PROYECTO FINAL DE ESTRUCTURAS DE CONCRET1

PROYECTO DE
ESTRUCTURAS
DE CONCRETO
Especialización Tecnología de
la Construcción de
Edificaciones

Arq. Cristian David Pinzón
Ing. Mariana Alvarado
Arq. Edisson Cruz

PROYECTO FINAL DE ESTRUCTURAS DE CONCRETO

Imagen 1 y 2 Diagramas en Planta de Losa

1

FLEXION

Imagen 3. Diagrama de Momentos

DATOS DE DISEÑO
VIGA
b
h

30 x 30

r1
r2
d
f´y
f´c
ɸ

300 mm
300 mm
30
30
240
420
28
0,9

mm
mm
mmMpa
Mpa

FORMULACION:

a=
𝐾=

𝜌 ∗𝑓´𝑦
∅ ∗𝑓´𝑐

xd

𝑀
𝑏 𝑥 𝑑2

𝐴𝑠𝑆𝑢𝑝 =
𝜌𝑚𝑖𝑛 =

𝑀𝑠𝑢𝑝
∅ ∗ 𝑓´𝑦 ∗ (𝑑 − 𝑟)

0.85 ∗𝑓´𝑐
𝑓´𝑦

*β*

600

600 −𝑓´𝑦

∅ ∗ 𝑀𝑛 = ∅ ∗ 𝜌 ∗ 𝑓´𝑦 ∗ ( 1 − 0.59 ∗

*

𝑟1
𝑑

𝜌 ∗ 𝑓´𝑦
) ∗ b ∗ 𝑑2
𝑓´𝑐

Calculo de 𝜌 por tabla

2

VIGAS 1ER NIVEL
VIGA VOLADIZO 1-2
Refuerzo Superior
Mn

Sup

1,9687 Ton * m

Ref. Sup

Mn

Sup

19,687 KN * m

2 No. 4

As Sup

0,00024801 m2

As Sup

248,0095742 mm2258 mm2

Cumple

258 mm2

Cumple

Refuerzo Inferior
Mn

Inf

0 Ton * m

Mn

Inf

0 KN * m

k

0 kN/m2

ρ

0,0033333 minimo

a

55,555 cm

As
As Inf

0,00024801 m2

Ref. Inf

248,0095742 mm2

2 No. 4

VIGA 2-2´
Refuerzo Superior
Mn

Sup

6,9128 Ton * m

Ref. Sup

Mn

Sup

69,128 KN * m

2 No. 6 +2 No. 5

As Sup

0,000870849 m2

As Sup

870,8490804 mm2

966 mm2

Cumple

966 mm2

Cumple

RefuerzoInferior
Mn

Inf

1,6798 Ton * m

Mn

Inf

16,798 KN * m

k

972,1064815 kN/m2

ρ

0,0033333 minimo

a

55,555 cm

As Inf

0,000869235 m2

Ref. Inf

As Inf

869,2353118 mm2

2 No. 6 +2 No. 5

3

VIGA 2´-3
Refuerzo Superior
Mn

Sup

6,9128 Ton * m

Ref Sup

Mn

Sup

69,128 KN * m

2 No. 6 +2 No. 5

As Sup

0,000870849 m2

As Sup

870,8490804 mm2

966 mm2

Cumple

966 mm2

Cumple

398 mm2

Cumple

398mm2

Cumple

Refuerzo Inferior
Mn

Inf

5,4144 Ton * m

Mn

Inf

54,144 KN * m

k

3133,333333 kN/m2

ρ

0,00856

a

142,6666667 cm

As Inf

0,000868834 m2

As Inf

868,834291 mm2

Ref Inf
2 No. 6 +2 No. 5

VIGA 3-4
Refuerzo Superior
Mn

Sup

2,4665 Ton * m

Ref Sup

Mn

Sup

24,665 KN * m

2 No. 5

As Sup

0,000310721 m2

As Sup

310,7205845 mm2

Refuerzo Inferior
Mn

Inf

4,36 Ton * m

Mn

Inf43,6 KN * m

k

2523,148148 kN/m2

ρ

0,0033333 minimo

a

55,555 cm
As Inf

0,000306532 m2

Ref Inf

As Inf

306,5319721 mm2

2 No. 5

4

VIGA 4-5
Refuerzo Superior
Mn

Sup

1,32 Ton * m

Ref Sup

Mn

Sup

13,2 KN * m

2 No. 4

As Sup

0,000166289 m2

As Sup

166,2887377 mm2

258 mm2

Cumple

258 mm2

Cumple

966 mm2

Cumple

966 mm2

Cumple

Refuerzo Inferior
Mn

Inf

Mn

Inf

k

1,42 Ton * m14,211 KN * m
822,3958333 kN/m2

ρ

0,0033333 minimo

a

55,555 cm

As Inf

0,000164923 m2

Ref Inf

As Inf

164,9234998 mm2

2 No. 4

VIGA 5-6

Refuerzo Superior
Mn

Sup

6,7573 Ton * m

Ref Sup

Mn

Sup

67,573 KN * m

2 No. 6 +2 No. 5

As Sup

0,00085126 m2

As Sup

851,2597632 mm2

Refuerzo Inferior
Mn

Inf

Mn

Inf

k

4,44 Ton * m
44,366 KN * m
2567,476852 kN/m2

ρ

0,00656

a

109,3333333cm

As Inf

0,000849103 m2

Ref Inf

As Inf

849,1032767 mm2

2 No. 6 +2 No. 5

5

VIGA 6-7
Refuerzo Superior
Mn

Sup

6,7573 Ton * m

Ref Sup

Mn

Sup

67,573 KN * m

2 No. 6 +2 No. 5

As Sup

0,00085126 m2

As Sup

851,2597632 mm2

966 mm2

Cumple

966 mm2

Cumple

656 mm2

Cumple

656 mm2

Cumple

Refuerzo Inferior
Mn

Inf

Mn

Inf

k

5,04 Ton * m
50,437 KN * m
2918,80787 kN/m2

ρ

0,00756

a126 cm

As Inf

0,000849134 m2

Ref Inf

As Inf

849,1337081 mm2

2 No. 6 +2 No. 5

VIGA 7-8
Refuerzo Superior
Mn

Sup

4,34 Ton * m

Ref Sup

Mn

Sup

43,4 KN * m

2 No. 5 + 2 No. 4

As Sup

0,000546737 m2

As Sup

546,7372134 mm2

Refuerzo Inferior
Mn

Inf

Mn

Inf

k
ρ
a

0,00 Ton * m
0 KN * m
0 kN/m2
0,00756
126 cm

As Inf

0,000546737 m2

Ref Inf

As Inf

546,7372134 mm2

2 No. 5 + 2 No. 46

VIGAS 2DO NIVEL

VIGA
b
h
r1
r2
d
f´y
f´c
ɸ

30 x 25
250 mm
300 mm
30 mm
30 mm
240 mm
420 Mpa
28 Mpa
0,9

VIGA 4-5
Refuerzo Superior
Mn

Sup

-5,56 Ton * m

Ref Inf

Mn

Sup

-55,6 KN * m

2 No. 6 +2 No. 5

As Sup

-0,000919312 m2

As Sup

-919,3121693 mm2

966 mm2

Cumple

966 mm2

Cumple

Refuerzo Inferior
Mn

Inf

Mn

Inf
k

1,88 Ton * m
18,825 KN * m
2085,872576 kN/m2

ρ

0,0033333...