NON-LINEAR NUMERICAL MODELLING OF A POST · PDF fileNON-LINEAR NUMERICAL MODELLING OF A...

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NON-LINEAR NUMERICAL MODELLING OF A POST-TENSIONED

TIMBER FRAME BUILDING WITH DISSIPATIVE STEEL ANGLE

DEVICES

Michele SIMONETTI1, Tobias SMITH

2, Felice C. PONZO

3, Antonio DI CESARE

4, Stefano

PAMPANIN5 and Domenico NIGRO

6

ABSTRACT

This paper describes the numerical modelling of post-tensioned timber (Pres-Lam) frame systems

under non-linear dynamic and static loading. From the conception of the post-tensioned jointed ductile

concept it has been clear that the nature of its controlled rocking mechanism leant itself well to the use

of a lumped plasticity approach. This approach combines the use of elastic elements with springs

representing plastic rotations in the system. Two experimental testing campaigns have been used in

order to confirm the effectiveness of this modelling technique in predicting both the global (frame)

and local (beam-column) response of these systems.

The first of these tests was a full scale beam-column joint tested quasi-statically and the second

was a 3-dimensional, 3-storey, 2/3rd scale multi-storey post-tensioned timber frame building tested

dynamically. During the testing programmes the specimens were tested both with and without the

addition of dissipative steel angles which were designed to yield at a certain level of drift. These steel

angles release energy through hysteresis during lateral frame movement thus increasing damping.

Both structures were modelled using a lumped plasticity approach with springs that were calibrated

against the moment rotation design procedure used for post-tensioned timber connections.

This work has proved the adequacy of the use of two numerical modelling programs,

RUAUMOKO and SAP2000, in providing accurate representation of structural response when

calibrated against current design procedures. All testing was performed in the structural laboratory of

the University of Basilicata in Potenza, Italy. This experimental campaign is part of a series of

experimental tests in collaboration with the University of Canterbury, Christchurch, New Zealand.

INTRODUCTION

Increasingly in the design of structures, engineers rely on the use of Non-linear Time History Analysis

(NTHA) in order to verify building performance under design seismic loading. During the use of these

models several trade-offs are made between complexity, accuracy, programming time, and processing

time. In design it is crucial that simple models exist which provide sufficiently accurate building

response without requiring a large amount of time in processing or programming.

1 PhD Candidate, University of Basilicata, Potenza, Italy, [email protected]

2 PhD Graduand, University of Canterbury, Christchurch, New Zealand, [email protected]

3 Prof, University of Basilicata, Potenza, Italy, [email protected]

4 Dr Eng, University of Basilicata, Potenza, Italy, [email protected]

5 Prof, University of Canterbury, Christchurch, New Zealand, [email protected]

6 Mr, University of Basilicata, Potenza, Italy, [email protected]

2

The post-tensioned timber concept (under the name Pres-Lam) was developed at the University

of Canterbury and has been extensively tested in the structural laboratories of the university

(Buchanan et al. 2008; Palermo et al. 2005a; Smith et al. 2007). The system, originally conceived for

use in concrete structures (Priestley et al. 1999), combines post-tensioning and dissipative reinforcing

in order to provide moment resistant connections. During the course of the post-tensioned timber

project several authors have used lumped plasticity modelling to replicate experimental testing

however the predictive dynamic abilities of this approach, with regards to post-tensioned timber

frames, have not been studied.

This paper presents the numerical modelling of two test specimens: a full-scale beam-column

joint, and a 2/3rd

scale, three-storey post-tensioned timber frame building both tested in the structural

laboratory of the University of Basilicata (UNIBAS) in Potenza, Italy. Numerical models of both

structures were created prior to testing in order to predict lateral response. Models were calibrated

against current post-tensioned timber design procedures and adequately predicted non-linear static

(beam-column) and dynamic (frame) response.

DESIGN CONCEPT

Post-tensioned timber uses post-tensioning technology (frequently applied to concrete structures) in

order to connect structural timber elements. While the post-tensioning provides desirable recentering

properties, the dissipative reinforcing devices allow adequate energy dissipation from the system as

well as increased moment resistance. During lateral frame movement, controlled rocking occurs at the

beam-column and column-foundation interface which provides flag-shaped hysteretic behaviour. Post-

tensioned timber technology enables the design of buildings having large bay lengths (8-12m) and

reduced structural sections.

Key to the post-tensioned frame connection is the ratio β between the moment resistance

provided by the post-tensioning Mpt and the total moment resistance provided by the frame Mt (Figure

1). Clearly, during design this choice affects both the damping and moment capacity of the system and

therefore changing this value will have a direct impact on both capacity and demand under seismic

loading. During both experimental campaigns the size of the structural members, building layout and

mass was not altered, however different values of post-tensioning and steel moment capacity

contributions (thus variations in the value β) have been investigated.

Figure 1. Moment response with varying levels of the parameter β

The design procedure

The numerical models used were calibrated against the current post-tensioned timber design

procedure. Although a codified procedure exists for the calculation of the moment-rotation response of

post-tensioned ductile concrete structures (fib 2004), several additions and considerations must be

made in order to account for the increased flexibility of timber. The moment capacity of a post-

tensioned timber joint is a function of the rotation at that joint. This rotation must be calculated from

the total building drift (θT) and is made up of five separate rotation contributions as shown in Figure 2.

The first three rotation contributions comprise of the elastic rotations of the beam (θb), column (θc) and

joint panel (θj) (Buchanan and Fairweather 1993; Newcombe et al. 2010a). The beam and column

rotations can be simply calculated in relation to the moment at the connection using common member

deflection equations. Due to the low shear modulus of timber, the large axial forces in the beams

induced by the post-tensioning result in large elastic shear deformations in the joint panel which must

M. Simonetti T. Smith F. C. Ponzo A. Di Cesare S Pampanin D Nigro 3

also be accounted for. The final two rotation contributions make up the total rotation of the connection

(θcon). These two contributions are defined as the interface rotation (θint) and the gap rotation (θgap) and

are calculated and act separately. Before decompression occurs an initial stiffness relating to the

compression perpendicular to the grain on the column face is present. This initial stiffness is not

captured by the design procedure used to calculate the post decompression behaviour and therefore

must be evaluated separately. This ‘interface rotation’ thus acts before the decompression point of the

beam (i.e. before the gap opens) and the gap rotation occurs after decompression.

Following decompression the Modified Monolithic Beam Analogy (MMBA) is used (Palermo

2004). This method draws an analogy between the deformations and stresses in a hybrid joint and

those occurring in a standard concrete connection. This procedure can be simply applied to the design

of a post-tensioned timber connection provided a few simple considerations are made. The procedure

involves the imposing of the gap rotation (θgap) and the initial estimation of a neutral axis value (c).

Using the design procedure, the forces in the post-tensioning tendon, compression in the timber, and

the force in any dissipative element are calculated. Force equilibrium is then checked and if not

satisfied a new value of c is selected. Once force equilibrium is verified the moment contributions are

added in series about a common point.

Figure 2. Deformation in a post-tensioned timber frame

NUMERICAL MODELLING

Modelling of post-tensioned timber beam/column-foundation connections (local modelling)

From the conception of the post-tensioned jointed ductile concept it has been clear that the nature of

the controlled rocking mechanism lent itself well to the use of a lumped plasticity approach in

modelling (Palermo et al. 2005b). This method of modelling has been used in the design predictions

of the beam-column and column-foundation joint with and without the dissipating steel angles.

Recently two methods of modelling the member interface (i.e. the lumped plasticity) have been

studied and applied to post-tensioned timber; the first a series of parallel rotational springs, the second

a more complex multi-spring model (Figure 3). Although when not considering secondary effects such

as beam elongation or timber crushing the simpler rotational spring model has been shown to be

sufficiently accurate (Newcombe et al. 2010b), the rotational spring model does not predict directly

the value of post-tension force (Tpt) or the neutral axis depth (c) nor does it directly calculate the force

(Ts or Cs) or displacement (∆s) of dissipative elements.

Figure 3. The multi-spring (left) and rotational spring (right) interface model

4

As mentioned above the joint panel rotations of a post-tensioned timber frame are not negligible

and in order to model this a rotational spring is added in the joint panel region. Previously all

modelling of post-tensioned timber beam-column joints has been performed using the finite element

program RUAUMOKO (Carr 2006) using both multi-spring and rotational spring approaches

(Newcombe et al. 2010b). During this research, the more widely used SAP2000 structural calculation

program (Computers and Structures 2004) was used and compared with testing results.

Spring calibration

All analysis results presented have been calibrated against the moment rotation response provided by

the design procedure described above with the parameters of the rotational springs being set to match

the predicted rotational response. Post-tensioning was represented using tri-linear elastic elements for

both models with bounded Ramberg-Osgood (Kaldjian 1967) and Buoc-Wen (Wen 1980) rotational

spring models used to represent the steel elements in the RUAUMOKO and SAP2000 model,

respectively.

Calibration of the multi-spring element was performed by altering the stiffness of the spring

elements until the three parameters of moment (Mt), post-tension force (Tpt) and neutral axis depth (c)

accurately replicated analytical values for a set level of initial post-tensioning force. Following

calibration it was simply necessary to change the initial compression value across the gap (due to post-

tensioning elements) in order to predict the performance of the different initial testing states. As the

multi-spring model can accurately predict the gap opening, and consequent displacements, axial

springs were used to represent the performance of the yielding steel angle reinforcement. These were

calibrated against testing results obtained for a single angle element subjected to cyclic axial loading

and a Bounded Ramberg-Osgood hysteric rule was used. SAP2000 does not contain a multi-spring

model therefore only a rotational spring model was used at the beam-column joint interface. The input

of the interface elements into the two models is essentially identical however the length of the

rotational spring differed slightly. In the RUAUMOKO analysis the standard practice of setting the

spring length to 1 mm was employed however this proved unstable when applied to the SAP model

and a 10 mm spring length was used.

Modelling of a post-tensioned timber frame (global modelling)

Full post-tensioned timber beam-column joints and frames are modelled through the combination of

the rotational/multi-spring elements described above with elastic beam elements. Post-tensioned

timber frames are represented with a combination of rotational springs being assembled to represent

the post-tensioning, reinforcement and joint panel contributions (Figure 4).

Figure 4 shows a perfectly pinned based column-foundation connection for the frame. When

dissipative reinforcement is applied to the column base it provides moment capacity. This moment

capacity acts in addition to the moment capacity provided by gravity (through the column axial load).

Due to this moment capacity, a truly pinned assumption is likely to over-predict displacement and

under-predict base shears. Figure 5 shows possible options, of increasing complexity, which can be

used in order to better represent the response of the column-foundation connection. The use of a fixed

based solution is considered adequate in predicting response until column-base gap opening, however,

following gap opening it is likely to under-predict displacement and over-predict base shear. This is

due to the fixed based model being infinitely stiff and not being able to account for the sudden drop in

stiffness when gapping and steel yielding occurs.

The third option shown in Figure 5 allows for the drop in stiffness due to gap opening through

the use of a rotational spring calibrated against the post-tensioned timber design procedure described

above. During this calibration the static value (i.e. without lateral earthquake loading) of column axial

load is used, however, during seismic loading this value will not remain constant, a factor which is not

considered in the rotational spring column-foundation model. The use of a calibrated multi-spring as

shown in the far right diagram in Figure 5 provides the most accurate representation of column

response. This option accounts for the sudden loss of stiffness due to gap opening but also allows for

the change in capacity due to changing axial load. As mentioned above SAP2000 does not have a

proprietary multi-spring model however two axial gapping springs (gap elements as defined in

SAP2000) can be used to create a similar effect. This two-spring approach is, however, considered to

crude for use at the beam-column joint interface.

b)


Figure 4. SAP2000 and RUAUMOKO frame numerical models

Figure 5. Base connection modelling options considered for frame numerical model

EXPERIMENTAL TEST SET UP

Beam-column joint quasi-static testing

The full-scale beam-column joint (Smith et al. 2014), shown in Figure 6, was made from glulam grade

GL32h (EN 1995-1-1 2004) and both column and beam were 483 x 240 mm. The high strength steel

tendon (Fy = 1530 N/mm2; ft = 1760 N/mm

2) placed at the centre of the beam had a diameter of 15.2

mm and was replaced by a 26.5 mm high strength steel (fy = 1050 N/mm2 E = 170 kN/mm

2) bar when

initial post-tensioning forces were above 150 kN. Due to the nature of timber as an orthotropic

material it is undesirable to have excessive loading in the perpendicular to grain direction. As

displayed in Figure 6b, the column section (where compression was perpendicular to the grain) was

reinforced using ϕ 8 mm, 120 mm length screws. A steel tube of 100 mm diameter was glued into the

beam with a protruding length of 40 mm. This transferred a vertical load to the column.

On completion of a series of post-tensioned only testing, dissipation was provided through the

use of steel angles which were reduced in a certain area to a design width in order to obtain desired

hysteretic performance. This method of dissipation is based on the DIS CAM concept developed by

Dolce et al. (2006). A section of mild steel equal angle 100x100x10 mm was milled down to provide a

region of concentrated yielding and thus hysteretic energy dissipation. The variables used to control

the characteristics of angle performance were the thickness of the worked area (tA), the height of the

worked area (LA) and the length of the angle (bA). The width of the angle used in testing was bA = 80

mm and the strength of steel was fyk = 355 MPa. To characterize the stand alone performance of the

steel angle testing was performed along with finite element analysis (Ponzo et al. 2011).

The test specimen was loaded quasi-statically with a load protocol which applied increasing

levels of inter-storey drift (as top of column displacement) with two cycles being applied at each drift

level. A maximum drift level of 2.5% was reached in each test.

6

Figure 6. a) Beam-column joint and b) details showing dissipating elements and shear transfer system

Three storey dynamic frame testing

The three storey test frame (Ponzo et al. 2012) shown in Figure 7 was made from glulam grade

GL32h. A scale factor of 2/3 was applied to a prototype structure resulting in an interstorey height of 2

m and a building footprint of 4 m x 3 m. The building was designed to represent an office structure

(live loading Q = 3 kPa) with the final floor being a rooftop garden. All design was performed in

accordance with the current version of the Italian design codes (NTC 2008).

Figure 7. Experimental model constructed in UNIBAS lab

Beam-column joints were detailed in the same manner as the beam-column testing with the use

of internal tube shear keys and horizontal screw reinforcing. The flooring of the building was made

from solid glulam panels. As with the beam-column, testing was performed with and without the

addition of dissipative steel reinforcing angles at the beam-column connections. Instrumentation of the

structure consisted of a combination of potentiometers, load cells and accelerometers.

Seismic inputs

The testing input was a set of 7 spectra compatible earthquakes selected from the European strong-

motion database. The code spectrum used to select the set of seven earthquakes was defined in

accordance with the current Eurocode for seismic design (EN 1998-1:2003 2003) giving a PGA for the

design spectrum of ag = 0.44 g (Soil class B – medium soil). A smaller set of three ground motions

was selected which provided the best representation of the design spectra as shown on the left of Table


1. This smaller set of seismic intensities was progressively increased in acceleration until the design

performance criterion was achieved.

Table 1. Characteristics of selected earthquakes and comparison with the code spectrum

EXPERIMENTAL TESTING RESULTS

Beam-column joint quasi-static testing

The moment/force – inter-storey drift/displacement responses of a selection of beam-column specimen

testing are shown in Figure 8. The post-tensioned only testing plots, shown in Figure 8a, display the

significant increase in moment resistance that occurred with the increase in initial tendon load. It can

be seen that an increase in initial tendon load from 50 kN to 250 kN led to a four times increase in

connection capacity at a drift of 2.5%. This graph also displays that without the addition of special

dissipation devices the fact that all materials in the system remain elastic meant that nominal energy

release occurred.

-80 -40 0 40 80Displacement (mm)

-3 -2 -1 0 1 2 3

Drift (%)

-30

-25

-20

-15

-10

-5

0

5

10

15

20

25

30

Forc

e to C

olu

mn T

op (

kN

)

-100

-80

-60

-40

-20

0

20

40

60

80

100

Mom

ent (k

Nm

)

50kN Initial

100kN Initial

150 kN Initial

200kN Initial

250kN Initial

Moment/Force to Column Top v Drift/Displacement


-3 -2 -1 0 1 2 3

Drift (%)

-30

-25

-20

-15

-10

-5

0

5

10

15

20

25

30

Forc

e to C

olu

mn T

op (

kN

)-100

-80

-60

-40

-20

0

20

40

60

80

100

Mom

ent (k

Nm

)

PT ONLY 100kN Initial

PT 100kN Initial Double Angle



-3 -2 -1 0 1 2 3

Drift (%)

-30

-25

-20

-15

-10

-5

0

5

10

15

20

25

30

Forc

e to

Colu

mn T

op (

kN

)

-100

-80

-60

-40

-20

0

20

40

60

80

100

Mom

ent (k

Nm

)

PT ONLY 150 kN Initial

PT 150 kN Initial Double Angle



-3 -2 -1 0 1 2 3

Drift (%)

-30

-25

-20

-15

-10

-5

0

5

10

15

20

25

30

Forc

e to

Colu

mn T

op (

kN

)

-100

-80

-60

-40

-20

0

20

40

60

80

100

Mom

ent (k

Nm

)

PT ONLY 200 kN Initial

PT 200 kN Initial Double Angle


Figure 8. Post-tensioned (PT) beam-column connection testing results: a) PT Only Testing, b) 100 kN Initial

with and without Dissipation, c) 150 kN Initial with and without Dissipation and d) 250 kN Initial with and

without Dissipation

Three storey dynamic frame testing

A series of shaking table tests with increasing PGA levels were performed both with and without

dissipative devices. Figure 9 shows the total input force as measured by the dynamic actuator versus

first floor drift at 75% and 100% of PGA intensity for model without and with dissipative steel angles,

respectively, considering three seismic inputs. The figure clearly shows the development of the typical

flag-shaped behaviour when dissipative steel angles were added as was seen for the beam-column

ID Code Location Mw PGA (g)

001228x Izmit, Turkey

7.6 0.357

000196x Montenegro

6.9 0.454

000535y Erzican,

Turkey

6.6 0.769 0

10

20

30

0 1 2 3Tsc (sec)

Sa (m/sec2) 196

535*1.5

1228*1.5

Average

Code Spectrum

8

quasi-static testing described above. Figure 10 shows photos of the maximum response of the structure

during testing with the dissipative reinforcing subjected to ground motion 000535y at a PGA intensity

level of 100%.

-4 -2 0 2 4

-150

-100

-50

0

50

100

150

Ram

forc

e (

kN

)

-4 -2 0 2 4

First floor drift (%)

-4 -2 0 2 4

001228x 000196x 000535y

Shaking foundation ram force versus first floor drift

-4 -2 0 2 4

-150

-100

-50

0

50

100

150

Ram

forc

e (

kN

)

-4 -2 0 2 4

First floor drift (%)

-4 -2 0 2 4

001228x 000196x 000535y

Shaking foundation ram force versus first floor drift

Figure 9. Shaking foundation ram force versus first floor drift for test model a) without dissipation (75%PGA)

and b) with dissipation (100%PGA)

Figure 10. Maximum positive and negative drift response of the structure with dissipation (000535y at 100%).

NUMERICAL MODELLING COMPARISONS

Non-linear static modelling of beam-column joint

Comparisons between the results of the numerical analysis and testing for the non-linear static beam

column are shown in Figure 11. As can be seen the performance comparison of the PT ONLY test

response is good for all cases and models studied. The initial stiffness of the beam-column joint, an

important parameter in time-history analysis, is accurately predicted for all cases. Comparisons of the

models with the inclusion of the steel dissipative angles are displayed in terms of the penultimate test

and numerical analysis cycle. This cycle has been chosen as the ultimate cycle of testing had reduced

capacity due to the onset of angle failure. As shown, all of the modelling methods provided adequate

prediction of the beam-column joint loading behaviour. It can be noted however that both rotational

b)

a)


models do not adequately reproduce the unloading behaviour of the joint. This is due to the way in

which the angle elements are modelled. In the multi-spring model only positive displacement is

applied which creates a larger hysteretic area than the rotational spring model where loading is also

reversed (+ve and –ve rotations).

The failure to replicate unloading impacts on the hysteretic damping prediction of the model,

and the value of equivalent viscous damping (related to the ability of joints to dissipate input energy

through yielding). For the test cycle shown in Figure 11 the values of equivalent viscous damping are

shown in Table 2. As shown, both rotational spring models tend to under estimate the value of

damping while the multi-spring model overestimates damping.

The models presented all provide reasonably accurate predictions of the non-linear static

response of the beam-column joint. The rotational spring models have been shown to be almost

identical between the two programmes used with the only difference being the selection of hysteric

rule used based on the available hysteric rules of each selected calculation program.

0 20 40 60 80Displacement (mm)

0

5

10

15

20

25

Forc

e (

kN

)

Test Results SAP2000 Rotational Ruaumoko Rotational Ruaumoko Multi-Spring

50 kN Initial


0

5

10

15

20

25

Fo

rce

(kN

)

150 kN Initial


0

5

10

15

20

25

Forc

e (

kN

)

250 kN Initial


0

10

20

30

Fo

rce

(kN

)

PT 100 kN2 Angles


0

10

20

30

Forc

e (

kN

)

PT 150 kN2 Angles


0

10

20

30

Fo

rce

(kN

)

PT 250 kN2 Angles

Figure 11. Comparison between Testing Results and Modelling Options

Table 2. Values of equivalent viscous damping (in %) for testing and numerical predictions

Test SAP2000

Rot.

RUA.

Rot.

RUA.

Multi

100 kN 2 Angle 14.7 13.2 11.6 17.2

150 kN 2 Angle 12.5 9.9 9.8 14.4

250 kN 2 Angle 7.8 5.7 6.6 10.5

Dynamic model identification of three-storey frame

Dynamic model identification testing was carried out in order to find the natural frequencies of

vibration considering two different excitation sources: hammer impact excitations and sine-sweep

ground motion. In Table 2 the first three periods of the frame, considering the hammer impact test

response on the third floor of the structure with dissipative devices, are compared with the 2-D

SAP2000 and RUAUMOKO numerical predictions. The numerical blind predictions (Ti,num) for both

models matched well with experimental results Ti,exp

Table 3. Comparison between dynamic experimental behaviour and SAP2000 blind predictions

Mode Ti,exp (sec) Ti,num SAP (sec) Ti,num RUA (sec)

1 0.53 0.53 0.50

2 0.13 0.12 0.12

3 0.06 0.05 0.05 0 5 10 15 20 25

Frequency (Hz)

T3 =

0.0

6s

T2 =

0.1

3s

T1 =

0.5

3s

10

Dynamic comparisons

As mentioned above the fixity of the base of the column has a significant impact on the total response

of the non-linear dynamic numerical model. In this section the experimental outcomes are compared

with SAP2000 and RUAUMOKO numerical results considering the more accurate, but most complex,

multi-spring base model.

The experimental outcomes of the dynamic testing are compared in Figure 3 with the SAP2000

and RUAUMOKO NTHA results considering the 3rd floor displacements for three test cases

(000196xa, 000535ya and 001228ya) with an intensity level of 75% of the design PGA with and

without dissipative steel angles. As shown both models provided very similar and sufficiently accurate

results when compared to testing. It can be seen however that during certain sections of structural

response the models were out of phase with the test structure. In all cases however this was during the

tail of the response and did not impact on the prediction of maximum values.

0 5 10 15 20

-0.15

-0.05

0.05

0.15

0 5 10 15 20

-0.15

-0.05

0.05

0.15

0 5 10 15 20

-0.15

-0.05

0.05

0.15

0 5 10 15 20

-0.15

-0.05

0.05

0.15

0 5 10 15 20

-0.15

-0.05

0.05

0.15

0 5 10 15 20

-0.15

-0.05

0.05

0.15

Figure 12. 3rd floor displacement comparisons between SAP2000, RUAUMOKO and testing results without (on

the left) and with (on the right) dissipative

Three key indicators have been selected for comparison between the testing results and the

numerical models and are displayed in Figure 13: the maximum 1st level drift, the maximum 3rd level

acceleration and the maximum base shear for the configuration with and without steel angles at

varying PGA intensity levels. As shown in Figure 13, the numerical predictions provided an accurate

representation of the experimental performance for both numerical models showing differences of less

than 20 – 25% when compared with experimental outcomes. For this test frame the SAP2000 model

provided a more accurate prediction of maximum test response.

SAP2000

EXPER.

RUAU.

535

1228

196


0 20 40 60 80 100

0

0.4

0.8

1.2

1.63rd

Leve

l a

cc. (g

)With dissipation

0 20 40 60 80 100

0

20

40

60

80

100

Ba

se s

he

ar

(Vb, kN

)

0 20 40 60 80 100

0

0.5

1

1.5

2

2.5

1st

Leve

l dri

ft (

rad)

Average Testing

Average SAP

Average RUA

0 20 40 60 80 100

0

0.4

0.8

1.2

1.6

3rd

Leve

l acc. (g

)

Without dissipation

0 20 40 60 80 100

Percentage of PGA

0

20

40

60

80

100B

ase s

hea

r (V

b,

kN

)

0 20 40 60 80 100

0

0.5

1

1.5

2

2.5

1st L

eve

l dri

ft (

rad

)

Average Testing

Average SAP

Average RUA

Figure 13. Comparison between SAP2000, RUAUMOKO and experimental results.

CONCLUSIONS

This paper has presented an overview of the non-linear static and dynamic modelling for the

prediction of post-tensioned timber frame response. Recent quasi-static and dynamic post-tensioned

timber testing performed at the University of Basilicata in Potenza Italy has then been used to assess

the adequacy of these models in predicting response.

The models consisted of a series of elastic elements and non-linear springs which have been

calibrated against the current post-tensioned timber design procedure that has also been briefly

described. Two analysis programmes, RUAUMOKO and the more widely spread SAP2000 were used.

The ability of the non-linear model to predict the static local (beam-column joint) behaviour has

been verified through comparison against quasi-static beam-column testing. All models considered

accurately represented initial and non-linear stiffness as well as providing sufficiently accurate

representation of hysteretic energy dissipation.

The ability of the non-linear model to predict dynamic global (frame) response has been verified

through comparison against 2/3rd

scale dynamic frame testing. Firstly the dynamic characteristics (first

three natural periods) of the test frame were compared favourably against results provided by the

numerical models. Secondly the key parameters of third floor displacement, maximum base shear,

maximum drift and maximum third floor acceleration were compared. All values were accurately

(within 20%) predicted with the SAP2000 programme providing improved accuracy for this test

frame. During testing a complex multi-spring model was used at the base of the column which may

not be feasible for use outside of research applications.

In a world were practicing engineers are relying increasingly on the use of non-linear static

(push-overs) and dynamic (NLTH) analysis it is important that the models used are robust and able to

predict system response. Current methods for the non-linear analysis of post-tensioned timber

buildings have been compared against a selection of test results. This comparison has shown that the

modelling techniques were able to predict with sufficient accuracy both local and global response

providing further confidence in their use in design.

12

ACKNOWLEDGEMENT

Authors would like to acknowledge the financial support of the Structural Timber Innovation

Company (STIC, New Zealand) and FederLegnoArredo (FLA, Italy).

REFERENCES

Buchanan, A., Deam, B., Fragiacomo, M., Pampanin, S., and Palermo, A. (2008). "Multi-Storey Prestressed

Timber Buildings in New Zealand." Journal of the International Association for Bridge and Structural

Engineering, 18(2), 166-173.

Buchanan, A. H., and Fairweather, R. H. (1993). "Seismic Design of Glulam Structures." Bulletin of the New

Zealand Society for Eathquake Engineering, 26(4), 415-436.

Carr, A. (2006). "RUAUMOKO." A. Carr, Christchurch, New Zealand, Inelastic Dynamic Analysis Software.

fib Bulletin 27. (2004). "Seismic Design of Precast Concrete Building Structures." fib

CSI Computers and Structures Inc. (2004). "SAP2000: Static and Dynamic Finite Analysis of Structures."

Berkeley, CA, USA.

Dolce, M., Moroni, C., Nigro, D., Ponzo, F. C., Santarsiero, G., Croce, M. D., Canio, G. D., Ranieri, N.,

Caponero, M., Berardis, S., Goretti, A., Spina, D., Lamonaca, B., and Marnetto, R. (2006). "TREMA

Project Experimental Evaluation of the Seismic Performance of a R/C 1/4 Scaled Model Upgraded with

the DIS-CAM System " 2nd International fib Congress, Naples, Italy.

NTC. (2008). "Norme Tecniche per le Costruzioni." Il Ministro delle Infrastrutture.

Kaldjian, M. J. (1967). "Moment-curvature of Beams as Ramberg-Osgood functions." Journal of the Structural

Division, American Society of Civil Engineers, 93(ST5), 53-65.

Newcombe, M., Cusiel, M., Pampanin, S., Palermo, A., and Buchanan, A. H. (2010a). "Simplified Design of

Post-tensioned Timber Frames." CIB W18 Workshop on Timber Structures, Nelson, New Zealand.

Newcombe, M. P., Pampanin, S., and Buchanan, A. H. (2010b). "Numerical Modelling and Analysis of a Two-

Storey Post-Tensioned Timber Frame with Floor Diaphragms." 14th European Conference on

Earthquake Engineering, Ohrid, Republic of Macedonia.

Palermo, A. (2004). "The Use of Controlled Rocking in the Seismic Design of Bridges," Politecnico di Milano,

Milan.Doctor of Engineering.

Palermo, A., Pampanin, S., Buchanan, A., and Newcombe, M. (2005a). "Seismic Design of Multi-Storey

Buildings using Laminated Veneer Lumber (LVL)." 2005 New Zealand Society for Earthquake

Engineering Conference, Wairakei Resort, Taupo, New Zealand.

Palermo, A., Pampanin, S., and Carr, A. (2005b). "Efficiency of Simplified Alternative Modelling Approaches to

Predict the Seismic Responce of Precast Concrete Hybrid Systems." fib symposium "Keep Concrete

Attractive, Budapest, Hungary.

Ponzo, F., Di Cesare, A., Nigro, D., and Smith, T. (2011). "Dissipative Steel Angles Devices for the Increased

Seismic Performance of Low Level Damping Systems." XXIII Congresso CTA, Lacco Ameno, Ischia,

Italy.

Ponzo, F. C., Smith, T., Di Cesare, A., Pampanin, S., Carradine, D., and Nigro, D. (2012). "Shaking Table Test

of a Multistorey Post-tensioned Glulam Building: Design and Construction." 12th World Conference on

Timber Engineering, Auckland, New Zealand.

Priestley, N., Sritharan, S., Conley, J., and Pampanin, S. (1999). "Preliminary Results and Conclusions From the

PRESSS Five-Story Precast Concrete Test Building." PCI Journal(November-December 1999), 42-67.

Smith, T., Ludwig, F., Pampanin, S., Fragiacomo, M., Buchanan, A., Deam, B., and Palermo, A. (2007).

"Seismic Response of Hybrid-LVL Coupled Walls Under Quasi-Static and Pseudo-Dynamic Testing."

2007 New Zealand Society for Earthquake Engineering Conference, Palmerston North, New Zealand,

8.

Smith, T., Ponzo, F. C., Di Cesare, A., Pampanin, S., Carradine, D., Buchanan, A. H., and Nigro, D. (2014).

"Post-tensioned Glulam Beam-Column Joints with Advanced Damping Systems: Testing and

Numerical Analysis." Journal of Earthquake Engineering, 18(1), 147 - 167.

EN 1998-1:2003. (2003). "Design of structures for earthquake resistance - Part 1: General rules, seismic actions

and rules for buildings." European Committee for Standardization.

EN 1995-1-1:2004. (2004). "Design of Timber Structures Part 1-1: General - Common Rules and Rules for

Buildings." European Committee for Standardization.

Wen, Y. (1980). "Equivalent Linearization for Hysteretic Systems under Random Excitation." ASME Journal for

Applied Mechanics, 47(1), 150-154.

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