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• Victor Hugo Paredes

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DISENO DE VIGA POR ACI Datos: Dimensiones de la viga h ≔ 45 cm

b ≔ 30 cm

Datos: Peso de la losa:

Peso de acabados:

Peso de tabiqueria - muro :

kg Losa ≔ 300 ―― m2

kg Acab ≔ 100 ―― m2

kg Tab ≔ 270 ―― m2

Peso especifico del concreto:

Sobrecarga:

Concreto:

Fluencia del acero:

kg γ ≔ 2400 ―― m3

kg Sc ≔ 200 ―― m2

kg fc ≔ 210 ―― cm 2

kg fy ≔ 4200 ―― cm 2

Longitud de tramos de la viga: L1 ≔ 5.15 m L2 ≔ 4.35 m

L3 ≔ 5.20 m

⎛ 3.08 m 2.70 m ⎞ Ancho tributario de la viga analizada: Anchotrib ≔ ⎜――― + ――― ⎟ = 2.8900 m 2 2 ⎝ ⎠ Solucion: Cargas que actuan sobre la viga: Peso propio de la viga:

Peso propio del aligerado:

ton Pviga ≔ b ⋅ h ⋅ γ = 0.3571 ―― m

ton Plosa ≔ Losa ⋅ Anchotrib = 0.9557 ―― m

Tabiqueria - Muro:

Carga viva:

ton Ptab ≔ Tab ⋅ Anchotrib = 0.8601 ―― m

ton Cv ≔ Sc ⋅ Anchotrib = 0.6371 ―― m

Acabados: kg Pacab ≔ Acab ⋅ Anchotrib = 289.0000 ―― m Carga muerta: ton Cm ≔ Pviga + Plosa + Ptab + Pacab = 2.4916 ―― m Verificacion para usar coeficientes: Numero de tramos: 3 tramos > 2 tramos: Diferencia de tramos menor a 0.20: 5.15 - 4.55 ――――― = 0.1319 4.55

OK

OK

5 - 4.55 ―――= 0.0989 4.55

OK

Cargas uniformemente distribuidas: Relacion Cv/Cm < 3: Cv ―― = 0.2557 Cm

OK

Elementos pristmaticos:

OK

Cumple con las condiciones para la aplicacion de los coeficientes: ton Wu ≔ 1.5 ⋅ Cm + 1.8 ⋅ Cv = 4.8842 ―― m Momento positivos: d ≔ h - 6 cm = 39.0000 cm MOMENTOS Y ACEROS POSITIVOS: Momentos positivo AB Wu ⋅ L1 2 MAB ≔ ――― = 9.2529 ton ⋅ m 14 Calculo de acero positivo AB: ⎛ ⎞ 4200 9.25 ⋅ 10 5 solve , As ⎡ 5.5616337006679266161 ⎤ 2 →⎢ ⎜―――― ⎟ ⋅ As - ⎛⎝4200 ⋅ 44⎞⎠ ⋅ As + ――― ――― ⎥ ⎣ 471234.43836629933207 ⎦ 0.9 ⎝ 1.7 ⋅ 210 ⋅ 30 ⎠ Momentos positivo BC Wu ⋅ L2 2 MBC ≔ ――― = 5.7763 ton ⋅ m 16 Calculo de acero positivo BC: ⎛ ⎞ 4200 5.91 ⋅ 10 5 solve , As ⎡ 3.5534178481843727087 ⎤ 2 ⎛ ⎞ ⋅ As 4200 ⋅ 44 ⋅ As + ――― →⎢ ―――― ――― ⎝ ⎠ ⎜ ⎟ ⎥ ⎣ 471236.44658215181563 ⎦ 0.9 ⎝ 1.7 ⋅ 210 ⋅ 30 ⎠ Momentos positivo CD Wu ⋅ L3 2 MCD ≔ ――― = 9.4334 ton ⋅ m 14 Calculo de acero positivo CD: ⎛ ⎞ 4200 9.66 ⋅ 10 5 solve , As ⎡ 524784.78452866643566 ⎤ 2 →⎢ ⎜―――― ⎟ ⋅ As - ⎛⎝4200 ⋅ 49⎞⎠ ⋅ As + ――― ――― ⎥ ⎣ 5.2154713335643423682 ⎦ 0.9 ⎝ 1.7 ⋅ 210 ⋅ 30 ⎠

MOMENTOS NEGATIVOS: Calculo de momento negativo A: Wu ⋅ L1 2 MA ≔ ――― = 8.0963 ton ⋅ m 16 Calculo de acero negativo A: ⎛ ⎞ 4200 8.29 ⋅ 10 5 solve , As ⎡ 524785.52420326970845 ⎤ 2 →⎢ ⎜―――― ⎟ ⋅ As - ⎛⎝4200 ⋅ 49⎞⎠ ⋅ As + ――― ――― ⎥ ⎣ 4.4757967302915532344 ⎦ 0.9 ⎝ 1.7 ⋅ 210 ⋅ 30 ⎠ Calculo de momento negativo B: 2

⎛ L1 + L2 ⎞ ⎜――― ⎟ ⎝ 2 ⎠ MB ≔ Wu ⋅ ―――― = 11.0199 ton ⋅ m 10 Calculo de acero negativo B: ⎛ ⎞ 4200 11.29 ⋅ 10 5 solve , As ⎡ 524783.90447514480727 ⎤ 2 ――― →⎢ ⎜―――― ⎟ ⋅ As - ⎛⎝4200 ⋅ 49⎞⎠ ⋅ As + ―――― ⎥ ⎣ 6.0955248551927315797 ⎦ 0.9 ⎝ 1.7 ⋅ 210 ⋅ 30 ⎠ Calculo de momento negativo B: 2

⎛ L1 + L2 ⎞ ⎜――― ⎟ ⎝ 2 ⎠ MB' ≔ Wu ⋅ ―――― = 10.0181 ton ⋅ m 11 Calculo de acero negativo B: ⎛ ⎞ 4200 10.26 ⋅ 10 5 solve , As ⎡ 524784.46058292813983 ⎤ 2 ⎛ ⎞ ⋅ As 4200 ⋅ 49 ⋅ As + ――― →⎢ ―――― ―――― ⎝ ⎠ ⎜ ⎟ ⎥ ⎣ 5.5394170718601650486 ⎦ 0.9 ⎝ 1.7 ⋅ 210 ⋅ 30 ⎠ Calculo de momento negativo B: 2

⎛ L2 + L3 ⎞ ⎜――― ⎟ ⎝ 2 ⎠ MB' ≔ Wu ⋅ ―――― = 10.1238 ton ⋅ m 11 Calculo de acero negativo B: ⎛ ⎞ 4200 10.37 ⋅ 10 5 solve , As ⎡ 524784.40119283273621 ⎤ 2 ⎛ ⎞ ⋅ As 4200 ⋅ 49 ⋅ As + ――― →⎢ ―――― ―――― ⎝ ⎠ ⎜ ⎟ ⎥ ⎣ 5.598807167263787174 ⎦ 0.9 ⎝ 1.7 ⋅ 210 ⋅ 30 ⎠ Calculo de momento negativo C: 2

⎛ L2 + L3 ⎞ Wu ⋅ ⎜――― ⎟ ⎝ 2 ⎠ MC ≔ ――――― = 11.1362 ton ⋅ m 10

Calculo de acero negativo C: ⎛ ⎞ 4200 11.41 ⋅ 10 5 solve , As ⎡ 524783.83968581184049 ⎤ 2 ⎛ ⎞ ⋅ As 4200 ⋅ 49 ⋅ As + ――― →⎢ ―――― ―――― ⎝ ⎠ ⎜ ⎟ ⎥ ⎣ 6.1603141881595117527 ⎦ 0.9 ⎝ 1.7 ⋅ 210 ⋅ 30 ⎠ Calculo de momento negativo D: Wu ⋅ L3 2 MD ≔ ――― = 8.2543 ton ⋅ m 16 Calculo de acero negativo D: ⎛ ⎞ 4200 8.45 ⋅ 10 5 solve , As ⎡ 524785.4378180221211 ⎤ 2 →⎢ ⎜―――― ⎟ ⋅ As - ⎛⎝4200 ⋅ 49⎞⎠ ⋅ As + ――― ――― ⎥ ⎣ 4.5621819778788962245 ⎦ 0.9 ⎝ 1.7 ⋅ 210 ⋅ 30 ⎠ Calculo de As min: 0.8 ⋅ ‾‾‾‾ 210 Asmin ≔ ――――⋅ b ⋅ d = 3.22950682 cm 2 4200