Predimencionamiento y Diseño de Vigas [PDF]

Zitiervorschau

PREDIMENSIONAMIENTO CALCULO DEL PERALTE Luz critica Categoria A 5.2 Categoria B 5.2 Categoria C 4.5

h 0.52 0.47 0.38

h 0.60 0.50 0.40

b1 0.30 0.25 0.20

b2 0.30 0.25 0.20 cumple

A. Tributario 4.00 5.00 4.40

A. Tributario 4.00 5.00 4.40

b3 0.20 0.25 0.22

A

B

0.25

5.50

C

0.25

5.80

V-P (25×50)

3

V-P (25×50) V-S (25×35)

V-S (25×35)

V-S (25×35)

V-P (25×50)

2

V-P (25×50) V-S (25×35)

V-S (25×35)

1

0.25

V-S (25×35)

V-P (25×50)

V-P (25×50)

METRADO DE CARGAS V-P (25×50 cm)

SEGÚN ING. MERCA -

Carga muerta (WD) CARGA MUERTA (WD) Peso propio de losa Piso terminado Tabiqueria Cielo raso P.p. Viga

Peso/m2 300 kg/m2 100 kg/m2 150 kg/m2 0 kg/m2

At 6.35 6.60 6.60 6.60

m m m m

WD = -

Carga viva (WL) CARGA VIVA (WL) Sobre carga según uso

Peso/m2 200 kg/m2

At 6.60 m

WD = -

Peso/m 1905 Kg/m 660 Kg/m 990 Kg/m 0 Kg/m 300 Kg/m 3855 Kg/m

WD = WD = WL =

Peso/m 1320 Kg/m 1320 Kg/m

Carga ultima (Wu) Wu=1.5WD+1.8WL

ACI

Wu=1.4WD+1.7WL

RNE

8158.5 kg/m ###

A.T

A

1.25

7641 kg/m

A.T

2.25

B

A.T

2.25

C

A

B

0.25

5.50

C

0.25

5.80

V-P (25×50)

3

V-P (25×50) V-S (25×35)

V-S (25×35)

V-S (25×35)

V-P (25×50)

2

V-P (25×50) V-S (25×35)

V-S (25×35)

V-S (25×35)

V-P (25×50)

1

0.25

V-P (25×50)

METRADO DE CARGAS V-P (25×35 cm)

SEGÚN ING. MERCA -

Carga muerta (WD) CARGA MUERTA (WD) Peso propio de losa Piso terminado Tabiqueria Cielo raso P.p. Viga

Peso/m2 300 kg/m2 100 kg/m2 150 kg/m2 0 kg/m2

At 2.00 m 2.25 m 2.25 m 2.25 m

WD = -

Carga viva (WL) CARGA VIVA (WL) Sobre carga según uso

Peso/m2 200 kg/m2

At 2.25 m

WD = -

Peso/m 600 Kg/m 225 Kg/m 337.5 Kg/m 0 Kg/m 300 Kg/m 1462.5 Kg/m

WD = WD = WL =

Peso/m 450 Kg/m 450 Kg/m

Carga ultima (Wu) ACI

Wu=1.5WD+1.8WL 3003.8 kg/m ###

RNE

Wu=1.4WD+1.7WL 2812.5 kg/m

D 5.20

0.25

V-P (25×50)

0.40

V-S (25×35)

VIGA PRINCPAL h b

V-S (25×35)

0.50

6.20

V-P (25×50)

0.40

V-S (25×35)

V-S (25×35) 6.20

V-P (25×50)

0.40

SEGÚN ING. MERCADO -

WD = WD =

0.65 0.65

6.60

4.29 Tn/m

WL =

0.2

6.60

1.32 Tn/m

RNE

0.75

Tn/m2

Wu=1.4WD+1.7WL 8.25 Tn/m

Wu=1.4WD+1.7WL kg/m

A.T

1.25

D

A.T

6.60

0.25

D 5.20

0.25

V-P (25×50)

V-S (25×35)

0.30

0.50

V-S (25×35) 4.00

V-P (25×50)

0.30

V-S (25×35)

V-S (25×35) 4.20

V-P (25×50)

0.30

SEGÚN ING. MERCADO -

WD = WD =

0.65 0.65

0.00

0.00 Tn/m

WL =

0.2

0.00

0.00 Tn/m

RNE

0.75

Tn/m2

Wu=1.4WD+1.7WL 0.00 Tn/m

Wu=1.4WD+1.7WL kg/m

VIGA SECUNDARIA h b 0.25

CALCULO DE MOMENTOS Wu= 8158.5 Kg/m

VIGA PRINCIPAL 8.16

ACI M(-)

15.42 Tn-m

26.04

Luz M(-) Factor M (-)

5.50 0.06 A

5.65 0.10 B

Factor M (+) Luz M(+)

0.07 5.50

ACI M(+)

Tn-m

0.06 5.80

1.05

17.63 Tn-m

Tn/m

24.68 Tn-m

13.79

5.50 0.10 C

5.20 0.06 D

1.12

17.15 Tn-m

15.76

ACI

3.31

Luz M(-) Factor M (-)

4.20 0.06

APOYO A

15.42

TRAMO AB

17.63

APOYO B

26.04

TRAMO BC

17.15

APOYO C APOYO D

24.68

15.76

13.79

TRAMO CD TRAMO DE

APOYO E

26.04

TRAMO EF

17.63

APOYO F

15.42

3.00

Tn/m

Tn-m

3.00

4.10 0.11

0.07 4.20 3.78

Tn-m

5.08

4.00 0.06

2

Factor M (+) Luz M(+)

17.15

VIGA SECUNDARIA

5.61

1

ACI M(+)

ACI MOMENTOS POSITIVOS Tn-m

Tn-m

1.12

Tn-m

MOMENTOS NEGATIVOS Tn-m

CALCULO DE MOMENTOS Wu= 3003.8 Kg/m

ACI M(-)

0.07 5.20

5.20 0.06 4

3 0.07 4.00

0.95

Tn-m

3.43

0.07 5.20

0.77

Tn-m

ACI

5.80

Tn-m

ACI

MOMENTOS NEGATIVOS Tn-m

MOMENTOS POSITIVOS Tn-m

APOYO 1 APOYO 2

TRAMO 1-2 TRAMO 2-3

3.31 5.61

3.78 3.43

1.12

APOYO 3

3.00

TRAMO 3-4

5.80

APOYO 4

5.08

TRAMO 4-5

6.32

APOYO 5 APOYO 6

9.59

TRAMO 5-6

6.49

5.68

Tn-m

0.06 5.80

26.04 Tn-m

15.42 Tn-m

5.65 0.10 E

5.50 0.06 F

1.05

17.15 Tn-m

Tn-m

6.32

17.63 Tn-m

9.59

0.06 5.80 Tn-m

0.07 5.50

Tn-m

5.68

5.65 0.10

5.50 0.06

5

6 0.07 5.50

1.05 6.49

Tn-m

Tn-m

VIGAS PRINCIPALES

CALCULO DEL AREA DE ACERO (cm2)

h

b 50

25

F'c = 210 Kg/cm2

a 1

2 3

a 1 2

9 10.08 9.48

Mu=

12.71

cm

As cm2

9

8.30

8.30

7.814

7.814 8.18 7.701

8.18 7.701 8.17

Mu=

15.42

cm

As cm2 10.08 9.48 10.14

Fy = 4200 Kg/cm2 b = base d = Peralte efectivo h = Peralte a = d/5 Ø=

a 1 2

9 17.01 16.01

Mu=

26.04

cm

As cm2

a

17.01 16.01

1

18.62

2

Mu=

24.68

cm

As

9

16.12

16.12

15.17 17.45

15.17

3 4

10.14 9.54 10.14 9.55

9.54 10.14 9.55 10.14

18.62

3 4

17.53 19.01 17.90

15.42 A

17.53 19.01

3

17.90 19.11

4

26.04 B

Mu=

a

2 3 4

9 11.51 10.84 11.78 11.09 11.82 11.12

cm

16.42 17.75 16.70 17.82 24.68 C

17.63

1

17.45 16.42 17.75 16.70

17.15 Mu=

17.63

As cm2

a 1

11.51 10.84 11.78 11.09 11.82 11.12 11.83

2 3 4

cm

9 11.20 10.55 11.42 10.75 11.45 10.78

ACI

17.15

As cm2 1

11.20 10.55 11.42 10.75 11.45 10.78 11.46

2 3 4

ACI

AREAS DE ACERO NEGATIVO cm2

AREAS DE ACERO POSITIVO cm2

APOYO A APOYO B

10.14

11.83

19.11

TRAMO AB TRAMO BC

APOYO C

17.82

TRAMO CD

10.39

APOYO D APOYO E

8.94

11.46

19.11

TRAMO DE TRAMO EF

APOYO E

10.14

CALCULO DEL AREA DE ACERO (cm2)

11.46

11.83

VIGAS SECUNDARIA

h

b 50

a 1

2 3

Mu=

a 1 2 3 4

cm

9 2.16 2.04 1.99 1.87 1.99 1.87

Mu=

12.71

cm

As cm2

9

8.30

8.30

7.814

7.814 8.18 7.701

8.18 7.701 8.17

25

Mu=

3.31

As cm2

a 1

2.16 2.04 1.99 1.87 1.99 1.87 1.99

2 3 4

3.31 1

cm

9 3.66 3.45 3.43 3.23 3.42 3.22

Mu=

5.61

As cm2

2 3 4

Mu=

a

2

9 2.47 2.33

cm

As 1.96 1.85 1.80 1.70 1.80 1.69 1.80

3.00 3 3.43 Mu=

3.78

As cm2 2.47 2.33 2.28

cm

9 1.96 1.85 1.80 1.70 1.80 1.69

5.61 2 3.78

1

a 1

3.66 3.45 3.43 3.23 3.42 3.22 3.42

3.00

a 1 2

9 2.24 2.11

cm

3.43

As cm2 2.24 2.11 2.07

1 2

3 4

2.28 2.15 2.28 2.15

2.15 2.28 2.15 2.28

3 4

2.07 1.95 2.06 1.94

ACI

1.95 2.06 1.94 2.06

3 4 ACI

AREAS DE ACERO NEGATIVO cm2

AREAS DE ACERO POSITIVO cm2

APOYO 1 APOYO 2

1.99

2.28

3.42

TRAMO 1-2 TRAMO 2-3

APOYO 3

1.80

TRAMO 3-4

3.54

APOYO 4 APOYO 5

3.08

TRAMO 4-5 TRAMO 5-6

3.87

APOYO 6

3.46

6.02

2.06

3.98

NCIPALES

ACI

ACI

MOMENTOS NEGATIVO Tn-m

MOMENTOS POSITIVOS Tn-m

APOYO A

15.42

TRAMO AB

17.63

APOYO B APOYO C

26.04

17.15

24.68

TRAMO BC TRAMO CD

APOYO D

13.79

TRAMO DE

17.15

APOYO E APOYO E

26.04

TRAMO EF

17.63

15.76

15.42

F'c = 210 Kg/cm2

210

kg/cm2

Fy = 4200 Kg/cm2 b = base d = Peralte efectivo h = Peralte a = d/5

4200 25 45 50 9 0.9

kg/cm2

a

cm2 1 2

9 9.01 8.477

Mu=

13.79

cm

As cm2 9.01 8.477 8.95

cm cm cm cm

a 1 2

9 17.01 16.01

Mu=

26.04

cm

As cm2 17.01 16.01 18.62

1 2

3 4

8.95 8.422 8.94 8.42

8.422 8.94 8.42 8.94

3 4

18.62 17.53 19.01 17.90

13.79 D

a 9 10.29 9.688 10.38 9.77 10.39 9.78

cm

Mu=

As cm2

SECUNDARIAS

4

17.15

15.76

10.29 9.69 10.38 9.77 10.39 9.78 10.39

3

26.04 E

15.76 Mu=

17.53 19.01 17.90 19.11

a 1 2 3 4

9 11.20 10.55 11.42 10.75 11.45 10.78

cm

17.63 Mu=

17.15

As cm2 11.20 10.55 11.42 10.75 11.45 10.78 11.46

a 1 2 3 4

9 11.51 10.84 11.78 11.09 11.82 11.12

cm

17.63

As cm2 11.51 10.84 11.78 11.09 11.82 11.12 11.83

ACI

ACI

MOMENTOS NEGATIVO Tn-m

MOMENTOS POSITIVOS Tn-m

APOYO 1

3.31

TRAMO 1-2

3.78

APOYO 2

5.61

TRAMO 2-3

3.43

APOYO 3

3.00

TRAMO 3-4

5.80

APOYO 4

5.08

TRAMO 4-5

6.32

APOYO 5

9.59

TRAMO 5-6

6.49

APOYO 6

5.68

F'c = 210 Kg/cm2 Fy = 4200 Kg/cm2

210 4200

kg/cm2

b = base

25

cm

d = Peralte efectivo

45

cm

h = Peralte a = d/5

50 9 0.9

cm

Ø=

Mu=

a

cm2 1 2 3 4

cm

9 3.32 3.12 3.09 2.91 3.08 2.90

kg/cm2

cm

Mu=

5.08

As cm2

a 1

3.32 3.12 3.09 2.91 3.08 2.90 3.08

2 3 4

5.08 4

a 9 3.79 3.57

cm

As cm2 1

6.26 5.90 6.03 5.68 6.02 5.66 6.02

2 3 4

9.59 5

5.80 Mu=

cm

9 6.26 5.90 6.03 5.68 6.02 5.66

9.59

6.32 Mu=

5.80

As cm2 3.79 3.57 3.55

a 1 2

9 4.13 3.88

cm

6.49 Mu=

6.32

As cm2 4.13 3.88 3.88

a 1 2

9 4.24 3.99

cm

6.49

As cm2 4.24 3.99 3.99

3.55 3.34 3.54 3.33

3.34 3.54 3.33 3.54

3 4

3.88 3.65 3.87 3.64

3.65 3.87 3.64 3.87

3 4

3.99 3.76 3.98 3.75

3.76 3.98 3.75 3.98

a 9 10.08 9.483

Mu=

15.42

cm

As cm2 10.08 9.483 10.14

10.14 9.54 10.14 9.55 15.42 F

9.54 10.14 9.55 10.14

Mu=

a 9 3.71 3.49 3.47 3.27 3.46 3.26 5.68 6

cm

5.68

As cm2 3.71 3.49 3.47 3.27 3.46 3.26 3.46

VIGAS PRINCIPALES 100%

97%

Ø

AREAS DE ACERO NEGATIVO cm2 APOYO A APOYO B

10.14

9.84

19.11

18.54

AS(a)=4Ø(5/8'') AS(a)=4Ø(5/8'')+2Ø(3/4'')

APOYO C

17.82

17.28

AS(a)=4Ø(5/8'')+2Ø(3/4'')

APOYO D APOYO E

8.94

8.67

19.11

18.54

AS(a)=4Ø(5/8'') AS(a)=4Ø(5/8'')+2Ø(3/4'')

APOYO F

10.14

9.84

AS(a)=4Ø(5/8'')

AREAS DE ACERO POSITIVO cm2

TRAMO AB

11.83

11.47

AS(a)=4Ø(5/8'')

TRAMO BC

11.46

11.11

AS(a)=4Ø(5/8'')

TRAMO CD TRAMO DE

10.39

10.08

11.46

11.11

AS(a)=4Ø(5/8'') AS(a)=4Ø(5/8'')

TRAMO EF

11.83

11.47

AS(a)=4Ø(5/8'')

VIGAS SECUNDARIAS 100%

97%

Ø

AREAS DE ACERO NEGATIVO cm2 APOYO 1

1.99

1.93

AS(a)=2Ø(5/8'')

APOYO 2 APOYO 3

3.42

3.32

1.80

1.75

AS(a)=5Ø(1/2'') AS(a)=5Ø(1/2'')

APOYO 4

3.08

2.99

AS(a)=2Ø(5/8'')

APOYO 5

6.02

5.84

AS(a)=5Ø(1/2'')

APOYO 6

3.46

3.36

AS(a)=2Ø(5/8'')

AREAS DE ACERO POSITIVO cm2

TRAMO 1-2

2.28

2.21

AS(a)=4Ø(1/2'')

TRAMO 2-3

2.06

2.00

AS(a)=4Ø(1/2'')

TRAMO 3-4

3.54

3.44

AS(a)=4Ø(1/2'')

TRAMO 4-5 TRAMO 5-6

3.87

3.75

3.98

3.86

AS(a)=4Ø(1/2'') AS(a)=4Ø(1/2'')

VIGAS PRINCIPALES

CORTE DE VARILLAS

b1 b2

a1

a2

b4 b5

b3

c1 c2

b6

c3

L1 m

L2 m

0.25

0.25

1.83 1.85 1.38 1.40

1.93 1.95

1.38

0.786

0.25

1.93 1.95

1.45

0.92

1.45

0.967

0.967

5.5

5.8

0.25

0.25

0.25

VIGAS SECUNDARIAS

CORTE DE VARILLAS

a1

b1 b2

b4 b5

c1 c2

a2

b3

b6

c3

L1 m

L2 m

0.30

0.30

1.40 1.40 1.05 1.05

1.33 1.35

1.05

0.6

1.33 1.35

1.00

0.70

1.00

0.667

4.2

0.30

0.30

0.667 4

0.30

0.30

c4 c5

d1 d2

c6

d4 d5

d3

e1

d6

e2

L3 m

L4 m

0.25

0.25

1.73 1.75

1.73 1.75

1.30

1.73 1.30

1.30

0.87

0.25

1.3 0.80

1.30

0.87

0.87

0.743

5.2

5.2

0.25

0.25

c4 c5

d1 d2

0.25

d4 d5

e1

c6

d3

d6

e2

L3 m

L4 m

0.30

0.30

1.33 1.35

1.33 1.35

1.00

1.33 1.30

1.00

0.67

1.00 0.80

1.00

0.67

0.67

4

0.30

0.30

0.571 4

0.30

0.30

Varillas longitudinales

Ø 3/8'' 1/2'' 5/8'' 3/4'' 1'' 1 1/4''

2@5cm- 3@10cm- 4@15cm- res

ngitudinales

Estribos

Ø 8mm 3/8'' 3/8'' 1/2'' 1/2'' 1/2''

m- 3@10cm- 4@15cm- resto @20cm