Escalonado Es. Especiales

7/25/2019 Escalonado Es. Especiales

1/29

UNIVERSIDAD NACIONAL DE INGENIERIA

ACULTAD DE ARQUITECTURA URBANISMO Y ARTES

PROYECTO

ESCALONADO

INTEGRANTES

-Ibarra Huaranga Guillr!ina

-Fl"r# Si$un%# Lui#

-Ya!una&u' Ta(ia Ir)ingG5

-

CTEDRA

Ing, M"#"#"

Ing, Pa"ra.

Car!n


2/29

/NDICE

OB0ETIVOS

ESTRUCTURAS ESPECIALESPr"1%" #al"na2" *

UNIVERSIDAD NACIONAL DE INGENIER/A Faul%a2 2 Ar&ui%%ura. Urbani#!" 1

I, In%r"2ui3n 4444444 56II, Ob7%i)"# 4444444 58III, D#ri(i3n 2l 2i9i" #%u2ia2" 4444444 6:IV, Fur;a #


3/29

DESCRIPCION DEL EDIFICIO

ESTRUCTURAS ESPECIALESPr"1%" #al"na2" 6


P"nr n (r%ia #"br un a#" ral l"# ri%ri"# 1 "n"i!in%"# "b%ni2"#n la# la## %3ria#,

A9an;ar 1 "!(l!n%ar l a(rn2i;a7 "b%ni2",

C"n%ra#%ar 1 r"n"r la# 2i$rnia# @i#%n%# n%r un 7!(l" %3ri" 1

un (r"1%" ral ral,

Ti(" 2l 2i9i" Pr%n a la la#i9ai3n 2 la )i)in2a 2 %i("!ul%i$a!iliar "n#%rui2" ("r 2(ar%a!n%"#,

Ubiai3n g"gr9a La "bra # nun%ra ubia2a n la A), Srgi"

Brnal# :8 n l 2i#%ri%" 2 Sur&uill". Li!a,


4/29



Di!n#i"n# La "bra "n#i#% n l 2i9i" !ul%i$a!iliar 2 65 (i#"#

#in #3%an"# n un ra "n#%rui2a 2 : !6, Su $"r!a # irrgular Si#%!a #%ru%ural Su #i#%!a #%ru%ural # 2ual =(laa#. "lu!na# 1

)iga#> "n l u#" 2 "nr%" (r!;la2",


5/29

ESTRUCTURAS ESPECIALESPr"1%" #al"na2" :



6/29

ESTRUCTURAS ESPECIALESPr"1%" #al"na2" +



7/29

DISTRIBUCION DE LA FUERA SISMICA EN ALTURA

FUERA SISMICA POR PISO

ESTRUCTURAS ESPECIALESPr"1%" #al"na2"


Si l (ri"2" $un2a!n%al T. # !a1"r &u 5,una (ar% 2 la $ur;a "r%an%V. 2n"!ina2a Fa. 2br a(liar# "!" $ur;a "nn%ra2a n la (ar%#u(ri"r 2 la #%ru%ura,

Hallan2" la $ur;a a2ii"nal Fa

En nu#%r" a#"

T hn

CT 59

45 *,8*# J 5,#

Fa 5,5@T@V K 5,*+V

Fa 5,5@*,8*@*8+::*,:88

Fa = 124 206.8247 302173.7157

Ya &u la $ur;a a2ii"nal Fa n" #u(ra l 5,*+V 2 la $ur;a #


8/29

LONGITUD DE PLACAS DE CORTE S/SMICO



13 8,55 655+,+

6+:*,555

5,5+6 ,*58

8:,+*6

12 88,6+ 655+,+

66+*86,+

5,5+688: :,8+*+

,8

11 85,+5 655+,+

6+56:,+5

5,5:55+ +,5+*8

+,588

10 6,+ 655+,

+

68+6:5,*

6+

5,5:+6+* ++,*5

*5*8,5+8

5 6,55 655+,+

6*88+:8,555

5,5:568 +5,8:8

*5:,5+66:

8 68,6+ 655+,+

*55,+

5,58+: :+,56*58+

**5,586*

7 65,+5 655+,+

*66:*6,+5

5,5866 8,88

**:,::

6 *,+ 655+,+

*:++:,6+

5,568 8:,8*6

**8,*:*88

5 *+,55 655+,+

*68556,+55

5,5685 6,5:+

*6*6,**6+

4 *6,6+ 655+,+

*55+6:*,8+

5,5*6* 68,6***

*68+,56:8

3 ,+5 655+,+

++6,6+5

5,5*:+6 *,8+6*

*6+:,858:+

2 ,+ 655+,+

++85,*6+

5,5*56: *8,55+::

*6,8:558

1 :,55 655+,+

866:66,555

5,556 ,:+6 *6+,**+

PiHi +6*86*,+

Para alular la# 2i!n#i"n# !

-R#i#%nia 2 la (laa *+ g!6 =gran r#i#%nia>

-S un%a "n la $ur;a # (r)ia!n% alula2a

Lug". !(la!"# la #iguin% $3r!ula

V= H

L

D3n2

V R#i#%nia 2 (laa

H Fur;a #


9/29



L L"ngi%u2 2 (laa,

E E#(#"r 2 (laa

PARA EL PRIMER PISO

15Kg/cm2=1354491.4383

L 30cm .

L= 1354491.4383

15Kg /cm2 30cm.

L=3009.98097 cm.L=31m .

La# (laa# a "n#i2rar n" #iun%an "n !


10/29




11/29

CENTRO DE RIGIDEESTRUCTURAS ESPECIALES

Pr"1%" #al"na2" *5


Para l lul" 2l n%r" 2 rigi2; # 2%%an n la (lan%a %


12/29

+

ESTRUCTURAS ESPECIALESPr"1%" #al"na2" **


al%ura 2l l!n%"A ra =b@>2 2i#%ania 2l 7 2 #i!%r


13/29

ESTRUCTURAS ESPECIALESPr"1%" #al"na2" *6


C" A b h3

12

A d2 I KB

Ci

C4 **5 6+ 6+5 *6,+ *:866,*

:6,+ +6*,

855 *5,6666

C8 :5 :5 *55 65 6*8888,888

:5555 +8888,888

855 6::,:::::

A11 665 6+ ++55 *6,+ 6:+,888 +8+ **:+88,88 855 8*,:::::A12 * 655 8:55 **6,+ **888888

,8:858*6+

5+:8:+8

,8855 **6*+,6

A13 665 6+ ++55 66+ 6:+,8

886:8+

55668+

855 65,

*C17 :5 :5 *55 *6,+ 6*8888,8

886+5555 :8888,8

88855 *+::,::::

:C22 **5 6+ 6+5 5 *:866,*

5 *:866,*

855 :,:85++

C26 :5 :5 *55 65 6*8888,8

88:5555 +8888,8

88855 6::,::::

:A21 665 6+ ++55 66+ 6:+,8

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55668+

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*A22 * 655 8:55 **6,+ **888888

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5+:8:+8

,8855 **6*+,6

A23 665 6+ ++55 5 6:+,8

885 6:+,8

88855 +:,***

*C35 :5 :5 *55 65 6*8888,8

88:5555 +8888,8

88855 6::,::::

:C40 **5 6+ 6+5 *6,+ *:866,*

:6,+ +6*,

855 *5,666

6

C" A

bh3

12 A d

2

I KCCi

C3 :5 :5 *55 65 6*8888,888 :5555 +8888,888 855 6::,:::::C7 6+ *+5 88 ++5 *+5 68+55 855 C12 :5 :5 *55 65 6*8888,88

8:5555 +8888,88

8855 6::,:::::

C16 6+ *+5 88 ++5 *+5 68+55 855 C21 :5 :5 *55 5 6*8888,88

85 6*8888,88

8855 **,******

C25 6+ *+5 88 ++5 *+5 68+55 855 C30 :5 :5 *55 65 6*8888,88

8:5555 +8888,88

8855 6::,:::::

C34 6+ *+5 88 ++5 *+5 68+55 855 C3 :5 :5 *55 65 6*8888,88

8:5555 +8888,88

8855 6::,:::::

9 44032.888

C" A bh3

12

A d2 I KD

Ci

C2 6+ **5 6+5 ++ 66*,

8*+5 **5*,

855 86,6666

C6 :5 :5 *55 65 6*8888,888

:5555 +8888,888

855 6::,:::::

C11 **5 6+ 6+5 5 *:866,*

5 *:866,*

855 :,:85++

C15 :5 :5 *55 65 6*8888,888

:5555 +8888,888

855 6::,:::::

C20 **5 6+ 6+5 5 *:866,*

5 *:866,*

855 :,:85++

E E C

E E D

D 7421.1

A 061.11111

: 22373.24


14/29

;

ESTRUCTURAS ESPECIALESPr"1%" #al"na2" *8


C24 :5 :5 *55 65 6*8888,888

:5555 +8888,888

855 6::,:::::

C2 **5 6+ 6+5 *6,+ *:866,*

:6,+ +6*,

855 *5,6666

C33 :5 :5 *55 65 6*8888,888

:5555 +8888,888

855 6::,:::::

C38 **5 6+ 6+5 ++ *:866,*

8*+5 :*,*

855 665,+6

C" A

bh3

12 A d

2

I KECi

C1 **5 6+ 6+5 *6,+ *:866,*

:6,+ +6*,

855 *5,6666

C5 6+ **5 6+5 ++ 66*,

8*+5 **5*,

855 86,6666

C10 **5 6+ 6+5 5 *:866,*

5 *:866,*

855 :,:85++

C14 6+ **5 6+5 ++ 66*,

8*+5 **5*,

855 86,6666

C1 **5 6+ 6+5 5 *:866,*

5 *:866,*

855 :,:85++

C23 6+ **5 6+5 ++ 66*,

8*+5 **5*,

855 86,6666

C28 **5 6+ 6+5 5 *:866,*

5 *:866,*

855 :,:85++

C32 6+ **5 6+5 ++ 66*,

8*+5 **5*,

855 86,6666

C37 **5 6+ 6+5 *6,+ *:866,*

:6,+ +6*,

855 *5,6666

DIRECCIN


15/29

ESTRUCTURAS ESPECIALESPr"1%" #al"na2" *:


1 68386.1111

2 41723.583

E E :

C" A

bh3

12 A d

2

I K2Ci

C 6+**

5 6+5 ++66*,

8*+5**5*

,85

586,66

66

C :5 :5 *55 *6,+ 6*8888,888 6+5555 :8888,888 855 *+::,:::::

C 6+ *+5 5 +8,+ 5 +8,+85

56,:+8

88

C :5 :5 *55 ,+6*8888,8

88 5555858888,8

8885

5*5**,***

**

C+**

5 6+ 6+5*6,

+*:866,*

:6,

++6*,

85

5*5,66

66

C" A

b h3

12 A d

2

I K3Ci

C*8 :5 :5 *55 +6*8888,8

88 5555556*8888,

8885

585**,**

**

A** 6+665 ++55 **5

66*8888,8 ++5555

88888,8

855

6+,

A*665

5 * 8:55 ,+*8,88

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5*5*,

A*8 6+665 ++55 **5

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855

6+,

C*6 :5 :5 *55 ,+6*8888,8

88 5555858888,8

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5*5**,***

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C** 6+**5 6+5

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+88,+:

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6+66*,*6+

C*5 6+**5 6+5 ++

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86,6666

3 686562.06


16/29

ESTRUCTURAS ESPECIALESPr"1%" #al"na2" *+


5 0458.1611

6 41723.583

C" A

b h3

12 A d

2

I K4Ci

C* 6+**5 6+5 ++

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86,6666

C* :5 :5 *55 *6,+6*8888,8

88 6+5555:8888,8

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5*+::,:::

::

C* 6+ *+5 5 +8,+ 5 +8,+85

56,:+8

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C*+ :5 :5 *55 ,+6*8888,8

88 5555858888,8

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5*5**,***

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I K

5

Ci

C66 6+**5 6+5 :,+

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65:,+

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8*6,+

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86,6666

C" A

b h3

12 A d

2

I K6Ci

C6 6+**5 6+5 ++

66*, 8*+5

**5*,

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86,6666

C6 :5 :5 *55 *6,+6*8888,8

88 6+5555:8888,8

8885

5*+::,:::

::

C6+ 6+ *+5 5 +8,+ 5 +8,+85

56,:+8

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C6: :5 :5 *55 ,+6*8888,8

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5*5**,***

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5 6+ 6+5 *6,+*:866,*

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4 41723.583


17/29



7 685744.073

8 41723.583

C" A

b h3

12 A d

2

I K7Ci

C8* :5 :5 *55 +6*8888,8

88 5555556*8888,

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A6* 6+ 665 ++55 **566*8888

,8 ++555588888

,885

56+,

A66655 * 8:55 5

*8,8888 5

*8,8888

855

66,:::::

A68 6+ 665 ++55 **566*8888

,8 ++555588888

,885

56+,

C85 :5 :5 *55 ,+6*8888,8

88 5555858888,8

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5*5**,***

**

C6 6+ **5 6+5:*,

+66*,

:8:6*,

+88,

+:85

56+66*,*6

+

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8*+5**5*

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12 A d

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5 5:+,*** 5,:+***6 :*68,+8 :*,68+87 +::,58 +,::588 :*68,+8 :*,68+8 +:86,* +,:86*


18/29



C"n l"# 2a%"# "b%ni2"#. (u#%"# n la l%i!a %abla r#u!n. alula!"# ln%r" 2 rigi2;,

EE,

+ ; + ; + . < ; .

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+

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*D ,:6**5+

+ 8,*5+5

8E *+8,*:56+ 5 51 ,8**** 5 52 :*,68+8 ,++ 68,6*6

3 ,+65 *8,*+

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4 :*,68+8 *,+

6:,5:*

5 5,:+*** 6,6

68,*:+5

6 :*,68+8 86,:

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7 +,::58 8,::

65:+,:6

8 :*,68+8 : **,8565

+,:86* +6,+

8,6:*

6+6+,8+5:6

*8,:55 6*5,*:5

:5+,8*


19/29

FUERAS TROSIONALES POR E0E



XR= (ky x ) (ky)

=46805.3169

1773.48007=26.3917919

YR= (kx y )

(k

x )

= 28180.1408

2525.395042=11. 158706


20/29

E?CENTRICIDAD

FUERAS TORSIONALES POR E0E



S 29n "!" la 2i#%ania n%r l Cn%r" 2 Rigi2; 1 l Cn%r" 2 Ma#a,La alula!"# #gn la 2iri3n 2 a2a 7,

E@n%rii2a2 =Cn%r" 2 Rigi2; Cn%r" 2 Gra)2a2>

E@n%rii2a2 =?r - ?g Yr - Yg>

@ ?r - ?g 6,8 6,6 5,*56 !

1 Yr - Yg **,* ,+ :,656 !

E@n%rii2a2 (ex )2+(ey)2 (0.102)

2+(4.202)2 :,6 !

E# n#ari" "!(r"bar &u la @n%rii2a2 #a !n"r al 65 2 lal"ngi%u2 !n"r 2l 2i9i"

65 =La2" !n"r>

5,6 =*:,+>

6,

S "b#r)a &u la @n%rii2a2 @2 l )al"r (r!i%i2",

EE " " "." "."2 T F"A ,5*****

*8,8 6,5* ,++ +:,5

::6,5686:*+

: 668,86:

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+:,5:

88566,6:8

C ::,586

6, **, 865, +:,5:

*5*,**8

D ,:6**5

,*6 :,5+6+ 6:,6

+:,5:

+,5:*+8

E *+8,*:56+

**,*+ *5,+* *58,6+:

+:,5:

6:::6,565

1 ,8****

6,8 *5:,5: :6,68 +:,5:

6+88,668

2 :*,68+8

*,: 6,58888 *:68,**

+:,5:

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8+6,6:58+


21/29

RIGIDE TORCIONAL



7 +,::58

*8,5+ :,5*+ **8,8 +:,5:

*65,:88

8 :*,68+8

*,+ *,+* ***5,++*

+:,5:

**8+,:

+,:86*

6,* *+,+* +*:5,

+:,5:

66,85:

S>*AT?RI

A

8:68,++

Fi=T kii

ki d i2

EE " " "."2A ,5****** 8,8 ,++: 668,86: *,58 68,*88C ::,586 6, 865,D ,:6**5 ,*6 6:,6E *+8,*:56+ **,*+ *58,6+:1 ,8**** 6,8 :6,682 :*,68+8 *,: *:68,**

3 ,+65 *8,6: *658+6,84 :*,68+8 ,: *8,+685 5,:+*** 5,* 5,5:+**6 :*,68+8 ,:+ *8+,657 +,::58 *8,5+ **8,88 :*,68+8 *,+ ***5,++* +,:86* 6,* +*:5,

S>*AT?RIA 8:68,++


22/29

PREDIMENSIONAMIENTO DE VIGAS

E0E A =6-8>

ESTRUCTURAS ESPECIALESPr"1%" #al"na2" 6*


Para l (r 2i!n#i"na!in%" 2 )iga#. %an%" (rini(al# "!" 2 "n@i3n# %n2r la #iguin% "n#i2rai3n. #gn l rgla!n%",

SEC @300, mB 500,mB 500,mB L** L*5 L L66 L65 L*

Al #r un 2i9i" 2 )i)in2a "n"!"# &u la #"brarga # !n" 2

855g!6. ("r #%" !(lar!"# la #iguin% al%rna%i)a (ara l(r2i!n#i"na!in%",

Ob%n!"# la# lu# 2 a2a )iga !2ian% !2ii3n 2ir%a 2l (lan" ."n#i2ran2" la# 2i!n#i"n# 2 la# "lu!na# #%abli2a# n laar&ui%%ura,

La# )iga# n"n%ra2a# 1 la# 2i!n#i"n# 2 la# #i"n# # !u#%ran n la#iguin% %abla,

D"n2

H Pral%

B An"

VIGAS HORIONTALES

IGA > )=,11

) :=,22

:

EE A 2/3

,* 5,+555

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8

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5

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++

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Tra!" "!(rn2i2" n%r l"#7# "r%"g"nal#

Alinai3n 2 la)iga n l

L**

L66


23/29



EE : 2/3

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EE C 4/5

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5, 5,6**6

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5, 5,6**6

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EE D 7/8

5,+:+:+:++

5,++ 5,6666

5,8

EE D 8/

+,:: 5,::+:+:+

5,+ 5,6:668

5,6+

EE E 1/2

,6 5,+***

5, 5,6+55

5,8

EE E 2/3

+,8 5,:**6

5,+ 5,6::55*

5,6+

EE E 3/

4

+,8 5,:**

6

5,+ 5,6::55

*

5,6+

EE E 4/5

,:6 5,+888

5, 5,6***

5,8


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EE E 5/6

,:6 5,+888

5, 5,6***

5,8

EE E 6/7

+,8 5,:**6

5,+ 5,6::55*

5,6+

EE E 7/8

+,8 5,:**6

5,+ 5,6::55*

5,6+

EE C 8/ ,6 5,+*** 5, 5,6+55 5,8

VIGAS VERTICALES


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ESTRUCTURAS ESPECIALESPr"1%" #al"na2" 6:


IGA > )=,11

) :=,22

:

EE1 :/C

6,+ 5,68888

5,6+ 5,****

5,*+

EE1 C/D

8 5,6666

5,8 5,*888:

5,*+

EE1 D/E

8,6 5,8:668

5,8+ 5,*888

5,6

EE 2 A/:

*,* 5,* 5,* 5,5+ 5,5+

EE2 :/C

8,6 5,6668

5,8 5,*:88

5,*+

EE2 C/D

8,* 5,6**6

5,8 5,*::55*

5,*+

EE 2 D/E

:,+ 5,:555*

5,:+ 5,65:+:+:+

5,6+

EE 3 A/:

*,6+ 5,**888

5,*+ 5,5+**

5,*

EE3 :/C

*,: 5,*8888

5,*+ 5,5**

5,*

EE 3 C/

D

6,* 5,***

6

5,6 5,555

*

5,*

EE 3 D/E

8,6 5,8:668

5,8+ 5,*888

5,6

EE 4 A/:

*,* 5,* 5,* 5,5+ 5,5+

EE 4 :/C

8,6 5,6668

5,8 5,*:88

5,*+

EE4 C/D

8,* 5,6**6

5,8 5,*::55*

5,*+

EE 4 D/E

:,+ 5,:555*

5,:+ 5,65:+:+:+

5,6+

EE 5 :/C 6,+ 5,68888 5,6+ 5,**** 5,*+

EE 5 C/D

6,6 5,65+:+:++

5,6+ 5,*5666

5,*+

EE 5 D/E

8, 5,8:+:+:++

5,8+ 5,*666

5,6

EE 6 A/:

*,* 5,* 5,* 5,5+ 5,5+

EE 6 :/C

8,6 5,6668

5,8 5,*:88

5,*+

EE 6 C/D

8,* 5,6**6

5,8 5,*::55*

5,*+

EE 6 D/E

:,+ 5,:555*

5,:+ 5,65:+:+:+

5,6+

EE 7 A/:

*,6+ 5,**888

5,*+ 5,5+**

5,*

EE 7 :/C

*,: 5,*8888

5,*+ 5,5**

5,*

EE 7 C/D

6,* 5,***6

5,6 5,555*

5,*

EE 7 D/E

8,6 5,8:668

5,8+ 5,*888

5,6

EE 8 A/:

*,* 5,* 5,* 5,5+ 5,5+

EE 8 :/C

8,6 5,6668

5,8 5,*:88

5,*+

EE 8 C/D

8,* 5,6**6

5,8 5,*::55*

5,*+

EE 8 D/E

:,+ 5,:555*

5,:+ 5,65:+:+:+

5,6+

/


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PREDIMENCIONAMIENTO DE LOSAS

ESTRUCTURAS ESPECIALESPr"1%" #al"na2" 6+


Una ); "b%ni2a# #%a# 2i!n#i"n# la# a(%a!"# %nin2" n un%a &ula# 2i!n#i"n# !


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L8 :,+ ! * ! 6+ !L: *,5 ! ,6 ! 6+ !L+ 8,+5 ! *: ! 6+ !L 8,* ! *6, ! 6+ !L :,+ ! * ! 6+ !L *,6+ ! + ! 6+ !L ,68 ! 6:, ! 6+ !L*5 8,* ! *6, ! 6+ !L** :,+ ! * ! 6+ !L*6 8,+5 ! *: ! 6+ !L*8 8,* ! *6, ! 6+ !L*: :,+ ! * ! 6+ !L*+ 8,+5 ! *: ! 6+ !L* 8,* ! *6, ! 6+ !L* :,+ ! * ! 6+ !L* *,6+ ! + ! 6+ !L* ,68 ! 6:, ! 6+ !L65 8,* ! *6, ! 6+ !

L6* :,+ ! * ! 6+ !L66 *, ! ,6 ! 6+ !L68 8,+5 ! *: ! 6+ !L6: 8,* ! *6, ! 6+ !L6+ :,+ ! * ! 6+ !L6 8,+5 ! *: ! 6+ !L6 8,* ! *6, ! 6+ !

GL6 :,+ ! * ! 6+ !

LOSA MACIA

L"#a Mai;a Uni2iri"nal

Lu; 85

LOSA LU ESPESOR DELOSA

ESPESOR FINAL

L* 8,+5 ! **, ! 6*!L6 8,* ! *5,+ ! 6*!L8 :,+ ! *+,8 ! 6*!L: *,5 ! ! 6*!

L+ 8,+5 ! **, ! 6*!L 8,* ! *5,+ ! 6*!L :,+ ! *+,8 ! 6*!L *,6+ ! :,* ! 6*!L ,68 ! 65, ! 6*!L*5 8,* ! *5,+ ! 6*!L** :,+ ! *+,8 ! 6*!L*6 8,+5 ! **, ! 6*!L*8 8,* ! *5,+ ! 6*!L*: :,+ ! *+,8 ! 6*!L*+ 8,+5 ! **, ! 6*!L* 8,* ! *5,+ ! 6*!

L* :,+ ! *+,8 ! 6*!L* *,6+ ! :,* 6*!L* ,68 ! 65, 6*!


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CONCLUSIONES



L65 8,* ! *5,+ ! 6*!L6* :,+ ! *+,8 ! 6*!L66 *, ! ! 6*!L68 8,+5 ! **, ! 6*!L6: 8,* ! *5,+ ! 6*!L6+ :,+ ! *+,8 ! 6*!L6 8,+5 ! **, ! 6*!L6 8,* ! *5,+ ! 6*!L6 :,+ ! *+,8 ! 6*!

En l anli#i# 2 la 2i9ai3n (r#n% n #% in$"r!. #%u)" ba#a2" n#%u2i"# (r)i"# a(rn2i2"# n la#. #%" n"# #ir)i3 (ara 2%r!inar #i l

2i9i" u!(l "n l"# r&uri!in%"# b#i"# 2 "n#%rui3n 1 #u ("#ibla!(liai3n,

El r#ul%a2" 2 la @n%rii2a2 @2i3 l )al"r !@i!" (r!i%i2", E#%" #2bi3 a &u n"n%ra!"# a7a# 2 a#n#"r aia un la2" 2l 2i9i" 1 n"%in l!n%"# ("r%an%# #u9in%# &u "!(n#n la rigi2; aia l la2""(u#%", E@i#% $al%a #i!%r


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