DISEÑO DE MURO DE CONTENCION EN VOLADIZO TIPO I (M - 01)
DISEÑO DE MURO DE CONTENCION EN VOLADIZO TIPO I (M - 01)
Datos:
Datos:
t1t1P
Peesso o EEssppeeccífífiicco o ddeel l tteerrrreenno o ((TTnn//mm33)) PPs s == 1.601.60 øø P
Peesso o EEssppeeccííffiicco o ccoonnccrreetto o ((TTnn//mm33)) PPc =c = 2.402.40
An!lo fricci"n intern# o re
An!lo fricci"n intern# o reposo$ (%)poso$ (%) & & == 3030
An!lo/'oriont#lt#l!d de
An!lo/'oriont#lt#l!d del *#teri#l (%)l *#teri#l (%) ø ø == 00
T
T##ll!!d d ddeel l *#*#tteerrii##ll$$ + + == 00
,
,eessiisstteennccii# d# deel cl coonnccrreetto (o (--//ccmm22)) f f c =c = 210210 == 44..00
ll!!eennccii# # ddeel l AAcceerro o ((--//ccmm22)) ff = = 42004200
##pp##cciidd##d d PPoorrtt##nntte e ((--//ccmm22)) c =c = 0.500.50 t t
##ccttoor r dde e ee!!rriidd##d d dde e 77oolltteeoo 7 7 == 2.002.00
##ccttoor r ee!!rriidd##d d 88eessllii##mmiieennttoo 8 8 == 1.901.90
#ctor
#ctor de de fricci"n fricci"n f f =T =T & & f f == 0.950.95 t2t2 Alt!r# del *!ro$ (m)
Alt!r# del *!ro$ (m) == 4.04.0
p
pmm((ttnn//mm33))== ppmm == 2.102.10
E
Essppeessoor r ss!!ppeerriioor r ddeel l **!!rroo$ $ ((ccmm)) tt1 1 == 29.0029.00
,
,eecc!!::rriimmiieenntto o een n eel l mm!!rro o ((ccmm))$$ rr1 =1 = 4.004.00
,
,eecc!!::rriimmiieenntto o een n ll# # ##pp##tt# # ((ccmm)) ;;22 ;;11 #r#
#r# !perior$ !perior$ r1 r1 == 4.004.00
#r#r# <# <nnfeferrioior er en cn coontnt#c#cto to ccon on TTererrrenenoo rr2 2 == .90.90 ;;
(!#ndo el relleno tiene pendiente) (!#ndo el relleno tiene pendiente) --## --## == 00..3333 tt11 --##PPss --##PPss== 00..9933 * *! ! == 1199..99>> #dem?s$ E #dem?s$ E == 44..00 donde@ donde@ &
& & & == 0.>00.>0 t2t2
: :((ccmm)) :: == 100.00100.00 -# Ps -# Ps ((cc!!##nnttíí##)) == 0.0040.004 @@ ff//ffcc == 00..005500
ii!!##ll##nnddo o mmoommeennttooss$ $ rreeeemmppll####nnddo o BB##lloorrees s ddeessppeeCC##nnddo o dd 00..2299 d d ((ccmm) ) d d == 3322..>> tt22 == 33..00 44..3300 D Dss##rreemmooss@ @ tt2 2 ((ccmm)) tt2 2 == 49.0049.00 c
coon n eesstte e BB##lloor r dde e tt22$ $ sse e oo::ttiieennee$ $ d d ((ccmm)) d d == 4400..2211 d
d11((ccmm)) dd11 == 2200..2211 00..4400
Verii!a!i"# $or !orta#te
Verii!a!i"# $or !orta#te
0.490.497 7dd! ! == 55..3322 7 7! ! ((ttnn) ) @ @ 77dd!!//& & = = 77dd!!//00..5599 77! ! == >>..>> 7 7c c == 2299..22 00..2299
V
V!
! %
% V
V&
&
''O
O
øø ((ccmm) ) @ @ tt2 2 9 9 == 9900..0000 D Dss##rreemmooss@ @ ((ccmm)) == 90.0090.00 PP11 PP22 t t ((ccmm) ) @ @ t t == 99..2200 T T @ @ 8 8 ((--# # PPs s / / ((2 2 ppm m ff)) T T == 00..3333 : :1) 1) ;1;1//t t @ @ T T / / (1 (1 + + T) T) ;1;1//t t == 0.0.3333 ; ;11((mm)) ;;11 == 11..22 EE==--##PPssttFF22//22 ; ;1 1 ((mm) ) @ @ ;;1 1 ((tt2 2 tt11) ) / / 22 ;;1 1 == 11..5522 D Dss##rreemmooss$ $ ;1 ;1 ((mm)) ;;1 1 == 2.402.40 : :22) ) ;;22//t t GG= = ((ff//33))((77//88));;11//((22tt)) ;;22//t t == 00..003 3 tt//3 3 == 11..33 ; ;2 2 ((mm) ) GG= = ;;2 2 == 00..1166 PP33 D
Dss##rreemmooss$ $ ;;22mmíínn..((mm)) ;;2 2 == 1.101.10
A
A
Anco de +#p#t#$ ; (m)
Anco de +#p#t#$ ; (m) @ @ ;2 ;1;2 ;1 ; ; == 3.903.90 1.101.10 2.402.40 E
E == ..11 33..9900
a) Di*e#sio#a*ie#to +e, M&ro
a) Di*e#sio#a*ie#to +e, M&ro
-# = osø (cosø H(cosø)-# = osø (cosø H(cosø)22 (cos&) (cos&)22 I I1/21/2 ) / (cosø H ) / (cosø H (cosø)(cosø)22 (cos&) (cos&)22 I I1/21/2 ) )
*! *! (tnm) @ 1. (tnm) @ 1. -# Ps -# Ps 33 / 6 / 6 *! *! (-cm) = (-cm) = & : d& : d22 fc fc (1 0.9> )(1 0.9> ) *! 10 *! 1099 = & : d = & : d22 fc (1 0.9> ) fc (1 0.9> ) t2 (cm) @ d r1 t2 (cm) @ d r1 & 9/5J& 9/5J / 2 / 2 7d! (tn) @ 1.7d = 1.HPs-#(d) 7d! (tn) @ 1.7d = 1.HPs-#(d)22 /2I /2I 7c (tn) @ 0.93 (fc) 7c (tn) @ 0.93 (fc)1/21/2 : d : d
)
) Di*e#sio#a*ie#to
Di*e#sio#a*ie#to +e ,a Za$ata
+e ,a Za$ata
E @
DISEÑO DE MURO DE CONTENCION EN VOLADIZO TIPO I (M - 01)
EB @ E sen( ø ) EB = 0.00DISEÑO DE MURO DE CONTENCION EN VOLADIZO TIPO I (M - 01)
'# = .1 s(m)@ t/3 s = 1.3 *# (tnm/m) @ '# s *# = 12.4 Peso P$ (tn) K (m) (tnm)$ en el p!nto A P1 t1 Pc = 2.520 1.229 P1 K1 = 3.499 1/2( (t2t1) ) Pc 1.125 1.459 P1 K1 = 1.69 P2 (;1 t2) Ps = 14.660 2.929 P2 K2 = 3.01 P3 ; Pc = 4.200 1.90 P3 K3 = .390 EB E sen(ø) = 0.000 3.900 EB K4 = 0.000 Pr= 22.505 *r= 4>.4>6 7 @ *r/*# 7= 3.>> G 2.00O
8 @ Pr f / '# 8 = 1.54 G 1.90O
P!nto de p#so de l# res!lt#nte$ respecto # A@
KB (m) @ (*r *#) / Pr KB = 1.63 m ELcentricid#d@
e (m) @ (; /2) KB e = 0.12 m ; / 6$ de:e ser m#or M!e JeJ $ ; / 6 = 0.95 N-O
1 (tn/m2) @ (Pr / ;) (1 6 e / ;) 1 = .56 = 0.56 -/cm2 2 (tn/m2) @ (Pr / ;) (1 6 e / ;) 2 = 9.15 = 0.915 -/cm2 1 c = 0.5 -/cm2
'O
*! (tnm) @ 1. -# Ps 3 / 6 *! = 19.9> t1 (cm) t1 = 29.00 d (cm) d = 40.21 d1(cm) d1 = 20.21Re&er.o Verti!a,
AsB (cm2) = *! / H0.> f (d #/2)I # (cm) = AsB f / (0.59 fc :) #s!miendo M!e@ # = d / 9
AsB (cm2) @ *! / (0.> f 0.> d) AsB = 11.4 con este B#lor se c#lc!l# J#J
# (cm) # = 2.65 con este B#lor se rec#lc!l# el #cero AsB (cm2) @ *! / H0.> f (d #/2)I AsB = 10.61
/ 12 3 0410 *
,ef!ero *ínimo (cm2) s!perior @ 0.0015 : d AsBm= .24 & 1/2J Q 0.40 m ,ef!ero *ínimo (cm2) inferior @ 0.0015 : d1 AsBm= 3.64 & 1/2J Q 0.39 m !#ntí# @ R @ AsB / (: d) R = 0.0026 G Rmín. N-O
En este c#so el m!ro tiene secci"n B#ri#:le@ El per#lte del m!ro no B#rí# line#lmente$ los momentos t#mpoco B#rí#n$ Pero se p!eden tr##r líne#s de resistenci# p#r# determin#r p!ntos de corte
!) Verii!a!i"# +e Estai,i+a+
'# Tn/m) @ -# Ps t2 / 2+) Presio#es sore e, Terre#o
DISEÑO DE MURO DE CONTENCION EN VOLADIZO TIPO I (M - 01)
Deter*i#a!i"# +e ,a a,t&ra !r6ti!a o +e !orte (L!)
.>9 = 0.1902 c (m) c = 0.> Sc (m) = d c Sc = 1.3 Ds#remos@ Sc (m) Sc = 1.00 S(m) S = 1.0
Re&er.o 7ori.o#ta,
omo t G= 0.29 m$ !s#remos dos c#p# de #cero oriont#l Adem?s$ el espesor es B#ri#:le$ entonces@
Arri:# @ As (cm2) = 0.0020 : t1 As = 9.00
/ 12 3 048 *
8esde 1.0m #st# l# p#rte s!perior de l# p#nt#ll#2As/3 3.33
As / 3 1.6
<ntermedio @ As (cm2) @ 0.0020 : t3 As = .00
/ 12 3 0418 *
8esde 1.00m #st# 1.0m2As/3 4.6
As / 3 2.33
A:#Co @ As (cm2) @ 0.0020 : t1 As = >.00
/ 12 3 0410*
8esde l# :#se del m!ro #st# 1.00m2As/3 6.00 As / 3 3.00 ø Peso s!elo@ s (tn/m) @ Ps s = .92 Peso propio@ pp (tn/m) @ : Pc pp = 1.20 +#p#t# +#p#t# <nterior
Za$ata E9terior
ELterior!m?L. (tn/m) @ 1. 1 0.> pp !m = 12.25 s *! = 1.94 As (cm2) @ *! / (0.> f 0.> d) As = 1.13 cm2 # (cm) @ As f / (0.59 fc :) # = 0.2 pp As (cm2) @ *! / H0.> f (d # / 2)I As = 1.02 cm2 9.15 tn/m2 .56 tn/m2 M: M:
,ef!ero *ínimo (cm2) @ 0.0015 : d Asm =
4;
cm2 1.3d = 41.5 1.>9
Ds#remos@ Acero P#r#lelo (cm2/m) Asm = .24
/ 12 3 040*
Dniformi#ndo #l #cero de l# #p#t# interior@ #l eCe de l# #p#t#*! / 2 = 1. -# Ps ( c)3 /6 (3.>0c)3
) Dise5o +e Za$ata
*! (tnm) @ !m?L. 2 / 2
DISEÑO DE MURO DE CONTENCION EN VOLADIZO TIPO I (M - 01)
Za$ata I#terior
;3(m)@ ;1t ;3 = 1.>9 ;4 (m) @ (;1 t) ; / 6 ;4 = 1.3 M: (tn/m) @ (1 2) ;3 / ; M: = 1.4> M: (tn/m) @ M: 2 M: = 6.6 ;9 (m) @ ; ;4 ;9 = 2.13/ 12 3 0410 *
! (Tn/m) @ (s pp) ;9 ! = 15.60 *! = 12.34/ 12 3 048 *
As (cm2) @ *! / (0.> f 0.> d) As = >.02 cm2 # (cm) @ As f / (0.59 fc :) # = 2.12 As (cm2) @ *! / H0.> f (d #/2)I As = 5.34 cm2Ds#remos@ Acero p#r#lelo (cm2/m) As = >.02
/ 12 3 0418*
/ 12 3 0418 *
#l eCe de l# #p#t#Verii!a!i"# $or Corta#te
/ 12 3 0410*
Md (tn/m) @ M: ;9 / ;4 Md = 2.33 7d! (tn) @ (!2;9)(;3e) Md;4 7d! = 12.22/ 12 3 0418*
7! (tn) @ 7d! / & 7! = 14.35 7c = >.22 7c G 7! N-ORe&er.o Tra#s<ersa,
Astemp (cm2) @ 0.0015 : Astm = >.00Acero perpedic!l#r #l eCe (cm2/m) Astm= >.00
/ 12 3 0418*
de l# #p#t#$ en #m:#s c#r#s
/ 12 3 0418*
/ 12 3 040*
SECCION TRANSVERSAL DEL MURO
0.29 ø #r# ELterior #r# <nterior = 4.0 0.49 = 0.90 0.10 1.10 2.40 3.90
SECCION TRANSVERSAL DE MURO
(+i*e#sio#es e# *etros)
*! @ (!2;9);32 /2M:;9;32 / 6DISEÑO DE MURO DE CONTENCION EN VOLADIZO TIPO I (M - 01)
#r# ELterior #r# <nterior & 1/2J Q 0.29 m & 1/2J Q 0.29 m & 1/2J Q 0.10 m 4.0 &1/2JQ0.10m 4.0 & 1/2J Q 0.10 m 1.0 & 1/2J Q 0.10 m 1.00 0.90 ol#do 0.10 T,A*N 8E *D,N A8A >. 00mDISEÑO DE MURO DE CONTENCION EN VOLADIZO TIPO I (M - 0)
Datos:
t1Peso Específico del terreno (Tn/m3) Ps = 1.60 ø
Peso Específico concreto (Tn/m3) Pc = 2.40 An!lo fricci"n intern# o reposo$ (%) & = 30 An!lo/'oriont#lt#l!d del *#teri#l (%) ø = 0
T#l!d del *#teri#l$ + = 0
,esistenci# del concreto (-/cm2) f c = 210 = 3.10
l!enci# del Acero (-/cm2) f = 4200
#p#cid#d Port#nte (-/cm2) c = 0.50 t
#ctor de e!rid#d de 7olteo 7 = 2.00 #ctor e!rid#d 8esli#miento 8 = 1.90
#ctor de fricci"n f =T & f = 0.95 t2
Alt!r# del *!ro$ (m) = 3.10
pm(tn/m3)= pm = 2.10
Espesor s!perior del *!ro$ (cm) t1 = 29.00 ,ec!:rimiento en el m!ro (cm)$ r1 = 4.00
,ec!:rimiento en l# #p#t# (cm) ;2 ;1
#r# !perior$ r1 = 4.00
#r# <nferior en cont#cto con Terreno r2 = .90 ;
(!#ndo el relleno tiene pendiente)
-# -# = 0.33 t1 -#Ps -#Ps= 0.93 *! = 4.4 #dem?s$ E = 3.10 donde@ & & = 0.>0 t2 :(cm) : = 100.00 -# Ps (c!#ntí#) = 0.004 @ f/fc = 0.050
i!#l#ndo momentos$ reempl##ndo B#lores despeC#ndo d 0.29
d (cm) d = 1.61
t2 = 22.41 2.0
Ds#remos@ t2 (cm) t2 = 49.00
con este B#lor de t2$ se o:tiene$ d (cm) d = 40.21
d1(cm) d1 = 20.21 0.40
Verii!a!i"# $or !orta#te
0.497d! = 3.25 7! (tn) @ 7d!/& = 7d!/0.59 7! = 3.56 7c = 13.93 0.29
V! % V&
'O
ø (cm) @ t2 9 = 90.00 Ds#remos@ (cm) = 90.00 P1 P2 t (cm) @ t = 3.60 T @ 8 (-# Ps / (2 pm f) T = 0.33 :1) ;1/t @ T / (1 + T) ;1/t = 0.33 ;1(m) ;1 = 1.1> E=-#PstF2/2 ;1 (m) @ ;1 (t2 t1) / 2 ;1 = 1.2> Ds#remos$ ;1 (m) ;1 = 3.90 :2) ;2/t G= (f/3)(7/8);1/(2t) ;2/t = 0.23 t/3 = 1.20 ;2 (m) G= ;2 = 0.53 P3 Ds#remos$ ;2mín.(m) ;2 = 0.10A
Anco de +#p#t#$ ; (m) @ ;2 ;1 ; = 3.60 0.10 3.90 E = 3.43 3.60a) Di*e#sio#a*ie#to +e, M&ro
-# = osø (cosø H(cosø)2 (cos&)2 I1/2 ) / (cosø H(cosø)2 (cos&)2 I1/2 )
*! (tnm) @ 1. -# Ps 3 / 6 *! (-cm) = & : d2 fc (1 0.9> ) *! 109 = & : d2 fc (1 0.9> ) t2 (cm) @ d r1 & 9/5J / 2 7d! (tn) @ 1.7d = 1.HPs-#(d)2 /2I 7c (tn) @ 0.93 (fc)1/2 : d
) Di*e#sio#a*ie#to +e ,a Za$ata
E @ -# Ps t2 / 2DISEÑO DE MURO DE CONTENCION EN VOLADIZO TIPO I (M - 0)
EB @ E sen( ø ) EB = 0.00DISEÑO DE MURO DE CONTENCION EN VOLADIZO TIPO I (M - 0)
'# = 3.43 s(m)@ t/3 s = 1.20 *# (tnm/m) @ '# s *# = 4.12 Peso P$ (tn) K (m) (tnm)$ en el p!nto A P1 t1 Pc = 1.560 0.229 P1 K1 = 0.41> 1/2( (t2t1) ) Pc 0.44 0.459 P1 K1 = 0.361 P2 (;1 t2) Ps = 19.130 2.09 P2 K2 = 31.3>9 P3 ; Pc = 4.320 1.500 P3 K3 = .6 EB E sen(ø) = 0.000 3.600 EB K4 = 0.000 Pr= 22.094 *r= 3>.>90 7 @ *r/*# 7= >.0 G 2.00O
8 @ Pr f / '# 8 = 3.3 G 1.90O
P!nto de p#so de l# res!lt#nte$ respecto # A@
KB (m) @ (*r *#) / Pr KB = 1.62 m ELcentricid#d@
e (m) @ (; /2) KB e = 0.15 m ; / 6$ de:e ser m#or M!e JeJ $ ; / 6 = 0.60 N-O
1 (tn/m2) @ (Pr / ;) (1 6 e / ;) 1 = .>6 = 0.>6 -/cm2 2 (tn/m2) @ (Pr / ;) (1 6 e / ;) 2 = 4.2> = 0.42> -/cm2 1 c = 0.5 -/cm2
'O
*! (tnm) @ 1. -# Ps 3 / 6 *! = 4.4 t1 (cm) t1 = 29.00 d (cm) d = 40.21 d1(cm) d1 = 20.21Re&er.o Verti!a,
AsB (cm2) = *! / H0.> f (d #/2)I # (cm) = AsB f / (0.59 fc :) #s!miendo M!e@ # = d / 9
AsB (cm2) @ *! / (0.> f 0.> d) AsB = 3.2 con este B#lor se c#lc!l# J#J # (cm) # = 0. con este B#lor se rec#lc!l# el #cero AsB (cm2) @ *! / H0.> f (d #/2)I AsB = 2.> & 1/2J Q 0.40 m
,ef!ero *ínimo (cm2) s!perior @ 0.0015 : d AsBm= .24 & 1/2J Q 0.3> m ,ef!ero *ínimo (cm2) inferior @ 0.0015 : d1 AsBm= 3.64
/ 12 3 04=8 *
!#ntí# @ R @ AsB / (: d) R = 0.000 G Rmín. N-OEn este c#so el m!ro tiene secci"n B#ri#:le@ El per#lte del m!ro no B#rí# line#lmente$ los momentos t#mpoco B#rí#n$ Pero se p!eden tr##r líne#s de resistenci# p#r# determin#r p!ntos de corte
!) Verii!a!i"# +e Estai,i+a+
'# Tn/m) @ -# Ps t2 / 2+) Presio#es sore e, Terre#o
DISEÑO DE MURO DE CONTENCION EN VOLADIZO TIPO I (M - 0)
Deter*i#a!i"# +e ,a a,t&ra !r6ti!a o +e !orte (L!)
2.239 = 0.1902 c (m) c = 0.64 Sc (m) = d c Sc = 1.04 Ds#remos@ Sc (m) Sc = 1.00 S(m) S = 1.0
Re&er.o 7ori.o#ta,
omo t G= 0.29 m$ !s#remos dos c#p# de #cero oriont#l Adem?s$ el espesor es B#ri#:le$ entonces@
Arri:# @ As (cm2) = 0.0020 : t1 As = 9.00
/ 12 3 048 *
8esde 1.0m #st# l# p#rte s!perior de l# p#nt#ll#2As/3 3.33
As / 3 1.6
<ntermedio @ As (cm2) @ 0.0020 : t3 As = .00
/ 12 3 0418 *
8esde 1.00m #st# 1.0m2As/3 4.6
As / 3 2.33
A:#Co @ As (cm2) @ 0.0020 : t1 As = >.00
/ 12 3 0410*
8esde l# :#se del m!ro #st# 1.00m2As/3 6.00 As / 3 3.00 ø Peso s!elo@ s (tn/m) @ Ps s = 4.>6 Peso propio@ pp (tn/m) @ : Pc pp = 1.20 +#p#t# +#p#t# <nterior
Za$ata E9terior
ELterior!m?L. (tn/m) @ 1. 1 0.> pp !m = 12.49 s *! = 1.96 As (cm2) @ *! / (0.> f 0.> d) As = 1.14 cm2 # (cm) @ As f / (0.59 fc :) # = 0.2 pp As (cm2) @ *! / H0.> f (d # / 2)I As = 1.03 cm2 4.2> tn/m2 .>6 tn/m2 M: M:
,ef!ero *ínimo (cm2) @ 0.0015 : d Asm =
4;
cm2 2.49d = 41.5 3.09
Ds#remos@ Acero P#r#lelo (cm2/m) Asm = .24
/ 12 3 0418 *
Dniformi#ndo #l #cero de l# #p#t# interior@ #l eCe de l# #p#t#*! / 2 = 1. -# Ps ( c)3 /6 (3.>0c)3
) Dise5o +e Za$ata
*! (tnm) @ !m?L. 2 / 2
DISEÑO DE MURO DE CONTENCION EN VOLADIZO TIPO I (M - 0)
Za$ata I#terior
;3(m)@ ;1t ;3 = 3.09 ;4 (m) @ (;1 t) ; / 6 ;4 = 2.49 M: (tn/m) @ (1 2) ;3 / ; M: = 3.11 M: (tn/m) @ M: 2 M: = .40 ;9 (m) @ ; ;4 ;9 = 1.19/ 12 3 04=8 *
! (Tn/m) @ (s pp) ;9 ! = .05 *! = 4.44/ 12 3 048 *
As (cm2) @ *! / (0.> f 0.> d) As = 3.29 cm2 # (cm) @ As f / (0.59 fc :) # = 0.6 As (cm2) @ *! / H0.> f (d #/2)I As = 2.>9 cm2Ds#remos@ Acero p#r#lelo (cm2/m) As = 3.29
/ =>2 3 040 *
/ 12 3 0418 *
#l eCe de l# #p#t#Verii!a!i"# $or Corta#te
/ 12 3 0410*
Md (tn/m) @ M: ;9 / ;4 Md = 1.46 7d! (tn) @ (!2;9)(;3e) Md;4 7d! = 4.3/ =>2 3 040 *
7! (tn) @ 7d! / & 7! = 9.14 7c = 13.52 7c G 7! N-ORe&er.o Tra#s<ersa,
Astemp (cm2) @ 0.0015 : Astm = >.00Acero perpedic!l#r #l eCe (cm2/m) Astm= >.00
/ 12 3 0418*
de l# #p#t#$ en #m:#s c#r#s
/ 12 3 0418*
/ 12 3 0418 *
SECCION TRANSVERSAL DEL MURO
0.29 ø #r# ELterior #r# <nterior = 3.10 0.49 = 0.90 0.10 0.10 3.90 3.60