TUHH - Prof. Rombach
Introduction
Beam and truss structures
Spatial structures- shear walls- slabs- shells
Material nonlinear analysis
3-d models
Design of real concrete structures with finite element software- model problems and errors Prof. Dr.- Ing. Gnter A. Rombach
Hamburg University of TechnologyE-mail: [email protected]
TUHH - Prof. Rombach
Special problems of concrete structures
complex material behaviour (cracks, time dependant)
detailing arrangement of rebars significant
construction process significant
complex loading exact value not known
no mass product fast design
massive members (Bernoulli hypothesis not valid)
TUHH - Prof. Rombach 3
Zuse Z1 1936-38
Built the first programmable computer in the world
Argyris: Civil Engineer
Clough: Civil Engineer
Zienkiewicz: mathematician;lecturer in faculty of civil eng.
TUHH - Prof. Rombach
The Sleipner platform
accident
Collapse: August 1991
Financial loss: 250 Mio US$
TUHH - Prof. Rombach
The Sleipner platform accident
TUHH - Prof. Rombach
The Sleipner platform accident tricells
TUHH - Prof. Rombach
The Sleipner platform accident tricells
7
3.453.413.252.32Tension force T1 [MN/m]
1.661.671.350.95Tension force T1-D1 [MN/m]
N4N3N2N1Elementmesh
TUHH - Prof. Rombach
The Sleipner platform accident tricells
8
TUHH - Prof. Rombach
Sleipner platform accident
9
Consequences:
distorted 8-noded volume elementsshould not be used
qualified staff
indenpendant checks
Sea Troll Plattform, Bj. 1995, h=472 m (330m)
better hard- and software more elements
substructure techniques
adaptive mesh refinement
nonlinear material models
independant checks engineering knowledge required
Seite:
TUHH - Prof. Rombach
Software faults loadcase G had not been considered since version 10.0-96
minimum reinforcement had been estimated with fyk instead of fyd
Errors
10
Numerical errors 245 - 0,8 - 245 = 0,8008
250 - 0,8 - 250 = 0,00
TUHH - Prof. Rombach
Program errors
Software faults
Model errorsmaterial model reinforced concrete behaves nonlinear
loading FE-Model considers only nodal loads
design slab, shear wall, column, tension member, shear reinforcement
modelling size of elementstype of elementsupport conditionssingularities
ErrorsReales Bauwerk
Numerisches Modell
TUHH - Prof. Rombach
Modelling
12
u2v2
2u1
1
v1 MV
N
MBemessung
FsdFcdV
N
Spannung
Knotenlasten
reale Einwirkung Beam element
Beam element
stresses
design
loading
real structure
real loading
Numerical model
beam -, plate-, shell-,volume elements
TUHH - Prof. Rombach 13
Prof. Dr.-Ing. G. A. RombachHamburg University of Technology
E-mail: [email protected]
Design of real concrete structures with finite element software
Introduction
Beam and truss structures Spatial structures- shear walls- slabs- shells
Material nonlinear analysis
TUHH - Prof. Rombach 14
Beam or truss element
Beam element
Strains stresses
TUHH - Prof. Rombach
Hauptm omenteLastfall g=10 kN /m2 -146. 5-125. 0-100. 0-75 .0
-50 .0-25 .00 .0
25 .050 .075 .0100. 0
-190.
187.
-176.
124.
8.
-137.
138.
-178.
176.
-193.
259.
-139.
122.
-141.
142.
horizontal membrane force
System
Width of beam b = 0,22 cm
see detail
Loading q = 1 kN/m
2,5m
60 80
9,5m
Discontinuity regions
TUHH - Prof. Rombach 16
D-regions in beam or truss structures
TUHH - Prof. Rombach 17
Beam with opening
2max
2
810 12,5 195
8
q lM
kNm
= == =
max / 195 / 0,6325
N M zkN
= = ==
TUHH - Prof. Rombach
5,0m 5,0m
50
20
10kN/m
Opening 20/50cm 5050
Model 1 Model 2 Model 3
Beam with opening
TUHH - Prof. Rombach
50.0
-50.0
50.0
-50.0-49.8
49.7
50.4
-50.3
85.0
-15.0
29.1
-70.9
20.8
-41.7-41.7 -41.7
33.0
-76.5
20.7
-42.1-40.8
-42.8
Bending Moment
Shear Forces
5,0m 5,0m
50
20
10kN/m
Opening 20/50cm
Model 3Model 2Model 1
Beam with opening
TUHH - Prof. Rombach
Stress/Strainsection 1-1left
Stress/Strain section 1-1right
Model 1 Model 21
1
Beam with opening
Stressessection 1-1 right
Stressessection 1-1 left
TUHH - Prof. Rombach
Hauptm omenteLastfall g=10 kN /m2 -146. 5-125. 0-100. 0-75 .0
-50 .0-25 .00 .0
25 .050 .075 .0100. 0
compression forces tension forces
Beam with opening - Strut-and-Tie model
Tension tieCompression strut
TUHH - Prof. Rombach
Hauptm omenteLastfall g=10 kN /m2 -146. 5-125. 0-100. 0-75 .0
-50 .0-25 .00 .0
25 .050 .075 .0100. 0
Summary 1: Beam and truss structures (D-regions)
The Bernoulli-Hypothesis (linear strain distribution) is not valid in so-calleddiscontinuity regions. Thus beam elements, which are mostly based on a linear strain distribution, can not estimate the forces in discontinuity regions.
It is important to model the stiffness in the discontinuity regions.
D-regions can be designed by means of strut-and-tie models whereas themember forces of the truss systems at the boundaries can be used to estimate the forces in the struts.
TUHH - Prof. Rombach
Hauptm omenteLastfall g=10 kN /m2 -146. 5-125. 0-100. 0-75 .0
-50 .0-25 .00 .0
25 .050 .075 .0100. 0
Modelling of support - single span girder
rigid
TUHH - Prof. Rombach
Hauptm omenteLastfall g=10 kN /m2 -146. 5-125. 0-100. 0-75 .0
-50 .0-25 .00 .0
25 .050 .075 .0100. 0
Modelling of support
TUHH - Prof. Rombach
Hauptm omenteLastfall g=10 kN /m2 -146. 5-125. 0-100. 0-75 .0
-50 .0-25 .00 .0
25 .050 .075 .0100. 0
Modelling of support - single span truss
TUHH - Prof. Rombach
Hauptm omenteLastfall g=10 kN /m2 -146. 5-125. 0-100. 0-75 .0
-50 .0-25 .00 .0
25 .050 .075 .0100. 0
Schornbachtalbridge
Bridge column with pile foundation
11m
15m
1,8m
Ortbetonramm-pfhle d=61cm
3m
3,6m
6:1
5:1
50:1
2,6m
3,04m
1,5m
7,22m
1,6m
5,72m
1,665m
1,225m
50:1
16:1
BoredPiles
D=0.61 m
TUHH - Prof. Rombach
Hauptm omenteLastfall g=10 kN /m2 -146. 5-125. 0-100. 0-75 .0
-50 .0-25 .00 .0
25 .050 .075 .0100. 0
Bending stiffness of piles is neglected
Estimation of pile forces
TUHH - Prof. Rombach
Hauptm omenteLastfall g=10 kN /m2 -146. 5-125. 0-100. 0-75 .0
-50 .0-25 .00 .0
25 .050 .075 .0100. 0
Bridge column with pile foundation
Numericalmodel
TUHH - Prof. Rombach
Hauptm omenteLastfall g=10 kN /m2 -146. 5-125. 0-100. 0-75 .0
-50 .0-25 .00 .0
25 .050 .075 .0100. 0
HVM
beam
horizontalspring
Vertikal-feder
n=0
n=0,5
n=1n=2
ks
k (z)=k (d).(z/d)s sn
n= 0 bindiger Boden
n =1 nichtbindiger Boden
Elastic support of piles
Beam
Horizontal springs
Verticalsprings
Distribution of soilstiffness
n = 0 cohesive soiln = 1 non-cohesive soil
TUHH - Prof. Rombach
Hauptm omenteLastfall g=10 kN /m2 -146. 5-125. 0-100. 0-75 .0
-50 .0-25 .00 .0
25 .050 .075 .0100. 0
Bending moments in the piles
H = 870 kN
Base of pile fixed vertically
TUHH - Prof. Rombach
Hauptm omenteLastfall g=10 kN /m2 -146. 5-125. 0-100. 0-75 .0
-50 .0-25 .00 .0
25 .050 .075 .0100. 0
195.
C=400MN/m
pile cap cant move horizontally
Pile cap can move
+8
68
-22
H = 870 kN
Bending moments in the piles
TUHH - Prof. Rombach
Hauptm omenteLastfall g=10 kN /m2 -146. 5-125. 0-100. 0-75 .0
-50 .0-25 .00 .0
25 .050 .075 .0100. 0
Summary 02: Beam and truss models
32
Beam elements are based on a linear strain distribution member forces in discontinuity region can not be calculated but stiffness of the D-regions has to be considered
Nonlinear material behaviour of concrete should be considered (e.g. torsion stiffness)
A realistic model for the support condition has a significant influence on the memberforce of the system. Restraints, which may lead to high forces, should be omitted.
The basic parameters of an elastic support on ground should be checked. The stiffnessmodulus of the soil is estimated by an Oedometer test, where the soil is fixed by a horizontal stiff ring. Therefore the real soil stiffness can be significant smaller.
An inclined axis of gravity (haunches) should be modelled with regard to the shear design of a beam. System und Belastung
Querkraft
-747
kN
607k
N -375kN
-375kN
Normalkraft
