Tercer Parcial Caminos 2000-II (1)
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TEMA Nº 02 A I1 = POSITIVO / I2 = NEGATIVO
SOLUCION 5 CALCULO DE LAS ORDE
1 Cálculo de la diferencia de pendientes R
I1 = 4.00% Cot !"# P$to A 104&1.00 Para X1 = 0.00 m
I2 = '4.00%
D(). = *.00%
Para X2 = 6.75 m
2 Se calcula la Longitud de la Cura! para una
"isi#ilidad de Parada! para lo cual se de#e
$sar el grafico %&'2001 S("!o Para X( = 26.75 m
L+ = *0.00 V = 50.00 ,-/
Se calcula las odenadas Para X) = )6.75 m
m = *rdenadas del punto medio +P,"-
m =
L C#+$#o !" # +ot !" #
/00 6"!("t" !" +! t-o
P"!("t" D(t+(
m = /.00 /0.00
).00
00.00 =/00 06.75 =
26.75 =
m = 0./00 )6.75 =
P," =
4 Se calcula las odenadas a cada 20.00 m.
').00
5(.25 =
n = *rdenadas en un punto cualesuiera ((.25 =
1(.25 =
n = X3 0.00 =
200 L
7 C#+$#o !" # +ot +o"
P"!("t" D(t+(
).00
00.00 =
06.75
26.75 =
)6.75 =
P," =
').00
5(.25 =
((.25
1(.25 =
00.00 =
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ADAS
MAL IZQUIERDA RAMAL DEREC9A
/.00 0.003 1 = 0.000 m Para X1 = 0.00 m /.00 0.003
200 /0.00 200 /0.00
/.00 6.753 2 = 0.02( m Para X2 = 1(.25 m /.00 1(.253
200 /0.00 200 /0.00
/.00 26.753 ( = 0.(5/ m Para X( = ((.25 m /.00 ((.253
200 /0.00 200 /0.00
/.00 )6.753 ) = 1.04( m Para X) = 5(.25 m /.00 5(.253
200 /0.00 200 /0.00
$3t" t"("!o " +$"t #
Cot Po8"(: Po8"(: 0
10505./0 m 01 16 1(.25 m.0117(.25 6.75 6.7510506.60 m 01 1/ 00.00 m.0121/.00 20.00 26.75
10507.)0 m 01 20 00.00 m.01220.00 20.00 )6.75
1050/.20 m 01 22 00.00 m.01222.00 1(.25 60.00
10504.00 m 01 22 1(.25 m.012((.25 0
1050/.2 m 01 2) 00.00 m.0122).00 6.75 60.00
10507.) m 01 26 00.00 m.01226.00 20.00 5(.25
10506.6 m 01 2/ 00.00 m.0122/.00 20.00 ((.25
10505./ m 01 2/ 1(.25 m.0124(.25 1(.25 1(.25
0
8(! !" # $3t".
Cot Co"8. Po8"(: Po8"(:
10505./00 m 01 16 1(.25 m.0117(.25
10506.600 m 01 1/ 00.00 m.0121/.00
10507.(77 m 01 20 00.00 m.01220.00
10507./)2 m 01 22 00.00 m.01222.00
1050/.200 m 01 22 1(.25 m.012((.25
10507.6)7 m 01 2) 00.00 m.0122).00
10507.(12 m 01 26 00.00 m.01226.00
10506.600 m 01 2/ 00.00 m.0122/.00
10505./00 m 01 2/ 1(.25 m.0124(.25
1 = 1 =
2 = 2 =
( = ( =
) = ) =
6.75
26.75
)6.75
60.00
m 0
1 0 2 2 0 0 . 0
0
m 0
1 0 2 0 0 0 . 0
0
m 0
1 0 1 / 0 0 . 0
0
m 0
1 0 1 6 0 0 . 0
0
m 0
1 0 1 6 1 ( . 2
5
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1 = 0.000 m
2 = 0.0// m
( = 0.55( m
) = 1.)1/ m
m 0
1 0 2 2 1 ( . 2 5
m 0
1 0 2 ) 0 0 . 0
0
m 0
1 0 2 6 0 0 . 0
0
m 0
1 0 2 / 0 0 . 0
0
m 0
1 0 ( 0 0 0 . 0
0
m 0
1 0 2 / 1 ( . 2
5
1(.25
((.25
5(.25
60.00
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&; 4< 40<<
44; 1< 10<<
"d. =
CALCULO DE LOS ELEMENTOS DE CURVA
C$: NºANGULO R T L+ C E P
8! -( "8 GRAD RAD S +m- +m- +m- +m- +m- +m- +-
1 (48 )69 )099 (4.77/ 0.64)( % 2(4.422 /6.74/ 166.566 16(.2)1 15.21/ 1).(10 (.70
2 ))8 (19 1099 )).514 0.7770 % 2(4.422 4/.202 1/6.)22 1/1.767 14.(20 17.//0 (.70
POLIGONAL POR DEEL>IONES. CALCULO DE LAS COORDENADAS D
PI L!o D(t.ANGULO AZIMUT
G! M( S"8 GRAD S"t(!o G! M( S"8 GRAD
' P,1 250.00 5; 20< 25<< (5.()08
P,1 (48 )69 )099 (4.77/8 D
P,1 ' P,2 45.00 75° 079 0599 75.11/8
P,2 ))8 (19 1099 )).5148 D
P,2 ' P,( 40.00 119° (/9 1599 114.6(/8
P,(
I1 =
I2 =
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45.00 m:;.
L6 S/A P+- = <á 10.00
+m- +m- S: +m- = <>lt. 0.(0
(6.00 0.))1 n = 02 Carril
(6.00 0.241 L = 6.00 m
LOS PI
PRO?ECCIONES COORDENADAS
RAD Et" Not" ESTE NORTE
1000.000 2000.000
0.617 1)).60/ 20(.4((
11)).60/ 220(.4((
1.(11 41./1( 2).(44
12(6.)21 222/.((1
2.0// 7/.225 ')).506
1(1).6)7 21/(./25
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TEMA Nº 02 @ I1 = NEGATIVO / I2 = POSITIVO
SOLUCION 5 CALCULO DE LAS ORDENADAS
1 Cálculo de la diferencia de pendientes RAMAL IZQUIERDA
I1 = '5.50% Cot !"# P$to A 20&.7 Para X1 = 0.00 m 4.75 0.003 1 = 0.000 m
I2 = 4.25% 200 120.00
D(). = '&.75%
Para X2 = 6.75 m 4.75 6.753 2 = 0.014 m
2 Se calcula la Longitud de la Cura! para una 200 120.00
"isi#ilidad de Parada! para lo cual se de#e
$sar el grafico %&'2001 S("!o Para X( = 26.75 m 4.75 26.753 ( = 0.241 mL+ = 120.00 V = 40.00 ,-/ 200 120.00
Se calcula las odenadas Para X) = )6.75 m 4.75 )6.753 ) = 0./// m
m = *rdenadas del punto medio +P,"- 200 120.00
m =
L C#+$#o !" # +ot !" # $3t" t"("!o " +$"t #
/00 6"!("t" !" +! t-o
P"!("t" D(t+( Cot Po8"(:
m ='4.75
120.00
'5.50
00.00 = 2(1).16 m 01 16 1(.25
/00 06.75 = 2(1(.06 m 01 1/ 00.00
26.75 = 2(11.46 m 01 20 00.00
m = '1.)6( )6.75 = 2(10./6 m 01 22 00.00
P," = 2(04.76 m 01 22 1(.25
4 Se calcula las odenadas a cada 20.00 m.
).25
5(.25 = 2(10.61 m 01 2) 00.00
n = *rdenadas en un punto cualesuiera ((.25 = 2(11.)6 m 01 26 00.00
1(.25 = 2(12.(1 m 01 2/ 00.00
n = X3 0.00 = 2(1(.16 m 01 2/ 1(.25
200 L
7 C#+$#o !" # +ot +o"8(! !" # $3t".
P"!("t" D(t+( Cot Co"8. Po8"(:
'5.50
00.00 = 2(1).160 m 01 16 1(.25
06.75 2(1(.060 m 01 1/ 00.00
26.75 = 2(11.474 m 01 20 00.00
)6.75 = 2(11.151 m 01 22 00.00
P," = 2(0/.24/ m 01 22 1(.25
).25
5(.25 = 2(11.054 m 01 2) 00.00
((.25 2(11.5(1 m 01 26 00.00
1(.25 = 2(12.(10 m 01 2/ 00.00
1 =
2 =
( =
) =
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00.00 = 2(1(.160 m 01 2/ 1(.25
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RAMAL DEREC9A
Para X1 = 0.00 m 4.75 0.003 1 = 0.000 m
200 120.00
Para X2 = 1(.25 m 4.75 1(.253 2 = 0.071 m
200 120.00
Para X( = ((.25 m 4.75 ((.253 ( = 0.))4 m
200 120.00
Para X) = 5(.25 m 4.75 5(.253 ) = 1.152 m
200 120.00
Po8"(: 0
m.0117(.25 6.75 6.75
m.0121/.00 20.00 26.75
m.01220.00 20.00 )6.75
m.01222.00 1(.25 60.00m.012((.25 0
m.0122).00 6.75 60.00
m.01226.00 20.00 5(.25
m.0122/.00 20.00 ((.25
m.0124(.25 1(.25 1(.25
0
1(.25
Po8"(: 6.75
m.0117(.25 6.5
m.0121/.00
m.01220.00
m.01222.00
m.012((.25m.0122).00
m.01226.00
m.0122/.00
1 =
2 =
( =
) =
1(.25
26.75 ((.25
)6.75 5(.25
60.00
20.00 20.00 20.00 20.00 20.00 20.00 20.00
60.00
m 0
1 0 2 2 1 ( . 2
5
m 0
1 0 2 ) 0 0 . 0
0
m 0
1 0 2 6 0 0 . 0
0
m 0
1 0 2 / 0 0 . 0
0
m 0
1 0 ( 0 0 0 . 0
0
m 0 1
0 2 2 0 0 . 0
0
m
0 1 0 2 0 0 0 . 0
0
m 0
1 0 1 / 0 0 . 0
0
m 0
1 0 2 / 1 ( . 2
5
m 0
1 0 1 6 0 0 . 0
0
m 0
1 0 1 ) 0 0 . 0
0
m 0
1 0 1 6 1 ( . 2
5
6.75
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m.0124(.25
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TEMA Nº 0 A I1 = POSITIVO / I2 = NEGATIVO
SOLUCION 5 CALCULO DE LAS OR
1 Cálculo de la diferencia de pendientes
L1 = 5.50% Cot !"# P$to C 20&.7 Para X1 = 0.00 m
L2 = '4.25%
%if. = 4.75
Para X2 = ).75 m
2 Se calcula la Longitud de la Cura! para una
"isi#ilidad de Parada! para lo cual se de#e
$sar el grafico %&'2001 S("!o Para X( = 2).75 m
L+ = 1*0.00 V = 40.00 ,-/
Longitud de los ramales +i?uierda! derec;a- Para X) = )).75 m
#1 = *0.00
#2 = 100.00
Para X5 = 6).75 m
Se calcula las odenadas
m = *rdenadas del punto medio +P,"-
m = +L1 L2-
200 +L1 L2-
5 Cálculo de las cotas de l
m =4.75 /000.00 pendiente de cada tram
200 1/0.00
P"!("t" D(t+(
m = 2.167
5.50
00.00
0).75
4 Se calcula las odenadas a cada 20.00 m. 2).75
n@ = *rdenadas en un punto cualesuiera )).75
6).75
n@ =X3
mIB$("! P,"
L13
').25
45.25
75.25
Se calcula las odenadas a cada 20.00 m. 55.25
nA = *rdenadas en un punto cualesuiera (5.25
15.25
nA =X3
mD""+ 00.00
L23
Cálculo de las cotas cor
P"!("t" D(t+(
5.50
00.000).75
2).75
)).75
6).75
P,"
').25
45.25
75.25
55.25
(5.25
15.25
00.00
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ENADAS
RAMAL IZQUIERDO RAMAL DEREC9O
0.00 2.17 1 = 0.000 Para X1 = 0.00 m 0.00 2.17
6)00 10000
22.56 2.17 2 = 0.00/ Para X2 = 15.25 m 2(2.56 2.17
6)00 10000
612.56 2.17 ( = 0.207 Para X( = (5.25 m 12)2.56 2.17
6)00 10000
2002.56 2.17 ) = 0.67/ Para X) = 55.25 m (052.56 2.17
6)00 10000
)142.56 2.17 5 = 1.)14 Para X5 = 75.25 m 5662.56 2.17
6)00 10000
Para X6 = 45.25 m 4072.56 2.1710000
la su#rasante! teniendo en cuenta la C#+$#o !" # +ot !"#
siBCot !" C = 20&.
Cot Po8"(: Po8"(:
= 2((2.67 m 01 20 15.25 m.00215.25 L +C- = 625.0
= 2((2.4( m 01 22 00.00 m.00220.00 ,2 = ').25
= 2(((.7/ m 01 2) 00.00 m.002)0.00
= 2(().6( m 01 26 00.00 m.00260.00 D()""+( !" A#t$
= 2((5.)/ m 01 2/ 00.00 m.002/0.00 si
= 2((6.(2 m 01 2/ 15.25 m.00245.25 100 su#e ).25
= 2((6.12 m 01 (0 00.00 m.00(00.00 625 D
= 2((5.27 m 01 (2 00.00 m.00(20.00
= 2(().)2 m 01 () 00.00 m.00()0.00D =
2656.25= 26.
= 2(((.57 m 01 (6 00.00 m.00(60.00 100
= 2((2.72 m 01 (/ 00.00 m.00(/0.00
= 2((2.07 m 01 (/ 15.25 m.00(45.25 COTA DE @ 2.
regidas de la su#rasante.
Cot Co"8. Po8"(: Po8"(:
= 2((2.67 m 01 20 15.25 m.00215.25= 2((2.4( m 01 22 00.00 m.00220.00
= 2(((.5/ m 01 2) 00.00 m.002)0.00
= 2(((.46 m 01 26 00.00 m.00260.00
= 2(().06 m 01 2/ 00.00 m.002/0.00
= 2(().16 m 01 2/ 15.25 m.00245.25
= 2(().15 m 01 (0 00.00 m.00(00.00
2(().0) m 01 (2 00.00 m.00(20.00
2(((.76 m 01 () 00.00 m.00()0.00
2(((.(0 m 01 (6 00.00 m.00(60.00
2((2.67 m 01 (/ 00.00 m.00(/0.00
2((2.07 m 01 (/ 15.25 m.00(45.25
1 = 1 =
2 = 2 =
( = ( =
) = ) =
5 = 5 =
6 =
m 0
1 0 2 ) 0 0 . 0
0
m 0
1 0 2 2 0 0 . 0
0
m 0
1 0 2 0 0 0 . 0
0
m 0
1 0 2 0 1 5 . 2
5
)!75
2)!75
))!75
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6
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1 = 0.000
2 = 0.050
( = 0.264
) = 0.661
5 = 1.227
6 = 1.466
P(:
si si
100 su#e ).25 100 su#e ).25
0 20.00 ;2 L +- = 5)5.00 20.00 ;2
,1 = 5.50
;1 =/5
= 0./5 ;1 =/5
= 0.C 100 D()""+( !" A#t$ @A 100
si si si si
100 su#e ).25 100 su#e ).25 100 su#e 5.50 100 su#e 5.50
).75 ;1 15.25 ;2 15.25 ;1 ).75 ;2
6 ;1 =20.2
= 0.20 ;1 =6)./
= 0.65 ;1 =/(./75
= 0./) ;1 =26.1
= 0.100 100 100 100
2
m 0
1 0 ( 0
0 0 . 0
0
m 0
1 0 ( 2 0 0 . 0
0
m 0
1 0 ( ) 0 0 . 0
0
m 0
1 0 ( 6 0 0 . 0
0
m 0
1 0 ( / 0 0 . 0
0
m 0
1 0 ) 0 0 0 . 0
0
m 0
1 0 2 / 0 0
. 0 0
m 0
1 0 2 6 0 0 . 0
0
15!25
(5!25
55!25
m 0
1 0 2 /
1 5 . 2
5
m 0
1 0 ( / 1 5 . 2
5
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!75 75!25
/0 45!25
100
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/5
26
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TEMA Nº 0 A I1 = NEGATIVO / I2 = POSITIVO
SOLUCION 5 CALCULO DE LAS OR
1 Cálculo de la diferencia de pendientes
L1 = '.20% Cot !"# P$to C 104.&4 Para X1 = 0.00 m
L2 = 4.0%
%if. = '7.50
Para X2 = ).75 m
2 Se calcula la Longitud de la Cura! para una
"isi#ilidad de Parada! para lo cual se de#e
$sar el grafico %&'2001 S("!o Para X( = 2).75 m
L+ = 10.00 V = 50.00 ,-/
Longitud de los ramales +i?uierda! derec;a- Para X) = )).75 m
#1 = 0.00
#2 = 100.00
Para X5 = 6).75 m
Se calcula las odenadas
m = *rdenadas del punto medio +P,"-
m = +L1 L2-
200 +L1 L2-
5 Cálculo de las cotas de
m ='7.50 6000.00 pendiente de cada tram
200 160.00
P"!("t" D(t+(
m = '1.)06
'(.20
00.00
0).75
4 Se calcula las odenadas a cada 20.00 m. 2).75
n@ = *rdenadas en un punto cualesuiera )).75
6).75
n@ =X3
mIB$("! P,"
L13
).(0
45.25
75.25
Se calcula las odenadas a cada 20.00 m. 55.25
nA = *rdenadas en un punto cualesuiera (5.25
15.25
nA =X3
mD""+ 00.00
L23
Cálculo de las cotas cor
P"!("t" D(t+(
'(.20
00.000).75
2).75
)).75
6).75
P,"
).(0
45.25
75.25
55.25
(5.25
15.25
00.00
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ENADAS
RAMAL IZQUIERDO RAMAL DEREC9O
0.00 '1.)1 1 = 0.000 Para X1 = 0.00 m 0.00 '1.)1
(600 10000
22.56 '1.)1 2 = '0.004 Para X2 = 15.25 m 2(2.56 '1.)1
(600 10000
612.56 '1.)1 ( = '0.2(4 Para X( = (5.25 m 12)2.56 '1.)1
(600 10000
2002.56 '1.)1 ) = '0.7/2 Para X) = 55.25 m (052.56 '1.)1
(600 10000
)142.56 '1.)1 5 = '1.6(/ Para X5 = 75.25 m 5662.56 '1.)1
(600 10000
Para X6 = 45.25 m 4072.56 '1.)110000
la su#rasante! teniendo en cuenta la C#+$#o !" # +ot !"#
siBCot !" C = 104.
Cot Po8"(: Po8"(:
= 1247.42 m 01 20 15.25 m.00215.25 L +C- = 560.0
= 1247.77 m 01 22 00.00 m.00220.00 ,2 = ).(0
= 1246.41 m 01 2) 00.00 m.002)0.00
= 1246.05 m 01 26 00.00 m.00260.00 D()""+( !" A#t$
= 1245.14 m 01 2/ 00.00 m.002/0.00 si
= 124).70 m 01 20 00.00 m.00200.00 100 su#e ').(0
= 124).40 m 01 22 00.00 m.00220.00 560 D
= 1245.76 m 01 2) 00.00 m.002)0.00
= 1246.62 m 01 26 00.00 m.00260.00D =
'2)0/'= 2).
= 1247.)/ m 01 2/ 00.00 m.002/0.00 100
= 124/.() m 01 (0 00.00 m.00(00.00
= 1244.00 m 01 (/ 15.25 m.00(45.25 COTA DE @ 12*0.
regidas de la su#rasante.
Cot Co"8. Po8"(: Po8"(:
= 1247.42 m 01 20 15.25 m.00215.25= 1247.7/ m 01 22 00.00 m.00220.00
= 1247.15 m 01 2) 00.00 m.002)0.00
= 1246./( m 01 26 00.00 m.00260.00
= 10)70.76 m 01 2/ 00.00 m.002/0.00
= 10)64.1( m 01 20 00.00 m.00200.00
= 1246.1/ m 01 22 00.00 m.00220.00
1246.56 m 01 2) 00.00 m.002)0.00
1247.05 m 01 26 00.00 m.00260.00
1247.66 m 01 2/ 00.00 m.002/0.00
124/.(/ m 01 (0 00.00 m.00(00.00
1244.00 m 01 (/ 15.25 m.00(45.25
1 = 1 =
2 = 2 =
( = ( =
) = ) =
5 = 5 =
6 =
0 . 0
0
)!7
1 5 . 2
5
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m 0
1 0 2 2 0 0 . 0
0
m 0
1 0 2 0
m 0
1 0 2 0
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1 = 0.000
2 = '0.0((
( = '0.175
) = '0.)24
5 = '0.746
6 = '1.276
P(:
4 si si
100 su#e ').(0 100 su#e
0 20.00 ;2 L +- = (20.00 20.00
,1 = '(.20
;1 ='/6
'= 0./6 ;1 ='/6
C 100 D()""+( !" A#t$ @A 100
si si si si
100 su#e ').(0 100 su#e ').(0 100 su#e '(.20 100 su#e
).75 ;1 15.25 ;2 15.25 ;1 ).75
/ ;1 ='20
'= 0.20 ;1 ='66
'= 0.66 ;1 =')/./
'= 0.)4 ;1 ='15.2
100 100 100 100
0
0 0 . 0
0
0 ) 0 0 0 . 0 0
( / 1 5 . 2
5
(5!25
55!25
75!25
(5!25
45!25
))!75
100
6)!75
/0
15!25
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m 0
1 0 2
/ 0 0 . 0
0
m 0
1 0 2 6 0 0 . 0
0
m 0
1 0 2 ) 0 0 . 0
0
m 0
1
0 ( 0 0 0 . 0
0
m
0 1 0 ( 2 0 0 . 0
0
m 0
1 0 ( ) 0 0 . 0
0
m 0
1 0 ( 6 0 0 .
m 0
1 0 ( /
m 0
1
m 0
1
m 0
1 0 2
/ 1 5 . 2
5
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').(0
;2
'= 0./6
'(.20
;2
'= 0.15
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