Deflexion Volados

Datos Resumen
Dead + CM + L #DIV/0!
f'c= 280 [kg/cm²] L #DIV/0!
ρ= 2400 [kg/m³]
B = 30 [cm]
H = 80 [cm]
rec = 4 [cm]

Φ 18 -> As' = 28.80 [cm²] -> Compresion Mu = 30.34 [tf.m]

Φ 18 -> As = 28.80 [cm²] -> Tension c = 19.93 [cm] ΦMn = 72.54 [tf.m]

fy= 4200 [kg/cm²] NOTA: Asumir cuantia de refuerzo

CV = 200 [kg/m²]
CM = 0 [kg/m²]
e = 0.00 [cm] → espesor de losa

S = 225.00 [cm]
L = 650.00 [cm]

Limite (L) = 360

Limite (D+L) = 240

Camber = 0.00 [mm]

Calculos

n = 10.05
d = 16.00 [cm]
d' = 4.00 [cm]

W(D) = 5.76 [kg/cm] → Peso Propio sin CM → W(Solo Viga) = 5.76 [kg/cm]
W(CM) = 4.50 [kg/cm]
W(L) = 0.00 [kg/cm]
W(D+L) = 10.26 [kg/cm]
I = 1280000 [cm^4]
E = 217532 [kg/cm²]

M(D) = 1216800.00 [kg.cm] → M(D) = 12.17 [tf.m]

M(CM) = 950625.00 [kg.cm] → M(CM) = 9.51 [tf.m]
M(L) = 0.00 [kg.cm] → M(L) = 0.00 [tf.m]
M(L+D) = 2167425.00 [kg.cm] → M(L+D) = 21.67 [tf.m]

M(cr) = 206559.11 [kg.cm] → M(cr) = 2.07 [tf.m]

Ma % Agrietamiento c Icr Ie
D 0.00 0.00 8.39 27681.30 #DIV/0!
D+CM 0.00 0.00 8.39 27681.30 #DIV/0!
D+L 0.00 0.00 8.39 27681.30 #DIV/0!
Deflexion a Corto Plazo

Deflexion inicial Peso Propio

#DIV/0! → #DIV/0!

Deflexion inicial Peso Propio + Carga Muerta

#DIV/0!

Deflexion inicial Carga Viva

#DIV/0!

Deflexion a Largo Plazo

ξ = 2.00
ρ' = 6.000%
λ = 1.00

#DIV/0!

Chequeo Limites

δmax(D+L) = 54.17 [mm] #DIV/0!

δmax(L) = 36.11 [mm] #DIV/0!

Deflexion a Largo Plazo (Forzado el ρ' - Grafico)

ξ = 2.00
ρ' = 1.600%
λ = 1.11

#DIV/0!
 B δ(D+L)
### 25 30 35 40 45 50 55 60
20 100.00 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
25 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
30 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
35 90.00
#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
40 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
45 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
50 80.00
#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
55 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
60 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
65 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
70 70.00
#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
75 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
80 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
85 60.00
#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
90 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
95 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
100 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
δ(D+L)

50.00
105 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
110 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
115 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
120 40.00
#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!

30.00

20.00

6 [kg/cm] 10.00

0.00
20 25 30 35 40 45 50 55 60 65 70 75 80

B [cm]

30 35 40 45 50 55 60
70 75 80 85 90 95 100

15 549.82726 -5671.0726 0 54.17

Ratio c 120 54.17
#DIV/0! 8.39267025 -45.047821
#DIV/0!
#DIV/0!
 65 70 75 80 85 90 95 100
#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!

70 75 80 85 90 95 100 105 110 115 120

B [cm]

50 55 60 65
90 95 100 Limite
Deflexion Volados

Calculos de Cargas

Peso Propio
Elementos W Wl Wl
Plancha Deck 8.13 kg/m² 17.07 kg/m 0.17 kg/cm
Hor. Deck 207.36 kg/m² 435.46 kg/m 4.35 kg/cm
Losa Maciza 240.00 kg/m² 72.00 kg/m 0.72 kg/cm
Viga P. - 576.00 kg/m 5.76 kg/cm Σ(11.01 kg/cm)
Viga Sec. - 1209.60 kg 1209.60 kg
Viga Acero - 213.70 kg 71.23 kg [c/u]
Carga Muerta
Elementos Area Wl Wl
Rec. 15.48 m² 1068.12 kg 1.78 kg/cm
Paredes - 700.00 kg/m 7.00 kg/cm
Cielo Falso 15.48 m² 619.20 kg/m² 1.03 kg/cm Σ(9.81 kg/cm)

Datos Resumen
Dead + CM + L #DIV/0!
f'c= 280 [kg/cm²] L #DIV/0!
ρ= 2400 [kg/m³]
B = 30 [cm] Mu = 78.53 [tf.m]
H = 80 [cm] c = 14.69 [cm] ΦMn = 54.96 [tf.m]
rec = 4 [cm]

As' = 13.92 [cm²] -> Compresion ρ' = 0.610%

As = 21.22 [cm²] -> Tension ρ = 4.421%

fy= 4200 [kg/cm²]

CV = 200 [kg/m²]

S = 225.00 [cm]
L = 650.00 [cm]

Limite (L) = 360

Limite (D+L) = 240

Camber = 50.00 [mm]

Calculos

n = 10.05
d = 16.00 [cm]
d' = 4.00 [cm]

W(D) = 11.01 [kg/cm] → Peso Propio sin CM → W(Solo Viga) = 5.76 [kg/cm]
W(CM) = 9.81 [kg/cm]
W(L) = 4.50 [kg/cm]
W(D+L) = 6227161.36 [kg/cm]
I = 1280000 [cm^4]
E = 217532 [kg/cm²]
M(D) = 3203709.11 [kg.cm] → M(D) = 32.04 [tf.m]
M(CM) = 2072827.25 [kg.cm] → M(CM) = 20.73 [tf.m]
M(L) = 950625.00 [kg.cm] → M(L) = 9.51 [tf.m]
M(L+D) = 6227161.36 [kg.cm] → M(L+D) = 62.27 [tf.m]

M(cr) = 206559.11 [kg.cm] → M(cr) = 2.07 [tf.m]

Ma % Agriet. c Icr Ie Ratio

D 0.00 0.00 8.41 20677.59 #DIV/0! #DIV/0!
D+CM 0.00 0.00 8.41 20677.59 #DIV/0! #DIV/0!
D+L 0.00 0.00 8.41 20677.59 #DIV/0! #DIV/0!

Deflexion a Corto Plazo

Deflexion inicial Peso Propio

#DIV/0! → #DIV/0!

Deflexion inicial Peso Propio + Carga Muerta

#DIV/0!

Deflexion inicial Peso Propio + Carga Muerta + Carga Viva

#DIV/0!

Deflexion inicial Carga Viva

#DIV/0!

Deflexion a Largo Plazo

ξ = 2.00
ρ' = 2.899%
λ = 1.00

#DIV/0!

Chequeo Limites

δmax(D+L) = 54.17 [mm] #DIV/0!

δmax(L) = 36.11 [mm] #DIV/0!

Deflexion a Largo Plazo (Forzado el ρ' - Grafico)

ξ = 2.00
ρ' = 0.610%
λ = 1.53

#DIV/0!
Calculos de Momentos y Deflexiones

Momentos
Tipo Carga Resultante Palanca Momento
D - lineal 11.01 kg/cm 7153.44 kg 325.0 cm 2324868
D - puntual 1209.60 kg 1209.60 kg 650.0 cm 786240
D - P1 71.23 kg 71.23 kg 650.0 cm 46301
D - P2 71.23 kg 71.23 kg 433.3 cm 30867
D - P3 71.23 kg 71.23 kg 216.7 cm 15434 Σ(3203709)
CM - lineal 9.81 kg/cm 6377.93 kg 325.0 cm 2072827 Σ(2072827)
CV - lineal 4.50 kg/cm 2925.00 kg 325.0 cm 950625 Σ(950625)

Deflexion DEAD
Tipo Carga Resultante Ie Deflexion
D - lineal 11.01 kg/cm 7153.44 kg #DIV/0! #DIV/0!
D - puntual 1209.60 kg 1209.60 kg #DIV/0! #DIV/0!
D - P1 71.23 kg 71.23 kg #DIV/0! #DIV/0!
D - P2 71.23 kg 71.23 kg #DIV/0! #DIV/0!
D - P3 71.23 kg 71.23 kg #DIV/0! #DIV/0! #DIV/0!
CM - lineal 9.81 kg/cm 6377.93 kg - - -
CV - lineal 4.50 kg/cm 2925.00 kg - - -

Deflexion DEAD+CM
Tipo Carga Resultante Ie Deflexion
D - lineal 11.01 kg/cm 7153.44 kg #DIV/0! #DIV/0!
D - puntual 1209.60 kg 1209.60 kg #DIV/0! #DIV/0!
D - P1 71.23 kg 71.23 kg #DIV/0! #DIV/0!
D - P2 71.23 kg 71.23 kg #DIV/0! #DIV/0!
D - P3 71.23 kg 71.23 kg #DIV/0! #DIV/0! #DIV/0!
CM - lineal 9.81 kg/cm 6377.93 kg #DIV/0! #DIV/0! #DIV/0!
CV - lineal 4.50 kg/cm 2925.00 kg - - -
 Deflexion DEAD+CM+CV
Tipo Carga Resultante Ie Deflexion
D - lineal 11.01 kg/cm 7153.44 kg #DIV/0! #DIV/0!
D - puntual 1209.60 kg 1209.60 kg #DIV/0! #DIV/0!
D - P1 71.23 kg 71.23 kg #DIV/0! #DIV/0!
D - P2 71.23 kg 71.23 kg #DIV/0! #DIV/0!
D - P3 71.23 kg 71.23 kg #DIV/0! #DIV/0! #DIV/0!
CM - lineal 9.81 kg/cm 6377.93 kg #DIV/0! #DIV/0! #DIV/0!
CV - lineal 4.50 kg/cm 2925.00 kg #DIV/0! #DIV/0! #DIV/0!

Calculos de Area de Acero

Armadura Compresion
3 Φ 18 7.63
2 Φ 20 6.28 Σ(13.92)
Armadura Tension
3 Φ 22 11.40
2 Φ 25 9.82 Σ(21.22)
Calculo de Inercia Efectiva para Chequeo de Servicio en Vigas

B = 100 [cm]
H = 20 [cm]
f'c = 240 [kg/cm²]
rec = 4 [cm]

Φ -> As' = 20.00 [cm²] -> Compresion

Φ -> As = 20.00 [cm²] -> Tension

Ma = 5.69 [tf.m] -> Momento producto del "full service load"

Calculos

Ig = 66667 [cm^4]
fr = 30.98 [kg/cm²]
yt = 10.00 [cm]
Es = 2038700 [kg/cm²]
Ec = 202944 [kg/cm²]
n = 10.05
d = 16.00 [cm]
d' = 4.00 [cm]

Mcr = 2.07 [tf.m]

Calculo de Momentos Alrededor del Eje Neutro

50 . x² = 3938.24 - 381.82 . x

50.00 c²
381.82 c
-3938.24 b

c = 5.84 [cm]
-c = 13.48 [cm]

c = 5.84 [cm]

Icr = 27991.00 [cm^4]

Icr/Ig = 0.42

M 
3
 M 
3

I e   cr  I g  1   cr   I cr 
 Ma    M a  
Ie = 29846.15 [cm^4]

Ratio = 0.45

1.20

1.00

0.80
Mcr/Ma

0.60

0.40

0.20

0.00
0 0.2 0.4 0.6 0.8 1 1.2
%Ig
V40x60 5 y 10

0 0.42
0.1 0.42
0.2 0.43
0.3 0.46
0.4 0.51
0.5 0.60
0.6 0.73
0.7 0.91
0.8 1.00
0.9 1.00
1 1.00
Calculo de Inercia Efectiva para Chequeo de Servicio en Vigas

B = 100 [cm]
H = 20 [cm]
f'c = 240 [kg/cm²]
rec = 4 [cm]

Φ -> As' = 20.00 [cm²] -> Compresion

Φ -> As = 20.00 [cm²] -> Tension

Ma = 5.69 [tf.m] -> Momento producto del "full service load"

Calculos

Ig = 66667 [cm^4]
fr = 30.98 [kg/cm²]
yt = 10.00 [cm]
Es = 2038700 [kg/cm²]
Ec = 202944 [kg/cm²]
n = 10.05
d = 16.00 [cm]
d' = 4.00 [cm]

Mcr = 2.07 [tf.m]

Calculo de Momentos Alrededor del Eje Neutro

50 . x² = 3938.24 - 381.82 . x

50.00 c²
381.82 c
-3938.24 b

c = 5.84 [cm]
-c = 13.48 [cm]

c = 5.84 [cm]

Icr = 27991.00 [cm^4]

Icr/Ig = 0.42

M 
3
 M 
3

I e   cr  I g  1   cr   I cr 
 Ma    M a  
Ie = 29846.15 [cm^4]

Ratio = 0.45

1.20

1.00

0.80
Mcr/Ma

0.60

0.40

0.20

0.00
0 0.2 0.4 0.6 0.8 1 1.2
%Ig
0.20

0.00
0 0.2 0.4 0.6 0.8 1 1.2
%Ig
V40x60 5 y 10

0 0.42
0.1 0.42
0.2 0.43
0.3 0.46
0.4 0.51
0.5 0.60
0.6 0.73
0.7 0.91
0.8 1.00
0.9 1.00
1 1.00