Ejemplo3.3: ELEMENTOS GEOMÉTRICOS Y DEFLEXIONES DE UNA CURVA CIRCULAR SIMPLE DERECHA DATOS: oo!"e#$"$% "el PI:
N& '((( E& )(( A*+m,- "e l$ -$#e#-e "e e#-!$"$ & 3' / #,lo "e "e=e>+1# p!+#+p$l 89& 0( / o!+e#-$+1#: "e!e2$ A%+%$ "el PC & 45643.76( m R$"+o "e ,!<$-,!$ 8R 8 R9 & 7( m C,e!"$ ,#+"$" 89 & '( m CALCULAR: $9 Lo% "em$% eleme#-o% eom-!+o%;,e $!$-e!+*$# e%-$ ,!<$. 9 L$% "e=e>+o#e%. 9 L$% oo!"e#$"$% "el PC5 PT ? O SOLUCIÓN: a) Elementos geométricos G!$"o "e ,!<$-,!$: G G & (.'64@7@ !$" G & .'@4(7)'0 / T$#e#-e: T T&
6(.6')
m
L &
73.46'
m
CL &
7(
m
E&
'(.4@
m
Lo#+-," "e l$ ,!<$: L
C,e!"$ l$!$: CL
E>-e!#$: E
O!"e#$"$ me"+$: M M & @.37 @.374 44' 4'73 73) )m
&
/ ''B 3'.)4BB
A%+%$ "el PT: A%. PT &
456@0.@' m
b) Defeiones De=e>+1# po! me-!o: "/'(&
estaci!n
Abscisa
Lc
C
*+,*-./,0 *+,-0.000 *+,,0.000 *+,40.000 *+,30.000 *+,/0.000 *+,50.000 *+,60.000 *+,63.651
0 3.*30 13.*30 *3.*30 -3.*30 ,3.*30 43.*30 33.*30 /-.*,1
T
c) Coor"ena"as "el C+ T 9 O 8!o "el p!olem$9
(.6(@0(6370 /
efei!n #$) A%im&t #') # ' ( (( ) 0 0' 0( 0(( -1 *.43,1*-, *' --( 40.5,(( 3.33013/* 3' -6( -3.3(( 10./43*11 10 10' ,4( **.-3(( 1,.54**44 1,' 41( 5.1*(( 15.6,5*65 15 15' 43( 4-.5/(( *-.0,,-,* *-' *( -6.3-(( */.1,0-53 */' 5( *4.-6(( -0 -0' 0( 0(( 61
elementos $2 30 'D R2 /0 m c2 10 m 7c 2 5' 5' 11( -1.4*(( T 2 ,0.,14 m Lc 2 /-.*,1 m CL 2 /0 m E 2 10.5*6 m 8 2 6.-/5 m
Coo!"e#$"$% "el PC
&
4''
/
NPC & @0).3)7@@0 EPC &
Coo!"e#$$"$% "el PT
Coo!"e#$"$% "el e#-!o O "e l$ ,!<$
&
@'
67@.')
/
NPT &
@@@.4@)
EPT &
)6(.6(
&
'4'
NO &
@
[email protected]()
EO &
)3@.'7
/
Ejemplo3.6: ELEMENTOS GEOMÉTRICOS Y DEFLEXIONES DE UNA CURVA CIRCULAR SIMPLE IJKUIERDA DATOS: oo!"e#$"$% "el PI:
N& E& A%+%$ "el PI & A*+m,- "e l$ -$#e#-e "e e#-!$"$ & #,lo "e "e=e>+1# p!+#+p$l 89& o!+e#-$+1#: G!$"o "e ,!<$-,!$ 8G9& C,e!"$ ,#+"$" 89 &
'(((( )((( 45440.((( m 74.) / 0(.) / +*;,+e!"$ 0/ 4( m
CALCULAR: $9 Lo% "em$% eleme#-o% eom-!+o%;,e $!$-e!+*$# e%-$ ,!<$. 9 L$% "e=e>+o#e%. 9 L$% oo!"e#$"$% "el PC5 PT ? O SOLUCIÓN: a) Elementos geométricos R$"+o: R R&
'@'.(73
m
T&
'''.63'
m
L &
4('.007
m
CL &
'@4.)')
m
E&
3(.''
m
T$#e#-e: T
Lo#+-," "e l$ ,!<$: L
C,e!"$ l$!$: CL
E>-e!#$: E
O!"e#$"$ me"+$: M M&
40.('7 m
& &
74/ 3(B (BB 0(/ 3(B (BB
A%+%$ "el PC ? PT: A% PC &
45''6.)0@ m
A%. PT &
453'0.430 m
b) Defeiones De=e>+1# po! me-!o: "/4( &
estaci!n C
T
Abscisa *+11,.436 *+1*0.000 *+1,0.000 *+130.000 *+150.000 *+*00.000 *+**0.000 *+*,0.000 *+*30.000 *+*50.000 *+-00.000 *+-13.*-3
Lc 0 4.,-1 *4.,-1 ,4.,-1 34.,-1 54.,-1 104.,-1 1*4.,-1 1,4.,-1 134.,-1 154.,-1 *01.33/
c) Coor"ena"as "el C+ T 9 O 8!o "el p!olem$9
(.') /
"efei!n #$) #') # ' ( (( ) 0 0' 0( 0(( 0.51,4615 0' ,5( 4*.4-(( -.51,4615 -' ,5( 4*.4-(( 3.51,4615 3' ,5( 4*.4-(( 6.51,4615 6' ,5( 4*.4-(( 1*.51,4615 1*' ,5( 4*.4-(( 14.51,4615 14' ,5( 4*.4-(( 15.51,4615 15' ,5( 4*.4-(( *1.51,4615 *1' ,5( 4*.4-(( *,.51,4615 *,' ,5( 4*.4-(( */.51,4615 */' ,5( 4*.4-(( -0.*4 -0' 1,( 0((
&
A%im&t /*.4
1*
(/ @B (BB
elementos $2 30.4 R 2 161.0/c2 *0 7c 2 3 T 2 111.,-1 Lc 2 *01.33/ CL 2 16*.414,-5 E 2 -0.115 8 2 *3.01/
Coo!"e#$"$% "el PC
Coo!"e#$$"$% "el PT
&
&
74.)
/
NPC &
@@00.6@4
EPC &
6@3.747
'4
/ NPT & '('(.@@0 EPT &
Coo!"e#$"$% "el e#-!o O "e l$ ,!<$
&
)(43.'0
364.)
NO & '('6.744 EO &
630.47(
/
'I m m m m m m m
Ejemplo3.): ELEMENTOS GEOMÉTRICOS Y DEFLEXIONES DE UNA CURVAS CIRCULARES SIMPLES De!I*; DATOS: D+%-$#+$ "el PI' $l PI4 & 4((.3 m C' : A%+%$ "el PC' & 65476.((( m #,lo "e "e=e>+1# p!+#+p$l 89& 0.033336 / o!+e#-$+1#: "e!e2$ G!$"o "e ,!<$-,!$ 8G9& 0.) / C,e!"$ ,#+"$" 89 & '( m CALCULAR: $9 Lo% "em$% eleme#-o% eom-!+o%;,e $!$-e!+*$# e%-$ ,!<$. 9 L$% "e=e>+o#e%. SOLUCIÓN: a) Elementos geométricos R$"+o: R R&
.'@)
m
T&
3.')@
m
L &
'33.44
m
CL &
'4'.((
m
E&
33.(43
m
T$#e#-e: T
Lo#+-," "e l$ ,!<$: L
C,e!"$ l$!$: CL
E>-e!#$: E
O!"e#$"$ me"+$: M M&
46.(47 m
&
0/ 3B (BB
&
0/ 3(B (BB
A%+%$ "el PC ? PT:
A%. PT &
656(7.44 m
b) Defeiones De=e>+1# po! me-!o: "/'( &
estaci!n
Abscisa
(.34) /
C
,+*/,.000 ,+*50.000 ,+*60.000 ,+-00.000 ,+-10.000 ,+-*0.000 ,+--0.000 ,+-,0.000 ,+-40.000 ,+-30.000 ,+-/0.000 ,+-50.000 ,+-60.000 ,+,00.000
"efei!n #$) #') # ' ( (( ) 0 0 0' 0( 0(( 3.000 1.64 1' 4/( 0(( 13.000 4.* 4' 1*( 0(( *3.000 5.,4 5' */( 0(( -3.000 11./ 11' ,*( 0(( ,3.000 1,.64 1,' 4/( 0(( 43.000 15.* 15' 1*( 0(( 33.000 *1.,4 *1' */( 0(( /3.000 *,./ *,' ,*( 0(( 53.000 */.64 */' 4/( 0(( 63.000 -1.* -1' 1*( 0(( 103.000 -,.,4 -,' */( 0(( 113.000 -/./ -/' ,*( 0(( 1*3.000 ,0.64 ,0' 4/( 0((
T
,+,0/.*5*
1--.*5*
8!o "el p!olem$9
Lc
,-.-1333/ ,-' 16( 0((
&
A%im&t
(/ '@B 3(BB
elementos $ 2 53.3----, 'D R 2 55.164 m c2 10 m 7c 2 3.4 ' T 2 5-.146 m Lc 2 1--.*5* m CL 2 1*1.005-,- m E 2 --.0*- m 8 2 *,.0*/ m
DATOS:
C* : #,lo "e "e=e>+1# p!+#+p$l 89& 04.7 / o!+e#-$+1#: +*;,+e!"$ G!$"o "e ,!<$-,!$ 8G9& 6.600007 / C,e!"$ ,#+"$" 89 & )m CALCULAR: $9 Lo% "em$% eleme#-o% eom-!+o%;,e $!$-e!+*$# e%-$ ,!<$. 9 L$% "e=e>+o#e%. SOLUCIÓN: a) Elementos geométricos R$"+o: R R&
06.')3
m
T&
3@.(3
m
L &
7(.'7
m
CL &
00.7)3
m
E&
'(.@07
m
T$#e#-e: T
Lo#+-," "e l$ ,!<$: L
C,e!"$ l$!$: CL
E>-e!#$: E
O!"e#$"$ me"+$: M M&
@.300 m
&
04/ 64B (BB
&
6/ 4B (BB
A%+%$ "el PC ? PT: A% PC &
656).7' m
A%. PT &
65))0.()7 m
b) Defeiones De=e>+1# po! me-!o: "/) &
estaci!n C
T
Abscisa ,+,54.5/1 ,+,60.000 ,+,64.000 ,+400.000 ,+404.000 ,+410.000 ,+414.000 ,+4*0.000 ,+4*4.000 ,+4-0.000 ,+4-4.000 ,+4,0.000 ,+4,4.000 ,+440.000 ,+444.000 ,+443.04/
8!o "el p!olem$9
Lc 0 ,.1*6 6.1*6 1,.1*6 16.1*6 *,.1*6 *6.1*6 -,.1*6 -6.1*6 ,,.1*6 ,6.1*6 4,.1*6 46.1*6 3,.1*6 36.1*6 /0.15/
(.6600007 /
"efei!n #$) A%im&t #') # ' ( (( ) 0 0' 0( 0(( 1.5,,,40*3 1' 40( ,0.0*(( ,.0///5-/3 ,' ,( ,0.0*(( 3.-1111/*3 3' 15( ,0.0*(( 5.4,,,40/3 5' -*( ,0.0*(( 10.////5,- 10' ,3( ,0.0*(( 1-.01111/5 1-' 0( ,0.0*(( 14.*,,,41- 14' 1,( ,0.0*(( 1/.,///5,5 1/' *5( ,0.0-(( 16./11115- 16' ,*( ,0.0-(( *1.6,,,415 *1' 43( ,0.0-(( *,.1///54- *,' 10( ,0.0-(( *3.,111155 *3' *,( ,0.0-(( *5.3,,,4*- *5' -5( ,0.0-(( -0.5///545 -0' 4*( ,0.0-(( -1.-4 -1' *1( 0((
&
(/ 40B 6BB
elementos $2 3*./ R 2 3,.14c2 4 7c 2 ,.,3333/ T 2 -6.05Lc 2 /0.15/ CL 2 33./4--5,E 2 10.63/ 82 6.-33
'D m m m m m m m
Ejemplo3.0: ELEMENTOS GEOMÉTRICOS Y DEFLEXIONES CURVAS CIRCULARES SIMPLES De!e2$De!e2$ DATOS: D+%-$#+$ e#-!e PI' $l PI4 & C': A*+m,- "e l$ -$#e#-e "e e#-!$"$ & #,lo "e "e=e>+1# p!+#+p$l 89& o!+e#-$+1#: A%+%$ "el PC & R$"+o "e ,!<$-,!$ 8R9 & C,e!"$ ,#+"$" 89 &
'( m 3( / 0( / "e!e2$ (.((( m 0.64' m '( m
& &
3(/ (B (BB 0(/ (B (BB
CALCULAR: $9 Lo% "em$% eleme#-o% eom-!+o%;,e $!$-e!+*$# e%-$ ,!<$. 9 L$% "e=e>+o#e%. SOLUCIÓN: a) Elementos geométricos G!$"o "e ,!<$-,!$: G G & (.'')77747 !$" G & 0.033)60 / & T$#e#-e: T T&
6@.@)
m
L &
@(.66@
m
CL &
0.64'
m
E&
'3.30@
m
Lo#+-," "e l$ ,!<$: L
C,e!"$ l$!$: CL
E>-e!#$: E
O!"e#$"$ me"+$: M M & ''.)74'0 m
0/ 3B (.7BB
A%+%$ "el PT: A%. PT &
@(.66@ m
b) Defeiones De=e>+1# po! me-!o: "/'(&
estaci!n C1
T1
Abscisa 0.000 0.000 10.000 *0.000 -0.000 ,0.000 40.000 30.000 /0.000 50.000 60.000 60.,,6
8!o "el p!olem$9
Lc 0 0.000 10.000 *0.000 -0.000 ,0.000 40.000 30.000 /0.000 50.000 60.000 60.,,6
(.33'07766 /
&
"efei!n #$) A%im&t #') # ' ( (( ) 0 0' 0( 0(( -0 0 0' 0( 0(( -.-13//,,- -' 16( 0.-6(( 3.3--4,553 3' -5( 0./5(( 6.640-*-*6 6' 4/( 1.13(( 1-.*3/06// 1-' 13( 1.44(( 13.45-5/** 13' -4( 1.6,(( 16.6003,33 16' 4,( *.--(( *-.*1/,*1 *-' 1-( *./*(( *3.4-,164, *3' -*( -.1(( *6.5406366 *6' 41( -.,6(( -0 -0' 0( 0(( 60
(/ '@B )6.(6BB
elementos $2 30 R 2 53.,*1 c2 10 7c 2 3' -5( 0./5(( T 2 ,6.564 Lc 2 60.,,6 CL 2 53.,*1 E 2 1-.-36 8 2 11.4/5
DATOS: C4: A*+m,- "e l$ -$#e#-e "e e#-!$"$ & #,lo "e "e=e>+1# p!+#+p$l 89& o!+e#-$+1#: A%+%$ "el PC & R$"+o "e ,!<$-,!$ 8R9 & C,e!"$ ,#+"$" 89 &
@( / 6 / "e!e2$ '(.60@ m @(.(34 m '( m
& &
@(/ (B (BB 6/ (B (BB
CALCULAR: $9 Lo% "em$% eleme#-o% eom-!+o%;,e $!$-e!+*$# e%-$ ,!<$. 9 L$% "e=e>+o#e%. SOLUCIÓN: a) Elementos geométricos G!$"o "e ,!<$-,!$: G G & (.''''47@ !$" G & 0.3074'(6 / T$#e#-e: T T&
6(.()
m
L &
7).30
m
Lo#+-," "e l$ ,!<$: L
C,e!"$ l$!$: CL CL & 73.43040@ m
E>-e!#$: E
E&
.)4(
m
O!"e#$"$ me"+$: M M & 7.7307)30 m
&
A%+%$ "el PT: A%. PT &
4)).)0 m
b) Defeiones De=e>+1# po! me-!o: "/'(&
estaci!n 'D m m m m m m m
C*
T*
Abscisa 150.,36 160.000 *00.000 *10.000 **0.000 *-0.000 *,0.000 *40.000 *44.543
8!o "el p!olem$9
Lc 0 6.4-1 16.4-1 *6.4-1 -6.4-1 ,6.4-1 46.4-1 36.4-1 /4.-53
(.3'30()6 /
&
"efei!n #$) A%im&t #') # ' ( (( ) 0 0' 0( 0(( 60 -.0-,16363 -' *( -.11(( 3.*1/50*-5 3' 1-( ,.06(( 6.,01,0/5 6' *,( 4.0/(( 1*.45401-* 1*' -4( 3.04(( 14./353153 14' ,3( /.0-(( 15.64***,1 15' 4/( 5.01(( **.1-45*64 **' 5( 5.66(( *, *,' 0( 0(( 1-5
(/ '@B 0.'BB
$2 R2 c2 7c 2 T2 Lc 2 CL 2 E2 82
0/ 44B '.@0BB
elementos ,5 'D 60.0-* m 10 m 3' **( 1.63(( ,0.054 m /4.-53 m /-.*-53*36 m 5.4*0 m /./5, m