105010037 diseno de vigas de concreto reforzado

7/22/2019 105010037 Diseno de Vigas de Concreto Reforzado

1/13

ESTRUCTURA MODELADA

ESTADOS DE CARGA SEGN RNE:

CD = Carga muerta

CV = Carga viva

CS = Carga de sismo

COMBINACIONES SEGN RNE:

0.9MD+1.25Ms

0.9MD-1.25Ms

1.25(MD+Mv-Ms)

Combinacion

1.5MD+1.8Mv

1.25(MD+Mv+Ms)


2/13

Diseo de viga : V-101

Del anlisis realizado en el Programa Estructural SAP-2000

Escogemos los valores de momentos ms desfavorables

Mu extremo =

Mu centro =

Procedemos al diseo con los siguientes datos :

f'c =

fy =

Mu extremo = 3.72 Tn-m

Mu centro = 1.63 Tn-m

rec: 3 cm

Acero : 5/8 ''

Estribo : 3/8 ''

d = 35.25 cm

Cuanta balanceada :

= 0.02125

mx = 0.01063

Peralte del bloque rectangular equivalente de esfuerzos :

a = 8.8134

Momento resistente mximo :

Para acero negativo .

3.72 Tn-m < Mcmax

No necesita acero en compresion

Para acero positivo :

1.63 Tn-m < Mcmax


Acero mnimo : As min =

40

25

1.63 Tn-m

210 Kg/cm

3.72 Tn-m

4200 Kg/cm

2.94 cm

MC max =

Mu (-) =

10.92 Tn-m

D I S E O D E V I G AS

Mu (-) =

)6000

6000(

'*85.0

fyfy

cfb

cf

fyda

'*85.0

**max

baadcfMC **)2/('85.0*max


3/13

Para acero Negativo :

d = As1 = 1*b*d

d' = As1 =

a = As1*fy/(0.85*f'c*b) Mu1 = 0.9*As1*fy(d-a/2)

a = 8.813 Mu1 = 10.92 Tn-m

Mu2 = Mu-Mu1

Mu2 =

As2 =

Asumimos inicialmente : a =0.02d

0.705075 -5.1358 -4.7392 -4.7642 -4.7626

-5.4568 -5.0354 -5.0619 -5.0603 -5.0604

As2 =

cuantia = -0.00506

f's = 6(a-beta*d')/a

f's =

Acero en traccin :

As = As1+As2

As =

As =

Acero a util izar:2 5/8 ' '

Acero en compresion

As' = As2*fy/f's

As' = -6.53

Acero a util izar:

4 5/8 ' '

Para acero positivo

0.705075 1.1629 1.1705 1.1707 1.1707

1.2355 1.2437 1.2438 1.2438 1.2438

As =

cuantia = 0.00124

As =

Acero a util izar:

2 5/8 ' '

3.25 Tn/cm

4.75 cm

1.24 cm

9.36 cm

-7.20 Tn-m

-5.06 cm

Usar cuantia mnima : 2.94 cm

35.25 cm

As ( cm2

) =

-5.06 cm

a ( cm ) =

4.30 cm

==> As = 3.96 cm2

==> As = 7.92 cm2

Usar acero calculado : 4.30 cm

==> As = 3.96 cm2

As ( cm2

) =

a ( cm ) =

)2/(9.0 adfy

MuAs

bcf

fyAsa

*'*85.0

*


4/13

Del analisis realizado en el Programa Estructural SAP-2000

Escogemos los valores de cortantes ms desfavorables

Vu izquierdo =Vu derecho =

El cortante : Vx = Ra - WX

Cortante a la cara de la columna

Va = 4.650 Vb = 5.910

Cortante en el apoyo Vdu =Vb - w*d

Wd = 2.16 L = 5.00 m

Wv = 0.225 b= 25.0 cm

Wu = 3.65 Tn/m d = 35.3 cm

Luego : Vdu = 4.625 Tn

Cortante tomado por el concreto : Vc

Vc=0.53*f'c1/2

*b*d

Vc =

Vn = Vdu/0.85Vn=

Vs=Vn - Vc

Vs =

Vn Vc/2

Usar estribos:

3/8 '' : 1 @ 0.05, 6@10, 6@15 R @ 0.20

V-101

No se necesita ningn tipo de refuerzo transversal

4.65 Tn-m

Wu = 1.5Wd + 1.8Wv

6.769 Tn

-1.328 Tn

CLCULO DEL ACERO TRANSVERSAL

Diseo de viga :

5.91 Tn-m

5.441 Tn

Vs

dfyAvS ..


5/13

V-102



Mu extremo =

Mu centro =


f'c =

fy =



rec: 3 cm

Acero : 5/8 ''

Estribo : 3/8 ''

d = 35.25 cm

Cuanta balanceada :

= 0.02125

mx = 0.01063


a = 8.8134



2.61 Tn-m < Mcmax



1.54 Tn-m < Mcmax



40

25

Mu (-) =

Mu (-) =

2.94 cm

2.61 Tn-m

1.54 Tn-m

210 Kg/cm

4200 Kg/cm

Diseo de viga :

MC max = 10.92 Tn-m

)6000

6000(

'*85.0

fyfy

cfb

cf

fyda

'*85.0

**max



6/13

Para acero negativo :

d = As1 = 1*b*d

d' = As1 =


a = 8.813438 Mu1 = 10.92 Tn-m

Mu2 = Mu-Mu1

Mu2 =

As2 =


0.705075 -5.9277 -5.4133 -5.4500 -5.4473

-6.2981 -5.7516 -5.7906 -5.7878 -5.7880

As2 =

cuantia = -0.0058


f's =

Acero en traccin :

As = As1+As2

As =

As =

Acero a util izar:

2 5/8 ' '

Acero en compr esion

As' = As2*fy/f's

As' = -7.47175

Acero a util izar:

4 5/8 ' '

Para acero positivo

0.705075 1.0987 1.1049 1.1050 1.1050

1.1673 1.1739 1.1740 1.1740 1.1740

As =

cuantia = 0.00117

3.58 cm

==> As = 3.96 cm2

==> As = 7.92 cm2

a ( cm ) =

As ( cm2

) =

1.17 cm

-8.31 Tn-m

-5.79 cm

a ( cm ) =

As ( cm2

) =

-5.79 cm

3.25 Tn/cm

3.58 cm

Usar acero calculado :

35.25 cm

4.75 cm 9.36 cm

)2/(9.0 adfy

MuAs

bcf

fyAsa

*'*85.0

*


7/13

As =

Acero a util izar:

2 5/8 ' '



Vu izquierdo =

Vu derecho =



Va = 3.700 Vb = 4.360


Wd = 2.16 L = 5.00 m

Wv = 0.225 b= 25.0 cm

Wu = 3.65 Tn/m d = 35.3 cm



Vc=0.53*f'c1/2

*b*d

Vc =

Vn = Vdu/0.85

Vn=

Vs=Vn - Vc

Vs =

Vn Vc/2

Usar estr ibos:

3/8 ' ' : 1 @ 0.05, [email protected], [email protected] R @ 0.20

Wu = 1.5Wd + 1.8Wv

6.769 Tn

3.618 Tn

-3.151 Tn


==> As = 3.96 cm2

3.70 Tn-m



4.36 Tn-m



8/13

V-103



Mu extremo =

Mu centro =


f'c =

fy =

Mu extremo =


rec: 4 cm

Acero : 3/4 ''

Estribo : 3/8 ''

d = 49.10 cm

Cuanta balanceada :

= 0.02125

mx = 0.01063


a = 12.2738



12.00 Tn-m < Mcmax



6.00 Tn-m < Mcmax



12.00 Tn-m

210 Kg/cm

35

55

4200 Kg/cm

6.00 Tn-m

12.00 Tn-m

Diseo de viga :

MC max = 29.65 Tn-m

Mu (-) =

Mu (-) =

5.73 cm

)6000

6000(

'*85.0

fyfy

cfb

cf

fyda

'*85.0

**max



9/13


d = As1 = 1*b*d

d' = As1 =


a = 12.27375 Mu1 =

Mu2 = Mu-Mu1

Mu2 =

As2 =


0.9819 -6.4570 -5.9980 -6.0245 -6.0229

-9.6049 -8.9221 -8.9614 -8.9591 -8.9593

As2 =

cuantia = -0.004654


f's =

Acero en traccin :

As = As1+As2

As =

As =

Acero a util izar:

4 3/4 ' '

Acero en compresion

As' = As2*fy/f's

As' = -10.610589

Acero a util izar:

1 3/4 ' '

Para acero positivo

0.9819 2.1955 2.2232 2.2239 2.2239

3.2658 3.3071 3.3080 3.3080 3.3080

As =

cuantia = 0.0017185

-8.96 cm

18.26 cm

Usar acero calculado :

3.55 Tn/cm

9.30 cm

a ( cm ) =

9.30 cm

==> As = 11.40 cm2

==> As = 2.85 cm2

5.91 cm

As ( cm2

) =

-17.65 Tn-m

-8.96 cm

a ( cm ) =

3.31 cm

As ( cm2

) =

49.10 cm

29.65 Tn-m

)2/(9.0 adfy

MuAs

bcf

fyAsa

*'*85.0

*


10/13

As =

Acero a util izar:

2 3/4 ' '



Vu izquierdo =

Vu derecho =

cortante : x = a -


Va = 12.920 Vb = 14.370


Wd = 2.16 L = 5.00 m

Wv = 0.225 b= 35.0 cm

Wu = 3.65 Tn/m d = 49.1 cm



Vc=0.53*f'c1/2

*b*d

Vc =

Vn = Vdu/0.85

Vn=

Vs=Vn - Vc

Vs =

Vn Vc/2

Usar estr ibos:

3/8 '' : 1 @ 0.05, [email protected], [email protected] R @ 0.20




14.801 Tn

1.603 Tn

14.37 Tn-m

12.92 Tn-m

Wu = 1.5Wd + 1.8Wv

13.197 Tn


==> As = 5.70 cm2


11/13

V - A



Mu extremo =

Mu centro =


f'c =

fy =



rec: 3 cm

Acero : 1/2 ''

Estribo : 1/4 ''

d = 16.23 cm

Cuanta balanceada :

= 0.02125

mx = 0.01063


a = 4.0575



1.80 Tn-m < Mcmax



0.45 Tn-m < Mcmax



1.80 Tn-m

0.45 Tn-m

210 Kg/cm

4200 Kg/cm

Diseo de viga :

20

25

MC max = 2.31 Tn-m

Mu (-) =

Mu (-) =

1.35 cm

)6000

6000(

'*85.0

fyfy

cfb

cf

fyda

'*85.0

**max

)2/(9.0 adfy

MuAs


bcf

fyAsa

*'*85.0

*


12/13


d = As1 = 1*b*d

d' = As1 =


a = 4.0575 Mu1 = 2.31 Tn-m

Mu2 = Mu-Mu1

Mu2 =

As2 =


0.3246 -0.7969 -0.7700 -0.7706 -0.7706

-0.8467 -0.8181 -0.8188 -0.8188 -0.8188

As2 =

cuantia = -0.001638

f's = 6(a-beta*d')/af's =

Acero en traccin :

As = As1+As2

As =

As =

Acero a util izar:

3 1/2 ' '

Acero en compresionAs' = As2*fy/f's

As' = -2.72622684

Acero a util izar:

2 1/2 ' '

Para acero positivo

0.3246 0.6973 0.7055 0.7057 0.7057

0.7409 0.7496 0.7498 0.7498 0.7498

As =cuantia = 0.0015

As =

Acero a util izar:

2 1/2 ' '

16.23 cm

3.77 cm 4.31 cm

-0.51 Tn-m

-0.82 cm

a ( cm ) =

As ( cm2

) =

-0.82 cm

1.26 Tn/cm

3.49 cm

Usar acero calculado : 3.49 cm

==> As = 3.80 cm2

==> As = 2.53 cm2

a ( cm ) =

As ( cm2

) =

0.75 cm


==> As = 2.53 cm2


13/13



Vu izquierdo =

Vu derecho =



Va = 1.800 Vb = 2.000


Wd = 2.16 L = 5.00 mWv = 0.225 b= 25.0 cm

Wu = 3.65 Tn/m d = 16.2 cm



Vc=0.53*f'c1/2

*b*d

Vc =

Vn = Vdu/0.85

Vn=

Vs=Vn - VcVs =

Vn Vc/2

Usar estr ibos:

1/4 ' ' : 1 @ 0.05, [email protected], R @ 0.20

2.00 Tn-m

Wu = 1.5Wd + 1.8Wv

3.116 Tn

1.657 Tn

-1.459 Tn



Diseo de viga : V - A

1.80 Tn-m

105010037 diseno de vigas de concreto reforzado

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