Download pdf - Prof Rombach Presentation

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. Günter A. Rombach

Hamburg University of TechnologyE-mail: [email protected]


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.


The Sleipner platform

accident

Collapse: August 1991

Financial loss: 250 Mio US$


The Sleipner platform accident


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



8


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 checksengineering knowledge required

Seite:


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


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


Modelling

12

u2

v2

ϕ2

u1ϕ1

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


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



Beam or truss element

Beam element

Strains stresses


Hauptm omenteLastfall g=10 kN /m2 -146. 5-125. 0-100. 0-75 .0-50 .0-25 .00 .025 .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


D-regions in beam or truss structures


Beam with opening

2

max

2

810 12,5 195

8

q lM

kNm

⋅= =

⋅= =

max / 195 / 0,6325

N M zkN

= ± = ± == ±


5,0m 5,0m

50

20

10kN/m

Opening 20/50cm 5050

Model 1 Model 2 Model 3

Beam with opening


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


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



compression forces tension forces

Beam with opening - Strut-and-Tie model

Tension tieCompression strut



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.



Modelling of support - single span girder

rigid



Modelling of support



Modelling of support - single span truss



Schornbachtalbridge

Bridge column with pile foundation

11m

15m

1,8m

Ortbetonramm-pfähle 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



Bending stiffness of piles is neglected

Estimation of pile forces



Bridge column with pile foundation

Numericalmodel



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



Bending moments in the piles

H = 870 kN

Base of pile fixed vertically



195.

C=400MN/m

pile cap can’t move horizontally

Pile cap can move

+8

68

-22

H = 870 kN

Bending moments in the piles



Summary 02: Beam and truss models

32

• Beam elements are based on a linear strain distributionmember forces in discontinuity region can not be calculatedbut 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

-90kN

-121

3kN

-125

8kN

-45kN

-1176kN

Verformung

29,3mm26,3mm

2 3 4 5 6 7 8 9 101112131415161718192021 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 414243444546474849505152535455565758596061 4,0m

12,5m12,5m 25m50m

1,0m

(g+q)=30kN/m

-824

0kN

m

-652

0kN

m

-1190kNm

1150kNm

1100kNm

Biegemoment beide Trägerenden eingespanntund unverschieblich

beide Trägerenden eingespanntein Lager horizontal verschieblich

-1240kNm.

1


Pin Support

Corners

Point Loads

Singularities in shear walls


a2

a3a4

a5

v5 v4 v3 v2 v1

a1 v =ai i.ϕF =C ai i. .ϕM =F a =C ai i i i

2. . .ϕM= M = C a =CΣ Σ ϕ ϕi i

2. . .ϕC = C aϕ .Σ i

2

ϕ

lE ,IA

c c

v ϕ

lE ,IA

c c

Deep beam supported on columns


h/b=24/48cm

lx=7,20m

ly=3,60m

l=2,4m

d=24cm

System and Loadingq = 20 kN/m

Finite-Elemente-Model

X

Y

0.78

Main membrane forces and beam bending moments

Deformed Structure



Hau ptmembra nkräfte M embrank raft n (S chnitt in F eldmitte)x -50.5

54.8

Ve rschoben e Struktur

XY

membrane forces H orizontal membrane force n (section in midspan)x-50.5

54.8

Finite-Elemente-Model

Deformed Structure

X

Y

DeepBeam

supportedon

columns


Connection of different types of elements

u2

v2

u 1ϕ1

ϕ2

v1

Plane shell element (2-D) Beam element (2-D)

2 translation degrees of freedom 2 translation degrees of freedom +

1 rotation degree of freedom


shell element

Increase of truss length

truss element

shell element

Coupling of the mid joint

truss element

Connection of different types of elements


3.7

-2.5

-3.7

2.5

main membrane forces and truss bending moments

2.0

-1.6

-2.0

1.6

Deformations



1 12 2

3

3

4

4

-80. -60.

-99.-213.

-182.

-131.-142.

-152.-150.

-103

.

-214

.-117

.

-133

.

Schnitt 3-3

Schnitt 1-1Schnitt 2-2

Schnitt 4-4

X

Y

Detail

Stress distribution in a corner


2.0

2.0

5.0

10.0 15.0

1.0

1.0

horizontal reinforcement2.07

10.42

0.41

3.49

section in midspan

3.5

4.54 .5

3.0

2.0

1.0

1.0

2.0

3.0

0.5

4.0 4.0

vertical reinforcement

7 ,20 m

3,6 m

Reinforcement


Reinforcement


Summary: Shear walls

• Singularities (e.g. pin support, single forces) should be omitted

• Modelling of the support of deep beams should be done with great care

• ‚Numerical’ restraints should be omitted (e.g. supports, coupling of nodes)

• An incompatible element mesh should be omitted (e.g. connection of beamand plain shell elements)

• An automatic design of plain shells is not possible

• Elastic finite element analysis of shear walls are useful to develop a strut-and-tie model

Scheibenelement

Stab in Scheibeverlängern

Stabelement

Scheibenelement

Gelenkige Kopplungmit Mittenknoten

Stabelement

X

Y

Z

l +a4

x l +a4

x l +a4

x l +a4

x

lxa a

ly

z

z2

z1

Zugstrebe

com

pres

sion

stru

t

Dru

ckst

rebe

Druckstrebe

horizontale Membrankraftin Feldmitte (in kN/m)

Fc=31kN

z=3,

8m0,55m

Fs=31kN

-4.80

-3.96

-8.17

36.6

+

-


Design of real concrete structures with finite element software

Prof. Dr.-Ing. G. A. RombachHamburg University of Technology


• Introduction




• 3-d models



Stüt zenraster 1,50mStüt zen 24/24 cm

Slabs



HauptmomenteLastfall g=10 kN/m2

-146.5

-125.0

-100.0

-75.0

-50.0

-25.0

0.0

25.0

50.0

75.0

100.0

Main bending moments and shear forces

Loading: g = 10 kN/m2

Stützenraster 1,50mStützen 24/24cm

2.6

25.0

50.0

75.0

100.0

125.0

150.0

175.0

200.0

225.0

250.0

728.0

Main Shear ForceLoading g=10 kN/m2

Corners

Pin support


Missing Support

Missing Support

Corner

Corner

Pin Support

Opening

Singularities

HauptquerkraftHauptmomente

1m

Y

Xm =0y,r

m =0x,r

10. 10.

10.

10.

90.


Singularities - point load

noyes

yesyes

X Y

Z

F

Fv = F U

Detail


Starre Scheibe

a) 2D resp. 3D Model

b) Pin support of one node

c) Pin support of all supported nodes

d) restraint of the end nodes

e) Pin support of stiff slab

f) Elastic support

Modelling of wall support


X

Z

Node

Coupling

Slab

Column

RestraintDeformation

One way slabLoad on left span only

Bending moments


Walls - partially missing support


Single-column footing

52


Single-column footing – shell analysis

Membrankraft in horizontaler Richtung in kN/m

Membrankräfte

3010.2900.

1302. 2 816.

281 7.

Setzung in mm

2.83

mm

2.45

mm

5,0m

Membrane forces

Membrane forces in horizontal direction

Settlements


Circular Slab


Shells

25m

28m

28m

pp

SSh

2r

pppp

Fle ckenlast

Ve rtikalschnit t Horizontalschnitt

Patchload


Anzahl der Elemente in Umfangsrichtung bzw. über die HöheElementnetz A

16 x 11 32 x 22 64 x 44

Elementnetz B Elementnetz C

N x

200 kN/m

C B A

X

Y

Z

Mx

100 kNm/m

X

Y

Z

CB A

Shells

Inner forces in circumferentialdirection

Mesh A Mesh B Mesh C16x11 32x22 64x44



Nonlinear analysis of concrete structures

• Introduction



• Material nonlinear analysis• 3-d models




Aims• more realistic model

• correct deflections (e.g. slabs)

• more economical design due to load redistribution

• reduce restraint forces

• more realistic analysis of damages

• analysis of experiments

Problems• reinforcement must be known (e.g. linear analysis)

• load combination is not possible

• numerical model



Nonlinear analysis of beams and columns

59

f /yk sγ

f /tk,cal sγBetonstahlσs

εsu

εs

Material modelssteel

resistance

Strains stresses andstress resultant




60

Tension

Stiffening

Effect




61

tension stiffening effect

modification of steel strains concrete tension




62

Tension Stiffening Effect

fI = 25,4 mm stage I – elastic

fII,1 = 88,0 mm stage II – without TSfII,2 = 83,0 mm stage II – with TS – modification of steel strainsfII,3 = 48,0 mm stage II mit TS – concrete tension

Big differences




63

Safety concept



Material models

concrete: uniaxial and triaxialtensile strengthlong term behaviour (s+c)load historycracking

reinforcement: elastic - plastic

64




bond: with/without slip„tension stiffening“

Kornverzahnung Dübelwirkung

Numerical Modellingreinforcement bars: discret – smearedbond: fixed - softcracks: discret - smeared

65


Material models

concrete: uniaxial and triaxialtensile strengthlong term behaviour (s+c)load historycracking

reinforcement: elastic - plastic



66


Material parameters of concrete:• Compressive strength fck

• Tensile strength fct

• Shrinkage and creep• Elastic-Modulus• Poisson‘s ratio• ........



25 120

180

150

550

670cm

Draufsicht

Ansicht

67

plan view

Side-view



180

150

d=28/10 + s d=16/10s

d=28/10 + sd=28/10s

d=16/10s

Special ColumnSES – Bangkok

Rebar



The conclusion of the various analyses is that the offset colum heads, as detailed, are able to carry the design service and ultimate loads....




Aims• More realistic analysis

• Fast analysis and design

• Simplifications seems not to be required

Problems• Manpower for input

• Difficult to check the results

• Important details may be overseen

• Calculation of reinforcementnot possible (e.g. shear walls) ......

• Relevant load arrangement ?

Modelling of whole structures


Arch bridge

Plan view

Side view

3-D (1. BA)

26,4 m

Bored piles d = 1.20m

Wing wall t = 1.0 mwall t = 0.4 m

Beam

2,2x2,0 m


Arch bridge

Flow of forces

detailing wrong correct


Arch bridge

loads

restraints

Dead load

Soil pressure

Temperature ∆ = 16 K


Arch bridge

Shear design

Seite:

Stirrups [cm2/m]

Bored piles d = 1.20 m

Section

A-A


Arch bridge

Shear design


Arch bridge

design

Seite:


Arch bridge

design


Arch bridge

Parametric studies on truss system


Arch bridge

Parametric study: soil stiffness


Summary: Complex 3-D-shell analysis

• Detailing and flow of forces (e.g. in frame corners oder massive members) should be considered.

• Restraint forces should be checked with regard to the cracked state.• Stiffness change of members due to cracking of concrete and variation of

possible soil stiffnesses should be considered in the design.• The numerical model should be to checked for D- and singularity regions.• Automatic design (bending, shear) of shear walls or shell structures is not

possible. Truss forces are needed for design.• Great effort is needed for checking the analysis and for the graphical and

numerical output.• Modifications of the structure requires the analysis of the whole structure.


Finite Element Design of Concrete Structures

Prof. Dr.-Ing. Günter A. RombachHamburg University of Technology


Rombach G.: Finite elementdesign of concrete structures

Thomas TelfordISBN: 0 7277 3274 9

Published 2004

Thanks you for your attention!