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: rombach@tu-harburg.de

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

3.453.413.252.32Tension force T1 [MN/m]

1.661.671.350.95Tension force T1-D1 [MN/m]

N4N3N2N1Elementmesh

Sleipner platform accident

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

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

MBemessung

FsdFcdV

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: rombach@tu-harburg.de

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

horizontal membrane force

System

Width of beam b = 0,22 cm

see detail

Loading q = 1 kN/m

Discontinuity regions

D-regions in beam or truss structures

Beam with opening

810 12,5 195

⋅= =

max / 195 / 0,6325

N M zkN

= ± = ± == ±

5,0m 5,0m

10kN/m

Opening 20/50cm 5050

Model 1 Model 2 Model 3

Beam with opening

-50.0-49.8

-41.7-41.7 -41.7

-42.1-40.8

Bending Moment

Shear Forces

5,0m 5,0m

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

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

Modelling of support

Modelling of support - single span truss

Schornbachtalbridge

Bridge column with pile foundation

Ortbetonramm-pfähle d=61cm

1,665m

1,225m

BoredPiles

D=0.61 m

Bending stiffness of piles is neglected

Estimation of pile forces

Bridge column with pile foundation

Numericalmodel

horizontalspring

Vertikal-feder

n=1n=2

k (z)=k (d).(z/d)s sn

n= 0 bindiger Boden

n =1 nichtbindiger Boden

Elastic support of piles

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

C=400MN/m

pile cap can’t move horizontally

Pile cap can move

H = 870 kN

Bending moments in the piles

Summary 02: Beam and truss models

• 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

N -375kN

-375kN

Normalkraft

-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

(g+q)=30kN/m

-1190kNm

1150kNm

1100kNm

Biegemoment beide Trägerenden eingespanntund unverschieblich

beide Trägerenden eingespanntein Lager horizontal verschieblich

-1240kNm.

Pin Support

Corners

Point Loads

Singularities in shear walls

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

lE ,IA

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

Main membrane forces and beam bending moments

Deformed Structure

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

Ve rschoben e Struktur

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

Finite-Elemente-Model

Deformed Structure

DeepBeam

supportedon

columns

Connection of different types of elements

u 1ϕ1

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

main membrane forces and truss bending moments

Deformations

1 12 2

-80. -60.

-99.-213.

-131.-142.

-152.-150.

Schnitt 3-3

Schnitt 1-1Schnitt 2-2

Schnitt 4-4

Detail

Stress distribution in a corner

10.0 15.0

horizontal reinforcement2.07

section in midspan

4.54 .5

4.0 4.0

vertical reinforcement

7 ,20 m

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 l +a4

Zugstrebe

Druckstrebe

horizontale Membrankraftin Feldmitte (in kN/m)

Fc=31kN

8m0,55m

Fs=31kN

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

HauptmomenteLastfall g=10 kN/m2

-146.5

-125.0

-100.0

Main bending moments and shear forces

Loading: g = 10 kN/m2

Stützenraster 1,50mStützen 24/24cm

Main Shear ForceLoading g=10 kN/m2

Corners

Pin support

Missing Support

Corner

Pin Support

Opening

Singularities

HauptquerkraftHauptmomente

Xm =0y,r

m =0x,r

10. 10.

Singularities - point load

yesyes

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

Coupling

Column

RestraintDeformation

One way slabLoad on left span only

Bending moments

Walls - partially missing support

Single-column footing

Single-column footing – shell analysis

Membrankraft in horizontaler Richtung in kN/m

Membrankräfte

3010.2900.

1302. 2 816.

281 7.

Setzung in mm

Membrane forces

Membrane forces in horizontal direction

Settlements

Circular Slab

Shells

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

200 kN/m

100 kNm/m

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

f /yk sγ

f /tk,cal sγBetonstahlσs

Material modelssteel

resistance

Strains stresses andstress resultant

Tension

Stiffening

Effect

tension stiffening effect

modification of steel strains concrete tension

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

Safety concept

Material models

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

reinforcement: elastic - plastic

bond: with/without slip„tension stiffening“

Kornverzahnung Dübelwirkung

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

Material models

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

reinforcement: elastic - plastic

Material parameters of concrete:• Compressive strength fck

• Tensile strength fct

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

25 120

Draufsicht

Ansicht

plan view

Side-view

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

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

d=16/10s

Special ColumnSES – Bangkok

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

2,2x2,0 m

Arch bridge

Flow of forces

detailing wrong correct

Arch bridge

restraints

Dead load

Soil pressure

Temperature ∆ = 16 K

Arch bridge

Shear design

Seite:

Stirrups [cm2/m]

Bored piles d = 1.20 m

Section

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!

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