Losa Alivianada en Una Direccion

7/23/2019 Losa Alivianada en Una Direccion

1/77

Nombre: Ramrez Cabrera Wladimir Jos

Semestre: sextosegundo

Materia: Hormign armado 2

!S"#$R %$ S!&'!"N(" %)S$ (!*) $%!+!$N$$ ) N"R+$$

A

B

C

D

1 2 3 4

3,4

3,5

3,3

7,2 7,5 7,4

1,2

1,4

1 2

34 5

6 7


2/77

Si m < 0.5 se disea como losa armada en una direccion

m=S/L

Tablero No. Sm!

Lm!

m=S/L

1 3.40 7.20 0.472 3.40 7.40 0.4"3 3.50 7.20 0.4#4 3.50 7.50 0.475 3.50 7.40 0.47" 3.30 7.50 0.447 3.30 7.40 0.45

e,ini-ion de ,a.as ti/o

$a%a &i'o l

( ) *

3.53.40


3/77

) * +

1.20 3.5 3.3

$a%a &i'o ll

$a%a &i'o lll

( ) * +

1.4 3.40 3.50 3.30

*redimensionamiento de la altura de losa

losa= de-inido 'or la &abla #.5a del (* 31

l=3.5


4/77

hmin= l/21=350 cm/21=16.67 cm

l=1.40

hmin= l/8=140 cm/8=17.5 cm

adoptamos la condicion mas critica

hlosa17.5cm

hlosa20cm por facilidad constructiva ya u! los alivianami!ntos d!

nu!stro m!dio "!n!ralm!nt! ti!n!n un ancho d! 15 cm # $lou! d! pom!%&.

Cuantifcacion de las cargas actuantes en y sobre la losa

'= car"a mu!rta

( = car"a viva

)ar"a mu!rta #'&

tomamos una unidad d! ar!a r!pr!c!ntativa


5/77

1

2

3

4

5

"

7

/

#

10

10 cm 40 cm 40 cm10 cm

1.0 m

1.0 m

10 cm 40 cm 40 cm10 cm

15 cm

5cm

p.p.l= p!so hormi"on armado * p!so alivianami!ntos


6/77

+ormi"on armado

+a=,1-1-0.2010#0.40-.20-0.15&2.4 /m3

+a=0.12 /m2

livianami!ntos

livian.= 10#0.006 &

livian.= 0.06 /m2

p.p.l= 0.12*0.06 /m2

p.p.l= 0.252 /m2

nlucidos=2#1-1-0.015&2.2 /m3

nlucido=0.066 /m2

iso=#1-1-0.006&1/m3

iso=0.006 /m2

anpost!ria= 0.200/m2

nstalacion!s y otros= 0.018 /m2

)=0.542 /m2

)ar"a viva#(&

)=!sid!ncia= 0.250 /m2

)ar"as ultimas

9=1.2) *1.6)

:9=1.2#0.542& *1.6#0.25&

:9=1.05 /m2

u=:u#/m2&-#ncho d! fa;a !n m!tros&

u=1.05 /m2 - 1m

u=1.05/m

Cal-ulo de solisita-iones en las ,a.as ti/o 0$C! 1334

$a%a &i'o l


7/77

1/24 1/# 1/# 1/24

1/14 1/14( ) *

1/2

1.15/2

1.15/2

1/2

( ) *

omen&os

(=1/24!ul2

(=1/24!1.053.42

(= 0.51 T/m

)=1/#!ul1l2!/2!2

)=1/#!1.053.43.5!/2!2

)= 1.3# T/m


8/77

*=1/24!ul2

*=1/24!1.053.52

*= 0.54 T/m

()=1/14!ul2

()=1/14!1.053.42

()= 0.7 T/m

)*=1/14!ul2

)*=1/14!1.053.52

)*= 0.#2 T/m

*or&an&es

(=1/2!ul

(=1/2!1.053.4

(= 1.7 T

)=1.15/2!ul

)=1.15/2!1.053.4)= 2.05 T

)=1.15/2!ul

)=1.15/2!1.053.5

)= 2.11 T

*=1/2!ul


9/77

1/24 1/# 1/# 1/24

1/14 1/14) *

1/2

1.15/2

1.15/2

1/2

+

) * +

1/2

1

*=1/2!1.053.5

*= 1.4 T

$a%a &i'o ll

)=1/2!ul2

)=1/2!1.051.22

)= 0.7" T/m


10/77

)=1/24!ul2

)=1/24!1.053.52

)= 0.54 T/m

*=1/#!ul1l2!/2!2

*=1/#!1.053.33.5!/2!2

*= 1.35 T/m

+=1/24!ul2

+=1/24!1.053.32

+= 0.47 T/m

)*=1/14!ul2

)*=1/14!1.053.52

)*= 0.#2 T/m

*+=1/14!ul2

*+=1/14!1.053.32

*+= 0.2 T/m*or&an&es

)=1!ul

)=1!1.051.2

)= 1.2" T

)=1/2!ul

)=1/2!1.053.5

)= 1.4 T

*=1.15/2!ul

*=1.15/2!1.053.5

*= 2.11 T

*=1.15/2!ul

*=1.15/2!1.053.3


11/77

*= 1.## T

+=1/2!ul

+=1/2!1.053.3

+= 1.73 T

$a%a &i'o lll

( ) * +

1/24 1/10 1/11 1/24

1/14 1/14

1/2

1/2

1.15/2

1.15/2

1/21

1/11 1/10

1/1"

( ) * +

1/2

1/2

(=1/2!ul2


12/77

(=1/2!1.051.42

(= 1.02 T/m

(=1/24!ul2

(=1/24!1.051.42

(= 0.51 T/m

)=1/10!ul1l2!/2!2

)=1/10!1.053.43.5!/2!2

)= 1.25 T/m

)=1/11!ul1l2#!/2!2

)=1/11!1.053.43.5!/2!2

)= 1.14 T/m

*=1/11!ul1l2!/2!2

*=1/11!1.053.53.3!/2!2

*= 1.10 T/m

*=1/10!ul1l2#!/2!

2

*=1/10!1.053.33.3!/2!2

*= 1.21 T/m

+=1/24!ul2

+=1/24!1.053.32

+= 0.4 T/m

()=1/14!ul2

()=1/14!1.053.42

()= 0." T/m

)*=1/1"!ul2

)*=1/1"!1.053.52

)*= 0.0 T/m

*+=1/14!ul2


13/77

*+=1/14!1.053.32

*+= 0.2 T/m

*or&an&es

(=1!ul

(=1!1.051.4

(= 1.47 T

(=1/2!ul

(=1/2!1.053.4

(= 1.7 T

)=1.15/2!ul

)=1.15/2!1.053.4

)= 2.05 T

)=1./2!ul

)=1./2!1.053.5

)= 1.4 T*=1/2!ul

*=1/2!1.053.5

*= 1.4 T

*=1.15/2!ul

*=1.15/2!1.053.3

*= 1.## T

+=1/2!ul

+=1/2!1.053.3

+= 1.73 T

C5e6ueo del /redimensionamiento de la losa


14/77

10 cm 40 cm 40 cm10 cm

15 cm

5cm

Secci6n &ransersal real

Secci6n euialen&e

anc,o de -a%a

suma&oria de

ner7ios

1 .0m

20 cm

15cm

5 cm


15/77

8ara u !

S9 a

,-a

b?

8ara u !

(n:lisis como S.;.S.(. de anco b?

C5e6ueo a ,lexi7n

Solici&aciones cr@&icas


16/77

u ! cri&ico=1.3# Tm/m

u ! cri&ico=0.#2 Tm/m

(n:lisis u ! cri&ico=1.3# Tm/m

b?=20 cm

,=20 cm

b=100cm

d=17.4

d eAis&en&e=losa recubrimien&o libre B arillas/2

d eAis=2021.2/2 cmd eAis=17.4 cm

d necesario = Mu

b Ru

B=0.#C ;u=47.2# alor de &abla!Cb=20cm -a%a de anco uni&ario

d necesario = 1.39 exp5

0.92047.829

d necesario = 12.70"

d eAis. de nece.

17.4 12.70"

(n:lisis u ! cri&ico=0.#2 Tm/m


17/77

,- *c ala

Ts

D= d4 ,-/2

,-/2

(s

+iaEn6s&ico

nala!= *c ala D

nala!= 0.5-Fcb-d-/2!

nala!= 0.5210100517.45/2!

nala!= 132#25 GE cm

nala!= 13.2# T m/m

B nala!= 0.#13.2#!

B nala!= 11.#" T m/m

u cri&ico! s B nala!0.#2


18/77

8ara u != b de diseo = b?

8ara u != b de diseo = b

C5e6ueo /or -orte

b?

d

Kn el diseo al cor&e de unasecci6n T> se considera ue las alas no colaboran con resis&encia.

u B n

n= cs s= 0 no u&iliDamos es&ribos en losas!

n=c=0.53M-c!1/2b?d!1.1 C M=1 ormiEones de 'eso normal

c=0.531210!1/22017.4

c=2.#4 T

B n=0.752.#4!

B n=2.205 T

u cri&ico=2.11 T

u cri&ico B n

2.11 ? s

calc)m2/

s /n

)m2/n

smin

/n)m2/n

s

adop.

@arillas

/n


19/77

o m& m )m2/

n 0.5

1

20 17.

4

0.0446 0.04

6

0.002

3

0.80

0

0.40 0.58 0.58 1@10/n

A 0.8

7

10

0

17.

4

0.0152 0.01

5

0.000

75

1.30

5

0.65 0.58 0.65 1@10/n

A 1.3

20 17.

4

0.1215 0.13

2

0.006

6

2.2

7

0.15 0.58 1.15 1@12/n

A) 0.

2

10

0

17.

4

0.0161 0.01

6

0.000

8

1.3

2

0.70 0.58 0.70 1@10/n

) 0.5

4

20 17.

4

0.0472 0.04

0.002

45

0.85

3

0.43 0.58 0.58 1@10/n

ta$l

a

:fBc/f

y

scalc

/2

>=u/@$-d2fBc tramos

>=u/@$-d2fBc apoyos

s calc= ?-$-d= apoyos

s calc= ?-$-d= tramos

?min= 14/ fy

s min= ?min-$-d

s min= ?min-$-d

s min=0.0033-20-17.4 =1.16 cm2

s min/n=smin/2=1.16/2 =0.58 cm2

FAJA ll

poy

o

tramo

u

#

m&

$

#c

m&

d

#c

m&

> ? s

calc

)m2

/m

s /n

)m2/n

smin

/n

)m2

/n

s

adop

.)m2/

n

@arillas

/n

A 0.7

6

20 17.

4

0.06

64

0.06

0.003

5

1.21

8

0.61 0.58 0.61 1@10/n

A) 0.

2

10

0

17.

4

0.01

61

0.01

6

0.000

8

1.3

2

0.70 0.58 0.70 1@10/n

) 1.3

5

20 17.

4

0.11

80

0.12

8

0.006

4

2.22

7

1.11 0.58 1.11 1@12/n

)' 0.8

2

10

0

17.

4

0.01

43

0.01

40

0.000

7

1.21

8

0.61 0.58 0.61 1@10/n

' 0.4

8

20 17.

4

0.04

1

0.04

3

0.002

15

0.74

8

0.37 0.58 0.58 1@10/n


20/77

ta$la :fBc/f

y

scalc

/2

FAJA lll

poy

o

tram

o

u

#

m&

$

#c

m&

d

#c

m&

> ? s

calc

)m2/

m

s /n

)m2/n

smin

/n

)m2/n

s

adop

.

)m2/

n

@arillas

/n

1.0

3

20 17.

4

0.0

00

0.0

5

0.004

8

1.67

0

0.84 0.58 0.84 1@12/n

A 0.8

6

10

0

17.

4

0.01

50

0.01

5

0.000

8

1.3

2

0.70 0.58 0.70 1@10/n

A 1.2

5

20 17.

4

0.10

2

0.11

7

0.005

2.05

3

1.03 0.58 1.03 1@12/n

A) 0.8

0

10

0

17.

4

0.01

40

0.01

40

0.000

7

1.21

8

0.61 0.58 0.61 1@10/n

) 1.2

1

20 17.

4

0.10

57

0.11

3

0.005

7

1.8

4

0. 0.58 0. 1@12/n

)' 0.8

2

10

0

17.

4

0.01

43

0.01

4

0.000

7

1.21

8

0.61 0.58 0.61 1@10/n

) 0.4

8

20 17.

4

0.04

1

0.04

3

0.002

2

0.76

6

0.38 0.58 0.58 1@10/n

ta$la :fBc/f y

scalc/2

Esque ma de armado

FAJA l

( ) *

1O10 1O12 1O10

1O10


21/77

) *

1O10 1O12 1O10

1O10

+

FAJA ll

FAJA lll

( ) * +

1O12 1O12 1O12 1O10

1O10

Re,uerzo /or tem/eratura

P&em'era&ura=0.001


22/77

Ct!mp!raturaD #3h o 45cm&

s t!mp!ratura=P&em'era&ura10020

s t!mp!ratura=0.0011000.20

s t!mp!ratura=3." cm2

1@10E20 cm #valor sacado d! ta$la& #paral!los al lado lar"o d!l ta$l!ro&

Cal-ulo 8 dise9o de igas

)ar"as u! losa transmit! a vi"as

u transmitido por losa=:u#/m2ancho coop!rant! d! losa !n m&

F)+G )GGF


23/77

A

B

C

D

1 2 3 4

3,4

3,5

3,3

7,2

1,2

1,4

7,47,5

Ancho coop. 1 Ancho coop. 2

Ancho coop. 3 Ancho coop. 4 Ancho coop. 3

Ancho coop. 5 Ancho coop. 6 Ancho coop. 6

Ancho coop. 7Ancho coop. 7


24/77

H

ncho coop. 1=#3.4/2 *0.15&=1.85 m

ncho coop. 2=#3.4/2 *1.4&=3.10 m

H A

ncho coop. 3=#3.4/2 *3.5/2&=3.45 m

ncho coop. 4=#3.5/2 *1.2&=2.5 m

H )

ncho coop. 5=#3.5/2 *0.15&=1.0 m

ncho coop. 6=#3.5/2 *3.3/2&=3.40 m

H '

ncho coop. 5=#3.3/2 *0.15&=1.80 m

u1=1.051.5!

=1.#4 T/mu2=1.053.10!

=3.2" T/m

1 2 3 4

H


25/77

l !spacio !ntr! 2 y 3 s!rI calculado con !l p!so propio d! vi"a cuando ya

s! t!n"a !l pr!dim!nsionado

H A

u3=1.053.5!

=3."2 T/mu3=1.053.45!

=3."2 T/m

1 2 3 4

u4=1.052.#5!

=3.10 T/m

H )

u5=1.051.#0!

=2.0 T/m

1 2 3 4

u"=1.053.4!

=3.57 T/m


26/77

H '

u7=1.051.0!=1.# T/m

2 3 4

*redimensionamento de igas -on los momentos mas -riti-os 01334

Q( )

1=1/1"!ul2

1=1/1"!3."27.22

1= 11.73 Tm

12=1/14!ul2

12=1/14!3."27.22

12= 13.40 Tm

2=1/10!ul1l2!/2!2

2=1/10!3."27.27.5!/2!2

2= 1#.5" Tm

2=1/11!ul1l2#!/2!2

2=1/11!3.107.27.5!/2!2

2= 15.22 Tm


27/77

23=1/1"!ul2

23=1/1"!3.107.52

23= 10.#0 Tm

3=1/11!ul1l2#!/2!2

3=1/11!3.107.57.4!/2!2

3= 15."4 Tm

3=1/10!ul1l2#!/2!2

3=1/10!3."27.57.4!/2!2

3= 20.0# Tm

34=1/14!ul2

4=1/14!3."27.42

4= 14.1" Tm

4=1/1"!ul2

34=1/1"!3."27.42

34= 12.3# TmmaA = 3

cri&ico=20.0# Tm

d necesario = Mu

b R u

B=0.#C ;u=47.2# alor de &abla!C b=100cm -a%a de anco uni&ario

d necesario = 20.09exp5

0.9b47.829

$# cm& d#cm& h #cm& h/$25 43.21 55 2.230 3.44 50 1.6735 36.51 45 1.5

1.5Dh/$D2.0 $=30 cm Jh=50 cm

Q( *


28/77

1=1/1"!ul2

1=1/1"!2.7.22

1= ".4 Tm

12=1/14!ul2

12=1/14!27.22

12= 7.41 Tm

2=1/10!ul1l2!/2!2

2=1/10!27.27.5!/2!2

2= 10. Tm

2=1/11!ul1l2#!/2!2

2=1/11!3.577.27.5!/2!2

2= 17.53 Tm

23=1/1"!ul2

23=1/1"!3.577.52

23= 12.55 Tm3=1/11!ul1l2#!/2!2

3=1/11!3.577.57.4!/2!2

3= 1.03 Tm

3=1/10!ul1l2!/2!2

3=1/10!3.577.57.4!/2!2

3= 1#.1 Tm

34=1/14!ul2

34=1/14!3.577.42

34= 13.#" Tm

4=1/1"!ul2

4=1/1"!3.577.42

4= 12.22 Tm


29/77

maA = 3

cri&ico=1#.1 Tm

d necesario =

Mu

b Ru

B=0.# C ;u=47.2# alor de &abla!Cb=100cm -a%a de anco uni&ario

d necesario = 19.81 exp5

0.9b47.829

$# cm& d#cm& h #cm& h/$25 42.0 55 2.230 3.17 50 1.67

35 36.26 45 1.2

1.5Dh/$D2.0 $=30 cm Jh=50 cm

u ppv=#1-0.30-0.35&m-2.4 /m3=0.252 # d!scontamos h d! losa al h d!

vi"a&

u ppv=0.302 /m

u total= u trasmitido d! vi"a a losa* u ppv

NOTA:d!$ido a u! los mom!ntos K!ctor!s para !l dis!Lo d! los porticos

son s!m!;ant!s al d!l caso para la losa maci%a adoptamos los r!sultados y

dis!Los tanto a K!Mion como a cort! d! la losa maci%a.


30/77

1

1FGN l !su!ma d! ri"id!c!s !s !l mismo para los pOrticos PA y ).

P


31/77

i


32/77


33/77


34/77


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42/77


43/77

!S"#) " +!&$S

*)R(!C) $

2.45 T/m 0.302T/m 3.#" T/m

1 2 3 4

7.20m 7.50m 7.40m

Tm! ".# .52 2.75 ".73 15.34 11.41H .#5 .#5 1.13 1.13 14."5 14."5R 0.23 0.23 0.53 0.53 0.53 .53

THT(L .72 #.1 0." 1."" 15.1 14.12

maA. 3.51 3."# 1.## 5.51 3.3 3.57 maA. .45 7.#1 13.7"

o= ul/2=2.457.20!/2=.#5

R=.52".#!/7.20=0.23

maA=/'=.72/2.45=3.51

maA= m / 'd=.45

UT!

8.72 0.608 15.18


44/77

.172 1.657 14.21

#m&

".# .52 15.34 11.#1

8.45 7.1 13.76

ise9o a ,lexi7n

u cri&ico=c=15.34 Tm

d eAis&en&e=502 ca'as B 20

d eAis=50.25=41.75 cm

d necesario = Mu

b Ru

B=0.# C ;u=47.2# alor de &abla!


0.93047.829

d necesario =34.4"

d eAis. de nece.

41.7534.4" oG! S.;.S.(.


45/77

)/timiza-i7n 8 -;l-ulo del re,uerzo

poy

o

tram

o

u

#m&

$

#cm&

d

#cm&

Q ? ?min s arill

as

1 6.8 30 41.7

5

0.067 0.07

3

0.003

7

0.003

3

4.63 2@18

12 8.45 30 41.7

5

0.0855 0.0

0

0.004

5

0.003

3

5.64 2@20

2 8.82 30 41.7

5

0.0862 0.0

1

0.004

6

0.003

3

5.76 2@20

23 7.1 30 41.7

5

0.0800 0.08

5

0.004

3

0.003

3

5.3 2@18

3 15.3

4

30 41.7

5

0.1550 0.17

3

0.087 0.003

3

10.

0

4@18

34 13.76

30 41.75

0.130 0.153

0.0077

0.0033

.64 4@18

4 11.4

1

30 41.7

5

0.1154 0.12

5

0.063 0.003

3

7.8 3@18

u/@$d2f

Bc

ta$la :fBc/f

y

14/fy ?$d

ise9o /or -orte

Q( 12 u!

.72

3."# m

d


46/77

u

#.17

9.17

3.69=

Vu

(3.690.4175)

u=.13 T

u cri&ico= .13 T

n= u/B CB=0.75

c=0.53M-c!1/2b?d

c=0.531210!1/23041.75

c=#."2T

s=nc

n=.13/.75=10.4

s=10.4#."2

s=1.22 T

.62

10.84 12.23

s


47/77

s maA=2.2M-c!1/2b?d

s maA=2.21210!1/23041.75

s maA=3#.#3 T

s


48/77

Q( 23 u!

0 ."0

5.51 m

d

u

1."57

1.657

5.51 =

Vu

(5.510.4175)

u=1.53 T

u cri&ico= 1.53 T

n= u/B CB0.75

c=0.53M-c!1/2b?d

c=0.531210!1/2

3041.75c=#."2T

s=nc

n=1.53/0.75=2.04

s=2.04#."2


49/77

s= 7.5 Tre-uerDo norma&io!

2.04

2.21

#."2

La norma dice es&ribo norma&io en W

c/2 n c

8ero debido a ue el cor&an&e es muJ 'eueo no se 'uede ubicar c/2 J al&ra&arse de un es&ribo norma&io 'odemos colocar en &oda la iEa

Si s 1.1M-c!1/2b?d

S= d/2 21=20cm! o "00mm

1.1M-c!1/2b?d =1.11210!1/23041.75

=1#.#" T

s


50/77

(m@n.=3.5bws

fyt

(do'&o ( J calculo S

(=2B=1cm2

S=Avm nFyt

3.5bw

S=142003.5(30)

S=40 cm CSsmaA

S=Smin=20cm

1Bmm 2ramasV20cm &oda la iEa &iene es&e armado!

Q( 34 u!

15.1

u


51/77

d

3.3m 14.121

15.83

3.83=

Vu

(3.830.4175)

u=13.53 T

u cri&ico= 13.53 T

n= u/B CB=0.75

c=0.53M-c!1/2b?d

c=0.531210!1/23041.75

c=#."2T

s=nc

n=13.53/.75=1.04

s=1.04#."2

s=.42 T

20.24

1.04

#."2


52/77

s


53/77

( ) * +

2B1 2B20 4B1 3B1

2B20 2B1 4B1

Kl re-uerDo neEa&io 'or -leAi6n debe sobre 'asar una dis&ancia QX(L a LuD/3

Kl re-uerDo 'osi&io 'or -leAi6n debe sobre 'asar as&a la o&ra cara del a'oJo

*)R(!C) ? ?min s arillas

1 5.05 30 41.7

5

0.051 0.05

3

0.002

7

0.003

3

4.13 2@18

12 6.7 30 41.7

5

0.068 0.07

1

0.003

6

0.003

3

4.51 2@18

2 17.6

8

30 41.7

5

0.17 0.20

4

0.010

2

0.003

3

12.7

8

4@20

23 12.6

5

30 41.7

5

0.128 0.14

0

0.007 0.003

3

8.77 3@20


64/77

3 23.4

8

30 41.7

5

0.238 0.28

7

0.014

4

0.003

3

18.0

4

6@20

34 12.

30 41.7

5

0.1314 0.14

4

0.007

2

0.003

3

.01

8

3@20

4 10.4

5

30 41.7

5

0.106 0.11

4

0.005

7

0.003

3

7.14 2@22

u/@$d2f

Bc

ta$la :fBc/f

y

14/fy ?$d

ise9o /or -orte

Q( 12 u!

7.7

4.17 m

d

u

10."2

10.62

4.17= Vu(4.170.4175)

u=#.5" T

u cri&ico= #.5" T

n= u/B CB=0.75

c=0.53M-c!1/2b?d

c=0.531210!1/23041.75


65/77

c=#."2T

s=nc

n=#.5"/0.75=12.75

s=12.75#."2

s=3.13 T

.62

12.75 14.16

s


66/77

3.13


67/77

u=15.#2 T

u cri&ico= 15.#2 T

n= u/B CB=0.75

c=0.53M-c!1/2b?d

c=0.531210!1/23041.75

c=#."2T

s=nc

n=15.#2/0.75=21.23

s=21.23#."2

s=11."1 T

23."3

21.23

#."2

s


68/77

Si s 1.1M-c!1/2b?d

S= d/2 21=20cm! o "00mm

1.1M-c!1/2b?d =1.11210!1/23041.75

=1#.#" T

s


69/77

( ) * +

2B1 4B20 "B20 2B22

2B1 3B20 3B20



*)R(!C)

2.42" T/m 2.42"T/m

1 2 3

7.20m 7.50m

Tm! 5.33 13.0# 13.17 3.#5H .73 .73 #.10 #.10R 1.0 1.0 1.23 1.23

THT(L 7."5 #.1 10.33 7.7

maA. 3.15 4.05 4.2" 3.24 maA. ". .

43

21


70/77

UT!

7.65 10.33

.82

7.87

#m&

5.3313.17 3.#5


71/77

6.8 8.8

ise9o a ,lexi7n

u cri&ico=)=13.17 Tm

d eAis&en&e=502 ca'as B 20

d eAis=50.25=41.75 cm

d necesario = Mu

b R u

B=0.# C ;u=47.2# alor de &abla!


0.93047.829

d necesario =31.#3 cm

d eAis. de nece. HI!

41.75 31.#3 oG! S.;.S.(.

)/timiza-i7n 8 -;l-ulo del re,uerzo

poyo

tram

o

u#m&

$#cm&

d#cm&

> ? ?min s arillas

1 5.33 30 41.7

5

0.054 0.05

6

0.002

8

0.003

3

4.13 2@18

12 6.80 30 41.7

5

0.06 0.07

2

0.003

6

0.003

3

4.51 2@18

2 13.1

7

30 41.7

5

0.133 0.14

6

0.007

3

0.003

3

.14 4@18

23 8.80 30 41.7

5

0.08 0.0

5

0.004

8

0.003

3

6.01 2@20

3 3.5 30 41.7 0.040 0.04 0.002 0.003 4.13 2@18


72/77

5 1 1 3

ise9o /or -orte

Q( 12 = Q( 23u!

10.33

u

d

4.2" 7.7

10.33

4.26=

Vu

(4.260.4175)

u=#.32 T

u cri&ico= #.32 T

n= u/B CB=0.75

c=0.53M-c!1/2b?d

c=0.531210!1/23041.75

c=#."2T

s=nc

n=#.32/0.75=12.43


73/77

s=12.43#."2

s=2.1 T

13.77

12.43

#."2

s


74/77

S=AvFytd

Vs

S=1420041.75

2.81(1000)

S="2.45 cm CSsmaA

S=SmaA=20cm

1Bmm 2ramasV20cm &oda la iEa &iene es&e armado!

*ro/uesta de armado

l/3 l/3

( ) *

2B14B1 2B1

2B1 2B20



No&aW Kn el es'acio ue ueda en&re aliianamien&os se colocara re-uerDosnorma&ios en sen&ido lonEi&udinal de los &ableros 1B10 arriba J 1B10 aba%o

1 32


75/77


76/77


77/77

i

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