Losa Maciza-primer Piso

8/17/2019 Losa Maciza-primer Piso

1/38


2/38

ea la losa%

PAÑO Nº 1

L1=Lx

L 2 = L y


3/38

DETERMINACION DEL MOMENTO INTERNO ACT7ANTE POR EL METODO DE TRA8A9O 3IRT7AL

L4e"o ,allamos el !a/a:o e;e!no e ine!no< !eali=ado 5o! la 4e!=as e;e!nas< ales como so/!eca!"a > 5eso 5!o5io< ?4e ac

Zona A Z

Segmentos considerados para el analisis

A A

B2

B1

L1-X1-X2 X1 X2

Y2

Y1

B1 B1

B1B2

L2

Probables lineas de falla o de rotura

A A

B

B Y1

Y2

L1-2X1 X1 X1

∆=1

X

PeA

δ A=1!

X

L2

∆=1

X

A

"A=1x

L2

mm#

B2

P eB 1

B1

∆=1

Y

δ B1=1!

δ B2=12

P eB 2

PeB 1

B1

X2

L1-X1-X2

X1

( ) ALLA )2(2'222 θ


4/38

…(3)

Enonces i"4alando las ec4aciones 012 0*2< > 0$2 0+2< se de/e @e!iica! ?4e( m m

( )( ) 2212

2

BWuY X L δ ××××−×

....

2××=×

x

A 1=

=

θ


5/38

PRIMER PISO

PAÑO NB &1Ca!ace!isicas del 5ao(

&ongtu! D"eccon $ % &1=&= 3000mm +a"a el conc"eto 2.4E-5

&ongtu! D"eccon % &2=&y= 200mm +eso !e la &osa =

Espeso" !e la losa % f= 130mm +eso !e aca)a!os =

3e!iicacion de la !elacion de las lon"i4desDe)e cumpl"se% +.1*E-&

.&&E-&

Dee!

Entonces. &1/&2=1.034 2 Si c4m5le

a"acte"stcas !el pao%

&ongtu! D"eccon $ % &1=&= 3000mm $1 = 14*mm&ongtu! D"eccon % &2=&y= 200mm 1 = 1450mm

Espeso" !e la losa % f= 130mm 2 = 1450mm

a"ga !e !seo % u = 1.8E601N/mm

27 = 2.51E60 999:1; 2 = .8 m .....:2; 4gualan!o las ecuacones :3; = :4;? (ene

2.51E60 = .8m @ Entonces m $.*E& 2.*E60 =

G c M

G c@

ANALISIS ESTR7CT7RAL DE LA LOSA:Asan!o las fo"mulas ante"o"es tenemos;

( )( )212

12

42214

WuY X L

BWuY X

B B δ

×××−×

+×

×××=×+×

=C γ

22

1≤

L

L

CV CM W W Wu ×+×= 7.14.1

( ))1....(

2

222 A

Wu X L A δ ×

×××=×

( )

x A

mm

Am Lm L A

1

'

)2....(2'222

=

=

××+××=

θ

θ


6/38

DISEÑO DE LA LOSA

Daos 5a!a el diseo de la losa.f'c = 21Mpa fy = 420Mpa +a"a stemas !e &osas con ,gas se ,e"fca con la

f= 130mm Mu = 3.2E60*Mpa

" = 20.00mm Calc4lo de la 4e!=a co!ane !esiseneCalc4lo de 5e!ale eeci@o de la losa !) = 13.00mm sumen!o%

Befue"Co% N13 = mm

Becu)"mento% 20mm

Calc4lo del a!ea de ace!o As( Calc4lo de la Co!ane ac4aneAtlCamos el meto!o !e a"ga !e Botu"a

ompa"an!o tenemos%

@ a = :s7420;/:0.8572171000; 2.*E04 84**.*2*21 s =:2.82;/:-a/2;;

sumen!o a = 4.85mm

s=8.523mm2 a=2.11mm CALC7LO DE L s=88.243mm2 a=2.08mm

s=88.22mm2 a=2.08mm "ea !e ace"o calcula!o. s=323.

+a"a%

(oman!ose% As %%.*mm* a *.&%mm N13N10

Hallamos el Ace!o Minimo

El espacamento esta !a!a po"%

Entonces%

s?mm=2*4.58 = 323.333mm2

Ace!o 5o! em5e!a4!a

s?mm=234.000mm2

Enonces omanos( As$*$.$$$mm*

s =:3.5710 3 ;/:0.74207:-a/2;;

( )dbr hf d +−=

−××

=

2

ad fy

Mu As

φ bc f

fy Asa

×××

='85.0

fy

d bwd bw

fy

c f As ××>××

×=

4.1

4

'min

f hb As ××= ρ min

VnVu ×=φ

bc f

Vc ×××

=×6

'φ φ

+±

×=

L

M M LWuVu

21

2

Vu < φ

As

b AsbS

ω ×=


7/38

PAÑO NB &*

Ca!ace!isicas del 5ao(&ongtu! D"eccon $ % &1=&= 3500mm +a"a el conc"eto 2.4E-5



3e!iicacion de la !elacion de las lon"i4des

De)e cumpl"se% +.1*E-&

.&&E-& Dee


Ca!ace!isicas del 5ao(&ongtu! D"eccon $ % &1=&= 3500mm $1 = 110mm

&ongtu! D"eccon % &2=&y= 4240mm 1 = 2120mmEspeso" !e la losa % f= 130mm 2 = 2120mm

a"ga !e !seo % u = 1.8E601N/mm2

27 = 4.E60 999:1; 2 = 8.880 m .....:2; 4gualan!o las ecuacones :3; = :4;? (ene

4.E60 = 8.880m @ Entonces m '.+E& 3.5E60 =

G c M

G c@


( )( )212

12

42214

WuY X L

BWuY X

B B δ

×××−×

+×

×××=×+×

=C γ

22

1≤

L

L

CV CM W W Wu ×+×= 7.14.1

( ))1....(

2

222 A

Wu X L A δ ×

×××=×

( )

x A

mm

Am Lm L A

1

'

)2....(2'222

=

=

××+××=

θ

θ


8/38

DISEÑO DE LA LOSA


f= 130mm Mu = 5.4E60*Mpa

Calc4lo de la 4e!=a co!ane !esiseneCalc4lo de 5e!ale eeci@o de la losa sumen!o%

Befue"Co% N13 = mm

Becu)"mento% 20mm


ompa"an!o tenemos%

@ a = :s7420;/:0.8572171000; 3.1E04 1425.224*5 s =:13042.2;/:-a/2;;

sumen!o a = *.0*mm



+a"a%

(oman!ose% As 1+).mm* a $.'*mm N13N10

Hallamos el Ace!o MinimoEl espacamento esta !a!a po"%

Entonces%

s?mm=2*4.58 323.333mm2

Ace!o 5o! em5e!a4!a

s?mm=234.000mm2


s =:3.5710 3 ;/:0.74207:-a/2;;

( )dbr hf d +−=

−××

=

2

ad fy

Mu As

φ bc f

fy Asa

×××

='85.0

fyd bwd bw

fyc f As ××>××

×= 4.1

4'

min


VnVu ×= φ

bc f

Vc ×××

=×6

'φ φ

+±

×=

L

M M LWuVu

21

2

Vu < φ

As

b AsbS

ω ×=


9/38

PAÑO NB &$






.&&E-& Dee!




a"ga !e !seo % u = 1.8E601N/mm2

27 = 2.5E60 999:1; 2 = .* m .....:2; 4gualan!o las ecuacones :3; = :4;? (ene

2.5E60 = .*m @ Entonces m $.$E& 2.0E60 =

G c M

G c@


( )( )212

12

42214

WuY X L

BWuY X

B B δ

×××−×

+×

×××=×+×

=C γ

22

1≤

L

L

CV CM W W Wu ×+×= 7.14.1

( ))1....(

2

222 A

Wu X L A δ ×

×××=×

( )

x A

mm

Am Lm L A

1

'

)2....(2'222

=

=

××+××=

θ

θ


10/38

DISEÑO DE LA LOSA


f= 130mm Mu = 3.3E60*Mpa


Befue"Co% N13 = mm

Becu)"mento% 20mm


ompa"an!o tenemos%

@ a = :s7420;/:0.8572171000; 2.*E04 884*.2358* s =:2.82;/:-a/2;;

sumen!o a = *.0*mm



+a"a%

(oman!ose% As )*.*mm* a *.1mm N13N10


Entonces%

s?mm=2*4.58 323.333mm2

Ace!o 5o! em5e!a4!a

s?mm=234.000mm2


s =:3.5710 3 ;/:0.74207:-a/2;;

( )dbr hf d +−=

−××

=

2

ad fy

Mu As

φ bc f

fy Asa

×××

='85.0

fyd bwd bw

fyc f As ××>××

×= 4.1

4'

min


VnVu ×=φ

bc f

Vc ×××

=×6

'φ φ

+±

×=

L

M M LWuVu

21

2

Vu < φ

As

b AsbS

ω ×=


11/38

PAÑO NB &+






.&&E-& Dee!



&ongtu! D"eccon % &2=&y= 1200mm 1 = *00mmEspeso" !e la losa % f= 130mm 2 = *00mm

a"ga !e !seo % u = 1.8E601N/mm2

27 = 5.*E60* 999:1; 2 = 5.*4 m .....:2; 4gualan!o las ecuacones :3; = :4;? (ene

5.*E60* = 5.*4m @ Entonces m 1.&E& 2.31E60 =

G c M

G c@


( )( )212

12

42214

WuY X L

BWuY X

B B δ

×××−×

+×

×××=×+×

=C γ

22

1≤

L

L

CV CM W W Wu ×+×= 7.14.1

( ))1....(

2

222 A

Wu X L A δ ×

×××=×

( )

x A

mm

Am Lm L A

1

'

)2....(2'222

=

=

××+××=

θ

θ


12/38

DISEÑO DE LA LOSA


f= 130mm Mu = 1.0E60*Mpa


Befue"Co% N13 = mm

Becu)"mento% 20mm


ompa"an!o tenemos%

@ a = :s7420;/:0.8572171000; 1.1E04 20.3*114 s =:1.38;/:-a/2;;

sumen!o a = *.0*mm

s=2.488mm2 a=0.*mm CALC7LO DE L s=28.**mm2 a=0.*mm

s=28.***mm2 a=0.*mm "ea !e ace"o calcula!o. s=323.

+a"a%

(oman!ose% As *%.mm* a &.mm N13N10


Entonces%

s?mm=2*4.58 323.333mm2

Ace!o 5o! em5e!a4!a

s?mm=234.000mm2


s =:3.5710 3 ;/:0.74207:-a/2;;

( )dbr hf d +−=

−××

=

2

ad fy

Mu As

φ bc f

fy Asa

×××

='85.0

fyd bwd bw

fyc f As ××>×××=

4.14

'min


VnVu ×=φ

bc f

Vc ×××

=×6

'φ φ

+±

×=

L

M M LWuVu

21

2

Vu < φ

As

b AsbS

ω ×=


13/38

PAÑO NB &'






.&&E-& Dee



&ongtu! D"eccon % &2=&y= 1200mm 1 = *00mmEspeso" !e la losa % f= 130mm 2 = *00mm

a"ga !e !seo % u = 1.8E601N/mm2

27 = 5.*E60* 999:1; 2 = 5.*4 m .....:2; 4gualan!o las ecuacones :3; = :4;? (ene

5.*E60* = 5.*4m @ Entonces m 1.&E& 2.14E60 =

G c M

G c@


( )( )212

12

42214

WuY X L

BWuY X

B B δ

×××−×

+×

×××=×+×

=C γ

22

1≤

L

L

CV CM W W Wu ×+×= 7.14.1

( ))1....(

2

222 A

Wu X L A δ ×

×××=×

( )

x A

mm

Am Lm L A

1

'

)2....(2'222

=

=

××+××=

θ

θ


14/38

DISEÑO DE LA LOSA


f= 130mm Mu = 1.0E60*Mpa


Befue"Co% N13 = mm

Becu)"mento% 20mm


ompa"an!o tenemos%

@ a = :s7420;/:0.8572171000; 1.1E04 234.431243 s =:1.38;/:-a/2;;

sumen!o a = *.0*mm

s=2.0mm2 a=0.*8mm CALC7LO DE L s=28.20mm2 a=0.*mm

s=28.28mm2 a=0.*mm "ea !e ace"o calcula!o. s=323.

+a"a%

(oman!ose% As *%.$mm* a &.mm N13N10


Entonces%

s?mm=2*4.58 323.333mm2

Ace!o 5o! em5e!a4!a

s?mm=234.000mm2


s =:3.5710 3

;/:0.74207:-a/2;;

( )dbr hf d +−=

−××

=

2

ad fy

Mu As

φ bc f

fy Asa

×××

='85.0

fyd bwd bw

fyc f As ××>×××=

4.14

'min


VnVu ×=φ

bc f

Vc ×××

=×6

'φ φ

+±

×=

L

M M LWuVu

21

2

Vu < φ

As

b AsbS

ω ×=


15/38

PAÑO NB &






.&&E-& Dee

Entonces. &1/&2=0.**0 2 Si c4m5le



a"ga !e !seo % u = 1.8E601N/mm2


2.0E60 = .05m @ Entonces m $.&E& 3.12E60 =

G c M

G c@


( )( )212

12

42214

WuY X L

BWuY X

B B δ

×××−×

+×

×××=×+×

=C γ

22

1≤

L

L

CV CM W W Wu ×+×= 7.14.1

( ))1....(

2

222 A

Wu X L A δ ×

×××=×

( )

x A

mm

Am Lm L A

1

'

)2....(2'222

=

=

××+××=

θ

θ


16/38

DISEÑO DE LA LOSA


f= 130mm Mu = 3.0E60*Mpa

Calc4lo de la 4e!=a co!ane !esiseneCalc4lo de 5e!ale eeci@o de la losa

sumen!o%

Befue"Co% N13 = mmBecu)"mento% 20mm


ompa"an!o tenemos%

@ a = :s7420;/:0.8572171000; 2.2E04

812.8*453 s =:1.38;/:-a/2;;

sumen!o a = *.0*mm

s=83.143mm2 a=1.*mm CALC7LO DE s=81.3*5mm2 a=1.1mm


+a"a%

(oman!ose% As %1.$mm* a 1.)1mm N13N10


Entonces%

s?mm=2*4.58 323.333mm2

Ace!o 5o! em5e!a4!a

s?mm=234.000mm2


PAÑO NB &



s =:3.5710 3 ;/:0.74207:-a/2;;

( )dbr hf d +−=

−××

=

2

ad fy

Mu As

φ bc f

fy Asa

×××

='85.0

fy

d bwd bw

fy

c f As

××>××

×=

4.1

4

'min


VnVu ×=φ

b

c f

Vc ×××

=× 6'φ

φ

+±

×=

L

M M LWuVu

21

2

Vu < φ

As

b AsbS

ω ×=

=C γ


17/38



De)e cumpl"se% 1.&&E-&

.&&E-& Dee

Entonces. &1/&2=0.*28 2 Si c4m5le

G c M

G c@

22

1≤

L

L

CV CM W W Wu ×+×= 7.14.1


18/38

Ca!ace!isicas del 5ao(

&ongtu! D"eccon $ % &1=&= 3140mm $1 = 130mm&ongtu! D"eccon % &2=&y= 2500mm 1 = 1250mm

Espeso" !e la losa % f= 0mm 2 = 1250mm

a"ga !e !seo % u = 1.3E601N/mm2


1.54E60 = .14m @ Entonces m *.1E& 2.14E60 =

DISEÑO DE LA LOSA


f= 130mm Mu = 2.1E60*Mpa

Calc4lo de la 4e!=a co!ane !esiseneCalc4lo de 5e!ale eeci@o de la losa

sumen!o%

Befue"Co% N13 = mm

Becu)"mento% 20mm


ompa"an!o tenemos%

@ a = :s7420;/:0.8572171000; 1.E04

5*48.5121 s =:1.38;/:-a/2;;

sumen!o a = *.0*mm

s=*0.111mm2 a=1.41mm CALC7LO DE L s=58.**0mm2 a=1.38mm

s=58.*4mm2 a=1.38mm "ea !e ace"o calcula!o. s=323.

+a"a%

(oman!ose% As '%.mm* a 1.$%mm N13N10

Hallamos el Ace!o Minimo


s =:3.5710 3 ;/:0.74207:-a/2;;

( )( )212

12

42214

WuY X L

BWuY X

B B δ

×××−×

+×

×××=×+×

( )dbr hf d +−=

−××=

2

ad fy

Mu

Asφ bc f

fy Asa×××= '85.0

VnVu ×= φ

bc f

Vc ×××

=×6

'φ φ

+±×

= L

M M LWuVu

21

2

Vu < φ

( ))1....(

2

222 A

Wu X L A δ ×

×××=×

( )

x A

mm

Am Lm L A

1

'

)2....(2'222

=

=

××+××=

θ

θ


19/38

El espacamento esta !a!a po"%

Entonces%

s?mm=2*4.58 323.333mm2

Ace!o 5o! em5e!a4!a

s?mm=234.000mm2


fy

d bwd bw

fy

c f As

××>××

×=

4.1

4

'min


As

b AsbS

ω ×=


20/38


21/38


22/38

/!e el elemeno(

B1

∆=1

Y

B2L1

B1

mm#

"A=1Y

( ) Bm Lm L B )4...(1'122 ××+××= θ


23/38

Y B

mm

1=

=

θ


24/38

e!ados de ca!"as

N/mm3

3.12E-03 N/mm2

0.001N/mm2

4.12E-03

Nmm*

Nmm* :Dato;

minamos la ca!"a 4lima

?Entonces Wu = 1.%E-&*Nmm*

…(3)

ean los tanteos%

9..:3; 2< = 8.2* m999:4;

os

8.2*m m $.*E& si c4m5le

:f; : γ c;

2 Bδ ×

( )

Y B

mm

Bm Lm L B

1

'

)4...(1'122

=

=

××+××=

θ

θ


25/38

e!iicacion 5o! co!e.

sguente ep"eson%

del conc!eo

5.*E04N

Es smet"c?entonces u= 2.*E04 N

5.*E04 AM+&E Por lo tanto no necesita acero de refuerzo por corte

A DISTRI87CION DEL REF7ERZO

33mm2

s) n, (omamos

133 2.43 2

4.0 4

Elegmos%

= 244.328 244.32 2*0

2 f = 2*0

+o" lo tanto tomamos% = 220mm

N1& &.**m

VsVcVn +=

=×Vcφ

Vc×

≤

VcVu ×


26/38

e!ados de ca!"asN/mm3

3.12E-03 N/mm2

0.001N/mm2

4.12E-03

Nmm*

Nmm* :Dato;minamos la ca!"a 4lima


…(3)

Sean los aneos(

9..:3; 2< = *.*04 m999:4;

os

*.*04m m '.+E& FGHH

:f; : γ c;

2 Bδ ×

( )

Y B

mm

Bm Lm L B

1

'

)4...(1'122

=

=

××+××=

θ

θ


27/38

e!iicacion 5o! co!e. sguente ep"eson%

del conc!eo

5.*E04N

Es smet"c?entonces u= 3.1E04 N

5.*E04AM+&E Por lo tanto no necesita acero de refuerzo por corte


333mm2

s) n, (omamos

133 2.43 2

4.0 4

Elegmos%

= 244.328 244.32 2*0

2 f = 2*0


N1& &.**m

VsVcVn +==×Vcφ

Vc×

≤

VcVu ×< φ


28/38


3.12E-03 N/mm2

0.001N/mm2

4.12E-03

Nmm*



…(3)

Sean los aneos(

9..:3; 2< = 8.**2 m999:4;

os

8.**2m m $.$E& FGHH

:f; : γ c;

2 Bδ ×

( )

Y B

mm

Bm Lm L B

1

'

)4...(1'122

=

=

××+××=

θ

θ


29/38


del conc!eo

5.*E04N

Es smet"c?entonces u= 2.*E04 N



333mm2

s) n, (omamos

133 2.43 2

4.0 4

Elegmos%

= 244.328 244.32 2*0

2 f = 2*0


N1& &.**m

VsVcVn +==×Vcφ

Vc×

≤

VcVu ×< φ


30/38


3.12E-03 N/mm2

0.001N/mm2

4.12E-03

Nmm*



…(3)

Sean los aneos(

9..:3; 2< = 22.000 m999:4;

os

22.000m m 1.&E& FGHH

:f; : γ c;

2 Bδ ×

( )

Y B

mm

Bm Lm L B

1

'

)4...(1'122

=

=

××+××=

θ

θ


31/38


del conc!eo

5.*E04N




333mm2

s) n, (omamos

133 2.43 2

4.0 4

Elegmos%

= 244.328 244.32 2*0

2 f = 2*0


N1& &.**m

VsVcVn +==×Vcφ

Vc×

≤

VcVu ×< φ


32/38


3.12E-03 N/mm2

0.001N/mm2

4.12E-03

Nmm*



…(3)

Sean los aneos(

9..:3; 2< = 20.33 m999:4;

os

20.33m m 1.&E& FGHH

:f; : γ c;

2 Bδ ×

( )

Y B

mm

Bm Lm L B

1

'

)4...(1'122

=

=

××+××=

θ

θ


33/38


del conc!eo

5.*E04N




333mm2

s) n, (omamos

133 2.43 2

4.0 4

Elegmos%

= 244.328 244.32 2*0

2 f = 2*0


N1& &.**m

VsVcVn +==×Vcφ

Vc×

≤

VcVu ×< φ


34/38


3.12E-03 N/mm2

0.001N/mm2

4.12E-03

Nmm*



…(3)

Sean los aneos(

9..:3; 2< = 10.5*0 m999:4;

os

10.5*0m m $.&E& FGHH

:f; : γ c;

2 Bδ ×

( )

Y B

mm

Bm Lm L B

1

'

)4...(1'122

=

=

××+××=

θ

θ


35/38


del conc!eo

5.*E04N


5.*E04 AM+&E

Por lo tanto no necesita acero de refuerzo por corte


33mm2

s) n, (omamos

133 2.43 2

4.0 4

Elegmos%

= 244.328 244.32 2*0

2 f = 2*0


N1& &.**m


0.00E600 N/mm2 :f; : γ c;

VsVcVn +==×Vc

φ

Vc

≤

VcVu ×< φ


36/38

0.001 N/mm2

1.00E-03

Nmm*


?Entonces Wu = 1.$E-&*Nmm*


37/38

…(3)

Sean los aneos(

9..:3; 2< = 10.048 m999:4;

os

10.048m m *.1E& FGHH


del conc!eo

5.*E04N

Es smet"c?entonces u= 1.E04 N

5.*E04 AM+&E

Por lo tanto no necesita acero de refuerzo por corte


33mm2

s) n, (omamos

133 2.43 2

4.0 4

Elegmos%

2 Bδ ×

VsVcVn +==×Vcφ

Vc×

( )

Y B

mm

Bm Lm L B

1

'

)4...(1'122

=

=

××+××=

θ

θ

VcVu ×< φ


38/38

= 244.328 244.32 2*0

2 f = 2*0


N1& &.**m

≤

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