Pilote con carga transversal o lateral

ton :=
Pilotes con carga horizontal
Eb :=
1000kgf
kgf
300000
cm 2
Esfuezos que llegan al cabezal
Carga horizontal:
H := 5 ⋅ ton
Dimensiones de los pilotes:
Diámetro:
B :=
Largo
lpil :=
Longitud enterrada:
lpil.ent :=
Momento de inercia
0.60 ⋅ m
Jpil :=
14 ⋅ m
10 ⋅ m
B4
Jpil =
12
0.0108 m
4
El suelo donde se encuentran los pilotes es una arena densa. Este es
un suelo incoherente en el cual su módulo de elasticidad varía con la
profundiad z (Es=f(z)). Como la profundiad z no es grande se puede
suponer una variación de Es lineal (Es=cte*z).
Constante de la
reacción horizontal
del terreno:
nh :=
Máximo valor del
coeficiente de reacción de
la subrasante horizontal:
Kh := nh ⋅
Coeficiente de reacción
de la subrasante horizontal
en función dela profundidad:
1.1 ⋅
kgf
(arena densa sumergida)
cm 3
lpil.ent
Kh ( z) := nh ⋅
Kh =
B
kgf
18.33
cm 3
−z
B
1
Factor de
flexibilidad relativa:
 Eb ⋅ Jpil 
T := 

 nh 
5
T=
lpil.ent
2m
T
=
5.08
Cálculo de desplazamientos, rotaciones y solicitaciones :
z: Profundidad en análisis
Z: Coeficiente de profundidad (Z = z/T)
Longitud libre del pilote:
Esfuezo horizontal en el pilote:
−1.623
−1.618
−1.603
−1.545
−1.503
−1.454
−1.397
−1.335
−1.197
−1.047
−0.893
−0.741
−0.464
−0.04
 0.0 1.623
 −0.1 1.453

 −0.2 1.293
 −0.4 1.003
 −0.5 0.873
 −0.6 0.752

 −0.7 0.642
−0.8
0.54
B := 
 −1.0 0.364
 −1.2 0.223
 −1.4 0.112

 −1.6 0.029
 −2.0 −0.07
 −3.0 −0.089
 −4.0 −0.028

0
 −5.0
−1.75
−1.65
−1.55
−1.351
−1.253
−1.156
−1.061
−0.968
−0.792
−0.629
−0.482
−0.354
−0.155
0
1
0.1
0.989
0.198
0.956
0.379
0.84
0.459
0.764
0.532
0.677
0.595
0.585
0.649
0.489
0.727
0.295
0.767
0.109
0.052
0
−0.056
−0.193
−0.371
−0.349
−0.106
0.025
−0.033
0.013
1
0
0.057
0.049
0.011
0.772
0.746
0.628
0.225
1
0.999
0.987
0.976
0.96
0.939
0.914
0.852
0.775
0.688
0.594
0.404
0.059
−0.042
−0.026
Ll =
Mo := H ⋅ Ll
Momento en el pilote al NTN::
z
Para: z := 0 ⋅ m
* Z := T * Z = 0
 0.0 2.435
 −0.1 2.273

 −0.2 2.112
 −0.4 1.796
 −0.5 1.644
 −0.6 1.496

 −0.7 1.353
−0.8 1.216
A := 
 −1.0 0.962
 −1.2 0.738
 −1.4 0.544

 −1.6 0.381
 −2.0 0.142
 −3.0 −0.075
 −4.0 −0.05

 −5.0 −0.009
Ll := lpil − lpil.ent *
Ho := H
−0.007
−0.028
−0.095
−0.137
−0.181
−0.226
−0.27
−0.35
−0.414
−0.456
−0.477
−0.456
−0.213
0.017
0.029
0
−0.227
−0.422
−0.718
−0.822
−0.897
−0.947
−0.973
−0.962
−0.885
−0.761
−0.609
−0.283
0.226
0.201
0.046



































0.140 
0.268 

0.112

−0.002 
A := csort ( A , 0)
0
−0.145
−0.259
−0.401
−0.436
−0.451
−0.449
−0.432
−0.364
−0.268
−0.157
−0.047
B := csort ( B , 0)
4m
Z := A⟨0⟩
Ay := A⟨1⟩
Aθ := A⟨2⟩
AM := A⟨3⟩
AQ := A⟨4⟩
Aq := A⟨5⟩
By := B⟨1⟩
Bθ := B⟨2⟩
BM := B⟨3⟩
BQ := B⟨4⟩
Bq := B⟨5⟩
(
)
Aθ ( ξ ) := interp ( θ , Z , Aθ , ξ )
y := cspline ( Z , Ay)
Ay ( ξ ) := interp y , Z , Ay , ξ
Mom := cspline ( Z , AM)
AM ( ξ ) := interp ( Mom , Z , AM , ξ )
θ := cspline ( Z , Aθ)
Corte := cspline ( Z , AQ)
Reacc := cspline ( Z , Aq)
y. := cspline ( Z , By)
θ . := cspline ( Z , Bθ)
Mom := cspline ( Z , BM)
Corte := cspline ( Z , BQ)
Reacc := cspline ( Z , Bq)
Desplazamiento:
y ( Z) :=
AQ ( ξ ) := interp ( Corte , Z , AQ , ξ )
Aq ( ξ ) := interp ( Reacc , Z , Aq , ξ )
(
)
(
)
BM ( ξ ) := interp ( Mom , Z , BM , ξ )
BQ ( ξ ) := interp ( Corte , Z , BQ , ξ )
Bq ( ξ ) := interp ( Reacc , Z , Bq , ξ )
By ( ξ ) := interp y. , Z , By , ξ
Bθ ( ξ ) := interp θ . , Z , Bθ , ξ
Ay ( Z) ⋅ Ho ⋅ T 3
Eb ⋅ Jpil
Aθ ( Z) ⋅ Ho ⋅ T 2
+
Eb ⋅ Jpil
Bθ ( Z) ⋅ Mo ⋅ T
Rotación:
θ ( Z) :=
Momento:
M ( Z) := AM ( Z) ⋅ Ho ⋅ T + BM ( Z) ⋅ Mo
Corte:
Mo
Q ( Z) := AQ ( Z) ⋅ Ho + BQ ( Z) ⋅
T
Reacción lineal del suelo:
Eb ⋅ Jpil
+
By ( Z) ⋅ Mo ⋅ T 2
Eb ⋅ Jpil
Ho
Mo
q ( Z) := Aq ( Z) ⋅
+ Bq ( Z) ⋅
T
T2
Ho ⋅ Ll 3
Desplazamiento del
pilote debido a Ho:
yBeH :=
Desplazamiento total del
pilote en el extremo superior:
yB := y ( 0) + θ ( 0) ⋅ Ll + yBeH
3 ⋅ Eb ⋅ Jpil
*
yB =
22.4 mm
Gráficos de solicitaciones y deformaciones de los pilotes:
Z :=
Z
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
Z
5 3.5 2 0.5 1 2.5 4 5.5 7 8.5 10
0.2
0.13
2
14
22
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
Z
30
M ( Z)
ton ⋅ m
Momento (tn*m)
Factor de profundidad
Factor de profundidad
Factor de profundidad
6
Z
0
10
7
4
1
2
M ( Z) =
20 ton ⋅ m
21
21.9
22.8
23.5
0
24
24.4
24.6
24.7
24.5
24.2
6
4.4
5
Q ( Z)
ton
Corte (tn)
PRESIÓN DE CONTACTO
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
0.1
CORTE
0
10
0.05 0.025
θ ( Z)
deg
Rotaciones
MOMENTOS
Z
−5
0
y ( Z)
mm
Desplazamientos (m)
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
, −0.1 ..
ROTACIONES
Factor de profundidad
Factor de profundidad
DESPLAZAMIENTOS
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
0
2.8
1.2
0.4
2
q ( Z)
 ton 


 m 
Reacción lineal del suelo (tn/m)
23.7
23
22.3
21.4
20.3