PRACTICA N°1 REPLANTEO DE CURVA CIRCULAR SIMPLE (METODO DE DEFLEXIONES Y CUERDAS)
VÍAS I
DOCENTE
SEMESTRE VI
FACULTAD DE INGENIERÍAS DEPTO. DE INGENIERÍA CIVIL 17/09/201!2
TABLA DE CONTENIDO
INTRODUCCI"N.........................................................................1 #USTIFICACI"N..........................................................................2 O$#ETIVOS...............................................................................3 O$#EIVO GENERAL%...................... GENERAL%........................................................................................& ..................................................................& .1 MARCO TE"RICO .......................................................................
4
PROCEDIMIENTO Y E'UIPOS UTILIADOS ......................................... 5 RESULTADOS ............................................................................
6
SOLUCION DE PREGUNTAS. ..........................................................
7
ANLISIS DE RESULT RESULTADOS............................................................ 8 CONCLUSIONES.........................................................................
9
1. INTR INTROD ODUC UCCI CION ON.. L*+ ,-*+ ++ + 3 456 656++*8 ** * +:65*5 *:3*; +3 64*:6* *56:* * :+65*5 5 :436:*:6< =3 >6+ + 3+ 5 53::6< 53::6< ? :+34 ? + @* 64*: 64*: * :4-* 5 3* :635*5 *-+. E +*5 5 +*+ ,-*+ 63? +8 :4:6 5 *+ :*65*5+ 55 + :3; + +* 3* 5 *+ *B+ *+ :3*+ *+ :**+ 58 +3*+ +3*+ * 3+ *4+ *4+ 5 56+ :4 * +6:*; +6:*; :4565*5; :4565*5; :4-* ? +@365*5. P** 56+ 5 * ,-* + 6 :3* *:+ *486*+; 8*:6*+; :<46:+; :. *54+ 5 *+ +:66:*:6+ :6:*+ =3 ** 3+ :*+ + 5*5*+ *+ 4*+ INVIAS. S 46B* +::6*5 * 3* =3 5 *:35 * ++ *4+ + *3+ 4 * * +:6,* :+65*5 5 :43 :436 6:* :* 5+ 5+ 3 3+ + + +::-66:+ :+;; *+ *+ *B *B*5 *5 5 +* +* 3* 3* +3 +3* * *6*46+ :+ =3 566:3* * 4,665*5 5 + ,-:3+ :3* + *: :+*6 56+* :3,*+ =3 *:66 * *+6:6< 5 + 46+4+; +*+ :3,*+ 35 + +64+ 5 3 + *56; :43+*+ +6*6B*5*+. E + 64 + 8*+* * 5 3* :3,* :6:3* +64. S :5 * *+4* :*4 5*+ ,6*4 :*:3*5+ 6:6* ** 3@ 3@ *: *: :4* :4**:6 *:6+ + =3 + +*8 +*8: : * >*:6 >*:635 35 5 * :6 :6:* :* *6B*5*.
2. #UST #USTIF IFIC ICAC ACIO ION N E+* :6:* + *: : 86, 5 5+** ? :6:* + ::646+ 865+ <6:*4 *::* 5 3 :: 8+6: 56+ @46: 5 :**+ :4 + * :3,* :6:3* +64; :3* +*8: 8*++ ** ::+ ::+ *H 4+ *,*B*5+ *,*B*5+ + :*4 5 * 6@6-* 6@6-* ? 46 * + +356*+ **6B* 5 3* 3* 4** 43? :6:* ? :6 + +68+ 6:,6 6:,6+ + ? + =3 + 35 :* :* * 5 *8* *8* * * * 5 ,* * :*4 + 5*+ 865+ ,6*4 6:6*; :3* + 55-* * :*@ :*@6 6B* B* +* +* *:6 *:6,6 ,65* 5*5 5 :4 :4 3* 3* 5 *+ *+ 35 35*4 *4 * *+ + ** ** 3 +356* 5 6@6-* :6,6 =3 ,** :*46*5 *:6* 56+ 5 :**+.
&. O$#E O$#ETI TIVO VOS S &.1O$#ETIVO GENERAL
R*6B* ::3 ? * 5 3* :3,* :6:3* +64; 456* *+ *6:*:6+ 5 45 5 5>6+ ? :35*+ ? 5 *:35 * * 64*:6< ? * *+ 6+3::6+ @*5*+ 5:.
. MARC MARCO O TEO TEORI RICO CO CURVA CIRCULAR SIMPLE U* U* :3, :3,* * :6: :6:3 3* * +64 +64 + 3 *: *: 5 :6: :6:3 3 :6 :6* * *@ *@ * 5+ 5+ *6*46+ :+; * :3,* + 56 +3 *56 :3* + 5+6@*5 56+ 56+* *5 5; :4 :4 4 :, :, @* @* :45 45665*5 5*5 ? : :4 4-* -* 5 * :+ :+3: 3::6 :6< <;; 4* 4* 64 646 6 ? 3: 3:6 6* *46 46 ;; 58 58 + 4 4 * 656:*5 *+ 4*+ 5 INVIAS :4 : * ,:65*5 5 56+.
Imagen 1. E4+ 5 3* :3,* :6:3* +64.
E4+ @46:+ =3 :**:6B* 3* :3,* :6:3* +64% T4*5 T4*5 +65 5 *,*: 5 6B=365* * 5:*; 56:+ 4+ +% PI = 3 5 6+::6< 5 *+ *@+ ,6: 5 * :3,*. PC = 6:66 5 * :3,*% 3 55 46* * *@ 5 *5* ? 46B* * :3,*. PT = 6:66 5 * *@% 3 55 46* * :3,* ? 46B* * *@ 5 +*65* O = : 5 * :3,* :6:3*. J K @3 5 5>6< 5 *+ *@+% @3 5 5>6< 6:6*. E+ 6@3* * @3 :* +38565 *: PC.PT. R = *56 5* :3,* :6:3* +64. T = *@ +38*@% 56+*:6* 5+5 PI *+* PC 5+5 PI * PT. L = @635 5 * :3,* :6:3*% 56+*:6* 5+5 PC * PT * *@ 5 * :3,* :6:3*; 5 3 -@ 5 :35*+. CL = :35* *@*% 56+*:6* -* :* 5+5 PC * PT.
E = >*% 56+*:6* 5+5 PI * 3 456 5 * :3,* A M= 5*5* 456*% 56+*:6* 5+5 3 456 5 * :3,* A * 3 456 5 * :3,* $. REPLANTEO DE UNA CURVA CIRCULAR CIRCULAR SIMPLE:
E>6+ 45+ ** ** 3* :3,* :6:3* *@3+ 4+ 6:6+ =3 + ? 4+ :6:+; :6:+; ? + : *@3*+ 646*:6+ 646*:6+ =3 646:* * * * *6 5 PC *+* 3 456 ? * *6 5 PT *+* 3 456. 1.
S 35 :*6B* * :3,* * *6 5 PC ? *: :6 PT 66:6* PT ? :* * :3,* PC. PROCEDIMIENTO DE CAMPO DEFLEXIONES Y CUERDAS .
S 6,* =36 PI; + :* +65 :*6 * *8:6+*5 + 465 * +38*@ ? + 4*6*6B* PC : +*:* ? 36* 1.2. D+5 46+4 3 + 465 * 5>6< 6:6*; * +38*@ ? + 4*6*6B* PT : +*:* ? 36*. 1.3. S 6+** =36 PC; + :* PI :+; + 4*:* * 64* 5>6< ? + 465 * :35* 5+5 PC *+* 64 3. 1.4. S 4*:* * +6@36 5>6< ? * *6 5 64 3 :*6B*5 + 465 * 56+*:6* :+56 :*5 +@35 3. 1.5. L+ 54+ 3+ ** :*6B* * :3,* + :*6B* 46+4 :5646 *+* @* * PT 1.6. A @* * PT + +*8: + + 5 :6 *@3* ? :6 6*. A48+ + + +*8: :-4+. : -4+. 1.1.
. PROCEDIMI PROCEDIMIENTO ENTO Y E'UIPOS E'UIPOS UTILIADOS UTILIADOS M*6*+ 366B*5+ 1. 2. &. .
T5 566 T-5 2 #* #*+ C6 C6* * 4 46 6:* :*
. . 7. .
U* U* 4 4*5 *5* * I4* I4*:6< :6< 5 6:6 6:6* * (:: (::3 3+) +) E+* E+*:* :*++ ? 3 366* *++ U 4*B 4*B 4* 4*66
PROCEDIMIENTO DE CAMPO. 1. L:*6B* L:*6B* 3 3 3 *86*6 *86*6 :*4; :*4; :3* +* +* PI; :3* + *6B* * 6+**:6< 5 =36. 2. P** :+ :+ *:*546:+ *:*546:+;; +356* +356* 58 +*8 +*8: : 3 *86*6 *86*6; ; ?* +* 3 8 >6+ (8; +; :.) 4*6*6B*5 : 3* +*:*; ? 6* * *@ 5 *5* 386:*5 PC : 8*+ * 4565* 5 * +38*@; 5* 865 +356* * *6 5 + 5*+ 5*+ +3466 +3466+ +*5 *5++ 5: 5: ? 6 65 5 :3* :3* *+ 43*+ 43*+ +356*5*+ +356*5*+ :*++ <6:*+. E+ PC + 386:* :*4 : +*:* ? 36*. &. S 58 :*:3* :*:3* 348 348 5 * *@ *@ 5 5 +*65* +*65* 5 *:35 *:35 * + 348+ 348+ 5 *5* ? @3+ 5 5>6< @*5+ 5: ? 65 :3* :3* + :3*5*+ :3*5*+ 55 + :3* *+ *@+ ? + 4*:* + @3 + :*6B* 3 PT : +*:* ? 36* : * ,6+3* ? * @635 5 +38*@:6*. . A* A*;; + 6+* 6+** * =36 =36 PC PT; PT; * :6 :6< < 5 + + +3 +356 56* *+; +; + :* PI ? ::* :+ =36. . S 4*:* 4*:* * 64* 64* 5>6< 5>6< 4 =3 :+ :+5* 5* * * +38 :35* :35* *5? *5?*: *: * 6@ 6@ 5 5 * * ; ; 5* 5* =3 =3 58 58 + + * **5 *5 : : *665*5 + +356*+ : 8*+ * <43*+ +356*5*+. C * 56+*:6* 53: 5 * 56:6* * *8+:6+* 55* +36 66 <>64* * PC PT +:6,*4 +@H :*+ ? * *8+:6+* 5 PC PT + 386:* + 64 64 3 5 * :3,* : +*:*. . A : :6 63* 3*:6 :6< < + 386: 386:* * :*5* :*5* 3 3 5 + + ++ 3 3+ + +8 +8 * :3, :3,*; *; :+56+ * * :35* 36*6*; *@@*5 * * 5>6< *6 ,* 5 G/2 ,* :+56 * * +38 :35*; *+* @* * PT * PT. 7. E 3 3 6* 6* 55 55 46 46* * * :3,* :3,*;; + : :+* +*6 6 5 54 46 6* * + + ++ 5 :6 :6 *@3 *@3* * ? 6 6* *;; > >+ +*5 *5+ + @*5 @*5+ + 463 463 ++ ? +@35+ ? :-4+ +:6,*4. E+ 5 656:* + +3*5+ ? + H6 ** *6+6+ ? *+ ::3+6+. . P** P** :+ :+ 5 :4** :4** + +3* +3*5+ 5+ 865 865+ + * :6: :6:* * : + 865+ <6:*4 456 5 *+ 43*+ + 58 *6B* *+ 456:6 456:6+ + 5 + 4 4+ + +* +*+ + 3* ,B 6*6 6*6B*5 B*5* * * :6: :6:*. *. (:35* *@*; @635 5 * :3,*; >* ? 5*5* 456*).
. CALCUL CALCULOS OS Y RESUL RESULT TADOS C3,* :6:3* +64 * * 6B=365* R= 44 m Rumbo TE= N 88 88 ° E
∆ =86 °
| PC |= k 0 + 025.2 c =10
S38*@ (ST)% ST = 44 ∙ tan
86 ° = 41.03 m 2
E>* (E)% E= 44 ∙
(
1 cos
( ) 86 °
)
−1 =16.16
2
m
O5*5* M56* (M)%
(
M =44 ∙ 1−cos
)
86 ° =11.89 m 2
C35* L*@* (L)% CL=2 ∙ 44 ∙ sin
( )= 86 ° 2
60.015 m
G*5 5 * C3,* (G)% −1
G=2 ∙ sin
(
)
10 m ' =13 ° 2 59.85 2 ∙ 44 m
L@635 5 * C3,* (L)% '
13 ° 2 59.85 } right ) = 65.9 m 10 m ∙ 86 °
¿ L= ¿
D>6< C35* U6*6* (
δc
)
'
13 ° 2 59.85 } over over {2} {2} = 6°31'29.93'' 6°31'29.93''
δc=¿
D>6< M ( δ m )
'
13 ° 2 59.85 } over {210}
! δ = 0° {39} " {'} 8.99
δ m= ¿
A$CISAS AbsPC # K 0 0 + 025.2 , AbsPI # K 0 0 + 066.23 # ( K 0 0+ 025.2 )+ 65.9 , AbsPT # # K 0 0+ 091.1 AbsPT #
AbsPM # ( K 0 + 025.2 )+
65.2 , AbsP AbsPM M # K 0 + 058.15 2
CALCULO DE DEFLEXIONES δ =c ∙δ m + δ anteror '
$0=3°%'55.16''' δ Ko + 030 =4.8 ∙ 0 ° 39 8.99 $0=3°%'55.16'
L*+ 54+ 5>6+ + :*:3* 5 6@3* 4*. PUNTO
ABSCISA
CUERD A
DEFLEXION
PC
O2.2 O0&2
0 .
0 3 ° % ' 55.16 ' '
O00
10
9 ° 39 09 ' '
000
10
16 ° 10 55.01 ' '
00.1
.1
21 ° 29 59.3 ' '
000
1.
22 ° 42 24.94 ' '
0070
10
29 ° 13 54.86 ' '
000
10
35 ° 45 24.%9 ' '
0090
10
42 ° 16 54.%1 ' '
0091.1
1.1
42 ° 59 58.61 ' '
PM
PT
Taba 1. D*+ 5 6:6* Error !or "e#ecto= 0 ° 0 $ 2.%9 $ $
'
'
'
'
'
'
'
'
D*+ 5 :*4% E=16.1% m
Error Error %nea%=5 cm !or "e#ecto "e#ecto
7. SOLUCI SOLUCION ON DE PREGUN PREGUNTA TAS. S. 1. D!ga D!ga e "#$% "#$%e& e&!m !m!e !en' n'$ $ "a#a "a#a %(e) %(e)*e *ea# a# en e %am" %am"$ $ e +a$ +a$## &e a e,'e#na- %*e#&a a#ga $#&ena&a me&!a.
E :5646 5 :*4 ** :=3* * >*; 65 3 456 5 * @635 5 *:; + 465 : 3* :6* * 56+*:6* =3 ** 3 456 ? PI; *+- 84+ * >*. P** * :35* *@*; 65 PC ? PI 4*6 4*6* *6B 6B*5 *5+ + : : 3* 3* +*:* +*:* 456 4564 4++ * 56+ 56+* *:6 :6* * ++ ++.. Y ** ** :=3* * 5*5* 456*; 65 3 456 5 * @635 5 *: ? 65 * 46*5 5 * :35* *@*; 4564+ : * :6* ? 5 + 45 84+ * 5*5* 456*. 2. Pa#a Pa#a &e'e#m!n &e'e#m!na# a# e g#a&$ g#a&$ &e *na %*#+a %*#+a /e "*e&e (a%e# (a%e# "$# e m0'$&$ m0'$&$ &e a %*e %*e#&a *n!' n!'a#!a #!a "$# e a#%$ *n!'a#! 'a#!$ $. C* C* m0'$&$ #e%$men&a#a */'e& E,"!)*e a/ #a$ne/.
A48+ 45+ + + :6:*4 + 46+4; * +* 5 =3 + 43:*+ *+ 56:6*+ ++ 5+ 45+; + :465* 366B* 45 5 * :35* 36*6*; =3 + 45 + 4+ *:6: * * * 5 *6B* * 456:6+ :*4; 5865 * +3 :6 4* =3 + 46 + 4+ >*:+ : *:6< * + ::3+ *6B*5+. 3. E/'ab E/'abe%a e%a $/ "#$/ "#$/ $/ %$n'#a/ %$n'#a/ &e #e"an #e"an'e$ 'e$ &e %*#+a/ %*#+a/ %!#%*a#e %!#%*a#e/ / /!m"e/ "$# e m0'$&$ &e ng*$/ &ee,!$ne/. Pro:
S 35 *6B* 456:6+ :*4 ** 546* * >*:635 + ::3+ *6B*5+ *8* 5 6:6*; :4 ,* 5 * >*. E *8* 5 6:6* + +:6 ? 65 5 *:. Contra.
S 6 =3 6+** =36 5+ ,:+ =3 *: 4+ 56+ *8* 5 :*4 =3 *? =3 *6B* * 6,*:6< 5 =36 5+ ,:+; :+* =3 =36* 64.
. ANALIS ANALISIS IS DE RESUL RESULT TADOS. ADOS.
E 6* 865 :*4 3 5 :4 5:; :3* +6@66:* +6@66:* =3 * :3,* 4565* :*4 3, 3* @635 @635 4 * * :*:3*5* 6:6* ? : +: * * @635 * :* 5 3 5 0.07Q :3* + 43? 4-64 *:6< : *4* 5 * :3,*.
A *6B* :=3 5 * >* + 83, 3 5 0.014 :3* =36,* * 1:4; + +6@66:* =3 *+ 4565*+ :*4 + *?* :3*5 6::*4 5865 * =3 ,* + 43? 4-64 ? + * 565 +3:5 5865 * *+ *>64*:6+ *6B*5*+ * =36 * 44 5 *6B* *+ :3*+.
+ 35 **56 =3 + 5*+ :*:3*5+ 6:6* + -* *>64*:6+ 43? =3*+; *+ :3*+ * + 55*5*+ * * :*68*:6< 5 56 366B*5 (10 +@35+); :,* * =3 + 54+ + :465+ :6:* + 4*>646:.
E * 5 +* :3,* :6:3* +64 + *:* =3 + + :465+ 3 43? =3+.
9. CO CONC NCLU LUCI CION ONES ES.. •
L*+ L*+ :3, :3,*+ *+ :6: :6:3 3* *+ + +64 +64 ++ + + 5 @* @* 36 3665 65*5 *5 ** ** 56+ 56+ @46: 5 :**+; ?* =3 + +64+ ? 5 65* :4+6< *54+ 5 =3 ::3+ ? :++ =3 +* * + +64+ ? 5 :6
•
*6B*:6<. T* * *8* *8* 5 6:6* 6:6* :4 5 :*4 + *6B* 5 3* 4*5* *:*8 ?* =3 + + 5 :6 *@3* ? 6* 56 58*
•
10:4 =3 + 83 ** @**6B* 3 <64 *B*5 5 * ,-*. E 45 5 5>6+ ? :35*+ + 5 :6 5646 ? =3 46 3* 83* *6B*:6< 5 * 5 3* :3,* :6:3* +64.
