Diseno a corte

APOYO A
0 0 0 0
0
CANTIDAD
ACERO SUPERIOR
CAPA 1
0
0
ACARO INFERIOR
2
CAPA 2 CAPA 3
0 0
0 0
0 0 0 0
0 0
0 0 0
0
CAPA 3
CANTIDAD
0 00
CAPA 1
0
0 0
0
0 00 0
0 0
5 0
5
0
0
0 0
0
0
ACEROS ETABS
m m m
cm2 / m
0
0
0
Nº DE DIAMETRO
CABILLA
CAPA 2
APOYO A APOYO B
0
fyBcol2 Bcol1 Bcol2
APOYO A APOYO B
cm m
m
37,000.00
B H rSup rInf rLat L
cm2 / m
RAMAS
Kg/cm2 Kg/cm2
APOYO "B"
Vu
cm cm cm cm
0.08 0.0845.00 70.00 5.00 5.00 5.00 7.20
2
3/8" 0
APOYO "A"
γconcreto
Kg/m3
Bcol1
ESTRIBO
f'c
1/2" 0
5/8" 0
3/4" 2
1 3/8" 0
7/8" 0
1" 4 0
5 Ø7/8" +
ACEROS APOYO A
2 Ø3/4" +4 Ø1" +
5 Ø5/8" +
2 Ø1/2" +
Ss
m Kg/m2
Kg/m2
Kg/m2
1.00 0.00615.00 400.003.90
VIGA
At Wcm Wcv
f1
Vg
Kg
18,767.71
0.275 0.275 0.400 0.400 280.00 4,200.00 2,500.00
38,000.00
PESO DEL
CONCRETO

3/8" 0
CANTIDAD CANTIDAD
CAPA 1 CAPA 2 CAPA 3 CAPA 1 CAPA 2 CAPA 3
APOYO B
ACERO SUPERIOR ACARO INFERIOR
CABILLA
CANTIDAD CANTIDAD
CAPA 1 CAPA 2 CAPA 3 CAPA 1 CAPA 2 CAPA 3
3/8" 0 0 0 0 0 0 0 0
1/2" 0 0 0 2 0 0 0 0
5/8" 0 5 0 0 0 0 0 0
3/4" 2 0 0 0 0 0 0 0
7/8" 0 0 0 0 6 0 0 0
1" 5 0 0 0 0 0 0 0
1 3/8" 0 0 0 0 0 0 0 0
TRAMO A - B
ACERO SUPERIOR ACARO INFERIOR
CABILLA
0 0 0 0 0 0 0
1/2" 0 0 0 0 0 0 0 0
5/8" 0 0 0 0 0 0 0 0
3/4" 0 0 0 0 0 0 0 0
7/8" 0 0 0 0 4 0 0 0
1" 4 0 0 0 0 0 0 0
1 3/8" 0 0 0 0 0 0 0 0
4 Ø7/8" +
ACEROS APOYO B
2 Ø3/4" +5 Ø1" +
5 Ø5/8" +
2 Ø1/2" +
6 Ø7/8" +
ACEROS TRAMO A - B
4 Ø1" +

ACEROS DE REFUERZO.
AREA TOTAL x Y
AREA TOTAL
AREA TOTAL x Y
AREA TOTAL
7.22250 0.00000
11.19125 28.35345
7.22250 0.00000
8.01625 79.33386
7/8" 0 0.00 0.00 0 0.00000 10.55625 0.00000
0 0.00000 10.55625 0.00000
10.55625 0.000003/4" 0.75 0.00 0.00 0 0.00000
1/2" 0 1.27 1.27 2 2.53354
0 0.00000 7.22250 0.00000
7/8" 0 0.00 0.00 0 0.00000
5/8" 0 1.59 1.98 5 9.89663
0.00000
0.00000
39.36167
0.00000
1/2" 0 0.00 0.00 0 0.00000
6.90500
7/8" 0 0.00 0.00 0 0.00000 5.95250
3/4" 0.75 1.91 2.85 2 5.70046
0 0.00000 5.95250
5/8" 0 0.00 0.00 0 0.00000 5.95250
pulg cm cm2
∑
0.375 0.9525 0.71256
38.40 293.43678
ESTRIBO
DIAMETRO AREA
=
∑
= 7.64 cm
0.00000
1 3/8" 0 0.00 0.00 0 0.00000 10.55625 0.00000
0.00000 10.55625 0.00000
1" 1 0.00 0.00 0 0.00000 10.55625
3
3/8" 0 0.00 0.00 0
5/8" 0 0.00 0.00
0.00000
1 3/8" 0 0.00 0.00 0 0.00000 7.22250 0.00000
0.00000 7.22250 0.00000
1" 1 0.00 0.00 0 0.00000 7.22250
2
3/8" 0 0.00 0.00 0
3/4" 0.75 0.00 0.00
146.38779
1 3/8" 0 0.00 0.00 0 0.00000 5.95250 0.00000
0.00000 5.95250 0.00000
1" 1 2.54 5.07 4 20.26830 7.22250
1
3/8" 0 0.00 0.00 0
1/2" 0 0.00 0.00
AREA TOTAL Y AREA TOTAL x Y
pulg cm cm2 cm2 cm cm3
1.
CAPA TIPO
DIAMETRO AREA
CANTIDAD
CAPA TIPO
DIAMETRO AREA AREA TOTAL x Y
CANTIDAD
AREA TOTAL Y
1
3/8" 0 0.00 0.00 0
3/4" 0 0.00 0.00
0.00000 5.95250 0.00000
1/2" 0 0.00 0.00 0 0.00000 5.95250 0.00000
5/8" 0 0.00 0.00 0 0.00000 5.95250 0.00000
0 0.00000 5.95250 0.00000
7/8" 0.875 2.22 3.88 5 19.39740 7.06375 137.01835
1" 0 0.00 0.00 0 0.00000 5.95250 0.00000
1 3/8" 0 0.00 0.00 0 0.00000 5.95250 0.00000
2
3/8" 0 0.00 0.00 0 0.00000 7.06375 0.00000
1/2" 0 0.00 0.00 0 0.00000 7.06375 0.00000
5/8" 0 0.00 0.00 0 0.00000 7.06375 0.00000
3/4" 0 0.00 0.00 0 0.00000 7.06375 0.00000
7/8" 0.875 0.00 0.00 0 0.00000 7.06375 0.00000
1" 0 0.00 0.00 0 0.00000 7.06375 0.00000
1 3/8" 0 0.00 0.00 0 0.00000 7.06375 0.00000
3
3/8" 0 0.00 0.00 0 0.00000 9.60375 0.00000
9.60375 0.00000
0.00000
1/2" 0 0.00 0.00 0 0.00000
0 0.00 0.00 0 0.00000
0 0.00 0.00 0 0.00000
9.60375 0.00000
5/8"
7/8" 0.875 0.00 0.00 0 0.00000
3/4"
1" 0 0.00 0.00 0 0.00000
1 3/8" 0 0.00 0.00 0 0.00000
9.60375
137.01835
∑
= 7.06 cm
∑
9.60375 0.00000
19.40
0.00000
9.60375 0.00000
9.60375
APOYO "A" - ACERO SUPERIOR
APOYO "A" - ACERO INFERIOR
YgSuperior
YgInferior =
=
293.4368 cm3
38.3989 cm2
=
137.0184 cm3
19.3974 cm2

AREA TOTAL x Y
AREA TOTAL
AREA TOTAL x Y
AREA TOTAL
APOYO "B" - ACERO SUPERIOR
CAPA TIPO
DIAMETRO AREA
CANTIDAD
1
3/8" 0 0.00 0.00 0
3/4" 0.75 1.91 2.85
0.00000 5.95250 0.00000
1/2" 0 0.00 0.00 0 0.00000 5.95250 0.00000
5/8" 0 0.00 0.00 0 0.00000 5.95250 0.00000
2 5.70046 6.90500 39.36167
7/8" 0 0.00 0.00 0 0.00000 5.95250 0.00000
1" 1 2.54 5.07 5 25.33537 7.22250 182.98474
1 3/8" 0 0.00 0.00 0 0.00000 5.95250 0.00000
2
3/8" 0 0.00 0.00 0 0.00000 7.22250 0.00000
1/2" 0 0.00 0.00 0 0.00000 7.22250 0.00000
5/8" 0 1.59 1.98 5 9.89663 8.01625 79.33386
3/4" 0.75 0.00 0.00 0 0.00000 7.22250 0.00000
7/8" 0 0.00 0.00 0 0.00000 7.22250 0.00000
1" 1 0.00 0.00 0 0.00000 7.22250 0.00000
1 3/8" 0 0.00 0.00 0 0.00000 7.22250 0.00000
3
3/8" 0 0.00 0.00 0 0.00000 10.55625 0.00000
1/2" 0 1.27 1.27 2 2.53354 11.19125 28.35345
5/8" 0 0.00 0.00 0 0.00000 10.55625 0.00000
3/4" 0.75 0.00 0.00 0 0.00000 10.55625 0.00000
7/8" 0 0.00 0.00 0 0.00000 10.55625 0.00000
1" 1 0.00 0.00 0 0.00000 10.55625 0.00000
1 3/8" 0 0.00 0.00 0 0.00000 10.55625 0.00000
43.47 330.03372
ESTRIBO
YgSuperior =
∑
=
330.0337 cm3
= 7.59 cm
DIAMETRO AREA ∑ 43.4660 cm2
pulg cm cm2
0.375 0.9525 0.71256
YgInferior =
∑
=
164.4220 cm3
= 7.06 cm
∑ 23.2769 cm2
APOYO "B" - ACERO INFERIOR
CAPA TIPO
DIAMETRO AREA
CANTIDAD
1
3/8" 0 0.00 0.00 0
3/4" 0 0.00 0.00
0.00000 5.95250 0.00000
1/2" 0 0.00 0.00 0 0.00000 5.95250 0.00000
5/8" 0 0.00 0.00 0 0.00000 5.95250 0.00000
0 0.00000 5.95250 0.00000
7/8" 0.875 2.22 3.88 6 23.27687 7.06375 164.42202
1" 0 0.00 0.00 0 0.00000 5.95250 0.00000
1 3/8" 0 0.00 0.00 0 0.00000 5.95250 0.00000
2
3/8" 0 0.00 0.00 0 0.00000 7.06375 0.00000
1/2" 0 0.00 0.00 0 0.00000 7.06375 0.00000
5/8" 0 0.00 0.00 0 0.00000 7.06375 0.00000
3/4" 0 0.00 0.00 0 0.00000 7.06375 0.00000
7/8" 0.875 0.00 0.00 0 0.00000 7.06375 0.00000
1" 0 0.00 0.00 0 0.00000 7.06375 0.00000
1 3/8" 0 0.00 0.00 0 0.00000 7.06375 0.00000
3
3/8" 0 0.00 0.00 0 0.00000 9.60375 0.00000
1/2" 0 0.00 0.00 0 0.00000 9.60375 0.00000
5/8" 0 0.00 0.00 0 0.00000 9.60375 0.00000
3/4" 0 0.00 0.00 0 0.00000 9.60375 0.00000
7/8" 0.875 0.00 0.00 0 0.00000 9.60375 0.00000
1" 0 0.00 0.00 0 0.00000 9.60375 0.00000
1 3/8" 0 0.00 0.00 0 0.00000 9.60375 0.00000
23.28 164.42202

AREA TOTAL x Y
AREA TOTAL
AREA TOTAL x Y
AREA TOTAL
TRAMO "A - B" - ACERO SUPERIOR
CAPA TIPO
DIAMETRO AREA
CANTIDAD
1
3/8" 0 0.00 0.00 0
3/4" 0 0.00 0.00
0.00000 5.95250 0.00000
1/2" 0 0.00 0.00 0 0.00000 5.95250 0.00000
5/8" 0 0.00 0.00 0 0.00000 5.95250 0.00000
0 0.00000 5.95250 0.00000
7/8" 0 0.00 0.00 0 0.00000 5.95250 0.00000
1" 1 2.54 5.07 4 20.26830 7.22250 146.38779
1 3/8" 0 0.00 0.00 0 0.00000 5.95250 0.00000
2
3/8" 0 0.00 0.00 0 0.00000 7.22250 0.00000
1/2" 0 0.00 0.00 0 0.00000 7.22250 0.00000
5/8" 0 0.00 0.00 0 0.00000 7.22250 0.00000
3/4" 0 0.00 0.00 0 0.00000 7.22250 0.00000
7/8" 0 0.00 0.00 0 0.00000 7.22250 0.00000
1" 1 0.00 0.00 0 0.00000 7.22250 0.00000
1 3/8" 0 0.00 0.00 0 0.00000 7.22250 0.00000
3
3/8" 0 0.00 0.00 0 0.00000 9.76250 0.00000
1/2" 0 0.00 0.00 0 0.00000 9.76250 0.00000
5/8" 0 0.00 0.00 0 0.00000 9.76250 0.00000
3/4" 0 0.00 0.00 0 0.00000 9.76250 0.00000
7/8" 0 0.00 0.00 0 0.00000 9.76250 0.00000
1" 1 0.00 0.00 0 0.00000 9.76250 0.00000
1 3/8" 0 0.00 0.00 0 0.00000 9.76250 0.00000
20.27 146.38779
ESTRIBO
YgSuperior =
∑
=
146.3878 cm3
= 7.22 cm
DIAMETRO AREA ∑ 20.2683 cm2
pulg cm cm2
0.375 0.9525 0.71256
YgInferior =
∑
=
109.6147 cm3
= 7.06 cm
∑ 15.5179 cm2
TRAMO "A - B" - ACERO INFERIOR
CAPA TIPO
DIAMETRO AREA
CANTIDAD
1
3/8" 0 0.00 0.00 0
3/4" 0 0.00 0.00
0.00000 5.95250 0.00000
1/2" 0 0.00 0.00 0 0.00000 5.95250 0.00000
5/8" 0 0.00 0.00 0 0.00000 5.95250 0.00000
0 0.00000 5.95250 0.00000
7/8" 0.875 2.22 3.88 4 15.51792 7.06375 109.61468
1" 0 0.00 0.00 0 0.00000 5.95250 0.00000
1 3/8" 0 0.00 0.00 0 0.00000 5.95250 0.00000
2
3/8" 0 0.00 0.00 0 0.00000 7.06375 0.00000
1/2" 0 0.00 0.00 0 0.00000 7.06375 0.00000
5/8" 0 0.00 0.00 0 0.00000 7.06375 0.00000
3/4" 0 0.00 0.00 0 0.00000 7.06375 0.00000
7/8" 0.875 0.00 0.00 0 0.00000 7.06375 0.00000
1" 0 0.00 0.00 0 0.00000 7.06375 0.00000
1 3/8" 0 0.00 0.00 0 0.00000 7.06375 0.00000
3
3/8" 0 0.00 0.00 0 0.00000 9.60375 0.00000
1/2" 0 0.00 0.00 0 0.00000 9.60375 0.00000
5/8" 0 0.00 0.00 0 0.00000 9.60375 0.00000
3/4" 0 0.00 0.00 0 0.00000 9.60375 0.00000
7/8" 0.875 0.00 0.00 0 0.00000 9.60375 0.00000
1" 0 0.00 0.00 0 0.00000 9.60375 0.00000
0 0.00 0.00 0 0.00000 9.60375 0.00000
15.52 109.61468
1 3/8"

MOMENTO RESISTENTE.
APOYO "A"
= = = =
= = =
= - = - = =
( )
= ≤ =
= = ( )
+ +
= x = x = ( )
x
x x x x
= =
ACI 21.2.2, Fig R21.2
ACI 22.2.2.4.1
62.36 cm
20.27
7.59 cm
15.52 7.22 cmTRAMO "A - B"
APOYO "B"
APOYO "A"
SUPERIOR
38.40
ACERO DE REFUERZO
SUPERIOR INFERIOR
Yg
cm2 cm2 cm cm
7.06 cm
ZONA
RESUMEN
19.40 7.64 cm 7.06 cm
43.47 23.28 7.06 cm
INFERIOR
2.
d h Yg 62.36 cm
h r Yg 7.64 cm
Assup
Fy 4,200.00 Kg/cm2
b 45.00 cm
ß = 1.05 -
f'c
70.00 cm
0.65 = 0.85 = 0.851.05 -
280.00 Kg/cm2
Єcmax
Si f'c > 280.00 Kg/cm2
1400
ß 0.85 Si
≥
ß 0.85
Cmax =
Єcmax
x d =
f'c 280.00 Kg/cm2
0.003 Єcmin 0.005
Єcmax Єcmin
a =
Assup fy
=
a max ß Cmax 19.88 cm
0.85 F'c b
0.85 23.38 cm
a ≤ amax SI
SIMPLEMENTE
ARMADA
NO
DOBLEMENTE
ARMADA
C
ey =
fy
= 0.002
Es
f'c 280.00 Kg/cm2
=
45.00 cm
=
0.005
ACI 22.2.2.4.3
1400
x
0.003
280.00 Kg/cm2
x
2,100,000.00 Kg/cm2
4,200.00 Kg/cm2
=
2.1.
38.40 cm2
70.00 cm 7.64 cm
ecu 0.003 Es
0.003
4,200.00 Kg/cm2
0.85
= 15.06 cm
2,100,000.00 Kg/cm2
23.38 cm
38.40 cm2
Asinf 19.40 cm2

x x
x x x x
x
= = ( )
≤ = > =
> < = =
( )
As = As' = = =
- ( )
-
= x x x = x x x
= ( )
( )
ACI 21.2.1, 21.2.4
0.013684 4,200.00 Kg/cm2x
50.69 cm2
4,200.00 Kg/cm2 x 0.6236 m -
0.1988 m
x 0.90
2
Ø
2
As1 =
100,431.90 Kg x m
x
=
2
As1 =
Muc
Fy x d -
amax
ACI 22.2.2.4.1
2
Muc = C x d -
= 100,431.90 Kg x mMuc = 212,879.21 Kg x 0.6236 m -
212,879.21 Kg ACI ACI 22.2.2.4.1
0.1988 m
x 0.90
amax
x Ø
ACI
C 0.85 f'c b amax
C
19.88 cm
es = ecu x
ß 0.85 f'c
- 1 = 0.0075598
ρreal
0.003 x
0.85 0.85
=
Ascol
= 0.013684
ρreal fy
b d 45.00 cm 62.36 cm
ey 0.002 es 0.00756
es ey Ø 0.65 0.90
es ey es 0.005 Ø 1.11 0.90
x Ø
es 0.005 Ø
ACI 9.3.3.1, 21.2.2
= Ascolocada x fy x
a
Para Doblemente Armada
=
38.40 cm2
Para Simplemente Armada
2
d -Mr
Ø
0.90 =
38.40 cm2
=
79,583.17 Kg x m
280.00 Kg/cm2
=
38.40 cm2 x 4,200.00 Kg/cm2 x 0.62 m
- 1
Mr x
f's = Es x
-
0.15 m
2
0.85 280.00 Kg/cm2 45.00 cm
0.003 x
ACI
19.40 cm2
Єcmax x
Cmax d'
≤ Fy
f's = 4,200.00 Kg/cm2
9.2.1.2, 9.5.2.1, 20.2.2, 22.2.1.2
Cmax
f's = 2,100,000.00 Kg/cm2 x
23.38 cm 7.06 cm
= 4,396.95 Kg/cm2
23.38 cm
d' YgInferior 7.06 cm

= =
x x x x
x x x x
x x x x
x x x x
= - = - =d h Yg 70.00 cm 7.06 cm 62.94 cm
100,431.90 Kg x m= + -25,680.60 Kg x m 74,751.30 Kg x m=
59,250.40 Kg x m
0.85 f'c
-25,680.60 Kg x mMus x 0.90
= Muc + Mus
x 0.6236 m - 0.0706 m
Mr
=
- d' Øx
= -12.29 cm2 x 4,200.00 Kg/cm2
= -12.29 cm2
Mus = As2 x Fy x d
As2 = As - As1 = 38.40 cm2 - 50.69 cm2
x fy x
=
b
9.51 cm
Muinf = Ø x As inf
a =
As inf
=
x fy x λ x
= 106,737.57 Kg x m
0.85 f'c b
= Ø x As sup
1.00
a =
As sup fy
Musup
As sup = 38.40 cm2
λ
19.40 cm2
1.25
79,583.17 Kg x m
x 0.63 m
4,200.00 Kg/cm2 1.25
As inf =
38.40 cm2
Musup =
Mr =
4,200.00 Kg/cm2 x 1.25
18.82 cm
Ø 1.00 λ
=
-
19.40 cm2 x
280.00 Kg/cm2 45.00 cm0.85
fy λ
x 38.40 cm2 x 4,200.00 Kg/cm2
a
2
d -
a
2
d -
0.85 280.00 Kg/cm2 45.00 cm
x 1.25 x 0.62 m
=
0.0951 m
2
Muinf
0.1882 m
2
Musup
=
19.40 cm2 4,200.00 Kg/cm2 1.25
-Muinf = 1.00 x

APOYO "B"
= = = =
= = =
= - = - = =
( )
= ≤ =
= = ( )
+ +
= x = x = ( )
x
x x x x
= =
x x
x x x x
x
= = ( )
≤ = > =
> < = =Ø 0.90es ey es 0.005 Ø 1.01
es 0.00634 ACI 21.2.1, 21.2.4
Ø 0.65 es 0.005 Ø 0.90
0.0063361
ρreal fy 0.0154776 x 4,200.00 Kg/cm2
0.85 0.85 280.00 Kg/cm2
- 1 =
45.00 cm 62.41 cm
es = ecu x
ß 0.85
0.002
ρreal =
Ascol
=
43.47 cm2
= 0.0154776
b d
ecu 0.003 Es 2,100,000.00 Kg/cm2
ey =
fy
=
4,200.00 Kg/cm2
=
amax SI
SIMPLEMENTE
ARMADA
NO
DOBLEMENTE
ARMADA
C
Es 2,100,000.00 Kg/cm2
= 17.05 cm
0.85 F'c 0.85 280.00 Kg/cm2 45.00 cmb
ACI 22.2.2.4.1
a =
Assup fy
=
43.47 cm2 x 4,200.00 Kg/cm2
Єcmax Єcmin 0.003 0.005
a max ß Cmax 0.85 23.40 cm 19.89 cm
=
0.003
x 62.41 cm = 23.40 cm
ß 0.85
Єcmax 0.003 Єcmin 0.005 ACI 21.2.2, Fig R21.2
280.00 Kg/cm2
= 0.85 = 0.85
ß 0.85 Si f'c 280.00 Kg/cm2
f'c
≥ 0.65 = 1.05 -
Si f'c > 280.00 Kg/cm2
ACI 22.2.2.4.3
280.00 Kg/cm2
d h Yg 70.00 cm 7.59 cm 62.41 cm Fy 4,200.00 Kg/cm2
7.59 cm
Assup 43.47 cm2 Asinf 23.28 cm2 f'c
Yg
2.2.
h 70.00 cm b 45.00 cm r
1 = 0.003 x
es ey
f'c
-
ey 0.002
a ≤
xCmax =
Єcmax
d
14001400
ß = 1.05 -

( )
As = As' = = =
- ( )
-
= x x x = x x x
= ( )
( )
= -19,070.85 Kg x m
-119,660.26 Kg x m
Mr = Muc + Mus = 100,589.41 Kg x m + -119,660.26 Kg x m
4,200.00 Kg/cm2 x 0.6241 m - 0.0000 m x
50.73 cm2 = -50.73 cm2
Mus = As2 x Fy x d
x 0.90
As2 = As - As1 = 0.00 cm2 -
As1 =
100,589.41 Kg x m
= 50.73 cm2
4,200.00 Kg/cm2 x 0.6241 m -
0.1989 m
As1 =
Muc
Fy x d -
amax
x Ø
ACI 22.2.2.4.1
Muc = 213,046.08 Kg x 0.6241 m -
0.1989 m
x 0.90
d -
amax
x Ø
ACI
2
280.00 Kg/cm2 45.00 cm 19.89 cm
C 213,046.08 Kg ACI ACI 22.2.2.4.1
C 0.85 f'c b amax 0.85
7.06 cm
= 4,398.44 Kg/cm2
23.40 cm
0.003 x
23.40 cm
f's = 4,200.00 Kg/cm2
ACI 9.2.1.2, 9.5.2.1, 20.2.2, 22.2.1.2
Cmax
f's = 2,100,000.00 Kg/cm2 x
Єcmax x
Cmax d'
≤ Fy
= 88,532.77 Kg x m
43.47 cm2 23.28 cm2 d' YgInferior 7.06 cm
= 43.47 cm2 x 4,200.00 Kg/cm2 x 0.62 m
-
a
x Øx d
ACI 9.3.3.1, 21.2.2
Mr = Ascolocada x fy
=Mus = -50.73 cm2 x
- d' x Ø
2
2
= 100,589.41 Kg x m
2
Muc = C x
f's = Es x
2
-
0.17 m
x
0.90
0.90Mr
2

= =
x x x x
x x x x
x x x x
x x x x
= - = - =
1.25
0.1141 m
Muinf = 69,938.50 Kg x m
Yg 70.00 cm 7.06 cm 62.94 cm
Muinf = 1.00 x 23.28 cm2 x
x d -
a d h
4,200.00 Kg/cm2 1.25
= 11.41 cm
0.85 f'c b 0.85 280.00 Kg/cm2 45.00 cm
=
As inf fy λ
=
23.28 cm2
Musup = 118,100.02 Kg x m
2
x 1.25 x4,200.00 Kg/cm2
x fy
0.62 m -
0.2131 m
Musup = 1.00 x 43.47 cm2 x
x λ x d
= 21.31 cm
a
0.85 f'c b 0.85 280.00 Kg/cm2 45.00 cm
=
43.47 cm2 4,200.00 Kg/cm2 1.25
23.28 cm2
Ø 1.00 λ 1.25
a =
As sup fy λ
Mr = 88,532.77 Kg x m
As sup = 43.47 cm2 As inf =
Muinf = Ø x
2
As inf x fy
2
x 0.63 m -4,200.00 Kg/cm2 x
2
Musup
a
-= Ø x As sup

TRAMO "A - B"
= = = =
= = =
= - = - = =
( )
= ≤ =
= = ( )
+ +
= x = x = ( )
x
x x x x
= =
x x
x x x x
x
= = ( )
≤ = > =
> < = =
h 70.00 cm b 45.00 cm r
2.3.
Yg 0.00 cm
Assup 15.52 cm2 Asinf 20.27 cm2 f'c 280.00 Kg/cm2
Yg 70.00 cm 7.06 cm 62.94 cm Fy 4,200.00 Kg/cm2
Si f'c > 280.00 Kg/cm2
ACI 22.2.2.4.3
d h
1400
ß = 1.05 -
f'c
≥
1400
= 0.85 = 0.850.65 = 1.05
Si f'c 280.00 Kg/cm2
-
280.00 Kg/cm2
ß 0.85
Єcmax 0.003 Єcmin 0.005 ACI 21.2.2, Fig R21.2
ß 0.85
Cmax =
Єcmax
Єcmax Єcmin
x
ACI 22.2.2.4.1
d =
0.003
x 62.94 cm
0.003 0.005
=
15.52 cm2
= 23.60 cm
a max ß Cmax 0.85 23.60 cm 20.06 cm
4,200.00 Kg/cm2
= 6.09 cm
0.85 F'c b 0.85 280.00 Kg/cm2 45.00 cm
Assup
a ≤ amax SI
SIMPLEMENTE
ARMADA
x
NO
DOBLEMENTE
ARMADA
a =
fy
ecu 0.003 Es 2,100,000.00 Kg/cm2
ey =
fy
=
4,200.00 Kg/cm2
=
Es 2,100,000.00 Kg/cm2
0.002
ρreal =
Ascol
=
15.52 cm2
= 0.0054792
b d 45.00 cm 62.94 cm
- 1 = 0.003es = ecu x
ß 0.85
ρreal fy
0.85 0.85 280.00 Kg/cm2f'c
- 1 = 0.0233723
0.0054792 x 4,200.00 Kg/cm2
ey 0.002 es 0.02337 ACI
x
es ey Ø 0.65 es 0.005
ey es 0.005 Ø 2.43
21.2.1, 21.2.4
Ø 0.90
0.90es Ø
C

( )
As = As' = = =
- ( )
-
= x x x = x x x
= ( )
( )
Mr = Ascolocada x fy x d x Ø
ACI 9.3.3.1, 21.2.2
2
=
2
Mr = 15.52 cm2 x 4,200.00 Kg/cm2 x 35,132.18 Kg x m
0.63 m -
0.06 m
x
d' YgInferior 7.22 cm
0.90
f's = Es x Єcmax
ACI 9.2.1.2, 9.5.2.1, 20.2.2, 22.2.1.2
15.52 cm2
x
Cmax d'
≤ Fy
Cmax
20.27 cm2
-
a
4,372.05 Kg/cm2
23.60 cm
f's = 4,200.00 Kg/cm2
f's = 2,100,000.00 Kg/cm2 x 0.003
0.85 f'c b
23.60 cm 7.22 cm
=x
45.00 cm 20.06 cm
C 214,852.56 Kg ACI ACI 22.2.2.4.1
amax 0.85 280.00 Kg/cm2C
Muc = C x d -
amax
x Ø
ACI ACI 22.2.2.4.1
2
Muc = 214,852.56 Kg x 0.6294 m -
0.2006 m
x 0.90 = 102,302.49 Kg x m
2
4,200.00 Kg/cm2 x
As1 =
Muc
Fy x d -
amax
0.90
2
x Ø
2
As1 =
102,302.49 Kg x m
As - As1 =
= 51.16 cm2
0.6294 m -
0.2006 m
x
51.16 cm2 = -51.16 cm2
Mus = As2 x Fy
As2 =
x 4,200.00 Kg/cm2
x d - d' x
0.00 cm2 -
x 0.6294 m
Ø
Mus = -51.16 cm2 - 0.0000 m x 0.90 = -121,698.13 Kg x m
-121,698.13 Kg x m = -19,395.64 Kg x mMr = Muc + Mus = 102,302.49 Kg x m +

= =
x x x x
x x x x
x x x x
x x x x
= - = - =
48,174.97 61,514.56
ZONA
RESUMEN
SUPERIOR INFERIOR
Kg x m Kg x m
106,737.57 59,250.40-
RESISTENTE
88,532.77 - 118,100.02 69,938.50
- 35,132.18
APOYO "A"
APOYO "B"
TRAMO "A - B"
SUPERIOR
Kg x m
79,583.17
Kg x m
0.0994 m
2
Muinf = 61,514.56 Kg x m
INFERIOR
MAXIMO PROBABLE
MOMENTO
4,200.00 Kg/cm2 x 1.25 x 0.63 m -Muinf = 1.00 x 20.27 cm2 x
h Yg 70.00 cm 7.22 cm 62.78 cm
2
fy x d -
a d
Muinf = Ø x As inf x
0.85 f'c b 0.85 280.00 Kg/cm2 45.00 cm
=
20.27 cm2 4,200.00 Kg/cm2 1.25
= 9.94 cm
0.0761 m
2
Musup = 48,174.97 Kg x m
a =
As inf fy λ
4,200.00 Kg/cm2 x 1.25 x
a
2
0.63 m -Musup = 1.00 x 15.52 cm2 x
x λ x d -
35,132.18 Kg x m
As sup = 15.52 cm2 As inf = 20.27 cm2
Mr =
Ø 1.00 λ 1.25
a =
As sup fy λ
= =
0.85 f'c b 0.85
15.52 cm2
7.61 cm
280.00 Kg/cm2 45.00 cm
Musup = Ø x As sup x fy
4,200.00 Kg/cm2 1.25

DISEÑO A CORTE
CORTE ISOSTATICO. ( )
= = = =
= = = = =
= x = x =
= x x = x x =
= + = + =
= x = x =
= x = x =
= x + x x + x
= x + x x + x
=
x x
= =
= =
+ +
=
+ +
=
= ( ; ) = ( ; ) =
= + = + =
3.
3.1. ACI 18.4.2.4 ; Fig. R18.4.2
615.00 Kg/m2
Wcv 400.00 Kg/m2
400.00 Kg/m2
Wu 1.20 Cp f1
Ln 6.53 m
At Wcm 2,398.50 Kg / m
S At
3.90 m
787.50 Kg / m
f1 1.00
Cv 0.20 S
0.00 Kg / m
Cv At Wcv 1,560.00 Kg / m
Pp
615.00 Kg/m2
3.90 m
1,560.00 Kg / m 0.20 0.00 Kg / m
Wu Ln 6,319.20 Kg / m 6.53 m
Ss
Wu 6,319.20 Kg / m
At 3.90 m Wcm
3.90 m 0.00 Kg/m2
S 0.00 Kg/m2
γconcreto b h 2,500.00 Kg/m3 0.45 m
b 0.45 m h 0.70 m γconcreto 2,500.00 Kg/m3
1.60
1.60
0.70 m
Cp1
Cp Cp1 Pp 2,398.50 Kg / m 787.50 Kg / m 3,186.00 Kg / m
= 20,616.39 Kg
Vg = 18,767.71 Kg
Wu 1.20 3,186.00 Kg / m 1.00
2
Vp1 27,076.79 Kg
Vg = =
2
59,250.40 Kg x m
Mu apoyo "B" - Superior 118,100.02 Kg x m Mu apoyo "B" - Inferior 69,938.50 Kg x m
Mu apoyo "A" - Superior Mu apoyo "B" - Inferior
Mu apoyo "A" - Superior 106,737.57 Kg x m Mu apoyo "A" - Inferior
Ln
Vp1 =
106,737.57 Kg x m
=
69,938.50 Kg x m
6.525 m
Vp2 27,180.14 Kg
Vp2 =
Mu apoyo "B" - Superior Mu apoyo "A" - Inferior
Vp1 Vp2 max 27,076.79 Kg
59,250.40 Kg x m
Ln 6.525 m
=
118,100.02 Kg x m
27,180.14 Kg 27,180.14 Kg
Vu1 Vp Vg 27,180.14 Kg 18,767.71 Kg 45,947.85 Kg
Vp max

= =
= ( ; ; )
= ( ; ; ) =
=
Para Concretos de peso normal =
=
Para Concretos Livianos =
>
>
= x x x x x ( )
= x x x x x =
>
>
= =
= x x x x ( )
= x x x x =
+ x x x = + x x x
=
= + = + =
x x x x
x x
45,947.85 Kg
0.75
=
37,000.00 Kg Vu apoyo "B" 38,000.00 Kg
max Vu1 Vu apoyo "A" Vu apoyo "B"
λ
37,000.00 Kg 38,000.00 Kgmax 45,947.85 Kg
1.00
=
45,947.85 Kg
Ø
Vu apoyo "A"
Ø 0.75
ØVc Ø 0.53 f'c b
λ
λ 0.75
ACI 22.5.5.1
ØVc 0.75 0.53 280.00 Kg/cm2 45.00 cm 62.36 cm 18,664.75 Kg
ØVs Ø 2.12 f'c b d ACI 22.5.1.2
ØVc
ØVs 0.75 2.12 280.00 Kg/cm2 45.00 cm 62.36 cm
d 9,332.38 Kg
74,659.01 Kg
ØVc
=
18,664.75 Kg
= 9,332.38 Kg
2 2
0.75 3.5 45.00 cm 62.36 cm
2
16,698.44 Kg
ØVc Ø 3.5 b
ØVmax ØVc ØVs 18,664.75 Kg 74,659.01 Kg 93,323.77 Kg
0.0359 cm2/cm
S Fy 4,200.00 Kg/cm2
Av1min
=
0.2 f'c b
=
=
3.5
0.2 280.00 Kg/cm2 45.00 cm
=
45.00 cm
= 0.0375 cm2/cm
S Fy 4,200.00 Kg/cm2
Av2min
=
3.5 b
( 0.0359 cm2/cm
Avmin
= max (
Av1min
; ; 0.0375 cm2/cm )
S S S
Av2min
) = max
Avmin
= 0.0375 cm2/cm
S
Vumax
Vumax
λ
Vumax
Vg
61,263.80 Kg
1.00
Si
Si
18,767.71 Kg 45,947.85 Kg
d
1.00
Vu =
Vu1
Vg Vu1
18,767.71 Kg 45,947.85 Kg
ØVc 0.00 Kg 0.00 Kg

- -
x x x x
>
= =
Si Vu <
ØVc
2
45,947.85 Kg < 9,332.38 Kg
Av
= 0.0000 cm2/cm
S
ØVc
< Vu < ØVmax
2
4,200.00 Kg/cm2
9,332.38 Kg < 45,947.85 Kg < 93,323.77 Kg
ØVc
=
=
45,947.85 Kg 0.00 Kg
= 0.2339 cm2/cm
S Ø Fy d 0.75
)
62.36 cm
Av
= max (
Av
;
Avmin
)
Aumentar Sección
max ( 0.2339 cm2/cm ; 0.0375 cm2/cm
3 ramas
= 0.2339 cm2/cm
S S S
Si Vu > ØVmax
cm
45,947.85 Kg 93,323.77 Kg
DIAMETRO Separación "S"
N°
Diametro AREA "db" 2 ramas
0.71 0.95 6.00 9.00
4 ramas
pulg cm2 cm cm cm
12.00
4 1/2" 1.27 1.27 10.00 16.00 21.00
3 3/8"
36.00 48.00
5 5/8" 1.98 1.59 16.00 25.00
3.88 2.22 33.00 49.00
33.00
6 3/4" 2.85 1.91 24.00
66.00
8 1" 5.07 2.54 43.00 64.00 86.00
7 7/8"
11 1 3/8" 9.58 3.49 81.00 122.00
0.2339 cm2/cm
Av
=
Vu
Si
So min 6.00 cm So Av
163.00
Av
=
S
6.00 cm

LONGITUD DE CONFINAMIENTO ( Lo ). ( )
= - r = = - - =
= = ≤ =
= x = > =
= x = x =
SEPARACIÓN DE ESTRIBOS EN ZONA CONFINADA (So). ( )
= x = = =
=
SEPARACIÓN DE ESTRIBOS EN ZONA NO CONFINADA (S).
= x = =
APOYO "B" 88,532.77 -
TRAMO "A - B" - 35,132.18
Kg x m
APOYO "A" 79,583.17 -
RESUMEN
ZONA
MOMENTO
RESISTENTE
SUPERIOR INFERIOR
Kg x m
ACI 18.4.2.4
=
d
= 32.00 cm
2
< Ln / h
Si
0.275 m 0.275 m 0.400 m 0.400 m
ACI 18.4.2.4
S 12.00 cm
0.05 m 0.05 m
Ø 3/8" @ 0.12 m
Ø 3/8" @ 0.06 m Ø 3/8" @ 0.06 m
6.525 m
1.400 m 3.725 m 1.400 m
30.00 cm
So 6.00 cm
S1 So 2 12.00 cm
7.20 m
S2
4
So3 24 Ø del estribo 22.00 cm So4
= 8 x Ø de la barra long. de menor diametro = 10.00 cm
Lcf3 0.00 cm
Lo 140.00 cm
So1 =
d
= 16.00 cm So2
132.08 cm
6 h
Lo3
2 h
140.00 cm Si Ln / h 10
+ 2 = 132.08 cm Si 4
0.00 cm
Lo2 =
h
x
Ln
≤ 10 Lcf2 =
Lo1 h 70.00 cm Ln / h 4 Lcf1
0.400 m 6.525 m Ln
= 9.32143
h
d h 65.00 cm Ln 7.20 m 0.275 m
70.00 cm
2 h
3.2.
3.3.
3.4.
2
So Av 6.00 cm

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