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• Josimar Medina Aguilar

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Longitudes de desarrollo y empalmes del refuerzo - ACI 318 - 14 Datos kgf fy ≔ 4200 ―― cm 2

fy = 411.879 MPa

kgf f'c ≔ 210 ―― cm 2

f'c = 20.594 MPa

cb ≔ 50 mm

Donde: Ψt - Factor por ubicación Ψe - Factor para revestimiento epóxico

Ψs - Factor de tamaño de refuerzo λ - Factor de peso de concreto

1.3 1.0 1.5 1.2 1.0 0.8 1.0 0.75 1.0

Barras superiores Otras barras Con Tratamiento Epóxico rec 3db Otras barras con Epóxico Barras sin tratamiento superficial Barras de 3/4" y menores Barras mayores de 3/4" Concreto Liviano Concreto peso normal

Factor por ubicación Ψt = 1.3 - Barras superiores

Para ϕ 3/8"

db ≔ 9.53 mm

Ψt ≔ 1.3

Ψe ≔ 1

Ψs ≔ .8

λ≔1

Espaciamiento ≥ db, estribos a lo largo de ld, espaciamiento barras traslapadas ≥ 2 db, recubrimiento ≥ db f y ⋅ Ψt ⋅ Ψe ld ≔ ――――――― ⋅ db 2.1 ⋅ λ ⋅ ‾‾ f'c ⋅ MPa .5

ld = 0.54 m

ACI 318 14 - 25.4.2.2

ld = 0.8 m

ACI 318 14 - 25.4.2.2

ld = 0.16 m

ACI 318 14 - 25.4.2.3

Otros casos f y ⋅ Ψt ⋅ Ψe ld ≔ ――――――― ⋅ db 1.4 ⋅ λ ⋅ ‾‾ f'c ⋅ MPa .5

f y ⋅ Ψt ⋅ Ψe ⋅ Ψs ld ≔ ――――――――― ⋅d ⎛ cb ⎞ b 1.1 ⋅ λ ⋅ ‾‾ f'c ⋅ MPa .5 ⋅ ⎜―⎟ ⎝ db ⎠

Para ϕ 1/2"

db ≔ 12.7 mm

Ψt ≔ 1.3

Ψe ≔ 1

Ψs ≔ .8

λ≔1

Espaciamiento ≥ db, estribos a lo largo de ld, espaciamiento barras traslapadas ≥ 2 db, recubrimiento ≥ db f y ⋅ Ψt ⋅ Ψe ld ≔ ――――――― ⋅ db 2.1 ⋅ λ ⋅ ‾‾ f'c ⋅ MPa .5

ld = 0.71 m

ACI 318 14 - 25.4.2.2

ld = 1.07 m

ACI 318 14 - 25.4.2.2

ld = 0.28 m

ACI 318 14 - 25.4.2.3

Otros casos f y ⋅ Ψt ⋅ Ψe ld ≔ ――――――― ⋅ db 1.4 ⋅ λ ⋅ ‾‾ f'c ⋅ MPa .5

f y ⋅ Ψt ⋅ Ψe ⋅ Ψs ld ≔ ――――――――― ⋅d ⎛ cb ⎞ b 1.1 ⋅ λ ⋅ ‾‾ f'c ⋅ MPa .5 ⋅ ⎜―⎟ ⎝ db ⎠

Para ϕ 5/8"

db ≔ 15.88 mm

Ψt ≔ 1.3

Ψe ≔ 1

Ψs ≔ .8

λ≔1

Espaciamiento ≥ db, estribos a lo largo de ld, espaciamiento barras traslapadas ≥ 2 db, recubrimiento ≥ db f y ⋅ Ψt ⋅ Ψe ld ≔ ――――――― ⋅ db 2.1 ⋅ λ ⋅ ‾‾ f'c ⋅ MPa .5

ld = 0.89 m

ACI 318 14 - 25.4.2.2

ld = 1.34 m

ACI 318 14 - 25.4.2.2

ld = 0.43 m

ACI 318 14 - 25.4.2.3

Otros casos f y ⋅ Ψt ⋅ Ψe ld ≔ ――――――― ⋅ db 1.4 ⋅ λ ⋅ ‾‾ f'c ⋅ MPa .5

f y ⋅ Ψt ⋅ Ψe ⋅ Ψs ld ≔ ――――――――― ⋅d ⎛ cb ⎞ b 1.1 ⋅ λ ⋅ ‾‾ f'c ⋅ MPa .5 ⋅ ⎜―⎟ ⎝ db ⎠

Para ϕ 3/4"

db ≔ 19.05 mm

Ψt ≔ 1.3

Ψe ≔ 1

Ψs ≔ .8

λ≔1

Espaciamiento ≥ db, estribos a lo largo de ld, espaciamiento barras traslapadas ≥ 2 db, recubrimiento ≥ db f y ⋅ Ψt ⋅ Ψe ld ≔ ――――――― ⋅ db 2.1 ⋅ λ ⋅ ‾‾ f'c ⋅ MPa .5

ld = 1.07 m

ACI 318 14 - 25.4.2.2

ld = 1.61 m

ACI 318 14 - 25.4.2.2

ld = 0.62 m

ACI 318 14 - 25.4.2.3

Otros casos f y ⋅ Ψt ⋅ Ψe ld ≔ ――――――― ⋅ db 1.4 ⋅ λ ⋅ ‾‾ f'c ⋅ MPa .5

f y ⋅ Ψt ⋅ Ψe ⋅ Ψs ld ≔ ――――――――― ⋅d ⎛ cb ⎞ b 1.1 ⋅ λ ⋅ ‾‾ f'c ⋅ MPa .5 ⋅ ⎜―⎟ ⎝ db ⎠

Para ϕ 1"

db ≔ 25.4 mm

Ψt ≔ 1.3

Ψe ≔ 1

Ψs ≔ 1

λ≔1

Espaciamiento ≥ db, estribos a lo largo de ld, espaciamiento barras traslapadas ≥ 2 db, recubrimiento ≥ db f y ⋅ Ψt ⋅ Ψe ld ≔ ――――――― ⋅ db 1.7 ⋅ λ ⋅ ‾‾ f'c ⋅ MPa .5

ld = 1.76 m

ACI 318 14 - 25.4.2.2

ld = 2.72 m

ACI 318 14 - 25.4.2.2

ld = 1.38 m

ACI 318 14 - 25.4.2.3

Otros casos f y ⋅ Ψt ⋅ Ψe ld ≔ ――――――― ⋅ db 1.1 ⋅ λ ⋅ ‾‾ f'c ⋅ MPa .5

f y ⋅ Ψt ⋅ Ψe ⋅ Ψs ld ≔ ――――――――― ⋅d ⎛ cb ⎞ b 1.1 ⋅ λ ⋅ ‾‾ f'c ⋅ MPa .5 ⋅ ⎜―⎟ ⎝ db ⎠

Factor por ubicación Ψt = 1 - Otros casos

Para ϕ 3/8"

db ≔ 9.53 mm

Ψt ≔ 1

Ψe ≔ 1

Ψs ≔ .8

λ≔1

Espaciamiento ≥ db, estribos a lo largo de ld, espaciamiento barras traslapadas ≥ 2 db, recubrimiento ≥ db f y ⋅ Ψt ⋅ Ψe ld ≔ ――――――― ⋅ db 2.1 ⋅ λ ⋅ ‾‾ f'c ⋅ MPa .5

ld = 0.41 m

ACI 318 14 - 25.4.2.2

ld = 0.62 m

ACI 318 14 - 25.4.2.2

ld = 0.12 m

ACI 318 14 - 25.4.2.3

Otros casos f y ⋅ Ψt ⋅ Ψe ld ≔ ――――――― ⋅ db 1.4 ⋅ λ ⋅ ‾‾ f'c ⋅ MPa .5

f y ⋅ Ψt ⋅ Ψe ⋅ Ψs ld ≔ ――――――――― ⋅d ⎛ cb ⎞ b .5 ‾‾ 1.1 ⋅ λ ⋅ f'c ⋅ MPa ⋅ ⎜―⎟ ⎝ db ⎠

Para ϕ 1/2"

db ≔ 12.7 mm

Ψt ≔ 1

Ψe ≔ 1

Ψs ≔ .8

λ≔1

Espaciamiento ≥ db, estribos a lo largo de ld, espaciamiento barras traslapadas ≥ 2 db, recubrimiento ≥ db f y ⋅ Ψt ⋅ Ψe ld ≔ ――――――― ⋅ db 2.1 ⋅ λ ⋅ ‾‾ f'c ⋅ MPa .5

ld = 0.55 m

ACI 318 14 - 25.4.2.2

ld = 0.82 m

ACI 318 14 - 25.4.2.2

ld = 0.21 m

ACI 318 14 - 25.4.2.3

Otros casos f y ⋅ Ψt ⋅ Ψe ld ≔ ――――――― ⋅ db 1.4 ⋅ λ ⋅ ‾‾ f'c ⋅ MPa .5

f y ⋅ Ψt ⋅ Ψe ⋅ Ψs ld ≔ ――――――――― ⋅d ⎛ cb ⎞ b .5 ‾‾ 1.1 ⋅ λ ⋅ f'c ⋅ MPa ⋅ ⎜―⎟ ⎝ db ⎠

Para ϕ 5/8"

db ≔ 15.88 mm

Ψt ≔ 1

Ψe ≔ 1

Ψs ≔ .8

λ≔1

Espaciamiento ≥ db, estribos a lo largo de ld, espaciamiento barras traslapadas ≥ 2 db, recubrimiento ≥ db f y ⋅ Ψt ⋅ Ψe ld ≔ ――――――― ⋅ db 2.1 ⋅ λ ⋅ ‾‾ f'c ⋅ MPa .5

ld = 0.69 m

ACI 318 14 - 25.4.2.2

ld = 1.03 m

ACI 318 14 - 25.4.2.2

ld = 0.33 m

ACI 318 14 - 25.4.2.3

Otros casos f y ⋅ Ψt ⋅ Ψe ld ≔ ――――――― ⋅ db 1.4 ⋅ λ ⋅ ‾‾ f'c ⋅ MPa .5

f y ⋅ Ψt ⋅ Ψe ⋅ Ψs ld ≔ ――――――――― ⋅d ⎛ cb ⎞ b 1.1 ⋅ λ ⋅ ‾‾ f'c ⋅ MPa .5 ⋅ ⎜―⎟ ⎝ db ⎠

Para ϕ 3/4"

db ≔ 19.05 mm

Ψt ≔ 1

Ψe ≔ 1

Ψs ≔ .8

λ≔1

Espaciamiento ≥ db, estribos a lo largo de ld, espaciamiento barras traslapadas ≥ 2 db, recubrimiento ≥ db f y ⋅ Ψt ⋅ Ψe ld ≔ ――――――― ⋅ db 2.1 ⋅ λ ⋅ ‾‾ f'c ⋅ MPa .5

ld = 0.82 m

ACI 318 14 - 25.4.2.2

ld = 1.23 m

ACI 318 14 - 25.4.2.2

ld = 0.48 m

ACI 318 14 - 25.4.2.3

Otros casos f y ⋅ Ψt ⋅ Ψe ld ≔ ――――――― ⋅ db 1.4 ⋅ λ ⋅ ‾‾ f'c ⋅ MPa .5

f y ⋅ Ψt ⋅ Ψe ⋅ Ψs ld ≔ ――――――――― ⋅d ⎛ cb ⎞ b 1.1 ⋅ λ ⋅ ‾‾ f'c ⋅ MPa .5 ⋅ ⎜―⎟ ⎝ db ⎠

Para ϕ 1"

db ≔ 25.4 mm

Ψt ≔ 1

Ψe ≔ 1

Ψs ≔ 1

λ≔1

Espaciamiento ≥ db, estribos a lo largo de ld, espaciamiento barras traslapadas ≥ 2 db, recubrimiento ≥ db f y ⋅ Ψt ⋅ Ψe ld ≔ ――――――― ⋅ db 1.7 ⋅ λ ⋅ ‾‾ f'c ⋅ MPa .5

ld = 1.36 m

ACI 318 14 - 25.4.2.2

ld = 2.1 m

ACI 318 14 - 25.4.2.2

ld = 1.06 m

ACI 318 14 - 25.4.2.3

Otros casos f y ⋅ Ψt ⋅ Ψe ld ≔ ――――――― ⋅ db 1.1 ⋅ λ ⋅ ‾‾ f'c ⋅ MPa .5

f y ⋅ Ψt ⋅ Ψe ⋅ Ψs ld ≔ ――――――――― ⋅d ⎛ cb ⎞ b .5 ‾‾ 1.1 ⋅ λ ⋅ f'c ⋅ MPa ⋅ ⎜―⎟ ⎝ db ⎠

Resumen