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9/10/2021
1
PAVIMENTOS
SESIÓN N°05
Mgtr. ANDRÉS EDUARDO DE LA CRUZ HERRERA
ESCUELA PROFESIONAL DE INGENIERÍA CIVIL
PFA
TEMÁTICA
PFA
Tensión y deformación en el pavimento
9/10/2021
2
Pavimentos
El Pavimento es una estructura de varias capas construida sobre la subrasante del camino para resistir
y distribuir esfuerzos originados por los vehículos y mejorar las condiciones de seguridad y comodidad
para el tránsito. Por lo general está conformada por las siguientes capas: base, subbase y capa de
rodadura.
Capa de Rodadura:
Es la parte superior de un pavimento, que puede ser de tipo bituminoso (flexible) o de concreto de
cemento Portland (rígido) o de adoquines, cuya función es sostener directamente el tránsito.
Base:
Es la capa inferior a la capa de rodadura, que tiene como principal función de sostener, distribuir y
transmitir las cargas ocasionadas por el tránsito. Esta capa será de material granular drenante
(CBR ≥ 80%) o será tratada con asfalto, cal o cemento.
P P
єh
9/10/2021
3
P P
єh
Aplicación de cargas a un pavimento flexible
єh
єv єv
єv
єv
P
z
r
σz
σr
σθ
τzr
9/10/2021
4
𝜎𝑧 =
3𝑃
2𝜋 𝑧2 1 +
𝑟
𝑧
2 5/2
𝜎𝑟 =
𝑃
2𝜋
3𝑟2
𝑧
𝑟2 + 𝑧2 5/2 −
1 − 2𝜇
𝑟2 + 𝑧2 + 𝑧 𝑟2 + 𝑧2
𝜎𝜃 =
𝑃
2𝜋
1 − 2𝜇
𝑧
𝑟2+ 𝑧2 3/2 −
1
𝑟2+ 𝑧2+𝑧 𝑟2+ 𝑧2
𝜏𝑧𝑟 =
𝑃
2𝜋
3𝑟𝑧2
𝑟2 + 𝑧2 5/2
9/10/2021
5
μ = 0.40
E = 12 ksi
P = 4.5 kip
1.5 pies
1.0 pie
μ = 0.40
E = 12 ksi
W = 4.5 kip
μ = 0.40
E = 12,000 psi
P = 4,500 lb
z = 1.5 p = 18”
r = 1 p = 12”
𝜎𝑧 =
3𝑃
2𝜋 𝑧2 1 +
𝑟
𝑧
2 5/2
𝜎𝑧 =
3(4500)
2𝜋 (18)2 1 +
12
18
2 5/2
9/10/2021
6
𝜎𝑟 =
𝑃
2𝜋
3𝑟2𝑧
𝑟2 + 𝑧2 5/2
−
1 − 2𝜇
𝑟2 + 𝑧2 + 𝑧 𝑟2 + 𝑧2
𝜎𝑟 =
(4500)
2𝜋
3 12 2(18)
122 + 182 5/2
−
1 − 2(0.40)
122 + 182 + 18 122 + 182
𝜎𝜃 =
𝑃
2𝜋
1 − 2𝜇
𝑧
𝑟2+ 𝑧2 3/2 −
1
𝑟2+ 𝑧2+𝑧 𝑟2+ 𝑧2
𝜎𝜃 =
(4500)
2𝜋
1 − 2(0.40)
18
122+ 182 3/2
−
1
122+182+18 122+ 182
9/10/2021
7
𝜏𝑧𝑟 =
𝑃
2𝜋
3𝑟𝑧2
𝑟2 + 𝑧2 5/2
𝜏𝑧𝑟 =
(4500)
2𝜋
3 (12)(18)2
122 + 182 5/2
Ingeniería civil, profesión de Investigar, Analizar,
diseñar y ejecutar obras estructurales que sirven al público
en general, tales como presas, puentes, acueductos,
canales, carreteras, plantas de energía, sistemas
de alcantarillado y otra infraestructura. El término se utilizó
por primera vez en el siglo XVIII para distinguir la profesión recientemente reconocida
de la ingeniería militar, hasta entonces preeminente. Sin embargo, desde los
primeros tiempos, los ingenieros se han dedicado a actividades pacíficas y muchas
de las obras de ingeniería civil de la antigüedad y la época medieval, como los baños
públicos romanos, las carreteras, los puentes y los acueductos; los canales
flamencos; las defensas marítimas holandesas; las catedrales góticas francesas; y
muchos otros monumentos, revelan una historia de genio inventivo y experimentación
persistente.
9/10/2021
8

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Sesion 5 1

  • 1. 9/10/2021 1 PAVIMENTOS SESIÓN N°05 Mgtr. ANDRÉS EDUARDO DE LA CRUZ HERRERA ESCUELA PROFESIONAL DE INGENIERÍA CIVIL PFA TEMÁTICA PFA Tensión y deformación en el pavimento
  • 2. 9/10/2021 2 Pavimentos El Pavimento es una estructura de varias capas construida sobre la subrasante del camino para resistir y distribuir esfuerzos originados por los vehículos y mejorar las condiciones de seguridad y comodidad para el tránsito. Por lo general está conformada por las siguientes capas: base, subbase y capa de rodadura. Capa de Rodadura: Es la parte superior de un pavimento, que puede ser de tipo bituminoso (flexible) o de concreto de cemento Portland (rígido) o de adoquines, cuya función es sostener directamente el tránsito. Base: Es la capa inferior a la capa de rodadura, que tiene como principal función de sostener, distribuir y transmitir las cargas ocasionadas por el tránsito. Esta capa será de material granular drenante (CBR ≥ 80%) o será tratada con asfalto, cal o cemento. P P єh
  • 3. 9/10/2021 3 P P єh Aplicación de cargas a un pavimento flexible єh єv єv єv єv P z r σz σr σθ τzr
  • 4. 9/10/2021 4 𝜎𝑧 = 3𝑃 2𝜋 𝑧2 1 + 𝑟 𝑧 2 5/2 𝜎𝑟 = 𝑃 2𝜋 3𝑟2 𝑧 𝑟2 + 𝑧2 5/2 − 1 − 2𝜇 𝑟2 + 𝑧2 + 𝑧 𝑟2 + 𝑧2 𝜎𝜃 = 𝑃 2𝜋 1 − 2𝜇 𝑧 𝑟2+ 𝑧2 3/2 − 1 𝑟2+ 𝑧2+𝑧 𝑟2+ 𝑧2 𝜏𝑧𝑟 = 𝑃 2𝜋 3𝑟𝑧2 𝑟2 + 𝑧2 5/2
  • 5. 9/10/2021 5 μ = 0.40 E = 12 ksi P = 4.5 kip 1.5 pies 1.0 pie μ = 0.40 E = 12 ksi W = 4.5 kip μ = 0.40 E = 12,000 psi P = 4,500 lb z = 1.5 p = 18” r = 1 p = 12” 𝜎𝑧 = 3𝑃 2𝜋 𝑧2 1 + 𝑟 𝑧 2 5/2 𝜎𝑧 = 3(4500) 2𝜋 (18)2 1 + 12 18 2 5/2
  • 6. 9/10/2021 6 𝜎𝑟 = 𝑃 2𝜋 3𝑟2𝑧 𝑟2 + 𝑧2 5/2 − 1 − 2𝜇 𝑟2 + 𝑧2 + 𝑧 𝑟2 + 𝑧2 𝜎𝑟 = (4500) 2𝜋 3 12 2(18) 122 + 182 5/2 − 1 − 2(0.40) 122 + 182 + 18 122 + 182 𝜎𝜃 = 𝑃 2𝜋 1 − 2𝜇 𝑧 𝑟2+ 𝑧2 3/2 − 1 𝑟2+ 𝑧2+𝑧 𝑟2+ 𝑧2 𝜎𝜃 = (4500) 2𝜋 1 − 2(0.40) 18 122+ 182 3/2 − 1 122+182+18 122+ 182
  • 7. 9/10/2021 7 𝜏𝑧𝑟 = 𝑃 2𝜋 3𝑟𝑧2 𝑟2 + 𝑧2 5/2 𝜏𝑧𝑟 = (4500) 2𝜋 3 (12)(18)2 122 + 182 5/2 Ingeniería civil, profesión de Investigar, Analizar, diseñar y ejecutar obras estructurales que sirven al público en general, tales como presas, puentes, acueductos, canales, carreteras, plantas de energía, sistemas de alcantarillado y otra infraestructura. El término se utilizó por primera vez en el siglo XVIII para distinguir la profesión recientemente reconocida de la ingeniería militar, hasta entonces preeminente. Sin embargo, desde los primeros tiempos, los ingenieros se han dedicado a actividades pacíficas y muchas de las obras de ingeniería civil de la antigüedad y la época medieval, como los baños públicos romanos, las carreteras, los puentes y los acueductos; los canales flamencos; las defensas marítimas holandesas; las catedrales góticas francesas; y muchos otros monumentos, revelan una historia de genio inventivo y experimentación persistente.