Analysis of folded steel shell - earth bridge - ZSoil · Robot Milenium => ZSoil, with help of...
Transcript of Analysis of folded steel shell - earth bridge - ZSoil · Robot Milenium => ZSoil, with help of...
dr hab. inż. Aleksander Urbański, prof. PKdr inż. Karol Ryż
Michał WszołekPrzemysław Milczarek
POLITECHNIKA KRAKOWSKA im. T. KościuszkiWydział Inżynierii LądowejInstytut Materiałów i Konstrukcji Budowlanych Katedra Budowy Mostów i Tuneli
Analysis of folded steel shell - earth bridge
Diploma work of: Under supervision of:
General informationAnalytical design methodsZSoil modeling of folded shellConceptionComputer modeling of a bridge and results
ConstructionExploitation
Conclusions
Contents
Is=0,95-1,00
φ=36o-45o
typical shapes soil parameters
Main components of the structure
Folded steel shell Soil
geometry (almost) arbitrary, min depth of backfill 0.5m:plane strain conditionformulas for: N,M –forces and bending moments for dead weihgt and moving load
Analytical method of design:Sundquist-Pettersson („swedish method”)- 2010
Identification of folded shell model in ZSoil in Robot Milenium: how to deal with it in ZSoil ?
K[kN/m]
B[kNm]
H[kN/m]
9 module
⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
Γ
⋅
⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
=
⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
yxxyyyxxxy
EyyExx
hyyhxx
bxyxybyyyysbxxyybxxxx
kxyxykyyyyskxxyykxxxx
QyQxMxyMyyMxxNxyNyyNxx
ββκκκ
OO
OO
OO
=
plane stress orthotropic model in core layer
10 parameters:
2hXζ
2hXζ
2hYζ
2hYζ
h
kx
kxky
aaFEky =
κζζ kykxvEEGh YX ,,,1,2,1,0,
symetric reiforcements, different in x,y
Identification of folded shell model in ZSoil, cont.
εDσ ⋅=⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡⋅
⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢
⎣
⎡
⋅−−−
⋅−⋅
⋅−
=⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=
XY
YY
XX
XY
YY
XX
Gvv
Esvv
Evvv
E
γεε
σσσ
000
0211
2
0211
12211
11212
EEvv ⋅=
Robot Milenium => ZSoil, with help of MathCadGiven
G0 h⋅ kxyxy
G012
h3⋅ bxyxy
κhxx
G0 h⋅
1.
2. 1. E212
h3
1 v12 E2E1⋅−
⋅ 2 ky⋅y4⋅+ byyyy
2. E112
h3
1 v12 E2E1⋅−
⋅ 2 kx⋅x4⋅+ bxxxx
3. E1h
1 v12 E2E1⋅−
⋅ 2 kx⋅+ kxxxx
4. E2h
1 v12 E2E1⋅−
⋅ 2 ky⋅+ kyyyy
5. v1E2E1⋅ E1
h
1 v12 E2E1⋅−
⋅ 2 kx⋅+⎛⎜⎜⎝
⎞⎟⎟⎠
⋅ kxxyy
E1,E2, such as kx>0, ky>0:
G0 1630894847.794=
h 0.227 m=
κ 1.944= [-]
[m]
[kPa]
ζxx
[kPa]
[kPa]
[kNm]
[kNm]
[-]
[m2]
[m2]
h0.378=:=
ζxy
h0.378=:=
E1 2100=
E2 10=
x 0.007=
y 0.007=
kx 1233343.1=
ky 1172.1=
v1 0.0599=
Identification of folded shell model in ZSoil, cont.
Design conception of a bridge
ProfileSUPERCOR
Railway load(kl. 2)
R.C. foundation
10.013.0H=5.89
1.9
Backfill
5.0
381 140[mm]
7
Computer modeling in ZSoilGeneral assumptions
3D model, with materialsMohr-Coulomb (soil), elastic (shell, concrete)
small displacementuse of:
construction stages,contact (sheel-backfill),infinite elements,kinematic constraints
Nodes: 48880Nele : B8 - 37712
SQ4, CQ4 - 2304
embankment-old
rail-road bed
Model components
Continuum
embankment-backfill
oMPaE 36,175 == φ
oMPaE 41,250 == φ
Results - final construction stage displacement, bending moments and forces in shell
Mxx
Nxx
Mxx
|u|
Ux Uy Uz IUImax [cm] 6,477 7,611 0,801
min [cm] -6,477 -4,596 -0,799
8,096
Results - construction stage,
uplift Uy=6,00cmmaximal displacement
Simulation of moving railway load
loads in ZSoil set on the top independently from FE discretizationset of 129 LTF to simulate moving load
Results – exploitation phazeDeformation under moving load
Ux Uy Uz IUI
max [cm] 0,778 0,635 0,708
min [cm] -0,286 -1,816 -0,7071,845
Model Max. shell stress [MPa]Model 1 (basic) 246,36Model 2 (expanded) 168,63Model 3 (one shell) 129,81Swedish method 157,16
Model 1 Model 2
Model 3
ConclusionsResult comparison
Thank you for your attention
Michał WszołekPrzemysław Milczarek
Aleksander Urbański ( [email protected] ) Karol Ryż