Memoria de Cálculo de Muros de Contención

DISEÑO DE MURO DE CONTENCION EN VOLADIZO TIPO I (M - 01) Datos:

t1

Peso Específi ífico del terreno (Tn/m3) Peso Específico concreto (Tn/m3)  An!lo fricci"n intern# o reposo$ reposo$ (%)  An!lo/'oriont#lt#l!d del del *#teri#l (%) T#l!d del *#teri#l$ ,esistenci# d de el co concreto ((-/cm2) l!enci# del Acero (-/cm2) #p#cid#d Port#nte (-/cm2) #ctor de e!rid#d de 7olteo #ctor e!rid#d 8esli#miento #ctor de fricci"n f =T &  Alt!r# del *!ro$ (m) pm (tn/m3) = Espesor s!perior del *!ro$ (cm) ,ec!:rimiento en el m!ro (cm)$ ,ec!:rimiento en l# #p#t# (cm) #r# !perior$ #r# #r#  ) donde@ & & = 0.>0 : (cm) : = 100.00  (c!#ntí#)  = 0.004  @   f / fc  = 0.050 i!#l#ndo momentos$ reempl##ndo B#lores  despeC#ndo d 2

*!  109 = &  :  d 2  fc    (1  0.9>  ) d (cm) d = t2 (cm) @ d  r1  & 9/5J / 9/5J / 2 t2 = Ds#remos@ t2 (cm) t2 = con este B#lor de t2$ se o:tiene$ d (cm) d = d1 (cm) d1 =

4 . 0

t2 -#  Ps  

0 . 29

32.> 3.0 49.00 40.21 20.21

4.30

0.40

Verii!a!i"# $or !orta#te

0.49

7d! (tn) @ 1.7d = 1.HPs-#(d)  /2I 7! (tn) @ 7d!/& = 7d!/0.59 2

7c (tn) @ 0.93  (fc) 1/2  :  d

7 d! = 7! = 7c =

V! % V&

5.32 >.> 29.2

0 . 29

'O

ø

) Di*e#sio#a*ie#to +e ,a Za$ata  (cm) @ t2  9 Ds#remos@  (cm) t (cm) @    T @ 8  (-#  Ps / (2  pm  f) :1) :1) ;1/ ;1/tt @ T / (1  +  T) ;1 (m) ;1 (m) @ ;1  (t2  t1) / 2 Ds#remos$ ;1 (m) :2) ;2/t G= (f/3)(7/8);1/(2t) ;2 (m) G= Ds#remos$ ;2mín.(m)  Anco de +#p#t#$ ; (m) @ ;2  ;1

 =  = t = T = ;1/ ;1/tt = ;1 = ;1 = ;1 = ; 2 / t = ;2 = ;2 = ; =

90.00 90.00 9. 2 0 0 . 33 0.33 0.33 1 . 2 1 . 52 2.40 0. 0 3 0 .1 6 1.10 3.90

E @ -#  Ps  t2 / 2

E =

 .1 

P1

P2

E = -#PstF2/2

 t/ 3 = P3

 A 1.10

2.40 3 .9 0

1.3

DISEÑO DE MURO DE CONTENCION EN VOLADIZO TIPO I (M - 01) EB @ E  sen( ø )

EB =

0.00

DISEÑO DE MURO DE CONTENCION EN VOLADIZO TIPO I (M - 01) !) Verii!a!i"# +e Estai,i+a+ '# = s = *# =

'# Tn/m) @ -#  Ps  t2 / 2 s (m) @ t / 3 *# (tnm/m) @ '#  s

P1 P2 P3 EB

Peso P$ (tn) t1    Pc = 1/2( (t2t1)  )  Pc (;1  t2)    Ps = ;    Pc = E  sen(ø) = Pr =

2.520 1.125 14.660 4.200 0.000 22.505

7 @ *r /*# 8 @ Pr  f / '#

.1 1.3 12.4 K (m) 1.229 1.459 2.929 1.90 3.900

7 = 8 =

(tnm)$ en el p!nto A P1  K1 = P1  K1 = P2  K2 = P3  K3 = EB  K4 = *r =

3.>> 1.54

G G

2.00 1.90

KB =

1.63

m

e =

0.12

m

3.499 1.69 3.01 .390 0.000 4>.4>6

O O

+) Presio#es sore e, Terre#o P!nto de p#so de l# res!lt#nte$ respecto # A@ KB (m) @ (*r  *#) / Pr ELcentricid#d@ e (m) @ (; /2)  KB ; / 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

e) Dise5o +e, M&ro *! (tnm) @ 1.  -#  Ps  3 / 6 t1 (cm) d (cm) d1 (cm)

*! = t1 = d = d1 =

19.9> 29.00 40.21 20.21

Re&er.o Verti!a,  AsB (cm2) = *! / H0.>  f  (d  #/2)I #s!miendo M!e@ # = d / 9



# (cm) = AsB  f / (0.59  fc  :)

 AsB (cm2) @ *! / (0.>  f  0.>  d) # (cm)

AsB = # =

11.4 con este B#lor se c#lc!l# J#J 2.65 con este B#lor se rec#lc!l# el #cero

 AsB (cm2) @ *! / H0.>  f  (d  #/2)I

AsB =

,ef!ero *ínimo (cm2) s!perior @ 0.0015  :  d

AsBm=

.24 & 1/2J Q 0.40 m

,ef!ero *ínimo (cm2) inferior @ 0.0015  :  d1

AsBm=

3.64 & 1/2J Q 0.39 m

!#ntí# @ R @ AsB / (:  d)

R=

10.61 / 12 3 0410 *

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

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!) *! / 2 = 1.  -#  Ps  (  c)3 / 6

Ds#remos@

.>9

c (m) Sc (m) = d  c

c = Sc =

0.> 1.3

Sc (m) S (m)

Sc = S =

1.00 1.0

=

0.1902 (3.>0  c)3

Re&er.o 7ori.o#ta, omo t G= 0.29 m$ !s#remos dos c#p# de #cero oriont#l  Adem?s$ el espesor es B#ri#:le$ entonces@  Arri:# @

As (cm2) = 0.0020  :  t1 As = 2  As / 3  As / 3

9.00 / 12 3 048 * 3.33 1.6

8esde 1.0m #st# l# p#rte s!perior de l# p#nt#ll#

.00 / 12 3 0410* 6.00 3.00

8esde l# :#se del m!ro #st# 1.00m

s = pp =

.92 1.20

 ) Dise5o +e Za$ata

ø

Peso s!elo@ s (tn/m) @ Ps   Peso propio@ pp (tn/m) @   :  Pc

+#p#t#  pp

!m =

*! (tnm) @ !m?L.    / 2

*! =

1.94

 As (cm2) @ *! / (0.>  f  0.>  d) # (cm) @ As  f / (0.59  fc  :)

As = # =

1.13 cm2 0.2

 As (cm2) @ *! / H0.>  f  (d  # / 2)I

As =

1.02 cm2

,ef!ero *ínimo (cm2) @ 0.0015  :  d

Asm =

4; cm2

d (cm) @   (r2  & 1/2J / 2)

d =

Ds#remos@ Acero P#r#lelo (cm2/m) #l eCe de l# #p#t#

Asm =

2

12.25

s

pp 9.15 tn/m2 .56 tn/m2

41.5 .24 / 12 3 040*

M:

M: 1.3 1.>9

Dniformi#ndo #l #cero de l# #p#t# interior@

DISEÑO DE MURO DE CONTENCION EN VOLADIZO TIPO I (M - 01)

Za$ata I#terior  ;3 (m) @ ;1  t ;4 (m) @ (;1  t)  ; / 6 M: (tn/m) @ (1  2)  ;3 / ; M: (tn/m) @ M:  2 ;9 (m) @ ;  ;4 ! (Tn/m) @ (s  pp)  ;9

;3 = ;4 = M: = M: = ;9 = ! =

1.>9 1.3 1.4> 6.6 2.13 15.60

*! @ (!2;9);32 /2M:;9;32 / 6  As (cm2) @ *! / (0.>  f  0.>  d) # (cm) @ As  f / (0.59  fc  :)

*! = As = # =

12.34 >.02 cm2 2.12

 As (cm2) @ *! / H0.>  f  (d  #/2)I

As =

5.34 cm2

Ds#remos@ Acero p#r#lelo (cm2/m) #l eCe de l# #p#t#

As =

>.02 / 12 3 0418*

/ 12 3 0410 * / 12 3 048 *

/ 12 3 0418 *

Verii!a!i"# $or Corta#te / 12 3 0410* Md (tn/m) @ M:  ;9 / ;4 7d! (tn) @ (!2;9)(;3e)  Md;4 7! (tn) @ 7d! / &

Md = 7d! = 7! =

2.33 12.22 14.35

7c (tn) @ 0.93  (fc)1/2  :  e

7c =

>.22

Astm = Astm=

>.00 >.00 / 12 3 0418*

/ 12 3 0418* 7c G 7!

N-O

Re&er.o Tra#s  ) d (cm) d = t2 (cm) @ d  r1  & 9/5J / 2 t2 = Ds#remos@ t2 (cm) t2 = con este B#lor de t2$ se o:tiene$ d (cm) d = d1 (cm) d1 =

3.10

t2 -#  Ps  

0.29

1.61 22.41 49.00 40.21 20.21

2.0

0.40

Verii!a!i"# $or !orta#te

0.49

7d! (tn) @ 1.7d = 1.HPs-#(d)  /2I 7! (tn) @ 7d!/& = 7d!/0.59 2

7c (tn) @ 0.93  (fc) 1/2  :  d

7d! = 7! = 7c =

V! % V&

3.25 3.56 13.93

0.29

'O

ø

) Di*e#sio#a*ie#to +e ,a Za$ata  (cm) @ t2  9 Ds#remos@  (cm) t (cm) @    T @ 8  (-#  Ps / (2  pm  f) :1) ;1/t @ T / (1  +  T) ;1 (m) ;1 (m) @ ;1  (t2  t1) / 2 Ds#remos$ ;1 (m) :2) ;2/t G= (f/3)(7/8);1/(2t) ;2 (m) G= Ds#remos$ ;2mín.(m)  Anco de +#p#t#$ ; (m) @ ;2  ;1

 =  = t = T = ;1/t = ;1 = ;1 = ;1 = ;2/t = ;2 = ;2 = ; =

90.00 90.00 3.60 0.33 0.33 1.1> 1.2> 3.90 0.23 0.53 0.10 3.60

E @ -#  Ps  t2 / 2

E =

3.43

P1

P2

E = -#PstF2/2

t/3 = P3

 A 0.10

3.90 3.60

1.20

DISEÑO DE MURO DE CONTENCION EN VOLADIZO TIPO I (M - 0) EB @ E  sen( ø )

EB =

0.00

DISEÑO DE MURO DE CONTENCION EN VOLADIZO TIPO I (M - 0) !) Verii!a!i"# +e Estai,i+a+ '# = s = *# =

'# Tn/m) @ -#  Ps  t2 / 2 s (m) @ t / 3 *# (tnm/m) @ '#  s

P1 P2 P3 EB

Peso P$ (tn) t1    Pc = 1/2( (t2t1)  )  Pc (;1  t2)    Ps = ;    Pc = E  sen(ø) = Pr =

1.560 0.44 19.130 4.320 0.000 22.094

7 @ *r /*# 8 @ Pr  f / '#

3.43 1.20 4.12 K (m) 0.229 0.459 2.09 1.500 3.600

7 = 8 =

(tnm)$ en el p!nto A P1  K1 = P1  K1 = P2  K2 = P3  K3 = EB  K4 = *r =

>.0 3.3

G G

2.00 1.90

KB =

1.62

m

e =

0.15

m

0.41> 0.361 31.3>9 .6 0.000 3>.>90

O O

+) Presio#es sore e, Terre#o P!nto de p#so de l# res!lt#nte$ respecto # A@ KB (m) @ (*r  *#) / Pr ELcentricid#d@ e (m) @ (; /2)  KB ; / 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

e) Dise5o +e, M&ro *! (tnm) @ 1.  -#  Ps  3 / 6 t1 (cm) d (cm) d1 (cm)

*! = t1 = d = d1 =

4.4 29.00 40.21 20.21

Re&er.o Verti!a,  AsB (cm2) = *! / H0.>  f  (d  #/2)I #s!miendo M!e@ # = d / 9



# (cm) = AsB  f / (0.59  fc  :)

 AsB (cm2) @ *! / (0.>  f  0.>  d) # (cm)

AsB = # =

3.2 con este B#lor se c#lc!l# J#J 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!ero *ínimo (cm2) s!perior @ 0.0015  :  d

AsBm=

.24 & 1/2J Q 0.3> m

,ef!ero *ínimo (cm2) inferior @ 0.0015  :  d1

AsBm=

3.64 / 12 3 04=8 *

!#ntí# @ R @ AsB / (:  d)

R=

0.000 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

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 = 1.  -#  Ps  (  c)3 / 6

Ds#remos@

2.239

c (m) Sc (m) = d  c

c = Sc =

0.64 1.04

Sc (m) S (m)

Sc = S =

1.00 1.0

=

0.1902 (3.>0  c)3

Re&er.o 7ori.o#ta, omo t G= 0.29 m$ !s#remos dos c#p# de #cero oriont#l  Adem?s$ el espesor es B#ri#:le$ entonces@  Arri:# @

As (cm2) = 0.0020  :  t1 As = 2  As / 3  As / 3

9.00 / 12 3 048 * 3.33 1.6

8esde 1.0m #st# l# p#rte s!perior de l# p#nt#ll#

.00 / 12 3 0410* 6.00 3.00

8esde l# :#se del m!ro #st# 1.00m

s = pp =

4.>6 1.20

 ) Dise5o +e Za$ata

ø

Peso s!elo@ s (tn/m) @ Ps   Peso propio@ pp (tn/m) @   :  Pc

+#p#t#  pp

!m =

*! (tnm) @ !m?L.    / 2

*! =

1.96

 As (cm2) @ *! / (0.>  f  0.>  d) # (cm) @ As  f / (0.59  fc  :)

As = # =

1.14 cm2 0.2

 As (cm2) @ *! / H0.>  f  (d  # / 2)I

As =

1.03 cm2

,ef!ero *ínimo (cm2) @ 0.0015  :  d

Asm =

4; cm2

d (cm) @   (r2  & 1/2J / 2)

d =

Ds#remos@ Acero P#r#lelo (cm2/m) #l eCe de l# #p#t#

Asm =

2

12.49

s

pp 4.2> tn/m2 .>6 tn/m2

41.5

M:

M: 2.49 3.09

.24 / 12 3 0418 * Dniformi#ndo #l #cero de l# #p#t# interior@

DISEÑO DE MURO DE CONTENCION EN VOLADIZO TIPO I (M - 0)

Za$ata I#terior  ;3 (m) @ ;1  t ;4 (m) @ (;1  t)  ; / 6 M: (tn/m) @ (1  2)  ;3 / ; M: (tn/m) @ M:  2 ;9 (m) @ ;  ;4 ! (Tn/m) @ (s  pp)  ;9

;3 = ;4 = M: = M: = ;9 = ! =

3.09 2.49 3.11 .40 1.19 .05

*! @ (!2;9);32 /2M:;9;32 / 6  As (cm2) @ *! / (0.>  f  0.>  d) # (cm) @ As  f / (0.59  fc  :)

*! = As = # =

4.44 3.29 cm2 0.6

 As (cm2) @ *! / H0.>  f  (d  #/2)I

As =

2.>9 cm2

Ds#remos@ Acero p#r#lelo (cm2/m) #l eCe de l# #p#t#

As =

3.29 / =>2 3 040 *

/ 12 3 04=8 * / 12 3 048 *

/ 12 3 0418 *

Verii!a!i"# $or Corta#te / 12 3 0410* Md (tn/m) @ M:  ;9 / ;4 7d! (tn) @ (!2;9)(;3e)  Md;4 7! (tn) @ 7d! / &

Md = 7d! = 7! =

7c (tn) @ 0.93  (fc)1/2  :  e

7c =

1.46 4.3 9.14 13.52

/ =>2 3 040 * 7c G 7!

N-O

Re&er.o Tra#s.00 >.00 / 12 3 0418*

/ 12 3 0418* / 12 3 0418 * SECCION TRANSVERSAL DEL MURO

0.29

ø

#r# ELterior  #r#