficult to handle. For solving these equations the online version of the computational knowledge engine Wolfram Alpha was used. Using the equations that metamorphosed a range of numbers into a parabola allowed the controlling of the curvature and the length of the curve, as well as the starting and ending point, but regarding the tangents, although they could be regulated, there was no method found to insert their angles in advance. In other words, the later approach resulted in a situation similar with the one related to the catenary curve command, where a different approach was needed in order to optimise the curves. Thus the Galapagos solver was used, in combination with sliders that controlled the tangents and the length of the catenary curve, and the optimal shapes were achieved.
84
5.15. Relationship of shape and reaction forces in a catenary curve Digital Design and Computation
The New Kuip: Enfolding 24/7
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
5.16. The GH definition that was used to produce parabolic curves
5.17. The parabolas were first built in the xy plane and then aligned along each grid-line
5.18. The equation relating the range of an asymmetric parabola to the length of its base derives from the application of the Pythagorean Theorem in the shape in Fig. 5.17.
5.19. Using Galapagos to achieve the optimal configurations of the catenary curves
Digital Design and Computation
85
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
The New Kuip: Enfolding 24/7
5.2.4.4. Study of the reconfiguration of the generating curves Coming after, the reconfiguration of the airbeams was studied. Efforts were made to define the accurate shape the curves would obtain after being bended from the large configuration to the 2nd position, and the dimensions of their rolled up-condition. The results of this research chapter were then combined in an animation that simulated the movement of the strips in space, to achieve the 3 different configurations. Simulating the bending of the curves proved to be a challenging task that could very difficultly be accomplished using only Rhino or GH tools. Specifically, the Bend option in Rhino bends a given line into an arc segment that does not retain the length of the initial line and therefore could not be used in our case. In GH there were no commands that could meet the requirements. To solve the issue, firstly it was necessary to refer to the elastic curve theory, as formed by Euler and Bernoulli. In brief, when a long thin metal rod is compressed, it bends into an elastic curve, which is supposed to optimise the spatial distribution of bending stress. The curvature varies with the sin of distance along the curve, resulting in a curved form that needed to be customarily defined in GH. The complexity of the equations- often differential onesprevented from applying them in the GH model. Instead, various definitions uploaded in internet were explored, as well as the Physics Engine Kangaroo. In parallel the JavaView online application that demonstrates continuous generalized elastic curves, was used for getting familiar with the geometry of these lines. After considering the above possibilities, a new definition was created that borrowed elements from the script “Tapeworm”, found under the blog “The geometry of Bending”. The inserted equation chosen to influence the curvature of the bending was that of a line consisting of two parameters. The result was an elastic curve whose curvature smoothly altered along its length and there were no stressed peak points located at its middle point that could be translated to points were excess wrinkling is observed.
5.20. The theory of elastic curves explains the way a thin metal rod will be bended
5.21. The Tapeworm script (left) and how it was used to simulate the movement
86
Digital Design and Computation
The New Kuip: Enfolding 24/7
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
The Curvature Analysis Rhino command in combination with the Curvature Graph GH command illustrated the differences between a catenary, a parabola, an elastically bended curve and a random interpolate curve, and proved the appropriateness of the chosen geometries.
5.22. The curvature along a catenary line remain constant
5.23. In the parabola, a small intensity in the curvature can be observed
5.24. This elastic curve shows a constant augmentation of its curvature
5.25. In the interpolate curve, the peak is located in its middle part
5.24. Curvature graph for the elastic curve
5.25. Curvature graph for the interpolate curve
Applying the pattern of bending to a series of adjacent curves was useful in determining which curves were clashing with the roof. The problem was solved either by changing the length of the line (by moving the endpoint or changing the tangent angle of the catenary curve with the perpendicular z axis)), by altering the curvature parameters of the equation, or in extreme situations, by introducing a new proposal that curved the strip and passed it over the stands, to be pinned at the end of the 2nd stands level. When the third option was selected, the large cantilevers were minimised and with them the produced bending moments.
Digital Design and Computation
87
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
The New Kuip: Enfolding 24/7
5.26. The rolled-up configuration of the strip is defined by the geometry of an Archimedean Spiral
5.27. The above diagrams show the reconfiguration of the longest beam
5.28. Optimal catenary curve of smaller span
Lastly, the rolled-up configuration of the curve was defined by using the equations of the Archimedean spiral and the total thickness of the strip. The data from this analysis informed the structural designer about the dimensions of the rolling mechanism and help fixing the position of the intermediate horizontal rings.
5.2.4.5. Optimasation of the strip element Once the optimal shape for the main airbeams was defined, the entity of the strip was examined. The evaluation was done in terms of geometry and in correspondence with analytical calculations that assessed the performance of the curves and the values of the resulting internal forces and stresses. The above analysis aimed to define the span of the beams, the shape and size of their section, the thickness of the membrane, the amount of pressure, and the capability of the beams to carry the loads. Moreover, it dealt with the optimisation of the covering fabric and the achievement of a minimum usage of material. Concerning the method used to simulate and evaluate the performance of the inflated textile beams, the research was in the beginning focused on locating available Finite Element Analysis software that addressed inflatable structures. No suitable application, generally accessible on-line was found, however, and as concluded from the related papers published on this topic, most computer-aided analyses were conducted by using regular Finite Element Analysis software and creating analogues that approximated the performance of the airbeams according to the existing equations. Following the above method was considered unnecessary, since the simplicity of the geometry and the uniform distribution of the loads allowed the deduction of numeric values by simply applying the related equations and performing the calculations. The procedure was, even more, significant for realising the factors that influence the performance of the beam, and indicating which parameters should be altered in order to achieve the optimal behavior. 88
Digital Design and Computation
The New Kuip: Enfolding 24/7
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
In consequence, the theory of inflated beams was studied and a collection of important equations were set in an Excel spreadsheet, accompanied by a list of constants mostly related to the material properties, and a list of parameters that were dependent on the chosen geometry. These parameters were selected from the GH file, exported as .csv files and inserted in Excel to perform the calculations. The system was flexible enough to allow changes in the GH file and updates to the Excel spreadsheet (yet, the reloading of data needed to be done manually).
5.29. The parameters that were extracted to Excel
Regarding the choice of material, it was done with the assistance of the cladding expert and in correspondence with the material used on the faรงade and the roof louvers of the stadium. Using the CES database, the properties of the material were inserted in the Excel file, to run the first calculations. However, soon it was noticed that the exact same textile material used at the exterior of the building, consisted of woven glass fibers, could not be used for the deployable strips, as the glass fibers would be subjected to breakage after multiple rolling and unrolling. Even more, the pvc coating that was applied to the exterior textile surfaces was not necessary for the indoor-situated membranes of the strips. The material that was thus chosen was a translucent white textile out of polyester fibers.
Simultaneously to the evaluation performed in combination with the Excel calculations, the formation of the strip was guided by the geometry of the covering membrane. The case of a spatial airbeam frame was compared to the solution where no transversal airbeams were introduced to connect the main beams of the strip and additionally support the covering membrane. Both membranes were formed using the Minimal Surface GH add-on, a script that relaxes a mesh confined by four boundary edges to its optimal position, where the entire membrane material is subjected to tension. The anticlastic shape of the resulting surface is what contributes to the strength of the textile and makes the choice of using this plug-in more appropriate, than generating the surfaces using the standard Edge Surface GH command.
5.30. Comparisson of the minimal surface between two airbeams in the case of existance of transversal beams (up) and without inbetween supports (down)
Digital Design and Computation
89
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
The New Kuip: Enfolding 24/7
Following, the two membranes were compared in terms of curvature and area of used material. The area difference in the case of the longest strip was reaching the value of 385sq.m., clearly indicating the necessity of transverse airbeams. The number of the secondary beams was decided in relation to the distance between the main beams, in order for the subsurfaces to obtain a square shape that would result in an even distribution of stresses along both directions. Then, the curvature of the secondary beams was examined, in combination with the stress plot graphs produced by the Rhino Membrane plug-in. The results showed that an arc formation of the transversal beams, in comparison to a linear configuration, resulted to a better distribution of stresses along the material, whatever the direction of the arc was. Anyhow, the curved surfaces in the optimal solution could allow projections- if the material was hanged at the lower part of the beams instead of being rested on the top- making the usage of the upper stands as 3D cinemas possible.
5.31. Comparisson of the produced surface area in the case of no transversal beams (left) and with inbetween supports (right)
5.32. Analysis of the stresses when the transversal beams are linear (up) and when arcs (down) 90
Digital Design and Computation
The New Kuip: Enfolding 24/7
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
Proceeding to the next step, the way the main beams were divided, to create the starting points for the transversal arcs, was looked at. Starting with airbeams of a catenary curve configuration, with starting tangent parallel to the ground and ending tangent perpendicular (in other words, using the curves that resulted from the Galapagos solution), a division was made with the application of the Divide Length GH command, that introduced beforehand the desirable length of each surface. The point along each curve was then joined and the linear distance between each couple of points was compared to its projection to the xy plane. The big differences in the configuration of each main catenary curve sometimes resulted in a difference between the actual length of the lines and the projected one that augmented at the lower part, near the ground level and in some extreme cases reached the value of 4 meters. Practically this difference would produce serious implications during the unrolled and rolled phase of the strip and cause the material to bag in the second reconfiguration. Deriving from this, the ending tangent of the curves was revised, to minimise this difference. Galapagos was used to locate the suitable curves, whose ending tangent this time had an angle difference with the z axis that did not exceed the 26째 limit. The results from the Galapagos solution were satisfactory as the above differences were extremely minimised.
5.33. Positioning of the transversal airbeams in the beginning (up) and after applying Galapagos (down), and evaluation of their length in comparisson to the length of their projection on the xy plane
Using the above information the parameters for the Excel file were updated. First conclusion from the calculations showed that the strip element should be reduced to the half, which meant that a new organisational grid should be introduced to the already existing one. A value around 8 m. was opted for the distance between the main beams, which doubled the amount of transversal beams, so that the shape of the covering surfaces could remain square.
Digital Design and Computation
91
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
The New Kuip: Enfolding 24/7
5.34. The Excel spreadsheet that received the data from the GH file and performed the calculations. With red color are noted the problematic values
92
Digital Design and Computation
The New Kuip: Enfolding 24/7
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
The new calculations showed an efficient performance of the airbeams in the first configuration, where the catenary formation causes 0 zero bending stresses but indicated a surpassing of the yield strength of the material in the 2nd configuration, that could not be solved although various changes in the parameters and the GH file were applied. The reason was the large amount of bending moment that was produced in the second configuration, were practically more than the half of the curve is acting like a cantilever. By reducing the distance between the base of the elastic curve and the most far away situated point (by relocating, as discussed in the previous section, the ending point of some curves to the end of the 2nd level stands) the bending moment was significantly reduced but not enough to relief the structure. To efficiently solve the problem, the principle of the air-supported structures was used. By raising the internal air pressure in the spaces of the 2nd configuration to a relatively low value, estimated around 500Pa, we could support the strips and retain the slender proportions of the beams and the lightness of the structure that were already working properly in the 1st reconfiguration. 5.34. The strip after the feedback from the Excel calculations
5.35. Aspect of the interior as it resulted after the information provided from the computational analysis
Digital Design and Computation
5.36. The principle of the air-supported structures will be used to relief the structure in its 2nd configuration (air pressure inside the membrane is slightly raised)
93
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
The New Kuip: Enfolding 24/7
5.37. Plan and 3D aspect of the arena as it resulted after the information provided from the computational analysis
94
Digital Design and Computation
The New Kuip: Enfolding 24/7
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
5.38. Interior views of the “New Kuip” during the week days
5.2.5. Materialisation of the design through prototype making Along with the construction of the building in a digital realm, to assess its performance and omit unpleasant implications, the prototype making is an essential tool towards the achievement of the above goals. The model to be constructed, using a 2D CNC machine, is conceived as a means of discovering the way the building will be constructed, rather than a plain representational tool. In particularly, through the production of a quarter portion of the stadium in 1:200 scale, we aim to focus on the fabric façade- which envisages the main concept of enfolding, and study its configuration in 3 dimensional space. The accuracy of the 3D model is crucial for the conduction of meaningful results as well as for reducing the needed time for the prototype making. Using Rhino commands such as Unroll Surface, plug-ins that prepare the files for the CNC machine such as GibbsCAM/Rhino, and grasshopper definitions like the “Waffle Structural System” (for the production of the pieces that form the anticlastic surface of the roof) we plan to experiment and use the core model as much as possible, taking advantage of its accuracy.
Digital Design and Computation
95
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
The New Kuip: Enfolding 24/7
5.3. Conclusion and Reflection The presented research, conducted in the frame of the XXL Workshop 2011, dealt with the manner the digital and computational design can support the development of a complex project in a multidisciplinary environment. The unobstructed digital work flow in combination with an updated and accurate core model and a well organised database proved essential for the communication and coordination of the team members. Inconsistencies to the organisational rules as well as the unfamiliarity of all team members with some of the software to be used, slowed down the process and prevented from fully benefiting from the digital tools and the conveniences of an integrated core model. Considering the simulation of the behavior of the building, it was constantly intended throughout this research to not rely on the existing plug-ins and applications, but rather to get acquainted first with the theories and rules that lie behind the studied phenomena, and then look for solutions on how to apply them in a digital environment. The reason for this approach was based on the fact that most of the current applications are still under development and the given results cannot be guaranteed by their authors. In addition, usually the scripts are delivered to the potential users in the form of a so called â&#x20AC;&#x153;Black Boxâ&#x20AC;?, where no information can be provided for the algorithms that have been used and the approximations that were made. Nevertheless, deepening of knowledge on the addressed matters stressed the fundamental factors that influenced the performance and propelled interpretations that were closer to reality. Especially in the field of reconfigurable architecture, which deals with deployable and pneumatic structures, the use of accurate digital tools that will predict the behavior of these kinetic structures is crucial for realising the possibilities and restrictions and for achieving quality in the final product. Borrowing physic engines and software already tested and used in other scientific fields could set a path towards the development of reliable tools. Then, research topics such as the one presented in this report could be essentially supported and further developed using the input from meaningful computational analyses.
96
Digital Design and Computation
The New Kuip: Enfolding 24/7
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
5.4. References Apedo K.L., Ronel S., Jacquelin E., Bennani A., Massenzio M., 2010, “Nonlinear finite element analysis of inflatable beams made from orthotropic woven fabric”, International Journal of Solids and Structures, April 3, www. elsevier.com/locate/ijsolstr Apedo K.L., Ronel S., Jacquelin E., Massenzio M., Bennani A., 2009, “Theoretical analysis of inflatable beams made from orthotropic fabric”, Thin-Walled Structures www.elsevier.com/locate/tws, pp. 1507-1522 Barnes M., Dickson M., Happold E., 2000, “Widespan roof structures”, Thomas Telford books Beer F.P., Johnston E.R,Jr., DeWolf J.T., Mazurek D.F., 2009, “Mechanics of Materials”, 5th edition, The McGraw Companies Inc., pp. 2-790 Bonet J., Wood R.D., Mahaney J., Heywood P., 1999, “Finite element analysis of air supported membrane structures”, University of Wales, july 8. Borgart A., Graphic Statics of Arches and Shells, Lecture for course “CT5251-09 Structural Design, Special Structures (2010-2011 Q3)”, TU Delft Darwich W., Gilbert M., Tyas A., 2010, “Optimum structure to carry a uniform load between pinned supports”, Struct Multidisc Optim, pp. 33-44 Davids D.G., 2007, ” Finite-element analysis of tubular fabric beams including pressure effects and local fabric wrinkling”, University of Maine, Science Direct, September 27, www.science Direct.com Davids W.G., Hui Zhang; Turner A.W., Peterson M., 2007, “Beam Finite-Element Analysis of Pressurized Fabric Tubes”, JOURNAL OF STRUCTURAL ENGINEERING © ASCE, JULY 2007. Davids W.G., 2007, “Finite-element analysis of tubular fabric beams including pressure effects and local fabric wrinkling”, ScienceDirect, September 27, www.sciencedirect.com Davids W.G., 2009, “ In-Plane Load-Deflection Behavior and Buckling of Pressurized Fabric Arches”, Journal of Structural Encineering, November/1329, www. Ascelibrary.org FIFA, 2007, Football Stadiums, Technical recommendations and requirements, 4th edition. Goss V.G.A., June 2003, “Snap buckling, writhing and loop formation in twisted rods Center for Nonlinear Dynamics”, University College London, pp 1-226 Häuplik-Meusburger S., Sommer B., Aguzzi M., 2009, “Inflatable technologies: Adaptability from dream to reality”, ScienceDirect, www.sciencedirect.com Horn B.K.P., 1983, “The Curve of Least Energy”, Massachusetts Institute of Technology, ACM Transactions on Mathematical Software, Vol. 9, No. 4, December, pp.441-460 Khabazi Z., 2010, “Generative Algorithms”, www.MORPHOGENESISM.com Kilian A., “Linking Hanging Chain Models to Fabrication”, Massachusetts Institute of Technology, Cambridge, MA Digital Design and Computation
97
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
The New Kuip: Enfolding 24/7
Luchsinger R.H. , 2006, “Adaptable Tensairity”, International Conference On Adaptable Building Structures, Eindhoven The Netherlands 03-05 July, Adaptable Tensairity – R. Luchsinger & R. Crettol, Malm Ch.G., Davids W.G., Peterson M.L., Turner A.W., 2008, “Experimental characterization and finite element analysis of inflated fabric beams”, Construction and Building Materials, October 5. www.elsevier.com/locate/ conbuildmat McKinley S. and Levine M., Cubic Spline Interpolation Megson T.H.G., 1996, “Structural and Stress Analysis”, Second Edition, Elsevier Btterworth-Heinemann Module 5, “Cables and Arches”, Version 2 CE IIT, Kharagpur. Payne A. & Issa R., 2007, “Grasshopper Primer” Retik A. & Kumar B., 1995, “Computer-aided integration of multidisciplinary design information”, Univercity of Strathclyde, Glasgow,UK, November 7, TensiNews, 2006, Newsletter No 11, October www.tensinet.com/register_symposium.php The Tubaloon by Snøhetta, Kirketorget, Kongsberg Jazz Festival Pavilion, Norway, http://www.e-architect.co.uk/ norway/kongsberg_jazz_festival_pavilion.htm Thin-Walled Pressure Vessels, http://www.efunda.com/formulae/solid_mechanics/mat_mechanics/pres..., pp.1-2 Veldman S.L., 2005, “Design and Analysis Methodologies for Inflated Beams”, DUP Science , Delft University Press, June 17. Wielgos C., Thomas J. C., Le Van A., 2008, “Mechanics of Inflatable Fabric Beams”, vol.5, no.2, pp.93-98 Wikipedia, “Air-supported structure”, http://en.wikipedia.org/wiki/Air-supported_structure Wikipedia, Concurrent engineering, en.wikipedia.org/wiki/Concurrent_engineering http://thegeometryofbending.blogspot.com/ http://geometrygym.blogspot.com/ http://designexplorer.net/newscreens/cadenarytool/cadenarytool.html http://ocw.mit.edu/ans7870/4/4.463/f04/module/Start.html http://www.ixcube.com http://www.airlight.biz/ http://www.federalfabrics.com/ http://www.wolframalpha.com http://www.javaview.de/demo/PaElasticCurve.html http://digitaltoolbox.info/ http://www.food4rhino.com http://www.kangaroophysics.com http://www.grasshopper3d.com/ http://www.liftarchitects.com/journal/2008/10/27/waffle-structural-system-using-grasshopper-to-output-structu. html
98
Digital Design and Computation
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
Contents 6. Sustainable design 6.1.1 Storm-water management 6.1 Green roofs. 6.1.2 Energy conservation 6.1.3 Urban heat island. 6.2 Light weight materials. 6.2.1 Sustainability & tensile surface structures 6.3 Energy production 6.3.1 Use of PV Flexibles 6.3.2 Integration of PV cells in the roof 6.4 Daylight conditions 6.4.1 Slicing the envelope 6.4.2 Daylight Analysis
98
100 101 101 102 104 105 106 107
The New Kuip: Enfolding 24/7
99 100 102 104 106
Sustainable Design
The New Kuip: Enfolding 24/7
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
6. Sustainable design Sustainable design recognizes the interdependence of the built and natural environments; seeks to harness natural energy from biological processes and eliminate reliance on fossil fuels and toxic materials; and seeks to improve resource efficiency. As designers and builders it is our responsibility to create buildings which protect and potentially enhance the environment, physically and in any other possible way. Buildings change the flow of energy and matter through urban ecosystems, often causing environmentalproblems. These problems can be partially mitigated by altering the buildingsâ&#x20AC;&#x2122; surficial properties. In our proposal for the New Kuip aiming for a sustainable construction is our main goal and itâ&#x20AC;&#x2122;s closely integrated in the design concept. Special care is given to the use of materials throughout the structure, being Lightness the one with a strongest significance and defining the materiality and visual appearance of the architectural object. Moreover, energy production based on renewable sources, in this case the sun, is also an important part of the strategy.
OVERALL STRATEGIES Energy production by integrating flexible PV panels
Light weight tensile surface structure for facade construction Light weight tensile roof structure and cladding
Inner volume of the arena naturally ventilated though ground floor gap and facade openings Green slopes and roofs Reducing urban heat island effects
Sustainable Design
Earth and ground shaped to form stadium bowl which will be lower in the ground, reducing building costs and the movement of vehicles importing and removing materials 0 materials: Using materials from renewable sources (wooden deck), bulk materials or recycled materials as much as possible.
99
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
Green slopes on main acces side
The New Kuip: Enfolding 24/7
6.1 Green roofs. Green roofs are a mayor contribution for healthier cities and are a true and logical choice when considering the design of green buildings in urban areas. It is a layering system that incorporates the use of vegetation-covered roofs, providing social, economic and environmental, especially in urban areas. You can also incorporate new technologies, such as urban agriculture and food production, water recycling systems or installing solar panels.
Green roofs are divided into two categories: 1) extensive green roofs, which are 6 inches or shallower and are frequently designed to satisfy specific engineering and performance goals, and 2) intensive green roofs, which may become quite deep and merge into more familiar on-structure plaza landscapes with promenades, lawn, large perennial plants, and trees. The green-roof benefits investigated o date fall into three main categories: storm-water management, energy conservation, and urban habitat provision.These ecosystem services derive from three main components of the living roof system: vegetation, substrate (growing medium), and membranes. Plants shade the roof surface and transpire water, cooling and transporting water back into the atmosphere. The growing medium is essential for plant growth but also contributes to the retention of storm water. The membranes are responsible for waterproofing the roof and preventing roof penetration by roots.
6.1.1 Storm-water management Urban areas are dominated by hard, nonporous surfaces that contribute to heavy runoff, which can overburden existing storm-water management facilities and cause combined sewage overflow into lakes and rivers. Green roofs are ideal for urban storm-water management because they make use of existing roof space and prevent runoff before it leaves the lot. Green roofs store water during rainfall events, delaying runoff until after peak rainfall and returning precipitation to the land. Green roofs can reduce annual total building runoff by as much as 60% to 79% (Kรถhler et al. 2002), and estimates based on 10% green-roof coverage suggest that they can reduce overall regional runoff by about 2.7% (Mentens et al.2005). In general, total runoff is greater with shallower substrate and steeper slopes.
100
Water run off
Sustainable Design
The New Kuip: Enfolding 24/7
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
6.1.2 Energy conservation Green roofs reducethe amount of heat transferred through the roof,thereby lowering the energy demands of the buildingâ&#x20AC;&#x2122;s cooling system. In the summer, green roofs reduce heat flux through the roof by promoting evapotranspiration, physically shading the roof, and increasing the insulation and thermal mass. Of course, green roofs are not the only technology that can provide summer cooling: enhanced insulation may be able to provide equivalent energy savings and can be combined with green roofs to further advantage. Evaporative roofs are another example of such a technology; water is sprayed on the roof surface to induce evaporative cooling. Rigorous comparisons of multiple roofing systems are necessary to evaluate prospects for optimal building energy savings.
Energy conservation
6.1.3 Urban heat island. In urban environments, vegetation has largely been replaced by dark and impervious surfaces (e.g., asphalt roads and roofs). These conditions contribute to an urban heat island (Oke 1987), wherein urban regions are significantly warmer than surrounding suburban and rural areas, especially at night. This effect can be reduced by increasing albedo (the reflection of incoming radiation away froma surface) or by increasing vegetation cover with sufficient soil moisture for evapotranspiration. A regional simulation model using 50% green-roof coverage distributed evenly throughout Toronto showed temperature reductions as great as 2°C in some areas (Bass et al. 2002). Living roofs also provide aesthetic and psychological benefits for people in urban areas. Even when green roofs are only accessible as visual relief, the benefits may include relaxation and restoration (Hartig et al. 1991), which can improvehuman health. Other uses for green roofs include urban agriculture: food production can provide economic and educational benefits to urban dwellers. Living roofs also reduce sound pollution by absorbing sound waves outside buildings and preventing inward transmission (Dunnett and Kingsbury 2004).
Green roof layers
Sustainable Design
California A. of Science roof _ Renzo Piano
101
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
The New Kuip: Enfolding 24/7
6.2 Light weight materials. As far as materials used for the building constructiuon is concerned, there is a direct relationship between the weight of the different elements of the building and environmental impact of it. The following graph is a representaiton of the burden caused from the different parts, being hull and faรงade the ones with higer repercussion. Toguether they provide for thwe major part (80%) of the material bound environmental impact. Furthermore, 25% of all road transport is caused by the building industry
Environmental burden of a standard building, source: NIBE
With sustainable approach on the design for the New Kuip, lightness in the use of materials becomes a key principle guiding our design and architectural concept. During the design process we have managed to incorporate this idea in almost every level of the stadium, since the outer envelope formed by the roof and the facade, to the mechanism used in the reconfiguration of the interior space. Wrapping the multifunctional program with tensile material that is light weight has a considerable impact in the size of structure, reducing the dimensions and amount of material used in both the main structure and the building foundations.
Longitudinal seciton: Building envelope
Transversal seciton: Building envelope
6.2.1 Sustainability & tensile surface structures When it comes to tensile structures three major components in sustainable design: Design, Materials and Construction. Design Benefits of tensile structures include: natural lighting during the day which reduces the need for artificial lighting, UV protection which reduces the risk of skin cancer, water collection which is then used 102
Light weight envelope in roof and facade Sustainable Design
The New Kuip: Enfolding 24/7
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
for irrigating plants and other services, solar shading which reduces energy on a buildingâ&#x20AC;&#x2122;s mechanical system whic is rarely considered but is a growing trend of incorporating a fabric structure as an educational tool that teaches people about UV protection, recyclability, etc. Materials Designers look to the three basic components: the structural members, the membrane and the perimeter tensioning system. The structural system is primarily made of steel but aluminum and wood are being considered more often.
Roof cable net structure
Light structure: Facade supporting rings
These materials all have many recyclable attributes and can be specified to be manufactured locally to the site. Depending on the membrane chosen, some materials have short life spans while others are made of recyclable materials. You can also find materials with 20 to 30 year life spans and are more environmentally friendly than ever before. Construction Most tensioned fabric structures are designed, engineered and fabricated by â&#x20AC;&#x153;form findingâ&#x20AC;? which means they are designed to be not only structurally efficient but manufactured and installed with little to no waste and energy. Architectural fabric is considered one of the lightest building materials and can create the largest building envelope. The result can have significant impact from manufacture to site due to the lighter weight of the membrane, structural steel and components, the entire structural system can be shipped to site with fewer trucks and erected with less equipment. Properly designed tensile structures may have little impact on the ground with smaller concrete foundations for compression loads and the use of utility cable anchor technology for tension loads. These efforts can have significant saving when the site is being used for temporary structures or deployable structures where reuse is inevitable. The reconfiguration of the bowl interior is also addressed by using light weight structures more specifically a deployable and pneumatic structures formed by a textile membrane integrated to inflatable beams. Implementation of this system represented a minor extra effort in the existing supporting ring for the roof. There are several environmetal benefits: the whole inflatable structure is supplied in roll form which makes it easier to be transported; Many inflatable structures have a long life expectancy but when they do eventually reach the end of their service they can also be recycled; hey require no extra foundation when deployed, only minimum anchoring points; Finally the The low power requirement for these structures means that it is entirely possible to use solar power to provide the electricity required for their operation.
Sustainable Design
Reconfigurable tensile structure
Inflatable beams system
103
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
The New Kuip: Enfolding 24/7
3.1 Interior view of the roof.Translucency created from the combination of PV Flexibles and tensile membrane.
6.3 Energy production 6.3.1 Use of PV Flexibles The new Stadium introduces a big volume in an open part of the city that could constantly face to the sun and therefore solar energy would be a very suitable solution for energy production(3.4). The application of PV panels on the envelope of the Stadium would contribute with big sums of energy either for internal use of the Stadium or for the Energy Grid of the city of Rotterdam. Conventional PV panels alternate the dynamic shape of the Stadium and would not be easily intergraded in the textile surfaces of the cladding. On the other hand the integration of thin-film solar cells (3.2) to membrane materials has come to a more mature phase and is more suitable for our case. The PV Flexibles can provide a clean energy production , integrated shading and a unique architecture at the same time.PV Flexibles are suited for mechanically prestressed tensile membrane structures and with a pariculary developed joining technology they are assembled on large -scale membrane modules(3.3).
104
3.2
3.3
3.4
Sustainable Design
The New Kuip: Enfolding 24/7
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
3.9
3.5 3D Section ( West-East) of the Stadium. 78% 22%
6.3.2 Integration of PV cells in the roof In order not to disturb the image of the Stadium PV cells were integrated only in the roof (3.5). The creation of the enclosed roof created the opportunity to make use of the new big surface-about 30% bigger than any conventional Stadium roof(3.6)- that was created in order to produce solar energy. The particular shape of the roof is directed by the bowl of seats it covers and the architectural need for visual reduce of the Stadium’s volume (3.4).The roof is divided in two parts, only one of which is facing South and therefore was suitable for PV Panels. The manipulation of the textile membranes created zones that looked to the South and zones that looked to the North along the entire surface of the roof( see cladding). The “South” zones would host the PV Flexibles and the “North” zones would act as openings for natural light(3.8).Self-shading during peak times was anavoidable because of the paricular shape of the roof.Nevertheless the success was to make use of the part of the roof that looks to the North and this was achieved( 3.7). The total area that could be suitable for PV Flexibles in the roof is approximately 35.873sqm. Such a surface with PV Flexibles is able to produce up to 700.000 KWH/year (3.9). Sustainable Design
100%
3.6
3.7
3.8 105
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
The New Kuip: Enfolding 24/7
4.1 3D section ( North-South) of the Stadium
1%
6.4 Daylight conditions
20%
6.4.1 Slicing the envelope The full cover of the roof with PV Panels would reduce significantly the levels of daylight inside the field. Day light was of great importance for the interior of the Stadium(4.4) not only because of the creation of a pleasant environment that had the most desirable qualities of an open air space but also because of the reduce of the artificially light during the daytime( the biggest disadvantage of the Stadium when compared with conventional Stadiums). 20% of the roof is covered with ETFE foil facing to the North(4.2). The rest 80% is covered with coated fiberglass membrane with PV cells that create a translucent effect. The light coming from the roof cannot alone please the demands for daylight. The need for more sources of light penetration in the interior led to the exploit of the facade(4.5). The facade cladding is organized in translucent and transparent strips ( very similar to the way the roof is divided) so it is possible to influence the daylight levels but lighting in the field area can be achieved through specific areas. The big gaps between the rows of seats( East-North, East-South, West-North, West-South) are the links of the facade with the big interior space(4.1). Through these areas the facade succeeds to increase daylight in the field area. 106
80% 99% 4.2
4.3
4.4
4.5
Sustainable Design
The New Kuip: Enfolding 24/7
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
4.6 Model used for the daylight simulations:Presenattion of opaque( and translucent) zones in the facade and the roof.
6.4.2 Daylight Analysis
4.7
4.8
In the beginning a daylight analysis and incident radiation analysis was made only for the roof so that the cladding would be divided in zones that would face the South and not shade each other and zones that would face the North( 4.8). The amount of daylight was significally increased by creating big transparent zones in the facade(4.9). Their size and position became also an object of research( 4.6). The structural restrictions of the facade and the reduction of overheating( in the South part) created constraints that limited the spreading of the daylight inlets. Nevertheless big zones out of ETFE were created in the highest parts of the facade so that even gap between the last seat and the roof would be used to bring natural light in the big interior space( 4.10).
4.9
4.10
Sustainable Design
107
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
The New Kuip: Enfolding 24/7
Adaptability Design Contents 7.1 Introduction
109
7.2 Reconfigurability of the peripheral spaces
109
7.2.1 Switching functions
109
7.2.2 Business Boxes and Hotel Block
110
7.3 Reconfiguration in field area
111
7.3.1 Sliding Field
111
7.3.2 Inflatable beam structure and textile partitions
114
108
Adaptability Design
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3)
The New Kuip: Enfolding 24/7
Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
7.1 Introduction The â&#x20AC;&#x153;New Kuipâ&#x20AC;? was conceived not as a football stadium with additional functions, but rather as a multifunctional building with a football field in its core. Driving force behind this decision was the fact that such a building complex would not host a football match more than 3-4 times per month. It was necessary therefore to plan the intense use of this space during the no-match days, to ensure return on investment in a reasonable time frame, and to enrich the neighbourhood with recreational, educational and cultural resources. To achieve this goal, instead of adding new spaces, we opted for the adaptability of the peripheral functions and the arena, in a cost and energy efficient way.
7.2 Reconfigurability of the peripheral spaces 7.2.1 Switching functions Adaptability in the area around the bowl structure takes place in terms of switch of functions that do not require major reconfiguration. Functions that match with the existing volumes are introduced in the unused- during the no-match days- spaces, so that for example, The VIP boxes can convert to Hotel rooms, the FIFA meeting rooms to school classrooms, and the press and media rooms to supporting areas of the conference centre, quickly and without requiring excess effort. The selection of functions to be added is also taking into account the operation period of each space, to avoid overlapping in the weekly timetable.
7.1. Chart showing the percentage of space used during a match and a no-match day and the spaces that are reconfigured Adaptability Design
109
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
The New Kuip: Enfolding 24/7
7.2.2 Business Boxes and Hotel Block On the western tip of the Isle of Brienenoord Rotterdam there are plans for a conference hotel with a capacity of 180 rooms and 55 apartments. These plans are part of the development vision presented in 1999 with projections to the year 2030. By including this program into the New Kuip the natural environment from the island remains untouched without suffering any ecological impact. A total number of 120 rooms, 42 of which also function as business boxes during match games, are proposed on the north side of the stadium, overlooking to the Mass River and the Island.
7.2. Hotel proposal on Brienenoord island, 1999
Private boxes are quite similar in size to hotel bedrooms. By providing moveable walls between boxes or adjustable cabinets, these spaces can easily be reconfigured for such dual use from the outset. The Skydome in Toronto was a pioneering stadium in this context, and the more recent Galpharm stadium in Huddersfield is an example of a stadium incorporating private boxes that can be converted into hotel rooms. The use of movable walls between boxes, would also allow the area to be opened up into a larger dining room at times when the boxes are not in use.
7.3. Plan and section of the VIP boxes / Hotel Rooms 110
Adaptability Design
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3)
The New Kuip: Enfolding 24/7
Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
7.3 Reconfiguration in field area
One of the main principles of the design was to maximize the use of the field area for various functions on a no-match day, which was achieved by sliding the field outside and providing temporary inflatable beam and fabric partition system.
7.3.1 Sliding Field 7.4. Concept Sketch
Considering the programmatic implications, it was more logical to have a sliding field which is always placed outside of the building and slided in only before the games, which was only 2-3 times a month. The stadium has a grass playing field with standardized size of 75m x 115m. The field has integrated drainage system that carries away water during and after heavy rain fall. There are also special surface heaters so that the field can played on and used even in winter. So that the grass can be maintained free of snow and ice and relatively dry.
7.5. St. Petersburg Stadium, Russia
7.6. View from East side
Adaptability Design
111
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
It is logical to move the field outside towards its shorter side than a longer side, for this purpose 80 m of columnless space is provided towards the eastern side of the building. What makes it challenging is the live and dead load coming from top as there are five floors of functions above that. The solution proposed here is a double floor truss system placed 13m c/c, so that the whole two floors will act as a huge 3d truss. The trusses are also given additional hydraulic supports which are removed when the field is slided out. When the field is slided out the gaps in between will be covered with wooded planks to get an hard floor.
The New Kuip: Enfolding 24/7
7.7. The “New Kuip”. Columnless space using truss system
The level of the playing field is 4m below ground level, which when slided out is also 4m below ground level. Which allows us to have a sloped area around the grass field outside the stadium, further which can be used for the practice matches or any other smaller played outside which has limited spectators and in good weather conditions. Entire playing field including the substrate lies on a preferably trough shaped support frame that is mainly formed of concrete and/or steel members and the support frame is horizontally slidable via slide pads on stationary slide tracks. The slide tracks extend from fully covered stadium to an adjacent outside space. Design and detailing of sliding pitch is referred from ‘Horizontally slidable sports field patent’ (US 6,286,264 B1) by Raimund Peuler. According to the patent the number of slide pads is determined by the weight of the support structure and the playing field on it, which in our case with the grass field of the size 75m x 100m can be over 100,000 kN. With such great weights preferably slide pads with a track engaging surface of polytetrafloethyline (PTFE) and slide tracks of steel with special coating are used. Combination of PTFE and austenitic steel are infact already known in bridge construction as equalizing joints, but there the slide paths are relatively small. Surprisingly it has been determined that slide pads with PTFE plates that slide on a coated slide track provided with a slide film can be used for sliding great weights over great distances.
7.8. Examples of sliding pitches 112
Adaptability Design
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3)
The New Kuip: Enfolding 24/7
Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
For sliding lubricants, such as silicon oil or lithium soap can be used, preferably however a thin water soluble oil and/or grease film is used on the slide tracks. The slide pads, that is PTFE plates, have on their undersides lubricant pockets and/ or grease distributing grooves which increase the slidability while minimizing friction. With this combination of PTFE and lubricant or oil and coated steel sliding frictions of from 0.018 to 0.025 can be obtained. In order to overcome static friction the pushing force is such that a sliding up to a friction of 0.07 can be exerted for breaking free. In order to protect the parts underneath the support plates, in particular from dust and dirt, dirt scrappers are installed on the edges, turned toward the slide tracks. Thus during advance it is possible to preclean the slide tracks so that dirt on them does not mix with the grease and/or oil. Preferably in order to horizontally move the support frame there is a plurality of slide actuators that can each grab on the upper flange of a respective profile set in the ground parallel to the slide tracks at successive locations, preferably via clamping jaws, and that can exert horizontally directed push or pull forces laterally on the support frame when clamped by means of hydraulically actuated cylinders. As a result the required enormous sliding force necessary to move support frame with its load can be distributed over several slide actuators. The slide actuators are connected with a travel detecting device and stroke synchronizer. Thus a uniform sliding and uniform advance force is applied to the attachment points.
21 - Field including substrate 22 - Trough shaped support frame 23 - slide tracks 24 - outside area for the field 25 - Horizontal force actuators 26,27,28 - concrete anchor plates 29 - Support plate 30 - elastomeric layer 31 - elastomeric layer with embedded steel plates 32 - PTFE plates 33 - connection screws 34 - protective housing 35 - scrapers 36 - slide track 37 - oil / grease distributing grooves 38 - oil distributing strips 39 - recessed screws
Adaptability Design
The slide tracks themselves are formed of wide steel bars or sheet metal and are welded on their undersides to Nelsonhead bolts and/or are adjustable with respect to height by means of threaded sleeves and screws and/or are set in a thin bed of mortar. With these mountings which can be used together or separately, it is possible to ideally position and anchor the slide tracks in the existing horizontal surface. The slide tracks can be formed of several pieces with between adjacent pieces at their ends a long life elastic expansion joint.
113
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
The New Kuip: Enfolding 24/7
7.3.2 Inflatable beam structure and textile partitions Dividing the arena into smaller cells was considered important in order to ensure the intense usage of the bowl area throughout the week days. A series of functions were introduced not only to complimentary work with the functions situated in the periphery (hotel, school, conference centre) but more importantly to attract visitors into the interior of the stadium and transform this vast enclosed space into a vivid public space. In addition, reconfiguration needed to be addressed in the case where a smaller match would take place, leaving almost half of the seats empty. This disadvantageous situation, considering the atmosphere of the game could be avoided if part or the whole of the 2nd level stands were to be covered, and a more intimate space were to be created. To achieve the above reconfigurations we propose a system of inflatable translucent woven beams and a covering translucent textile surface, both out of polyester fibres, that extends the concept of “Enfolding 24/7” to the interior of the arena. This lightweight system consists of a continuous series of textile strips of 8m width, with airbeams along their boundaries, which are stored around a secondary ring structure situated above the end of the 2nd level stands.
7.9. Plan showing a reconfiguration option during the week days
In the situation where a big match is taking place, the strips are rolled-up and do not disturb the spectators. During the week, however, they are pulled down and pinned on the ground floor, to form an amphitheatre, a conference hall, a sports hall, and temporary spaces that might be necessary, or pinned at the start of the 2nd level stands to create 3D cinema spaces where 3D matches can be projected on the membrane surfaces. For the case where a small match is on, all the strips can end at the start of the 2nd level stands, to create the intimate space we opt for. The positioning of the strips is aided by cable-suspended crane hooks that are supported by the ring, and are digitally manoeuvred in the arena. This cranes function according to the principle of the “Spycam” camera system that is used in stadiums, and reassure that the strip element will be unfolded in the correct place, without getting damaged by the seats. Once the airbeams are pinned and inflated, the hooks facilitate the joining between two adjacent strips by pulling down their in-between translucent plastic zipper. Lastly, the hooks can work contrariwise, to help rolling up the system. The assembly and disassembly of the system is not time-consuming and therefore enables the switch from the no-match weekly condition to the match condition, during the weekends. 114
Adaptability Design
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3)
The New Kuip: Enfolding 24/7
Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
7.10. The strip element and its reconfiguration stages. During a big match, the strip is rolledup and stored under a secondary ring above the 2nd level stands. When smaller spaces need to be generated during the week, it can be pulled down, placed in the correct position, pinned on the ground and then inflated until it reaches its optimal shape, that of a catenary curve. In case of a smaller match, it can be reconfigured to cover the upper level of stands.
Adaptability Design
115
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3) Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
The New Kuip: Enfolding 24/7
7.11. Aspect of the interior during the week, as it is formed by the successive textile strips that are rolled down from the ring
Considering the enclosed spaces (music hall, conference hall, 3D cinemas), their access is achieved through the circulation areas behind the bowl and the entrancing slots to the stands. Their positioning is such so they can benefit from the existing supporting functions around the bowl (foyer, restaurants, toilets) or to support the functionality of those spaces (for example, the conference centre). Part of the ventilation of the enclosed areas is accomplished through the openings situated in the facade (especially at the part over the 2nd level stands), and the gap between the 1st and 2nd level stands that forms the main entrance level to the arena. These light partitions do not permit all combinations of functions to occur simultaneously, nor do they guarantee an excellent level of performance in terms of acoustics. This is not considered as a disadvantage because this enfolding of space aims to create intimate smaller space bubbles that encourage various activities, as if they were loose tents under a larger roof. The simplicity, lightness, and flexibility of the proposed system could not have been succeeded otherwise.
7.12. Interior views 116
Adaptability Design
TU Delft _ Faculty of Architecture _ AR0025 _ XXL Workshop (2010-2011 Q3)
The New Kuip: Enfolding 24/7
Team 5: Bristogianni Telesilla _ Calle Eduardo _ Sakkas Panos _ Shitole Harshad
7.12. Video simulating the reconfiguration of the textile strip elements (Click on the video to view)
More information on the development procedure of the interior partitions and technical data can be found on section 5.2.4 of the â&#x20AC;&#x153;Digital Design and Computationâ&#x20AC;? chapter.
Adaptability Design
117