Download - 30628365 Apuntes Caminos y Ferrocarriles
-
c
c
c
Y
!"#$ %Y&'("Y
%
%
&)
*
%
()++
,
$ , $ &"'Y &'-.'$'Y$ %,-/ &!&Y!-0&&"/&Y -#'&"$ %Y&'("Y
Y
& ! 1Y&!2 +
) 3
p Y'$-,'1Y'.'-,'2
p !
p ,(+
p Y++
p &4
p !
)
')5)
,+
+
'Y&!3
Sp $1$.&42
-
Sp $)1$.,Y!/&2
Sp $1&'40, 2
6
5
&%'Y"4"&'&"7$ %Y&'("Y
*+
3
Sp &
p &
p &12
p &
p !
Sp &3) 8
5
p & 9 )
5
p & 9
Y5
p & 9
12
p & 9 + 1&'40, 2 %
)
Sp & ) 3 & 1!$,'2
3
p !':!$,';?>
p !$!$,'?>>>
p ! !$,'?>>
Sp 3
p &
p &
p &
Y &&"!-'Y# -Y'%
&
+3
Sp Y+
Sp Y
Sp Y)
%3
-
p %
p Y
p &
p %
p %
1+2
3
mp '
p 4
mp '
p ,
mp '
p ,
mp
p
)
mp
p ,
mp &
p ,
mp &
p )
-
mp &
p .
mp &
p Y
mp &
p &
)
mp $
p $
mp $
p Y
+
mp .
p M*:>
mp .*+
p %*
*+
mp 8
p )
mp %
p
mp %
p *++
*+
mp %
p '
:
mp ,
p -:
mp ,
p
mp ,*+
p *+
mp ,
p
mp -
p ,
mp Y
p ,
mp Y
p
mp !+
p $
-
4 --&'--"% Y
0
*
&
p
p %
)
p
p
cp
p
%
%
p
p & +
*
p
p
p ,
p ,&
p &
?p #
:p $ )
;p $(*
=p $8*
p '
p
p (
p '
p
p c
p Y
p ,
p $
p -
p &
-
p cc
p &
p
p -
p !
p !
p ,
p .
p c
p .5
p (
p
c
$:3
'p 41@A2
p "12
':3
p %
p &
p %
p & *
12@A
#'-"'&"7$ %#%0( $ !-'Y"! %'8-'$ (M"('$ ('$'
, *+ *+ B48($C
*+ B#8($C *+ B0+C
(*+3
$3
D*+1?
-
48($ *+ *
*+
Y+*+#
*+
312
0*+
$48($
-
1"!2@
3
- - - -$3
1&!2
1!.2
1!$2
-:;?3
- - - - - - +
- - $3
!'D!1#8$(2
D!
D@
%
)
)
c
Sp '1',2
Sp &1'&2
Sp '512
Sp &:1&:2
Sp &;1&;2
Sp !
p !;9Y:
p !;9Y;
p !;9Y=
Sp !
p !;9Y:9-:
p !;9Y;9-;
p !;9Y=9-;
-
p !;9Y=9-=
Sp #
Y!0$"Y$ # %&"$'$
# %&"$'$
Y
%+3
!"! #%
BC
# %&"$'$"Y!'!M '$ ,0!
@&
:3
?p #9)
:p # 9 )
# %&"$'$$ ('-&8' $ &-0& -
# %&"$'$$ , -'&" 7
*+
)5
# %&"$'$$ - &--" $.%'%
1
2
# %&"$'$$ ,-/ &!$ $"Y J
*+
?3
0 '9'K9K&9&K$9$K
12 =
-
'9$6
$
'9'N9N
9N
9
N
9
N$9$N
'9'N$9$N
'9'N$9$N O
3
0 '9'K9K 9 K$9$K!"#""
$% LM !" #" " " '
9 K # * Y
'9$6
( Y0 %)
0'$ (
*3
0'"3+,3*$
- +#L + 3.
* '#
+,*"@3
%p/
%p %
-
!
0
"
L+*
@
2p
2p %
&,&"
%*+
%
*
2p &
2p &
%
%
*+
" % Y "&"
0
5
Y
#
& 4
5
%0 Y "&"
*+5
&,&",&" &" Y &"&0%&"&"0
%)
p &
p Y
- ;p &;#
-
3
DY
D%??:
3
03
p =1:2;M
p *?:>
p !
p #?>>LM
p #*+1#8($2?"+12
?>P?
-
9 / 3: & .53 / .59. .5: ; .596 / .59. .5.63.5 ( .5.6 54: 9/ 54 654D#$>
#M&D?
... ( ( ( .563 ( ( .58 9.7#$+3
- -*" 3
D?"1:>>"2
D@1+2
D12
- 34..5.84 < 897# 3
'@D:>>"
'@D:>?#
3
0*3
p #1;2;;>M
p ?
p !
p #">LM
p #8($:#;>+"P?"
-
@
@
!
4'Y Y$ 0'&'-- ! -'
3
?p ,
:p -
;p !
=p %
-
2p %
2p %
2p 0
,)
%
,
)+),
!
%3
?p
p '12
p ,12
:p *
p &**
;p
p "12
p +12
=p
-
"!@>"" A?)"!" #!"B #A # #!"B # ! c c
% $>L P
#!BC=>>>
p BC?>>
p B&C:>>>>
mp
p B'C;
p BC::
p B&C:
77 ( 7 ( 84 ( $3
Sp D#9
Sp "%D
Sp %D#
Sp D'
Sp D&
" EE 4. ( 8 ..5 ( 84 ( .58 8:944" E?E 4. ( 4.5 ( 84 ( .54 83:54" EE 4. ( ..5 ( 84 ( .54 8:944
A 8:944 83:54 8:944 8.:954,3
-
2
V
V
3
Sp &?9@5
Sp &:9@@
Sp &;914"!29@
@?>P@
$"C#=Q>>ML>>>>>>>
Sp &D129
,+ HIJ3D)D
Sp &"$9
Sp 0
Sp %
Sp &B
C&
/
! -"','-' '(
p $
p &
p R
p $
-
p &
p &
p 4
p R
p %
p !
p &
p %
p ,
EF
2
G
H
IJK LMN
OPQQRSS
TO
V
UV
VW W
XY
XY
#
- &&"(" !
12
3
"p -*1)2
p ,1:2 *
p
""p -&
"""p -,
,-& Y$ %- &&"( "!
p $
Y )**
*?
p Y
;3
Sp !12
Sp ')
-
Sp &
)
*
&3
2p '
2p $+
2p ,+
2p $
2p $*
2p $
p -
3
Sp "
Sp "
Sp "
Sp "*
Y3
Sp '
Sp
Sp Y
Sp &
Y3
Sp
p $
p
p +
p
p (
Sp "
p "
p $+
Sp "*
p
p $
p )
Sp "
p &)*
p 12
p $*
p &
p
&3
2p %5
2p #
2p :1Z2
-
p
%**
3 # #!!" # =!" # #!" % * )
@3
Sp '
Sp ' * *
*
Sp **
@
Sp @)
Sp
Sp $))
Sp %@
Sp %
3
Sp Y
Sp *)*
!-'S,- %"("'-
)+
)#
%&'%"S'&"
&%:
*
%3
?p %
:p !
;p 0
=p &
-
%&'%"S'&"$ %'%" '', %$ !" --'
Y12
*
%)
)
,3
2p 1'2
2p 12
2p ,
Y3
&**1
2
Y3
? ;
3
D$
3
'D?3?>>>
D:>>
&D:
-
!-'S$ !'. ! Y
&
&)*
*3
?2p $*
:2p R*+:
;2p R+
=2p R
-
0 3
+
)*
-'$"/, -'%! $ & 0-#'Y
&
'
%5 142
*
+
%Y1.2*
12 12
,1-21D:>2.+
3
$
K 8.LM@ 3..M@ 456@ N@ 456
3
-
Sp Y?>P9
Sp Y"P9
Sp Y#P9
*+1Y+2 *+
3
@OI .5..934K$O P O ...$O
K #
-'$"Y(""(Y/.-'$" ! Y('"(Y
\]^^_
`
_^]a b^c]d]a
Y Y Y
e
e
e
e
f
09
3
$ C@OI@ D$O *93
$! C$D
&'$ '(" !$ %'%" '
!*
*#
'! ,-/ &!$ Y0-'Y'! Y
03
)
/
*
$
-
$3
2p 5)
2p R
*+
2p *
2p '**
* * +
5)
- #"Y"$ Y &&" Y
, * *+
3
mp
mp &
mp $
mp &
mp 1? ! 2
22p )"
3
3
2p -@> ! 22
2p % QK / K GK / GK 2p $+,"?
-
$
%)+$
3
2p -
2p %1)2
2p %
,"
$;>*+
Sp Y>;>*+*
&0-#'YY"(,% Y
&:*
L
3
-
$3
+D+
D
D
D
D
D
D
D*+
D*
,D
D
D
D+
D
D
-D
-D
@ 456
456@ $- @ R- .R
@#R- @ S / ! # R- T @ U ! # RVK / W
5 5 / $-5- 5
0)
-
*+,&
"53
g c
.i?>Q :>
?>QT.T:>Q ?>
:>QT.T=>Q 3
RXYZ %+?>3
RXYZ %+
-
.49L4^8L 8359 83569# 49L4^ 84563 83569] / ! # 49L4^ _ 56 83569`a ! # bLcK d / e 4856
5 ...5.. / .359 . 965485- . 96548 8359 985.
$3
&D:>
,123
3.. / 96548 359985. / . 85.
RO 548 54LRXYZ 54. 54LRXYZ 8 54L
R-Z 49L4^ 3L89^8.^^ RfggVV5 54^359 .L83^39hhRKigVV5 54^85. .L46^hh
-
m
hi hi hi hi
j
kk
kk
jl
3
m! "
#
n
o
$p $p
n $ $
Y "
#
c %
%
m
c
c
&""&
-
m
'Y %R0 %" Y' Y"%
+
''
*m'&*+12
',"
'&3Dmq
$?12
'
?#j# ?#j#R ? ?#k# ?#k#R
3
Y,"
4?
)#
$3
-
"#rst
u
$rv wxyQz{|
} xy~{
"#rv$rv% Qzx|
} ~
"#rv%$rst
zQz|
} z~{
&rv xyz~z xyz~z
y~{y
'
x~{ #
m Q
Q
Q
"
&
( Q
3
412
&
m ! !!
V !
c
! ! j '
! ! ! !
c
c !! )* ! )+
! + ! +
i
!! !! !
c
,' !! !! i
c
, !! !! !
-
m
!! !! !! !!
!
!
!
! !
!
0-#'Y Y"-'% Y$ !-'Y""7
Y
%3
4!
!
3
>!
>m
>m
>cm
>m
Y
" "
~
~'
(
)
#
>
Y
-
~i
C~ii ~
~
~
~
~
~
~
~
~
~
~
!3
>
>
>
>
>
~
~
>
~i
C~ii ~
~
~
~
~
~
~
~
~
~
~
!!
%'Y- 4 - &"'Y
-
Y3,Y!,&,",!
1,-2
Y,-
*
&
%*+%**
% ,-*
&*:,-*
!
$?:12
%."!0$$ !-'Y"&"7$ %( '%'Y- % #'&"
%
,
.
+
)
&
P
%+
$
)!
'(,%"'&" &0-#'Y
Y
@''Y8!
1''4&!,52*
%3
l@ / Q@K / Km n@$3
-
'D
D
-D
%D1%D:>2
#DM
%''Y8!5>?>%
5)63
l@ / Q@K / Km .5.n@ 'D
D
-D
%D1%D#?>2
#DLM
$"Y!'&"'$ #"Y""% "$'$
%
) ;3
2p $
Y
+3 )$3
$D
D
D
D
2p $
2p $
,-& Y," #
,3+ +
,+
)
"36
3$
+,
#3
-
c
j j
) K / )K4) o .56 K4) o
$3
D
#D
#D
:
-
pg Q4 ( 45 / 5.
56 q83 ( %45 4 / 5.' )K q83 ( %45 4 / 5.' 56K 35.3r7
$
Y
%
4:
54$3
$D
=
-
$3
-D
D
'D'
;=D
%
6 5
5 ,
??=>?
-
""? s 77 ? / r? / r
%*L+'3
'D??=;>>6'D:>:>>>
D??;=>>6D:;">>>
&3
2p ,
7 ? / 85.. / 85.. /6 r? / r 83.5.. / ..5.. 8.5..""? 7 68. .5.4 54t
2p $
.5.4 ( . .542p %
c
!!
! !
! !
!
!
!!
!
!
!
!!
!!!
!!
!!
!!
!
!!
!
!
!
&,"#
4!
&0-#'Y# -!"&'% Y
-
% *
*%
$,"#3
2p &1,"#2
2p &1,"#2
& * *
3
Sp Y3y u;KSp %
% ( !Y$ %'Y&0-#'Y# -!"&'% Y
$3
!#?D
!#:D
,D
,PD
,"#D+
,!#D
-
%D
D,!#1,!#2
,D,!#
AD
KKKAKD
KKKAKDA
&$"&" Y,'-',-/ &!'-&0-#'Y# -!"&'% Y
?p Y >
;p %:>6
?=>
=p &,"# 5*
,"#
-
p ,
:
&M uK
&
*
r 83 .5..P 854.t5 85..P^ /594t 9.r7 P 8r7 P ) .584
?p
.568 8K4.584 .5.84 3958:p
-
t/ ^t 854 / /594 454;p ,3
.5..4K .5..44543958K 665=p
. 665. 564 v 4
-
.569 9K4.58. .5.48 54.:p
t/ ^t /458./ 53. /35.;p ,3
K. 854 35.54.K. 85454. 8.588&$i%6%D=>
=p
. 8.588. 54 v ( . .5..
-
.
c !! !!
!
!! !! !
! !!! !
!!
! !
!! !! !!
! !! !!
! !! !!
! ! !! ! !!
! !! ! !!
! !! ! !!
!! !!
! !!! !!
!! ! !!
! !! ! !!!
! !! ! !!!
3+3
u 3
%D
D*
!-
ccc
c
c c
c c
;> = ; = :>
=> = ;>
?: " ?> ;>
#> :; ?= ?
> ;# :> :> =>
"> 9 ;? : 9 =; ;?
?>> 9
??> 9 : =; #>
'D
-
!'- '3
&Y!-0&&"$ %, -4"%$ 0'Y0-'Y'!
0 *
3
$
:>
'3
-
&
&
&
'
%
!' ! ! !'
!
% ! ! ! * '! !! !
! !! ! !! ! ! !
! !
$! ! ! ! 3 !!! !
! !!!'
' !' !'!
-/ $
! !! !! ! ' ! !
!
( ! ! 3
p :>
p ,,&,!! && !1'& 2
p ,,,"#,!#
p ,*+
)
-
,
'
)
Y*
1,&,!2
%3
$ *
+
-
':>):>
3
'
'
>O >>
>
:
>O :>
>
:
>O
>
>
:
>O >
>
:
>O >
>
:
>O >>
>
::
,
)
'
'
>O >>
:
:
>O :>
::
>
>O
>
>
>O >
:
>
>O >
>
>O >>
>:
>
3
#
*+* !
! !
*,* !
! ! ** !
! ** !!
"
+ #
$
!
!
+
+
-
P%
&
%'
P%
&((
P%
&(
)
P%
&
'%
P%
&
'*
P%
&
+*
P%
&
,
-
. .
/
0 1 1 1
0 1 1
0 1
0 12 1 1
1
3
-
3
4
5
6
7
.8
.
9
: .;.
: => .*3
^ ( . . ^$3
-
''KD*
&*3
^ ( ^$3
D
&0-#'$"'.-'('$ ('Y'Y
Y*
Sp &?9L
Sp &:9
Sp &;9 *
12
Sp &=9
Sp &