Datos:F`c = 200 Kg/cm2Fy = 4200 Kg/cm2

d = 25 As = 3#4 3.81Ecu = 0.003Ey = 2E+06

flexion Ø = 0.90Cortante Ø = 0.70Aplastamient Ø = 0.60

b = 15

Revisar Asmin Formula

0,8 √ F`c (b)(d) = 1.0101525 cm2Fy

Asmax = ρmax(b)(d) = ρmax = 0,75ρb

1,05 - F`c = 0.9071429 ∴ 0.851400

ρb = 0,85F`c*Fy 6000 + Fy

ρb = 0.0202381

ρmax =

ρmax = 0.01517857

Asmax = 5.69196429 cm2

1 Tanteo

C = d/3C = 8.33333333

a = 7.08333333

β1 = β1 =

6000β1

0,75 * ρb

a = β1*C

Є = (a)(0,85*F`c)(b)Є = 18062.5 Kg

Es = Ecu(d- c)c

Es = 0.006

Ey = Fy ∴ Por lo tanto el Acero Fluye Ey

Ey = 0.002

T = As*FyT = 16002 Kg

Error = Є - TX 100%

TError = 12.8765154 %

2º Tanteo

C = T

C = 7.38269896 cm2

a =

a = 6.27529412 cm2

Є = (a)(0,85*F`c)(b)

Є = 16002 Kg

Es = Ecu(d- c)c

Es = 0.00715889

Ey = Fy ∴ Por lo tanto el Acero Fluye Ey

Ey = 0.002

Es > Ey

β1*0,85*F`c*b

β1*C

Es > Ey

T = As*Fy

T = 16002

Error = Є - TX 100%T

Error = 0

Nota: como el error es menor de 1 Procede el calculo

Z = d-(a/2)

Z = 21.8623529 cm2

Mn =

Mn = 349841.372 Kg

Mn = 3.49841372 Ton *metro

ØMn

3.14857235 Ton * metro

T*Z

MR =

MR =

cm2

Por lo tanto el Acero Fluye

Por lo tanto el Acero Fluye

Datos:

F`c = 250

d = 60 Fy = 4200

As = 5#8 25.35flexion Ø = 0.90Cortante Ø = 0.70Aplastamie Ø = 0.60

b = 25

Revisar Acero

Asmin = 0,8 √ F`c (b)(d)Fy

Asmin = 4.5175395

1,05 - F`c1400

0.8714286 ∴ 0.85

ρb = 0,85F`c*Fy 6000 + Fy

ρb = 0.0252976

ρmax =

ρmax = 0.0189732

Asmax = ρmax(b)(d)

Asmax = 28.459821

ρ = Asb*d

ρ = 0.0169

Kg/cm2

Kg/cm2

β1 =

β1 = β1 =

6000β1

0,75 * ρb

cm2

W = ρ*F`yF`c

W = 0.28392

Mn =

Mn = 5318095 Kg

Mn = 53.180947 Ton * metro

ØMn

47.862853 Ton * metro

b*d2*F`c*W(1-0,59(W))

MR =

MR =

cm2

Datos:

F`c = 200

d = 60 Fy = 4200As = 3#8 15Ecu = 0.003F*c = 0,8*F`cF*c = 160F``c = 0,85*F*c

b = 30 F``c = 136Ey = 2100000

flexion Ø = 0.90Cortante Ø = 0.70Aplastamie Ø = 0.60

Asmin = 0,7√F`c (b)(d)Fy

Asmin = 4.2426407

1,05-(F*c/1400)

0.9357143 ∴ 0.85

ρb = F``c*Fy 6000 + Fy

ρb = 0.0161905

ρmax = 0,70*ρb

ρmax = 0.0113333

Asmax = (0,70)*ρb*(b)(d)

Asmax = 20.4

1 Primer Tanteo

C = d3

C = 20 cm2

Kg/cm2

Kg/cm2

β1 =

β1 = β1 =

6000β1

a =

a = 17 cm2

Є = F``c * a * b

Є = 69360

Es = Ecu(d-c)c

Es = 0.006

Ey = Fy ∴ Por lo tanto el Acero Fluye Ey

Ey = 0.002

T = As * Fy

T = 63000 Kg

Error = Є - TT

Error = 10.095238 ∴ NO pasa

2º Segundo Tanteo

C = T

C = 18.16609 cm2

a =

a = 15.441176 cm2

Є = F``c * a * b

Є = 63000

β1*C

Es > Ey

β1*F``c*b

β1*C

Es = Ecu(d-c)c

Es = 0.0069086

Ey = Fy ∴ Por lo tanto el Acero Fluye Ey

Ey = 0.002

T = As*Fy

T = 63000 Kg

Error = Є - TX 100%T

Error = 0 %

Nota: como el error es menor de 1 Procede el calculo

Z = d - (a/2)

Z = 52.279412 cm

Mn =

Mn = 3293603 Kg

Mn = 32.936029 Ton * metro

ØMn

29.642426 Ton * metro

Es > Ey

T*Z

MR =

MR =

cm2

Datos:

F`c = 200

d = 60 Fy = 4200As = 3#8Ecu = 0.003F*c = 0,8*F`cF*c = 160F``c = 0,85*F*c

b = 30 F``c = 136Ey = 2100000

Revision del Acero flexion Ø =Cortante Ø =

Asmin = 0,7√F`c (b)(d) Aplastamie Ø =Fy

Asmin = 0

1,05-(F*c/1400)

0.9357143 ∴ 0.85

ρb = F``c*Fy 6000 + Fy

ρb = 0.0161905

ρmax = 0,70*ρb

ρmax = 0.0113333

Asmax = (0,70)*ρb*(b)(d)

Asmax = 20.4

Nota: una vez revisando el Acero minimo y maximo podemos proceder a:

ρ = Asbd

ρ = 0.0083333

q = ρ*FyF``c

β1 =

β1 = β1 =

6000β1

q = 0.2573529

Mn =

Mn = 3293603 Kg

Mn = 32.936029 Ton * metro

ØMn

29.642426 Ton * metro

b*d2*F``c*q(1-0,5(q))

MR =

MR =

15 cm2

0.900.700.60

Kg/cm2

Kg/cm2

Datos:

F`c = 200

d = 60 Fy = 4200As = 3#8Ecu = 0.003F*c = 0,8*F`cF*c = 160F``c = 0,85*F*c

b = 30 F``c = 136Ey = 2100000

flexion Ø =Cortante Ø =Aplastamie Ø =

ρ = Asb*d

ρ = 0.0083333

ρ*Fy W = ρ*FyF``c F`c

0.2573529 W =

De la Grafica

Mn= 0.23

Mn = Mn

Mn = 3378240 Kg

Mn = 33.7824 Ton * metro

ØMn

q =

q =

b*d2*F``c

(b*d2*F``c)

b*d2*F``c

MR =

30.40416 Ton * metroMR =

15 cm2

0.900.700.60

Formula RCDF Mn = b*d2*F``c*q*(1-0,5(q))

Formula ACI Mn = b*d2*F``c*w*(1-0,5(w))

Kg/cm2

Kg/cm2

b*d2*F``c*q*(1-0,5(q))

b*d2*F``c*w*(1-0,5(w))