Shaking Table Testing of a Multi-Storey Post-tensioned ... Table Testing of a Multi-Storey Post-tensioned Timber Building equipped with Advanced Damping System PONZO F ... drift (θd)

Shaking Table Testing of a Multi-Storey Post-tensioned Timber

Building equipped with Advanced Damping System

PONZO F.C.+, DI CESARE A., SIMONETTI M., NIGRO D. University of Basilicata

V.le Ateneo Lucano, 10 – 85100 Potenza, ITALY

+ [email protected] http://www2.unibas.it/ponzo/Sito/MAIN.html

SMITH T., PAMPANIN S. University of Canterbury,

Christchurch NEW ZEALAND

CARRADINE D. Branz,

Wellington NEW ZEALAND

Abstract: - This paper describes the main results of shaking table testing performed on a post-tensioned timber

frame building equipped with an advanced damping system. This experimental campaign, carried out in the

structural laboratory of the University of Basilicata in Potenza, Italy, is part of a series of experimental tests in

collaboration with the University of Canterbury in Christchurch, New Zealand. The specimen is 3-dimensional,

3-storey, 2/3rd scale and is made by using post-tensioned timber frames in both directions. During the testing

programme, the specimen was tested both with and without the addition of dissipative steel angle reinforcing

which was designed to yield at a certain level of drift. These steel angles release energy through hysteresis

during seismic loading, thus increasing damping. This paper discusses the main results of the experimental

testing and presents comparisons with numerical outcomes using two non-linear finite element codes: SAP2000

and RUAUMOKO.

Key-Words: - Shaking table test, Timber Buildings, Damping system, Post-Tensioning, Passive control, Steel dissipating devices, Pres-Lam technology.

1 Introduction This paper describes the main results of shaking

table testing performed on a multi-storey post-

tensioned timber frame building equipped with an

advanced damping system. The study evaluates the

feasibility of applying jointed ductile post-

tensioning technology, originally conceived for use

in concrete structure [11], to glue laminated timber

(glulam). The aim of the project is to evaluate the

seismic performance of the system and further

develop the system for use in multi-storey timber

frame buildings. The post-tensioned timber concept

(under the name PRES-LAM) has been developed at

the University of Canterbury and extensively tested

in the structural laboratory of the university [6, 12].

This technology enables the design of buildings

having large bay lengths (8-12m), reduced structural

sections and lower foundation loads with respect to

traditional construction methods. The PRES-LAM

concept uses post-tensioning technology in order to

connect structural timber elements. The structural

response of a post-tensioned timber frame centres

on the moment-rotation response of its connections.

In order to design all structural characteristics a

certain starting point must be selected as the design

drift (θd). From this point all of the elastic

contributions of the frame must be subtracted (beam

rotation, column rotation, joint panel rotation,

interface rotation). Having obtained the rotation to

be imposed at the beam-column joint the Modified

Monolithic Beam Analysis (MMBA) method is used

in order to calculate the moment capacity of the

Advances in Mathematics and Statistical Sciences

ISBN: 978-1-61804-275-0 308

rocking joint. From this, the required value of initial

post-tensioning and steel reinforcing can be defined

and the key to this type of system is made up of the

ratio β between the moment resistance provided by

the post-tensioning and the moment resistance

provided by the dissipation (Fig 1).

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

Although a simple concept, this ratio provides the

cornerstone in the understanding of system

performance. Clearly, during design this choice

affects both damping and moment capacity of the

system and therefore changing this value will have a

direct effect on both capacity and demand. In Stage

One of PRES-LAM project a full-scale beam-

column joint was designed, fabricated, constructed

and tested at the Structural Laboratory of UNIBAS.

This experimental programme was completed

midway through 2011 providing excellent results

[13] and began to answer key questions regarding

system performance. During testing the application

of the post-tensioned timber concept to glulam

timber was confirmed and the system displayed the

same excellent performance under static loading as

when the system was employed with laminated

veneer lumber (LVL). In the current stage of the

project a 3-dimensional, 3-storey timber structure

(Figg. 2 and 3) has been dynamically tested in real

time in the UNIBAS lab. During the experimental

campaign the size of the structural members,

building layout and mass was not altered, however

different values of post-tensioning and steel

reinforcing moment capacity contributions were

investigated. The dissipative devices used were

based on yielding steel angles which activate at low

drift levels, both increasing the moment capacity of

the system and adding energy dissipation (thus

reducing seismic load through damping) without

inducing plastic deformations in other elements.

This paper will describe briefly the detailing, the

testing set-up of the experimental model and the

testing results with and without dissipation. Finally,

comparisons between experimental outcomes and

SAP2000 and RUAUMOKO numerical predictions

will be also shown.

2 Testing Structure The prototype structure is three stories in height

and has a single bay in both directions. The

interstorey height of the prototype building is 3 m

and the frame footprint is 6 m by 4.5 m. The

building has been designed to represent an office

structure (live loading Q = 3 kPa) with the final

floor being a rooftop garden. The flooring of the

building is made by solid glulam panels. The lateral

resistance of the building is governed by seismic

loading. The test frame is made from glulam grade

GL32h (EN 1995-1-1 2004) and has been

constructed in the UNIBAS lab in the brief time of

two days by only four workers. All design has been

performed in accordance with the current version of

the Italian design code [7]. A scale factor of 2/3rd

has been applied to the prototype structure resulting

in an interstorey height of 2m and a building

footprint of 4m by 3m. In order to evaluate the

required amount of mass to be added to the test

frame the masses of the prototype building have

been scaled by the factor of 2/3rd observing mass

similitude related to the Cauchy-Froude similitude

laws. The additional mass required is made up of a

combination of concrete blocks and steel hold

downs with 12 blocks being spread out across each

floor. 50 sensors have been located in the test

structure to evaluate the experimental dynamic

behaviour and connection deformations in real time.

For more information regarding the specimen

design, connection detailing and testing set-up

please refer to [10].

The shaking table tests were carried out using the

testing apparatus (Fig4) of the seismic laboratory of

the University of Basilicata. The foundation had a

single degree of freedom in the N-S direction and

consisted of a steel frame made up of HEM300

structural steel sections.

Fig. 2. Frame assembling in UNIBAS lab


ISBN: 978-1-61804-275-0 309

Fig. 3. Experimental model built in UNIBAS lab

Fig. 4. Shaking foundation in UNIBAS lab.

The foundation was driven by an MTS 244.41

dynamic actuator characterized by a capacity of ±

500 kN and ± 250 mm stroke. The actuator was

fixed to a hinge at the base of the foundation and

pushed against the 6 m thick strong wall used during

the beam-column test programme. Pressure for the

actuator was provided by 3 MTS SilentfloTM 505-

180 hydraulic pumps. The foundation was situated

upon 4 SKF frictionless sliders (model LLR HC 65

LA T1) with one each situated under the four

columns. These sliders sat upon a series of levelling

plates set upon grout-pads to ensure that a system

with a coefficient of friction of less than 1% was

obtained. The table was displacement controlled and

therefore seismic input was supplied as table

displacement over a specific time interval.

2.1 Energy dissipating devices During dynamic testing energy dissipation devices

have been added to the structure in order to add

strength and damping and reduce displacements

without increasing of accelerations or base shears.

This passive hysteretic devices are made by yielding

steel angles and have been located in beam-column

and column-foundation connections (Fig. 5).

Fig. 5. Details of beam-column and column-foundation connections.

The dissipative system is based on the DIS-CAM

system [3] developed at the University of Basilicata

in Potenza, Italy and consists of the use of low

carbon steel angles designed to yield in a controlled

manner. These angles not only provide dissipative

capacity (thus reducing demand) but also

significantly contribute to capacity. An extended

experimental campaign has been performed at

UNIBAS in order to define the angle forms to be

used in the dynamic experimental model. Following

this two different methods of creating a

concentrated yield area were selected both based on

the concept of creating a controlled zone of

concentrated yielding. The first option (taken from a

section of square hollow section tube) involves the

removal of two holes and the second of these

involves the milling down of a certain section of an

equal steel and. Milled steel angle ID5 configuration


ISBN: 978-1-61804-275-0 310

has been chosen for dynamic testing with

dissipation adopting the angled cut as particular

form of transition. This type of transition proved to

be successful and simple and is now recommended

for all milled angle manufacture.

For more information regarding the experimental

campaign, please refer to [1].

Fig. 6. Steel angles device for beam-column joint selected for dynamic testing (with dissipation) and experimental Force-Displacement device characterisation.

2.1 Seismic Input The testing input was a set of 7 spectra compatible

earthquakes selected from the European strong-

motion database (Fig. 7).

0

10

20

30

0 1 2 3Tsc (sec)

Sa (m/sec2

) 196

535*1.5

1228*1.5

Average

Code Spectrum

Fig. 7. Spectral characteristics of selected earthquakes and comparison with the Code Spectrum considered

Seismic loading during testing has been mono-

directional applied along the north-south axis of the

building. The seismic intensities were progressively

increased until the design performance criterion was

achieved. The code spectrum was defined in

accordance with the current Eurocode for seismic

design (EN 1998-1:2003 2003) having a PGA of

ag= 0.35 and a soil factor of S = 1.25 (Soil class B –

medium soil) giving a PGA for the design spectrum

of ag= 0.4375. The elastic response spectra of three

accelerograms used in blind numerical predictions

SAP 2000 and RUAUMOKO are shown below with

their Average and Code Spectrum.

3 Numerical modelling From the conception of the post-tensioned jointed

ductile connection 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.

This approach combines the use of elastic

elements with springs, which represent plastic

rotations in the system. Recent studies have also

recognized the importance of modelling and

accounting for the elastic joint rotation in the

calculation of rocking connection rotation, therefore

a rotational spring was added in the joint panel

region.

Fig. 8. Numerical model of the test frame, beam-column joint and column/foundation interface.

This procedure can be applied to the design of a

timber hybrid connection provided a few simple

considerations are made. This method of modelling

has been used in the predictive modelling of the

structural behaviour under the planned input

loading. The specimen was modelled (Fig. 8)

considering rotational springs to predict the moment

rotation response and the effects of dissipation of

0 5 10 15 20 25

Displacement (mm)

-25

-20

-15

-10

-5

0

5

10

15

20

25

30

35

Fo

rce

(k

N)

ID5 A

ID5 B


ISBN: 978-1-61804-275-0 311

the post-tensioned beam-column joints and a multi-

spring column/foundation interface to match the

structural rocking movement. Rotational springs

have been calibrated against the design procedure

for the moment calculation of a hybrid joint

presented in Appendix B of the New Zealand Code

for the Design of Concrete Structures [8]. Post-

tensioning was represented using tri-linear elastic

elements for both models with bounded Ramberg-

Osgood and Buoc-Wen rotational spring models

used to represent the steel dissipative angles in the

RUAUMOKO and SAP2000 model respectively

[2].

3 Shaking Table Tests In the first series of tests, carried out on July 2013,

the structure was first tested with the addition of the

dissipative reinforcing angles. Upon completion the

angles were removed and testing without dissipation

was performed.

Figure 9 shows the maximum average drift of the

three levels of the test structure for the

configurations with and without dissipative

reinforcing. The figure clearly shows that under

dynamic loading the addition of the dissipative

angle reinforcing reduced maximum drifts under the

same input acceleration. The figure also shows that

the two systems responded very similarly in terms

of drift for low levels of the seismic action. This

indicated that the presence of dissipative reinforcing

will not impact on serviceability level response.

This is due to the fact that before this point gap

opening has not occurred and the dissipative

reinforcing remains nominally loaded.

Following the PGA50% intensity level the

response of the frame differed with a rapid increase

of drift levels in the case without dissipation while

for the dissipative case this rapid increase occurred

following PGA75% testing. The presence of the

steel dissipative angles led to a 32% decrease in

average first floor drift between testing with and

without the dissipative angles at PGA75%. The

point of gap-opening is a function only of the

amount of initial post-tensioning across the

interface, however in a dissipative reinforced

system, following gap-opening the joint also has the

stiffness and strength provided by the angles in

order to resist rotation leading to later onset of non-

linear behaviour.

Figure 9 shows also the average maximum floor

accelerations for the two test configurations with

increasing percentages of PGA. The figure also

shows that as levels of PGA% increased the

differences in floor acceleration between the case

with and without dissipation decreased.

0 20 40 60 80 100

0

1

2

3

4

5

Inte

rsto

rey d

rift (%

)

Average PT100_0.60

Average PT100_1.00

0 20 40 60 80 1000 20 40 60 80 100

1st Floor 2nd Floor 3rd Floor

Solid lines denote West

Dashed lines denote East

0 0.13 0.26 0.39 0.520 0.13 0.26 0.39 0.52

Average maximum PGA

0 0.13 0.26 0.39 0.52

(PGA %)

0 20 40 60 80 100

0

0.4

0.8

1.2

1.6

Flo

or

accele

ration (

g)

Average PT100_0.60

Average PT100_1.00

0 20 40 60 80 1000 20 40 60 80 100

1st Floor 2nd Floor 3rd Floor

Solid lines denote West

Dashed lines denote East

0 0.13 0.26 0.39 0.520 0.13 0.26 0.39 0.52

Average maximum PGA

0 0.13 0.26 0.39 0.52

(PGA %)

Figure 9. Comparison of maximum average drifts and acceleration for test frame increasing PGA levels.


ISBN: 978-1-61804-275-0 312

For low levels of PGA% a slight increase in floor

acceleration is observed. It is likely that this was due

to the increased stiffness of the structure before the

initial slipping of the floors and the failure of the

column base connection. These two factors led to a

reduced building stiffness as evidenced by a higher

building period. The base shear response of the

structure with and without dissipative reinforcing is

also shown in Figure 10. This was calculated using

the accelerations and the model masses. Although a

load cell was placed on the dynamic actuator these

readings included the weight of the shaking

foundation and provided higher values than what

was actually present during testing. As expected the

base shear display the same general trend as the

accelerations presented above. A maximum average

value of 97 kN was recorded for testing case with

dissipation corresponding to 100% of PGA intensity

which was similar to the design level base shear.

0 20 40 60 80 100Percentage PGA

0

40

80

120

160

Ba

se s

hea

r (V

b, kN

)

000196x

000535y

001228x

Average

a)

0 20 40 60 80 100Percentage PGA

0

40

80

120

160

Ba

se

sh

ea

r (V

b,

kN

)

000535y

000196x

001228x

Average

b)

Fig. 10. Maximum base shear of test frame at increasing levels of PGA for a) with and b) without dissipation testing

Although it was not possible to directly compare

this value to the design values and assuming a linear

trend to continue, a value of approximately 91 kN

(similar to the performance point) could be obtained

also for testing case without dissipation.

During the first series of testing, carried out on

2013, some slipping of the dissipative connection

was observed. This reduced the effectiveness of the

reinforcing by decreasing both stiffness and

dissipative capacity. Although the slipping shown is

approximately 3 mm this represented almost half of

the expected reinforcing displacement and was 6

times the yielding displacement. It is likely that this

fact led or at least was a contributing factor to the

increased drifts and displacements. Slipping

between the base of the dissipative reinforcing and

the connection plate also explains why the

dissipative loops were low in spite of the significant

levels of gap opening. It is unclear the degree to

which this slipping occurred during testing with

only one of the connections being recorded. In any

case, despite this anomaly, the system demonstrated

its overall effectiveness and thus its robustness.

The final study of the dynamic test results

involves the evaluation of the elastic and inelastic

damping of the frame. During a seismic event the

presence of damping reduces demand on a structure.

The total equivalent viscous damping of a structure

(ξ) is made up of two sources: the elastic (ξel) and

the hysteretic damping (ξhyst). Damping values are

evaluated and compared in this section.

Elastic damping is used to introduce damping not

captured by the hysteretic model represented by the

codified reduction methods. Many methods can be

used in order to evaluate the elastic damping of a

building. During the analysis of the test structure,

the half-power bandwidth (HPB) method [4] was

used. This method estimates the damping using the

frequency range, in combination with a Welch

Fourier analysis [14]. The HPB method returns

significant results in the analysis of a stationary

system (i.e. no significant non-linear response)

therefore it has been applied using the forced

vibration hammer identification testing. In the

application of the HPB method, firstly, the

amplitude of each (in this case the first) natural

frequency is obtained. Values of ξel = 1.49% and

1.84% were calculated for tests with and without

dissipation respectively.

Test configuration without reinforcing showed

slightly elevated elastic damping likely due to the

reduction in stiffness created by the series testing

with dissipation. It is important to note however that

an experimental model is without many of the

sources of elastic damping present in a normal

structure (partitions, cladding etc.).Values were

therefore expected to be lower than in a real post-

tensioned timber structure which contains these

elements.


ISBN: 978-1-61804-275-0 313

As with elastic damping, several methods are

available to evaluate inelastic damping [5]. The

evaluation of hysteretic damping (ξhyst) during

dynamic testing is complicated by the forced nature

of the system response. In order to have hysteretic

damping gap opening and dissipative reinforcing,

yield must occur. With increased displacement

beyond yield (i.e. increased ductility) the equivalent

viscous damping of a post-tensioned timber

structure also increases. During seismic response

therefore, damping increases with stronger ground

motion. Test without dissipation did not contain the

use of dissipative reinforcing at the beam-column

joint indicating that the timber system itself is

capable of providing nominal amounts of hysteretic

dissipation during strong motions [9]. The total

response of the system without dissipation was very

similar to the response of model with dissipation

(ξhyst=2.8% for PGA75%) tending to indicate that

the damping characteristics of the two

configurations are very similar. This is not

unexpected as the dissipative reinforcing will only

provide damping during the maximum frame

response cycle of which few occur during the total

frames responses. It can be seen that only one clear

flag shaped hysteretic loop occurred during all tests.

Performing the area EQV analysis method

suggested by [5], the equivalent viscous damping

value of this loop was ξhyst = 7.8 %.

The experimental outcomes of the dynamic

testing are compared in Figure 11 with the SAP2000

and RUAUMOKO multi-spring base model

considering the 3rd floor displacements for 000196x

test case with an intensity level of 75% of the design

PGA. As shown in the figure, numerical predictions

provided an accurate representation of the

experimental performance for both models.

Comparisons between RUAUMOKO and SAP2000

non-linear time history analysis have shown that the

results have the same trend in time.

Indeed, only a small difference in maximum

values (less than 10%) both for configurations with

and without dissipation has been observed. The

introduction of multi-spring base in modelling

reduces accelerations and base shears compared

with a fixed one but leads to large levels of drift

which can govern design of a flexible system such

as post-tensioned timber. It is clear however that

this discrepancy decreases with the addition of

additional damping to the structure which also has a

significant effect in reducing the values of all of the

key performance parameters studied.

Figure 12 shows SAP2000 and RUAUMOKO

multi-spring base model results in terms of a)

maximum interstorey drift (MID) and b) maximum

base shear (MBS) averaged across 3 input

accelerograms compared with the experimental tests

with and without dissipative steel angles

corresponding to an intensity level of 75% of the

design PGA. Comparisons between SAP2000 and

RUAUMOKO NTHA analysis show that both codes

provide adequate prediction of first floor drift with

the SAP2000 programme providing more accurate

results. Comparison of the maximum base shear

shows that SAP2000 does not accurately predict

values either with or without reinforcing however

RUAUMOKO does capture values well in both

cases. As can be seen NTHA confirmed the

interstorey drift and base shear in the structure

reducing in amplitude by 1.5 and 1.2 factor

respectively when additional steel angle devices are

introduced.

0 5 10 15 20Time (sec)

-0.15

-0.05

0.05

0.15D

isp

l. (

m)

0 5 10 15 20Time (sec)

-0.15

-0.05

0.05

0.15

Dis

pl. (

m)

Fig. 11. Comparison between SAP2000, RUAUMOKO and testing results a) without and b) with dissipative reinforcement.

0 0.5 1 1.5 2 2.5

Drift (%)

0 20 40 60 80

Base Shear (kN)

Figure 12. Average of a) MID and b) MBS provided by SAP2000 and RUAUMOKO modelling compared with experimental outcomes with and without dissipation.

WITH DISSIP._RUAU

WITH DISSIP._SAP

WITH DISSIP._EXP

WITHOUT DISSIP._RUAU

WITHOUT DISSIP._SAP

WITHOUT DISSIP._EXP


ISBN: 978-1-61804-275-0 314

4 Conclusion An extensive dynamic testing campaign has been

performed on a multistorey post-tensioned timber

building in the laboratory of the University of

Basilicata in Potenza, Italy. The aim of the project,

in collaboration with the University of Canterbury

in Christchurch, New Zealand is to develop the

innovative post-tensioned timber concept (under the

name PRES-LAM) by extending its application to

glulam timber with dissipative steel angle devices.

The experimental model has been tested both with

and without the addition of steel angles which are

designed to yield at a certain level drift. This paper

confirmed the validity of MMBA procedure used in

order to calculate the moment capacity of the

rocking joint selecting a certain starting point which

is taken as the design drift (θd). Testing results have

been shown in this paper proving the effectiveness

of post-tensioned system adding dissipative steel

devices in reducing seismic effects if compared to

that of the system without ones. The presence of the

steel dissipative angles allow a maximum reduction

of the seismic behaviour in the range values of 1.2-2

times in comparison with PT only configuration. By

varying post-tensioning force and the contribution

of steel dissipation devices in beam-column joints

and column/foundation interface a designer can

control the global seismic response of the system.

NTHA numerical outcomes using SAP2000 and

RUAUMOKO matched experimental results

confirming the effectiveness of dissipation with

hysteretic steel angles.

Acknowledgements The authors would like to acknowledge funding

from the Structural Timber Innovation Company

(STIC), FederlegnoArredo (FLA) and project DPC-

RELUIS 2014 and 2015.

References: [1] Di Cesare A., Ponzo F., Nigro D., Simonetti M.,

Smith T., Pampanin S. (2013a) "Experimental

modelling and numerical analysis of steel angles as

hysteretic energy dissipating systems". XV Italian

Conference of Earthquake Engineering, Padova,

Italy

[2] Di Cesare, A., Ponzo, F.C., Simonetti M., Smith, T.,

Pampanin, S., (2013b). "Numerical modelling of a

post-tensioned timber framed building with

hysteretic energy dissipation". 5th International

Conference on Structural Engineering, Mechanics

and Computation Cape Town, South Africa.

[3] 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.

[4] Ewins, J. D. "Modal testing: theorey and practise".

Reasearch Studies Press., 1994

[5] Jacobsen, L. S. "Damping in Composite Structures".

2nd World Conference on Earthquake Engineering,

Tokyo and Kyoto, Japan, 1960.

[6] Newcombe, M. P., Pampanin, S., and Buchanan, A.

H. (2010). "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.

[7] NTC08 (2008). "Norme Tecniche per le Costruzioni".

Ministero delle Infrastrutture, Roma, Italy.

[8] NZS 3101:1995 (2006). "Concrete Structures Part 1.

The Design of Concrete Structures" Secondary

Concrete Structures Part 1. The Design of Concrete

Structures, Secondary Zealand, S. N., ed., Standards

New Zealand.

[9] Pino Merino, D. "Dynamic Response of Post-

Tensioned Timber Framed Buildings". University of

Canterbury, Christchurch, New Zealand, 2011.

[10] Ponzo, F., Di Cesare A., Nigro D., Simonetti M,

Smith T., Pampanin S. (2013). "Shaking table

testing of a multi-storey post-tensioned timber

building". XIII EASEC, East Asia Pacific

Conference on Structural Engineering and

Construction, Sapporo, Japan

[11] 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.

[12] 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.

[13] Smith, T., Ponzo, F. C., Cesare, A. D., Auletta, G.,

Pampanin, S., Carradine, D., Palermo, A., and

Nigro, D. (2012). "Testing of a Post-Tensioned Glue

Laminated Beam to Column Joint: Experimental

and Numerical Results." 12th World Conference on

Timber Engineering, Auckland, New Zealand.

[14] Welch, P. D. "The Use of Fast Fourier Transform

for the Estimation of Power Spectra: A Method

Based on Time Averaging Over Short". IEEE

Transactions on Audio Electroacoustics, AU-15, 70-

73, 1967.


ISBN: 978-1-61804-275-0 315

Documents

Shaking Table Testing of a Multi-Storey Post-tensioned ... Table Testing of a Multi-Storey Post-tensioned Timber Building equipped with Advanced Damping System PONZO F ... drift (θd)