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Detailed and simplified non-linearDetailed and simplified non linear models for timber-framed

masonry structures

Prof Andreas J KapposProf. Andreas J. KapposLab. of Concrete and Masonry Structures , Dept. of

Civil Engineering Aristotle University of ThessalonikiCivil Engineering, Aristotle University of Thessaloniki

(Based on PhD work by L A Kouris)(Based on PhD work by L.-A. Kouris)

IST, Lisbon, 10IST, Lisbon, 10--1010--20112011

FACULTY OF ENGINEERINGFACULTY OF ENGINEERINGARISTOTLE UNIVERSITY OF THESSALONIKIARISTOTLE UNIVERSITY OF THESSALONIKI

At the heart of Aristotle’s landAt the heart of Aristotle’s land

HELLAS THE COYNTRYTHE COYNTRYTHE COYNTRY ––– THE THE THE CITYCITYCITY

THE COUNTRYTHE COUNTRY –– THE THE CITYCITY

The oldest E.U. member state in S.E. Europe THE UNIVERSITYTHE UNIVERSITYTHE UNIVERSITY HISTORY HISTORY HISTORY ---INSTITUTIONSINSTITUTIONSINSTITUTIONS

BELGRADE BUCHAREST HUMAN POTENTIALHUMAN POTENTIALHUMAN POTENTIAL INFRASTRUCTUREINFRASTRUCTUREINFRASTRUCTURE STUDIESSTUDIESSTUDIES THE REGION

2 continentsTHESSALONIKI

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RESEARCHRESEARCHRESEARCH SOCIETYSOCIETYSOCIETY THE DEPARTMENTSTHE DEPARTMENTSTHE DEPARTMENTS

Ci il E i iCi il E i iCi il E i i

2 continents7 countries7 capitals or major

b t THESSALONIKITHESSALONIKIATHENS

(CONSTANTINOPLE)TIRANA

••• Civil EngineeringCivil EngineeringCivil Engineering••• ArchitectureArchitectureArchitecture••• Rural and SurveyingRural and SurveyingRural and Surveying

EngineeringEngineeringEngineering

urban centers THESSALONIKITHESSALONIKIThe city isThe city is a center among centers of decision makinga center among centers of decision making

ARISTOTLE UNIVERSITY

EngineeringEngineeringEngineering••• Mechanical EngineeringMechanical EngineeringMechanical Engineering••• Electrical and ComputerElectrical and ComputerElectrical and Computer

EngineeringEngineeringEngineeringThe largest University of the

country dominates the city

EngineeringEngineeringEngineering••• Chemical EngineeringChemical EngineeringChemical Engineering••• General General General DepartmentDepartmentDepartment

A University at the heart of the cityA University at the heart of the cityFACULTY OF ENGINEERINGFACULTY OF ENGINEERINGARISTOTLE UNIVERSITY OF THESSALONIKIARISTOTLE UNIVERSITY OF THESSALONIKI

THE COYNTRYTHE COYNTRYTHE COYNTRY ––– THE THE THE CITYCITYCITY

The largest university in Greece

THE UNIVERSITYTHE UNIVERSITYTHE UNIVERSITY HISTORY HISTORY HISTORY ---INSTITUTIONSINSTITUTIONSINSTITUTIONS

THE UNIVERSITYTHE UNIVERSITYstudentsfaculty members

85.000 2.590

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GEOTECHNICAL HEALTH SIENCES

SCIENCES SCIENCES HEALTH SIENCES

FINE ARTSEDUCATION

THEOLOGYPHILOSOPHYLAW ECONOMIC AND POLITICAL SCIENCES

ENGINEERING

The largest and oldest The largest and oldest department department (1955) (1955)

FACULTY OF ENGINEERINGFACULTY OF ENGINEERINGARISTOTLE UNIVERSITY OF THESSALONIKIARISTOTLE UNIVERSITY OF THESSALONIKI

THE COYNTRYTHE COYNTRYTHE COYNTRY ––– THE THE THE CITYCITYCITY

( 955)( 955)DEPARTMENT DEPARTMENT OF CIVIL OF CIVIL ENGINEERINGENGINEERING

THE UNIVERSITYTHE UNIVERSITYTHE UNIVERSITY HISTORY HISTORY HISTORY ---INSTITUTIONSINSTITUTIONSINSTITUTIONS HUMAN POTENTIALHUMAN POTENTIALHUMAN POTENTIAL INFRASTRUCTUREINFRASTRUCTURE ORGANIZATIONORGANIZATION

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ORGANIZATIONORGANIZATION 10034

39

faculty membersteaching assistantsadministrative staff

RESEARCHRESEARCHRESEARCH SOCIETYSOCIETYSOCIETY

Structural EngineeringStructural Engineering

DIVISIONSDIVISIONS4

20divisionslaboratories

DEGREES DEGREES CONFERREDCONFERRED

• Civil Engineer’s

Diploma

g gg g

Hydraulics and Environmental Hydraulics and Environmental EngineeringEngineering

CONFERREDCONFERRED

p• Three postgraduate

specialization

Geotechnical EngineeringGeotechnical Engineering

Transport, Infrastructure,Transport, Infrastructure,Diplomas

• Doctoraldegree

Transport, Infrastructure, Transport, Infrastructure, Management and Regional Management and Regional PlanningPlanning

Additionally, the Department participates in two interdepartmental postgraduate programs

Timber framed construction in the course of history

Ancient Greek and Greek-

• Remains of T-F masonry buildings since the Bronze Age

Bronze Age Ancient Greek and GreekRoman Times Medieval Centuries Nowadays

Remains of T F masonry buildings since the Bronze Age in: Minoan Crete, Mycenae, and the island of Thera.

MycenaeThera

Crete




Salient features: Low degree of sophistication; a few vertical and/or horizontal


Low degree of sophistication; a few vertical and/or horizontal elements no diagonals (braces).

One timber framework on each face of the thick masonry wall One timber framework on each face of the thick masonry wall. Used only in critical parts of the building. In crossing walls joining them at the corners In crossing walls joining them at the corners.




A complete T-F masonry system: found in Thera; 7m high remains of the 3-story building Xeste-2


found in Thera; 7m high remains of the 3-story building Xeste-2. ordinary wooden frames with masonry infill (but no diagonals). section of timber elements; 20 cm square.; q vertical spacing about 0.8 m.

(Palyvou, Arch. Soc. of Athens, 1999)


Ancient Greek and Roman


In the town of Herculaneum, buried in

Bronze Age Ancient Greek and Roman Times Medieval Centuries Nowadays

the lava from the Vesuvius volcano in 79 AD, single-leaf T-F masonry b ildings ere fo ndbuildings were found

Vitruvius called this type of stucture“Opus Craticium”Opus Craticium .

Timber elements have square cross-section with side 1012cm and formsection with side 10 12cm and form panels of 11m.

the Trellis house




Horizontal timber elements incorporated in masonry walls

Bronze Age Ancient Greek and GreekRoman Times Middle Ages Nowadays

were commonly used in Byzantine churches, defense walls and other large stuctures.

(Moropoulou et al., SDEE, 2000)


Ancient Greek and Greek- th th


Timber-framed masonry was used h k i

Bronze Age Ancient Greek and GreekRoman Times 16th -19th century Nowadays

as an earthquake-resistant structure at least since the 18th

century in seismic-prone areascentury in seismic prone areas. In some interesting cases it was

introduced as a preventive measureintroduced as a preventive measure after strong seismic events.

After the 1755 catastrophic earthquake the centre of Lisbon After the 1755 catastrophic earthquake, the centre of Lisbon was rebuilt with new provisions: T-F masonry was used to enhance seismic capacity The ‘Pombalino’ = the externalenhance seismic capacity. The Pombalino the external masonry façade + an internal timber frame (‘gaiola’).




In Calabria (S. Italy), after a strong seismic sequence in 1783 the local


government decided the reconstruction of the earthquake-strikenarea with timber-framed masonry buildings (‘Casa Baraccata’).

Casa Baraccata also consisted of a wooden internal frame with Casa Baraccata also consisted of a wooden internal frame with diagonal braces invisible from the outside and the external masonry wall, connected to each other (‘dual’ system).

(Tobriner, The Journal of the Soc. of Arch. Historians, 1983)




Another timber-framed masonry system is found in LefkasLefkas,


Greece in which the dual system consists of the ground stone-masonry floor and the upper timber-framed storeys.

(Touliatos, NTUA, 1995)

Timber framed construction in the course of historyTimber framed construction in the course of history


Lefkas buildings: The upper storeys are carried by the stone-masonry ground floor but in case of collapse, a secondary load-


masonry ground floor but in case of collapse, a secondary loadcarrying system of timber columns is activated. These timber columns are fixed to the ground or, more usually, are free standing, but not embedded in the walls.

These two systems are initially interconnected.

(Touliatos, NTUA, 1995)


Ancient Greek and GreekAncient Greek and Greek-- thth thth


• Nowadays, many heritage buildings of timber-framed

Bronze AgeBronze Age Ancient Greek and GreekAncient Greek and GreekRoman TimesRoman Times 1616thth –– 1919thth Modern timesModern times

y , y g gmasonry stand in Lefkas (GR), Lisbon (PT), Calabria (IT) and other cities.

• These buildings are used as dwellings, and many of them are exposed to high seismic risk.

Seismic behaviour of timber-framed walls

4th step: separation of 3rd step: separation of

1st step: cracks in mortar 2nd step: fall of mortar

diagonals – infill failure masonry infills

Performance of timber framed structures in recent earthquakes

Lefkas Lefkas earthquake, 2002, M=6.4, epicenter near the city: 34% of buildings were timber-framed although the earthquake was strong (amax= 0.42g , many R/C buildings

damaged, one collapsed), damage to T-F buildings was limited to outout--ofof--plane fall of external mortarplane fall of external mortar, or, rarely, of masonry infillsmasonry infillsofof plane fall of external mortarplane fall of external mortar, or, rarely, of masonry infillsmasonry infills

In Turkey, during the strong Düzce Düzce (1999) earthquake the behaviour of T-F buildings was good (better than old R/C), the opposite occurred during the lower magnitude Orta Orta (2000) earthquake (reasons?..).

Performance of timber framed Performance of timber framed structures instructures in recent earthquakes

Performance of timber framed structures in recent earthquakes

As a rule: observed performance of T-F masonry buildings is rather goodgood,

for highhigh seismic intensities ability to dissipate earthquake energy efficiently through contact and friction

f d i ll i i h k i l li l l performance during lowlow intensity earthquakes not particularly not particularly goodgood, due to early cracking of the masonry infills

overall T F masonry seismic response is markedly nonnon linearlinear overall, T-F masonry seismic response is markedly nonnon--linearlinear.

Modelling of timber framed wallsModelling of timber framed walls

Masonry infillsinfills affect the performance of the walls primarily during the initial phase of elastic response.

In a model focusing on the inelasticinelastic response, masonry infills can be indirectly taken into account.

The result in the model is lower elastic stiffness, but better capturing of the overall response.


Wooden members are modelled with area (2D) elements. The adopted yield law (and plastic potential function) for timber is the p y ( p p )

orthotropic Hill law.2 2 2

2 2 2 2 2

1 1 1 1 1 1

x y xy za b a b c

The material law for monotonic and uniaxial stress is considered trilinear (for ±σ). Initiation of plastic deformation: at 40% of the final strength.

Flow rule: associated for work hardening (isotropic)Flow rule: associated for work hardening (isotropic).


Unreliable connection between timber elements it is assumed that there is simple contactsimple contact without any connectionassumed that there is simple contact simple contact without any connection.

Interface model for timber braces and posts: Mohr-Coulomb friction pmodel (friction coefficient 0.5), without cohesion (c 0).

For surface-to-surface contact asymmetric contact asymmetric contact is assumed.

Influence of masonry infills: Influence of masonry infills: (i)weight is taken into account indirectly, (ii) assumed to prevent y, ( ) pbuckling of diagonals.

Validation of the modelValidation of the model The proposed model is validated against the

results of laboratory tests performed at LNEC, Lisbon, by Santos (1997).

h l b h i In the laboratory tests three specimens were taken by an existing building of Lisbon.Th i h d l di i i h These specimens had large dimensions, with about 3.5m height (storey height), about 2 5m width and about 0 15m thickness2.5m width and about 0.15m thickness.

Validation of the model The experimental testing consisted in the

application of a reversed horizontal forcereversed horizontal force untilapplication of a reversed horizontal force reversed horizontal force until failure of the specimens.

The behaviour of the three specimens wasThe behaviour of the three specimens was similar; at the final stage of failure they showed unnailing of the wooden braces consequent sliding and partial expulsion of

masonry infills.

(Santos, LNEC, 1997)

Validation of the model LNEC specimens were modelled in ANSYS using

the proposed method (plasticity model) were subjected to monotonicallymonotonically increasing

horizontal loading (with displacement control). Th fi l d f d t t d The final deformed stage presents damage

similar to that observed in the test specimens: disengagement of the diagonals from the g g gsurrounding timber members

Validation of the model Analytical pushover curves are compared with

the hysteresis loops from the tests, good agreement is found

Elastic stiffness (kN/m), maximum strength (kN) and maximum displacement (cm) of the specimens.elastic stiffness max strength (%) max displacement

80 G1

G1LNEC test 6733.36 71.61 -60.61

8%12.50 -10.28

Proposed model 6564.29 65.77 10.00

LNEC test 7711.08 70.98 -63.42 12.28 -9.9340

60

G1G2 1%Proposed

model 7120.08 70.08 11.50

G3LNEC test 4361.08 46.77 -59.23

-4%11.76 -11.42

Proposed

20

40

G3 4%Proposed model 4049.97 48.81 9.00

-20

0

-150 -100 -50 0 50 100 150

kN

-60

-40LNEC model

-80

60

mm

Validation of the model Difference in the ultimate load capacity: 4% Difference in the ultimate deformation: 2 5% Difference in the ultimate deformation: 2.5% Difference in elastic stiffness: 5%

80G2

60

80G2

G2

20

40

-20

0

-150 -100 -50 0 50 100 150

kN

-40

LNEC model

-80

-60

mm

LNEC model

Validation of the model Pre-peak range of the response: not captured

properly in all specimensproperly in all specimens local imperfections and wear of the timber members. 80G3members.

60

G3

G3

20

40

-20

0

-150 -100 -50 0 50 100 150

kN

-60

-40

LNEC model

-80

60

mm

Simplified model for T F wallsSimplified model for T-F walls

Every timber post and lintel is modelled through a linear-elastic beam elementbeam elementlinear elastic beam elementbeam element.

The diagonals are modelled with a linklink (bar) element pinned at its ends, hence carrying onlyelement pinned at its ends, hence carrying only axial compressive forces.

A plastic axial spring plastic axial spring is incorporated in these link p p gp p g pdiagonals.

The inelastic constitutive law of this point plastic spring is then derived by means of the detailed model (bilinearization of the pushover curve).

2 2 2 2

, diag x diag

H L H Lu u N VL L

Simplified model of T F wallsSimplified model of T-F walls

Consideration of slidingsliding of the diagonals in the elastic range is required use results from refined modelrequired use results from refined model.

The correction factor ks is applied to the stiffnesses of the members of the beam modelmembers of the beam model.

3

2 2 32 1 H L H V 2

1 y

sy

H L H Vk

EA L u

Initial stiffness of detailed model

Validation of the simplified modelValidation of the simplified model

Model applied to LNEC specimens (six panels). 1 An elastic analysis is performed for the evaluation1. An elastic analysis is performed for the evaluation

of the axial stress in each column. 2 The pushover curves derived from the detailed2. The pushover curves derived from the detailed

model are transformed into bilinear curves for the estimation of yield and maximum strain and ystrength.

3. These quantities are then expressed in terms of axial force and deformation.

4. The correction factor ks is calculated for each panel.

Validation of the simplified modelValidation of the simplified model

Specimen G2: Good match (as expected, since link model was calibrated against the refined model)was calibrated against the refined model)

60

80

20

40

-20

0

-0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2

kN

-60

-40

-80m

LNEC TEST link model

Application to an existing building The simplified model is used for the analysis of

the façade of an actual building situated in the Ionian island of Lefkas GreeceIonian island of Lefkas, Greece.

• 'Berykiou‘ building: y g basement in stone masonry

of thickness 0.8m two storeys built in T-F

masonry ti f ti b section of timber

elements: 100mm square

Application to Lefkas building: results

failure mechanism; plastic hinges

Stone masonry piers

90

100

Stone masonry piers

60

70

80

90

N

20

30

40

50kN

pushover curve0

10

0,00 0,02 0,04 0,06 0,08 0,10 0,12

m

ConclusionsConclusions From the Bronze Age to modern times we find g

timber-framed buildings of different configurations.

The development of timber-framed structures is often closely linked to earthquakes.

It might be hypothesized that, at least in earthquake-prone areas timber-framed construction was developed as a technique toconstruction was developed as a technique to effectively resist earthquake loading.

Two modelsTwo models developed for the non linear static Two models Two models developed for the non-linear static analysis of T-F masonry buildings: detaileddetailed (plasticity–based finite element) detaileddetailed (plasticity based finite element) simplifiedsimplified (beams – links)

Conclusions Detailed model: orthotropic behaviour for timber

elements and a proper interface (Mohr-Coulomb), for their interaction small subassemblagestheir interaction small subassemblages.

Simplified model: beam elements for timber posts and lintels, and link elements with nonlinear axial hinges for the diagonals entire structures.

Masonry infill excluded from the model due to its i i ifi t t ib ti t i i l d i tinsignificant contribution to seismic load resistance.

The method was validatedvalidated using the cyclic tests performed at LNEC.performed at LNEC.

Good match found between results of numerical analysis and those of the tests.

The detailed model can capture the gradual softening in the response of the walls.

h h l f h l f d The pushover curve resulting from the simplified model has an essentially bilinear form.

Website: ajkap weebly comWebsite: ajkap.weebly.com

K i L d K A J “D t il d d i lifi d liKouris, L. and Kappos, A.J. “Detailed and simplified non-linear models for timber-framed masonry structures”, Jnl of Cultural

Heritage, doi:10.1016/j.culher.2011.05.009, July 2011.Heritage, doi:10.1016/j.culher.2011.05.009, July 2011.

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