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
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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
Timber framed construction in the course of history
Ancient Greek and Greek-
Timber framed construction in the course of history
Salient features: Low degree of sophistication; a few vertical and/or horizontal
Bronze Age Ancient Greek and GreekRoman Times Medieval Centuries Nowadays
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.
Timber framed construction in the course of history
Ancient Greek and Greek-
Timber framed construction in the course of history
A complete T-F masonry system: found in Thera; 7m high remains of the 3-story building Xeste-2
Bronze Age Ancient Greek and GreekRoman Times Medieval Centuries Nowadays
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)
Timber framed construction in the course of history
Ancient Greek and Roman
Timber framed construction in the course of history
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
Timber framed construction in the course of history
Ancient Greek and Greek-
Timber framed construction in the course of history
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)
Timber framed construction in the course of history
Ancient Greek and Greek- th th
Timber framed construction in the course of history
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’).
Timber framed construction in the course of history
Ancient Greek and Greek- th th
Timber framed construction in the course of history
In Calabria (S. Italy), after a strong seismic sequence in 1783 the local
Bronze Age Ancient Greek and GreekRoman Times 16th -19th century Nowadays
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)
Timber framed construction in the course of history
Ancient Greek and Greek- th th
Timber framed construction in the course of history
Another timber-framed masonry system is found in LefkasLefkas,
Bronze Age Ancient Greek and GreekRoman Times 16th -19th century Nowadays
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
Ancient Greek and Greek- th th
Lefkas buildings: The upper storeys are carried by the stone-masonry ground floor but in case of collapse, a secondary load-
Bronze Age Ancient Greek and GreekRoman Times 16th -19th century Nowadays
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)
Timber framed construction in the course of history
Ancient Greek and GreekAncient Greek and Greek-- thth thth
Timber framed construction in the course of history
• 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.
Modelling of timber framed wallsModelling of timber framed walls
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).
Modelling of timber framed wallsModelling of timber framed walls
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.