2 Scheiben und Träger - ETH Z · 2018-10-19 · Crack localization (size effect): stiffness of the...

2 Scheiben und Träger

18.10.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Vorlesung Stahlbeton III 1

2.6 Kontinuierliche Spannungsfelder

Kontinuierliche Spannungsfelder

Overview and nomenclature


2. Scheiben und Träger

2.1 Spannungsfelder = Stress fields (discontinuous)Equilibrium considerations: Lower bound solutions

2.2 Bruchmechanismen = Failure mechanismsKinematic considerations: Upper bound solutions

2.3 Träger – Verformungsvermögen= Beams – Deformation capacity

2.4 Scheibenelemente – Fliessbedingungen= Membrane elements – Yield conditions

2.5 Scheibenelemente – Last-Verformungsverhalten= Membrane elements – Load deformation behaviour

2.6 Kontinuierliche Spannungsfelder = Continuous stress fieldsEquilibrium & kinematic considerations:Exact solutions (simultaneously lower + upper bound)

Tedious hand calculations (iterations, many load cases)Digitalisation required!

Concepts only developed for particular elementsDeformation capacity?Serviceability checks(deformations, crack widths)?

Computer-aided tool for a general plane stress elementImplements same mechanical conceptsOvercomes the stated limitations

Application to real-life structures


Real-life structuresB Continuity/Bernouilli regionsD Discontinuity regions: static and geometric discontinuities are always present


[Tjhin & Kuchma, 2002]


Dimensioning/assesment of real-life structures

B Continuity/Bernouilli regions• Classic tools: hand calculations feasible; cover all verifications• Computer-aided tools:

Many available applications for member design: direct implementation of code verifications/mechanical models

D Discontinuity regions• Classic tools (discontinuous stress fields…): deformation capacity?; serviceability aspects?; hand calculations non-

feasible/productive• Computer aided-tools:

a) Linear elastic FE-calculations: Non-symmetric strength of concrete only accounted for in the last step (dimensioningbased on yield conditions); unable to predict realistic capacity in existing structures, nor cracking in new ones

b) Non-linear FE-calculations: complex, typically consider tensile strength for equilibrium (differ from classic mechanicalmodels), code compliant?

c) Gap between a & b for simple but realistic, code-compliant tool, consistent with classic mechanical models Continuous stress fields = Computer-aided stress fields = Simplified non-linear FE-calculation



Dimensioning/assesment of Discontinuity Regions: Existing computer-aided tools

[HanGil, 2017]

Idea StatiCa for specific details(corbels, piles caps…)

AStrutTie (HanGil) (strut-and-tie fc=? Realistic results?)

[IDEA, 2017]

CAST (Tjhin & Kutchma, 2002)(strut-and-tie fc=? Realistic results?)

[Mata-Falcón & Sánchez-Sevilla, 2006]

18.10.2018 ETH Zürich | Prof. Dr. W. Kaufmann | Eurostars – DR-Design 5




Stringer-Panel Models (Nielsen, 1971; Blaauwendraad & Hoogenboom, 1996; Marti & Heinzmann, 2012)

[Blauwendraad, 2006]


Experimental crack pattern

Hand-calculated stress fields

Numerical results EPSF


[Mata-Falcón, 2015]

[Mata-Falcón et al., 2014]

[Muttoni & Fernandez Ruiz, 2007]

EPSF elastic plastic stress fields (Fernández Ruiz & Muttoni, 2007)

Maintains advantages of hand calculations (transparent, safedesign with fct = 0, consistent detailing)Compressive strength fcdetermined automatically fromstrain state

Limited user-friendlinessLimited use for serviceability… no tension stiffening… no crack width calculationNo check of deformationcapacity (perfectly plastic material)



DRD (discontinuity region design) method - Implemented in commercial software IdeaStatiCa DetailContinuous stress fields = Computer-aided stress fields


Scope• Simple method for efficient, code-compliant design and assessment of discontinuity concrete regions• Including serviceability and deformation capacity verifications• Direct link to conventional RC design: standard material properties, concrete tensile strength totally neglected for

equilibrium (only its influence to the stiffness is accounted)

Inspirations• EPSF FE-implementation (strain compatibility, automatic determination of concrete reduction factor from strain state)• Tension Chord Model TCM and Cracked Membrane Model CMM (tension stiffening, ductility and serviceability checks)

Development / Credits

ETH Zürich | Prof

This project has received partial funding from Eurostars-2 joint programme, with co-funding from the European Union

Horizon 2020 research and innovation programme


DRD: design process


1) Definition of geometry, loads and load combinationsa) BIM connections: export data from a global model for the analysis of a detailb) Standalone application:

Full definition in standalone user-friendly application


DRD: design process


2) Reinforcement designa) Location of reinforcement: definition by user. Several design tools are provided to identify where the

reinforcement is required (for complex regions):

b) Amount of reinforcement: can be automatically designed for all or part of the reinforcement. Not yet releasedin current version (Idea Statica Detail 9.1)

3) Verification models to check all code requirementsa) Load-bearing capacityb) Serviceability verifications (deformations, crack width…)

Linear elastic stress flow

Topological optimization


DRD verification model: main assumptions


• AStruTie (HanGil)

based on [Kaufmann and Marti, 1998]

Main assumptions:

• Fictitious rotating-stress-free cracks( c1,r=0) without slip

• Average strains

• Equilibrium at cracks:

i. Maximum stresses:- c3,r / s,r

ii. Concrete tensilestrength neglectedexcept for tension-stiffening: m

Suitable for elements with minimum transversal reinforcement. Slender elements without shear reinforcement would lead to conservative results.


DRD verification model: concrete



Strain limitations of concrete specified by codes(explicitly considers the increasing brittleness ofconcrete with strength).Imposed to the average strain over a characteristiccrushing band length.

kc discrete values for hand calculations


DRD verification model: concrete



kc (compression softening) automatically computed basedon the transversal strain state.Use of fib MC 2010 / SIA 262:213 proposal for shearverifications (consistent with considered max. stresses)extended for general cases.

Strain limitations of concrete specified by codes(explicitly considers the increasing brittleness ofconcrete with strength).Imposed to the average strain over a characteristiccrushing band length.



DRD verification model: bond and reinforcement


Bond model used exclusively for bond verifications

Tension-stiffening:Does not affect thestrength of thereinforcementIncreases the stiffnessReduces the ductility(can reduce the strengthof the member)

explicit failure criteria *Bilinear naked steel input for design. More

realistic laws for assessment & experimental validation.


DRD verification model: tension stiffeningStabilized crack pattern


Implementation ofTension Chord Model(TCM) [Alvarez, 1998;Marti et al., 1998]

Average crack spacing:assumed =0.67

for > cr 0.6% Reinforcement is able to carry the cracking load without yielding 0

1 1sr y ctmcr

f f n


DRD verification model: tension stiffeningNon-stabilized crack pattern


for cr 0.6% Reinforcement is NOT able to carry the cracking load without yielding. Cracks are controlled by other reinforcement.

Independent cracks areassumed + bond model ofTension Chord Model.

Crack localization (sizeeffect): stiffness of thewhole rebar embedded inconcrete > local stiffnessnear the crack(considered average strainover lavg).

the cra.

for cr 0.6% Reinforcement is NOT able to carry yielding. Cracks are controlled by other reinforcement.


DRD verification model: effective area of concrete in tensionsuitable for numerical implementation and valid for automatic definition of c,eff in any region

Maximum concrete area each rebar can activate (concrete at fct)

(illustrated for rebars 3 and 4) Areas used in calculation



DRD verification model: crack width – stabilized crack pattern


WT4

[Walther, 1967]


DRD verification model: crack width – non-stabilized crack pattern


[Zhu et al., 2003]

Assumed independent cracks at SLS Considered for:a) Regions with <0.6%b) Cracks triggered by geometric

discontinuities at low loads

T6


DRD verification model: crack width – crack kinematic



DRD & IdeaStatiCa Detail implementation: additional information

Theoretical description of DRD method & experimental validation

• “Computer-aided stress field analysis of discontinuity concrete regions”, J. Mata-Falcón, D. T. Tran, W. Kaufmann, J.Navrátil; Proceedings of the Conference on Computational Modelling of Concrete and Concrete Structures (EURO-C2018), 641-650, London: CRC Press, 2018.

Use and installation of Idea StatiCa Detail software:

• Installation of the software: https://www.ideastatica.com/downloads/

Free educational license might be ordered in https://www.ideastatica.com/free-trial/

• Idea StatiCa Resource Center (tutorials, sample projects…): https://resources.ideastatica.com/Content/Home.htm

• Practical workshop will be organised for those students interested



DRD: practical examples in Idea StatiCa DetailDeep beam with distributed top load


Problem definition Design of reinforcement

x

z

tF

cF

A

B C

D

E

a

w cqa b f

Gqa

Fq


DRD: practical examples in Idea StatiCa DetailDeep beam with distributed top load


Continuous stress fields Discontinuous stress fields


DRD: practical examples in Idea StatiCa DetailDeep beam with distributed load


Top load: fan mechanism Suspended load: arch mechanism

Arch mechanism requires enough capacity of flexural reinforcement; otherwise, the load is suspended until top & fan action is generated

2 Scheiben und Träger - ETH Z · 2018-10-19 · Crack localization (size effect): stiffness of the...

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