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Research Collection
Report
Investigation of a post-tensioned timber connectiontest report
Author(s): Frangi, Andrea; Wanninger, Flavio
Publication Date: 2014
Permanent Link: https://doi.org/10.3929/ethz-a-010232009
Rights / License: In Copyright - Non-Commercial Use Permitted
This page was generated automatically upon download from the ETH Zurich Research Collection. For moreinformation please consult the Terms of use.
ETH Library
i b kInstitut für Baustatik und Konstruktion, ETH Zürich
Investigation of a post-tensioned timber connection
Flavio WanningerAndrea Frangi
IBK Bericht Nr. 355, Juni 2014
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KEYWORDS: Timber, hardwood, connection, post-tensioned, static tests, embedment failure
Dieses Werk ist urheberrechtlich geschützt. Die dadurch begründeten Rechte, insbesondere die der Übersetzung, des Nachdrucks, des Vortrags, der Entnahme von Abbildungen und Tabellen, der Funksendung, der Mikroverfilmung oder der Vervielfältigung auf anderen Wegen und der Speicherung in Datenverarbeitungsanlagen, bleiben, auch bei nur auszugsweiser Verwertung, vorbehalten. Eine Vervielfältigung dieses Werkes oder von Teilen dieses Werkes ist auch im Einzelfall nur in den Grenzen der gesetzlichen Bestimmungen des Urheberrechtsgesetzes in der jeweils geltenden Fassung zulässig. Sie ist grundsätzlich vergütungspflichtig. Zuwiderhandlungen unterliegen den Strafbestimmungen des Urheberrechts.
Flavio Wanninger, Andrea Frangi: Investigation of a post-tensioned timber connection
Bericht IBK Nr. 355, Juni 2014
© 2014 Institut für Baustatik und Konstruktion der ETH Zürich, Zürich
Gedruckt auf säurefreiem PapierPrinted in Switzerland
Investigation of a post-tensioned timber connection
Test report
Flavio Wanninger
Andrea Frangi
Institute of Structural Engineering
Swiss Federal Institute of Technology Zurich
Zurich
August 2014
i
Foreword
In the past decades, precast concrete frames were developed using tendons to connect columns
and beams. These systems showed favourable seismic behaviour, being able to avoid residual
deformations after an earthquake. The use of post-tensioned timber structures was recently
studied at the Institute of Structural Engineering at the ETH in Zurich in the framework of
the Master Thesis of Roman Schneider in cooperation with the industrial partner Haring & Co.
AG. As a result, an innovative post-tensioned beam-column timber joint was developed using
glued laminated timber made of spruce and local strengthening of the joint with hardwood.
The present report shows the results of a comprehensive series of static bending tests on the
developed post-tensioned beam-column timber joint. The experimental investigations were con-
ducted in the framework of the research project entitled ”Post-tensioned timber frame struc-
tures” and sponsored by the Commission of Technology and Innovation CTI and supported by
the industrial partner Haring & Co. AG, Eiken. The overall objective of the research project
is the development and implementation of post-tensioned timber frame structures. The project
fits into the overall research strategy of the institute on the development of innovative solutions
for timber structures. The tests presented in this report form one important step to evaluate
the moment-rotation-behaviour of the developed post-tensioned beam-column timber joint. The
test results demonstrate the high stiffness of the joint and the nonlinear structural behaviour
after the moment of decompression. Furthermore, even after large rotations, the timber column
showed only small residual deformations due to compression perpendicular to the grain.
I would like to thank Flavio Wanninger who has prepared and carefully conducted all tests
and has also processed and evaluated the large amount of data and edited this report. I would
also like to thank the team of the IBK testing and research lab (Patrik Morf, Christoph Gisler,
Thomas Jaggi, Pius Herzog and Dominik Werne) and Christian Nagy as well as Claudio Scan-
della for their support. Furthermore, I would like to gratefully acknowledge the support by the
Swiss Commission for Technology and Innovation (CTI) and the industrial partner Haring &
Co. AG.
Zurich, June 2014 Andrea Frangi
ii
iii
Summary
A post tensioned timber connection made of glulam has been developed at the ETH in Zurich.
The connection is made of spruce with ash reinforcement in the connection area where high
stresses perpendicular to the grain occur.
The moment-rotation-behaviour of this post-tensioned beam-column timber joint has been anal-
ysed with a series of static bending tests. The timber joint was loaded at the ends of the beams
in order to apply a moment to the connection. The tests were conducted with different forces
in the tendon, from 300 kN up to 700 kN. The bending tests were performed with a controlled
load level, so that no embedment failure perpendicular to the grain occurred in the column. The
intended self-centring behaviour could be verified and no damage could be observed during all
the tests.
A final bending test was conducted in order to study the failure mode of the post-tensioned tim-
ber connection. The vertical load on the beams was increased until the tendon-elongation got so
high that the test had to be aborted due to safety reasons. Nearly no damage occurred during
the last test, only minor residual deformations could be observed. The failure is an embedment
failure in the column due to exceedance of the strength perpendicular to the grain.
The specimen, test setup, instrumentation and the results of all performed tests are presented
in this technical report.
Keywords: Timber, hardwood, connection, post-tensioned, static tests, embedment failure
iv
v
Zusammenfassung
Einfache und wirtschaftliche biegesteife Verbindungen sind im Holzbau schwierig zu realisieren.
Am Institut fur Baustatik und Konstruktion der ETH Zurich wurde in Zusammenarbeit mit der
Firma Haring & Co. AG der Prototyp einer neuartigen vorgespannten Holzrahmenkonstruktion
entwickelt.
Der Trager-Stutze-Knotenanschluss aus Brettschichtholz mit lokaler Verstarkung aus Hartholz
uberzeugt durch den hohen Vorfertigungsgrad und dem zeitsparendem Zusammenfugen auf der
Baustelle dank des einfachen Aufbaus des Systems. Er zeigt das grosse Potential von vorges-
pannten Holzrahmenkonstruktionen insbesondere fur mehrgeschossige Holzbauten.
Der Prototyp wurde in einer Serie von Biegeversuchen auf sein Tragverhalten untersucht. Samtliche
Versuche wurden mit unterschiedlichen Vorspannkraften gefahren. Die Vorspannkraft variierte
- je nach Versuch - zwischen 300 kN und 700 kN. Die Versuche wurden mit einer Belastung
durchgefuhrt, welche zu keinen Schaden am Versuchskorper fuhrten. Neben einer symmetrischen
Belastung des Knotens wurden auch asymmetrisch Lastfalle gefahren, welche eine horizontale
Belastung des Knotens simulieren sollten (Windlasten, Erdbeben). Das selbst-zentrierende Ver-
halten des Knotens konnte bestatigt werden, ohne dass der Knoten beschadigt wurde.
In einem letzten Biegeversuch sollten die Lasten gesteigert werden, bis ein Versagen des Systems
eintritt. Durch die hohen Deformationen am Knoten wurde das Spannglied verlangert, was zu
einer Zunahme der Vorspannkraft fuhrte. Diese Zunahme wurde so gross, dass der Versuch
aus Sicherheitsgrunden abgebrochen wurde. Der Schaden am Knoten war sehr gering, lediglich
kleine bleibende Verformungen infolge Querdruck senkrecht zur Faserung in der Stutze waren
die Folge.
Dieser Versuchsbericht beinhaltet samtliche Informationen zum Versuchsaufbau und -korper,
sowie Versuchsbeschrieb und -auswertung aller durchgefuhrten Versuche.
vi
Contents
1 Introduction 1
2 Specimen and test setup 3
2.1 Material and dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Test setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.3 Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3.1 Linear variable differential transformers . . . . . . . . . . . . . . . . . . . 6
2.3.2 Inclinometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3.3 Pressure sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3.4 Hydraulic pump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3.5 Load cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3 Test overview 11
3.1 Testing program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.1.1 Test protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.2 Testing procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4 Experimental analysis - equations 15
4.1 Initial compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.2 Key variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
4.2.1 LVDTs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
4.2.2 Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.2.3 Moment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.2.4 Decompression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.2.5 Neutral axis depth from LVDTs . . . . . . . . . . . . . . . . . . . . . . . 21
4.2.6 Stresses in the column . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
5 Experimental analyis - test evaluation 23
5.1 Test 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
5.1.1 Initial compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
viii CONTENTS
5.1.2 Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
5.1.3 Evaluation symmetrical loading . . . . . . . . . . . . . . . . . . . . . . . . 25
5.1.4 Evaluation asymmetrical loading - constant load on right beam . . . . . . 27
5.1.5 Evaluation asymmetrical loading - constant load on left beam . . . . . . . 28
5.2 Test 14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
5.2.1 Initial compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
5.2.2 Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
5.2.3 Evaluation symmetrical loading . . . . . . . . . . . . . . . . . . . . . . . . 30
5.2.4 Evaluation symmetrical loading - constant load on right beam . . . . . . 31
5.2.5 Evaluation asymmetrical loading - constant load on left beam . . . . . . . 32
5.3 Test 15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
5.3.1 Initial compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
5.3.2 Rotation test 15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
5.3.3 Evaluation symmetrical loading . . . . . . . . . . . . . . . . . . . . . . . . 34
5.3.4 Evaluation asymmetrical loading - constant load on right beam . . . . . . 35
5.3.5 Evaluation asymmetrical loading - constant load on left beam . . . . . . . 36
5.4 Test 17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
5.4.1 Initial compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
5.4.2 Rotation test 17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
5.4.3 Evaluation symmetrical loading . . . . . . . . . . . . . . . . . . . . . . . . 39
5.4.4 Evaluation asymmetrical loading - constant load on right beam . . . . . . 40
5.4.5 Evaluation asymmetrical loading - constant load on left beam . . . . . . . 40
5.5 Test 21 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
5.5.1 Initial compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
5.5.2 Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
5.5.3 Evaluation symmetrical loading . . . . . . . . . . . . . . . . . . . . . . . . 43
5.5.4 Evaluation asymmetrical loading - constant load on right beam . . . . . . 44
5.5.5 Evaluation asymmetrical loading - constant load on left beam . . . . . . . 45
5.6 Test 22 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
5.6.1 Initial compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
5.6.2 Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
5.6.3 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
6 Test summary 51
A Drawings 53
A.1 Specimen and instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
A.2 Specimen and test setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
CONTENTS ix
B Test protocols 67
B.1 Test 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
B.2 Test 14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
B.3 Test 15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
B.4 Test 16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
B.5 Test 17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
B.6 Test 18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
B.7 Test 19 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
B.8 Test 20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
B.9 Test 21 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
B.10 Test 22 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
C Test evaluation 79
C.1 Test 16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
C.1.1 Initial compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
C.1.2 Rotation test 16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
C.1.3 Evaluation symmetrical loading . . . . . . . . . . . . . . . . . . . . . . . . 81
C.1.4 Evaluation asymmetrical loading . . . . . . . . . . . . . . . . . . . . . . . 82
C.2 Test 18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
C.2.1 Initial Compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
C.2.2 Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
C.2.3 Evaluation symmetrical loading . . . . . . . . . . . . . . . . . . . . . . . . 85
C.2.4 Evaluation asymmetrical loading . . . . . . . . . . . . . . . . . . . . . . . 86
C.3 Test 20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
C.3.1 Initial compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
C.3.2 Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
C.3.3 Evaluation symmetrical loading . . . . . . . . . . . . . . . . . . . . . . . . 89
C.3.4 Evaluation asymmetrical loading . . . . . . . . . . . . . . . . . . . . . . . 90
Nomenclature 93
x CONTENTS
Chapter 1
Introduction
In the past decades precast concrete frames were developed using tendons to connect columns and
beams [1–3]. These systems showed favourable seismic behaviour, being able to avoid residual
deformations after an earthquake. Furthermore a model, the monolithic beam analogy, was
developed to describe the connection behaviour [4]. A similar system for timber was introduced
in New Zealand at the University of Canterbury [5–11]. A timber frame made of laminated
veneer lumber was post-tensioned, resulting in a good structural behaviour. Design proposals
were published [12–16] and buildings using the post-tensioned timber frames were constructed
[17].
Post-tensioned timber joints are also being studied at the Institute of Structural Engineering at
the ETH in Zurich. An innovative post-tensioned beam-column timber joint has been developed
using glued laminated timber (spruce) and local strengthening of the joint with hardwood (ash).
No further steel elements are required for the moment-resisting timber joint, only a single straight
tendon is placed in the middle of the beam. The developed post-tensioned beam-column timber
joint is characterised by a high degree of pre-fabrication and easy assemblage on site.
The moment-rotation-behaviour of the post-tensioned beam-column timber joint has extensively
been analysed with a series of static bending tests. The timber joint was loaded at the ends
of the beams in order to apply a moment to the connection (see figure 1.1). The tests were
conducted with different forces in the tendon, from 300 kN up to 700 kN. The bending tests
were performed with a load level, so that no failure perpendicular to the grain in the column
occurred.
A final bending test was conducted in order to study the failure mode of the post tensioned
timber beam-column joint. The vertical load on the beams was increased until the tendon-
elongation got so high that the test had to be aborted. The results of the bending tests on the
structural behaviour of the post-tensioned timber joint are presented herein.
2 Chapter 1. Introduction
Fig. 1.1: Post-tensioned timber joint
Chapter 2
Specimen and test setup
2.1 Material and dimensions
The test specimen consists of two beams and a column made of glulam. The glulam beams
are made of spruce except three lamellae, which are made of ash (see figure 2.1, grey parts are
made of ash). The column is also a hybrid made of spruce and ash. The hardwood is used in
areas, where high stresses perpendicular to the grain occur, namely in the connection between
the column and the beam. The strength and stiffness values of the materials are summarised in
table 2.1.
An unbonded tendon is attached both ends of the specimen. A thick steel plate is necessary at
the end of the beam for the load transmission from the tendon to the beam.
The shear force between beam and column is transferred via friction. By cutting a small opening
into the column a support was created for safety reasons in case the friction would not be
sufficient.
1.62 0.36 1.62
0.040.04
0.6
0.4
0.6
F F1.24
0.59
0.12
Fig. 2.1: Specimen and load application, all dimensions in [m]
The properties of the tendon are summarised in table 2.2
4 Chapter 2. Specimen and test setup
Tab. 2.1: Strength and stiffness properties in [MPa] for strength grade GL24h [18] and D40 [19]
Description Abbreviation Strength grade
GL24h D40
Compressive strength parallel to the grain fc,0,k 22 26
Compressive strength perpendicular to the grain fc,90,k 3 8.3
Modulus of elasticity parallel to the grain E0,mean 11000 13000
Modulus of elasticity perpendicular to the grain E90,mean 300 860
Shear modulus Gmean 500 810
Tab. 2.2: Tendon properties according to [20].
Description Abbreviation Y1770 4-06
Number of strands [-] N 4
Area cross section [mm2] Ap 600
Tendon length [mm] Lp 4200
Young’s Modulus [MPa] Ep 197000
Tensile strength [MPa] fp,k 1770
Applicable design load [kN] Pmax 850
2.2 Test setup
All the tests were performed at the ETH Zurich on a strong floor. The strong floor has several
spots where loads up to 1200 kN can be transferred into the floor.
A rigid steel frame was build for the tests (see figure 2.2). The frame consists of two columns
which are connected to the floor with high-strength pre-stressed bolts. The columns are con-
nected to a strong wall with two beams, assembled from steel profiles HEB 300. The specimen
is attached to the columns with profiles UPE 270.
The force is applied by two cylinders of the type Emmen cylinder 206 kN, which are connected
with a beam. The cylinders allow to apply a force of 412 kN on each side of the specimen. The
cylinders are connected to the same hydraulic pump, but can be controlled separately, so that
several load cases can be investigated. It is therefore possible to apply the load only on one
beam while the other one is unloaded. One beam can also be loaded to a certain value while
the second beam is loaded to a different value. One beam with two cylinders attached weighs
480 kg, which has to be accounted for in the analysis.
The tendon and the press are shown in figure 1.1 and figure 2.2. The press is positioned between
the steel plate and the anchorage of the tendon. The press allows to change the force in the
tendon. Several tests with different levels of post-tensioning force can therefore be executed.
Scaled drawings of the specimen and the test setup can be found in appendix A.
2.2. Test setup 5
left right
Fig. 2.2: Test setup and specification of the beam (left or right)
Fig. 2.3: Test setup CAD (without tendon)
6 Chapter 2. Specimen and test setup
2.3 Instrumentation
To investigate the structural behaviour of the post-tensioned timber connection several types of
measuring devices are being used:
� linear variable differential transformers (LVDTs)
� inclinometers
� pressure sensors
� hydraulic pumps
� load cell
All the abbreviations and the most important information are summarized in table 2.3. The
abbreviations will be used in the entire document.
Tab. 2.3: Measuring Equipment
Description Abbreviation Range Error
LVDT TK-10 WRV1. . . ± 10 mm 0.25 %
LVDT D6 WRH1. . . ± 5 mm 0.25 %
LVDT TK-25 Durch L Durch R ± 25 mm 0.25 %
Inclinometer IL1 IL2 IR1 IR2 ± 5 ◦ ± 0.01 ◦
Pressure sensor FSR 0.2-20N ± 2 %
Load cell KMD 0-1250kN unknown
2.3.1 Linear variable differential transformers
The LVDTs record the displacements between the column and the beams. The rotation of the
connection (or the beam) can be calculated from the recorded values. One LVDT is also attached
at the bottom of each beam to measure its deflection (figure 2.4). The LVDTs being used at
the column-beam interface are of the type Precisor TK-10 and RDP D6/05000A with a range
of 10 mm and 5 mm, respectively.
2.3. Instrumentation 7
0.040.28
0.04
WLV3
WLO2
WLV1
WLV2
WRV3
WRO2
WRV1
WRV4
WRV2
1.251.25
0.7
0.6
0.7
0.061.6
0.36
0.02
5
0.30
1 0.43
7 0.57
1
0.64
4
0.62
2
0.57
4
0.29
90.
029
Durch L Durch R
IL2 IL1IR1
IR2
1.60.06
LVDT
Inclinometer
Test specimen with instrumentationFront view1:20 [m]
Fig. 2.4: Instrumentation: LVDTs and inclinometers, all dimensions in [m]
Figure 2.5 shows the LVDTs attached at the beam. The aluminium plate is needed to measure
the actual deformation between the column an the beam. It is attached to the rigid test frame. If
there would be no plate, the measured deformation would correspond to the relative deformation
between the column and the beam, the deformation of the column itself would not be measured.
Fig. 2.5: LVDTs at the beam-column interface
8 Chapter 2. Specimen and test setup
2.3.2 Inclinometers
Two inclinometers of the type NS-5/P are positioned on top of each beam. These devices allow to
measure the inclination of the beams directly. The rotation in the connection can be calculated
from these values if the elastic inclination of the beam is subtracted. There are therefore two
ways to calculate the rotation, which leads to more reliable results.
2.3.3 Pressure sensors
Two pressure sensors of the type FSR 400 are used to estimate the moment of decompression.
Figure 2.6 shows the sensor and its single components. Two substrate layers with a spacer in
between are the main components. As soon as a force acts on the head of the sensor, the two
substrate layers are pressed together. If there is a contact between the substrate layers, the
sensor measures a voltage, which increases as the pressure on the head increases. If there is no
pressure and therefore no contact, the measured voltage is zero.
Since the maximal applicable load on the sensors is only 20 N, the contact between the pressure
sensors and the beam is made after a certain tendon force has already been applied. This reduces
the force on the sensor but has to be taken into account in the analysis.
Fig. 2.6: Pressure sensor FSR 400
The pressure sensors are only attached on the right beam, as can be seen in figure 2.7. The
pressure sensor is positioned right under the top edge of the beam and is connected to an
adjustable screw. The screw is necessary to create a clearly defined contact area. If the pressure
is zero, the point of decompression has been reached and a gap will start to open between the
beam and the column interface.
2.3.4 Hydraulic pump
Three hydraulic pumps are used for the tests. The main pump is from the manufacturer Amsler,
which is connected to the cylinders that are pulling the beams down.
Two more pumps of the type Bieri HP 2.2D−15110 are being used during the tests. One pump
is needed to pre-stress the tendon. The second one is being used for the asymmetrical loading,
where one beam is loaded to a constant value.
2.3. Instrumentation 9
Fig. 2.7: FSR at the connection interface
The oil pressure is measured for each press separately. These values are necessary to calculate
the forces in the cylinders and the tendon, respectively.
2.3.5 Load cell
A load cell of the type ForceCell BaMa 1250 is positioned between the tendon and the anchorage.
The load cell measures the force in the tendon in addition the the tendon force obtained from
the oil pressure.
10 Chapter 2. Specimen and test setup
Chapter 3
Test overview
3.1 Testing program
A total of 22 tests were performed at the ETH Zurich. The tests one to twelve are preliminary
tests, which where performed to calibrate the measuring equipment and will not be presented
herein. Test 19 is not considered due to an error in the hydraulic system.
Tab. 3.1: Performed tests
Test No. Tendon force [kN] Load application Applied load [kN]
13 518 B,C,O 80
14 416 B,C,O 60
15 612 B,C,O 80
16 325 B,C,O 50
17 683 B,C,O 70
18 560 B,C,O 80
20 462 B,C,O 75
21 554 B,C,O 90
22 557 B 157
The tests were performed with different post-tensioning-forces and different kind of load appli-
cations. The maximal applied load varies from test to test. Three different load applications
were performed (figure 3.1):
� (B) Load is applied on both beams, symmetric loading. Both beams are loaded and
unloaded at the same time.
� (O) Load is applied on one beam, asymmetric loading. The second beam remains un-
loaded.
� (C) Combined load application. One beam is pre-loaded to a certain, constant value. The
second beam is then loaded and unloaded to different (higher) values.
12 Chapter 3. Test overview
By applying the load only on one beam, a load combination is generated, which is closer to a
horizontal load on a post-tensioned timber frame (earthquake, wind loads).
The analysis often refers to a load level (for example 80 kN). This values always corresponds
to the peak value of a load cycle. I.e. in the test shown in figure 3.1 the value 80 kN would
correspond to the peak at 1600 sec.
3.1.1 Test protocol
All the tests, except test 22, consist of the three parts:
� 1. Symmetrical loading, 3-4 loading and unloading cycles.
� 2. Asymmetrical loading, right beam under constant load. The right beam is loaded to a
certain value, the left beam is then loaded to 40 kN, unloaded and reloaded again up to
60 kN. This is repeated with different loads levels on the right beam.
� 3. Asymmetrical loading, left beam under constant load. The left beam is loaded to a
certain value, the right beam is then loaded to 40 kN, unloaded and reloaded again up to
60 kN. This is repeated with different loads levels on the left beam.
The force-time-diagram for test 13 can be seen in figure 3.1. The symmetric loading ends at
t = 1700 sec. The asymmetric loading with constant load on the right beam starts at t = 1700 sec
and ends at t = 3100 sec. At the end of the test, the asymmetric loading with a constant load
on the left beam is performed.
It shall be noted, that the loads are not exactly constant. Since one beam is loaded more
than the other one, the beam with the heavier load is being pulled down, the beam with less
load would like to move upwards, but is restrained by the cylinders. Therefore the load in the
cylinders increases slightly.
500 1500 2500 3500 45000
20
40
60
80
100
Time [sec]
Load
[kN
]
symmetricload left beamload right beam
Fig. 3.1: Load-time diagram for a typical test
3.2. Testing procedure 13
Detailed protocols for all the perfromed tests can be found in appendix B.
3.2 Testing procedure
The same procedure was applied for all the tests. The following steps were always performed in
the following order:
� Step 1: Starting the computer for the measuring equipment. The beams are temporarily
supported, the force in the tendon is about 5 to 10 kN
� Step 2: The force in the tendon is increased up to 100 kN
� Step 3: The supports under the beams are being removed
� Step 4: The force in the tendon is increased up to 2/3 of the value to be achieved. The
pressure sensors are connected to the beam by adjusting the screw
� Step 5: The tendon force is being increased up to the value to be achieved
� Step 6: The steel beams with the cylinders are mounted on the specimen (first on the right
beam, then on the left beam). The cylinders are connected to the strong floor
� Step 7: Performing the tests (loading and unloading cycles)
� Step 8: Removing the cylinders (first from the left beam, then from the right beam)
� Step 9: Reducing the force in the tendon to 100 kN. Mounting the supports under the
beams of the specimen
� Step 10: Reducing the force in the tendon to approximately 5 to 10 kN
14 Chapter 3. Test overview
Chapter 4
Experimental analysis - equations
4.1 Initial compression
The beams are being pressed against the column when force is applied on the tendon. This leads
to a initial compression in the interface, which has to be estimated. It is therefore essential, that
the measuring equipment is recording, before load is applied on the tendon. Figure 4.1 shows
the LVDTs at the beam-column interface during pre-stressing the tendon.
−1 −0.5 0 0.50
100
200
300
400
500
600
Displacement [mm]
P [k
N]
WLOWL1WL2WL3
−1 −0.5 0 0.50
100
200
300
400
500
600
Displacement [mm]
P [k
N]
WROWR1WR2WR3WR4
Fig. 4.1: Compression during pre-stressing the tendon
The displacements recorded by the LVDTs are linear for a force greater than 100 kN. At the
beginning of pre-stressing the tendon, the recorded displacements are not linear, which is due
to a rotation of the beams. The beams are supported at the beginning of each test, preventing
it from falling down (see section 3.2). The beams are not perfectly horizontal, while being
supported. By applying the force on the tendon, the beams are rotating at the beginning before
they are being pressed into the column.
In order to estimate the amount of compression, the displacements recorded by the LVDTs are
approximated linearly between 100 kN and the maximal force in the tendon. The straight lines
are then shifted, so that they go through the origin of the coordinate system. This procedure
is supposed to remove the rotation of the beam from the data and has to be done for each set
16 Chapter 4. Experimental analysis - equations
of LVDTs separately. The values at the initial pre-stressing-force (for figure 4.1 the value would
be at approximately 520 kN) is then read from the diagram. The values are of course different
for the different LVDTs. To estimate an initial compression the mean value is calculated.
This value for the initial compression is then applied to all LVTDs, meaning that at the beginning
of each test the beam is compressed uniformly into the column. Figure 4.2 shows the LVDTs
plotted against their position (measured from the lower edge of the beam) for different load
levels applied to the beam. After applying the force on the tendon the beam is being pressed
into the column by approximately 0.4 mm. By loading the beam with 20 kN up to 80 kN the
beam is rotating. The lines connecting the LVDTs (circles in figure 4.2) can be interpreted as
the cross section of the beam at the interface.
−1 −0.5 0 0.5 1 1.5 2 2.5 30
100
200
300
400
500
600
Displacment [mm]
Pos
ition
[mm
]
0 kNinterp.20kNinterp.40kNinterp.60 kNinterp.80 kNinterp.
Fig. 4.2: Measured displacements with LVDTs for different load levels. I.e. F = 0 kN after post-
tensioning, F = 20 kN applied load on the beam 20 kN, etc.
It is important to mention, that by defining a uniform compression, the calculated rotation is
not altered, since the rotation only depends on the incremental change in displacements of the
LVDTs. The initial compression only influences the moment of decompression. It is possible to
check if the uniform compression was chosen accurately: If the moment of decompression does
not correspond to the results of the pressure sensors, the compression was selected too low or too
high, depending if the decompression occurs at a too low load or a too high load, respectively.
4.2 Key variables
4.2.1 LVDTs
The LVDTs are attached at the beams on both sides. For the experimental analysis the average
value from the LVDTs at the same position are used, i.e. for the two LVDTs positioned in the
middle of the left beam:
4.2. Key variables 17
WL2 =WLV 2 +WLH2
2(4.1)
4.2.2 Rotation
The rotation between the column (see figure 4.3) and the beam is the most important parameter
that has to be estimated. One possibility is to use the LVDTs and calculate the rotation, another
possibility is to use the inclinometers to calculate the rotation in the connection interface. Both
ways are described in the following.
Calculation with LVDTs
The rotation is calculated by using the upper LVDTs (WLO) and the ones in the middle of the
beam (WL2). By assuming that the section remains plain, the rotation can be calculated as
follows:
θ =WLO −WL2
f(4.2)
With f defining the distance between the LVDTs WLO and WL2.
Since there are eight LVDTs mounted at the left interface and ten LVDTs at the right interface
there is a more accurate way to calculate the rotations. The position of each LVDT with
reference to the lower edge of the beam is known. By assuming that the section remains plain,
the following three equations can be written (as an example only for the left beam, see figure
2.4):
yWLO = θ · (622− x) = θ · 622− θ · x = θ · 622− n (4.3)
yWL1 = θ · (574− x) = θ · 574− θ · x = θ · 574− n (4.4)
yWL2 = θ · (299− x) = θ · 299− θ · x = θ · 299− n (4.5)
The values correspond to the position of the LVDTs, measured in mm from the lower edge of
the beam. The value y is the mean measured deformation for each set of LVDTs. The LVDTs
at the lower edge of the beam are not taken into account, since they are in the compressive zone,
where the deformations may not be linear (due to embedment failure in the column).
The unknown variables are the rotation θ and the neutral axis depth x, which have to be
calculated.
18 Chapter 4. Experimental analysis - equations
With two unknown variables and three equations (respectively four for the right beam) the
problem can be solved. The equations (4.3)-(4.5) can be transposed into:
yWLO
yWL1
yWL2
=
[θ
n
]·
622 −1
574 −1
299 −1
(4.6)
The variables θ and n can be calculated with a right division. The value for x is calculated from
n (which would be a displacement at the lower edge of the column) by a back substitution:
n = x · θ → x =n
θ(4.7)
Calculation with inclinometers
The rotation at the interface is determined by using the inclinometers, which are attached on
top of each beam. The inclinometers measure the inclination of the beam during the tests.
However, the rotation in the interface does not correspond exactly to the measured inclination,
since the elastic inclination of the beam is also measured. Thus, the recorded values have to be
corrected. The inclination of the beam can be calculated as follows:
w′ =F · Lcant
EI
[xincl −
x2incl2 · Lcant
](4.8)
The position of the inclinometers (xincl), measured from the interface, is equal to 200 mm for
the first set of inclinometers and 900 mm for the second set (see figure 2.4).
Comparison of rotations
The rotations calculated with the LVDTs and the inclinometers can be verified with the measured
deflection of the beams. The rotations have to be multiplied with the length of the beam in
order to get a deflection. After adding the elastic deflection of the beam, the obtained value
should correspond to the measured deflection under the beam:
wcalc = θ · Lcant (4.9)
wcalc + wel,beam = θ · Lcant +F · L3
cant
E · I≈ wmeasured (4.10)
If the difference between the measured and calculated deflection is negligible, the rotations cal-
culated from the LVDTs and the inclinometers are considered as validated and usable. This
check is performed for every single test, since the rotation is the key variable needed to describe
4.2. Key variables 19
the structural behaviour of the connection.
In case of the asymmetrical loading there is an additional term, which has to be calculated.
The two different loads acting on the beam lead to a rotation of the column. This rotation can
be calculated as follows:
θasymmetric =Masymmetric,col · Lcant
8 · E · Icol(4.11)
With Masymmetric,col being the resulting moment due to the two different loads acting on the
column. This rotation influences the measured deflections of the beams. If the rotations are
estimated with the inclinometers the rotation of the column is included, since the inclinometers
measure the absolute inclination according to a horizon. If the rotation is estimated with the
LVDTs the rotation is also included, since the reference point is the testing frame, which is
fixed and does not move during the test. Since the focus is on the structural behaviour of the
beam-column interface, the deflection due to column rotation has to be subtracted from the
measured ones under the beam:
wasymmetric = θasymmetric · Lcant (4.12)
4.2.3 Moment
The structural behaviour of the connection is best described using the moment in the connection
instead of the load applied to the beam. The moment can be calculated with:
M = F · Lcant (4.13)
It is useful to plot the moment against the rotation in order to evaluate the tests, since the two
parameters correspond to the characteristics of a rotational spring and are therefore widely used
and comprehended.
4.2.4 Decompression
The moment of decompression can be estimated with the pressure sensors. As soon as there is
no pressure, the sensors will loose contact to the beam and therefore not measure any voltage.
Figure 4.4 shows the voltage of the pressure sensor as a function of the load on the beam. The
voltage of the sensor is zero that at a load of approximately 20 kN. This would mean, that the
moment of decompression is reached at a load of 20 kN on the beam.
Since the sensor is not exactly positioned on the top edge of the beam but slightly lower (10 mm),
the moment of decompression is estimated to occur at a value of 0.5 V.
20 Chapter 4. Experimental analysis - equations
11
11
11
11
11
11.31°
0.11
x
inf
Fig. 4.3: Definition of the rotation θ, maximal compressive stresses σinf and the neutral axis depth x
at the connection interface
As already mentioned in section 2.3.3 and 3.2, the pressure sensors are not activated from the
beginning on, in order to protect the sensitive sensors. If the tendon force to be achieved is
600 kN the pressure sensors are activated at a tendon force of 400 kN, corresponding to 2/3 of
the value to be achieved. This has to be taken into account during the analysis, since the sensors
do not experience the full pressure of the beam. This means, that the moment of decompression
would be measured too early. In order to take into account this influence a factor is introduced,
which interpolates the pressure up to the target value (600 kN in the mentioned case):
fFSR =P0
P0 − PFSR=
600kN
600kN − 400kN= 3 (4.14)
If decompression would occur at an applied load of 20 kN, the value would be fFSR-times the
measured one. In the example shown in figure 4.4 decompression would actually occur at 60 kN.
Since the deformations in the column remain elastic during pre-stressing, the linear interpolation
should not lead to any mistakes during the analysis.
In addition to the pressure sensors a 0.2 mm thick feeler gauge was used to check for the
gap opening between the column-beam interface during the tests. As soon as the feeler gauge
could be pushed between the column and beam, a note was made in the testing protocol. This
information can be used to check the moment of decompression.
4.2. Key variables 21
0 20 40 60 80 1000
1
2
3
4
5
Load [kN]
Vol
tage
[V]
Fig. 4.4: Recorded voltage from the pressure sensor while applying a load F on the beams
4.2.5 Neutral axis depth from LVDTs
The neutral axis depth can be estimated with two LVDTs directly, instead of calculating it with
the linear regression as described in section 4.2.2. By assuming a plain section in the interface,
the neutral axis depth can be estimated as follows:
x = 622mm− WLO
θ(4.15)
4.2.6 Stresses in the column
The stresses in the column (perpendicular to the grain) are very important for the design. With
the equilibrium of forces and the assumption of a linear-elastic stress distribution it is possible
to calculate the maximal compressive stresses in the interface (figure 4.3).
σinf =2P
x · b(4.16)
The width b of the beam is known, the force in the tendon (P) is being measured during the
tests. The neutral axis depth x is estimated according to section 4.2.2.
Equation (4.16) is only valid after decompression. Until decompression the following equation
has to be used in order to calculate the maximal stresses in the column:
σinf =P
A+M
W(4.17)
22 Chapter 4. Experimental analysis - equations
Chapter 5
Experimental analyis - test
evaluation
5.1 Test 13
5.1.1 Initial compression
The initial compression is estimated as described in section 4.1. The procedure is performed for
both beams separately (see figure 5.1). The compression is not linear at the beginning, since both
beams are rotating. As soon as the force in the tendon reaches 100 kN the compression is linear.
The small deviation, which is visible at 300 kN is due to a break during the post-tensioning
process. The pressure sensors are connected during this break. This deviations occurred during
each test as soon as the post-tensioning process was interrupted. The reason is that the pump
looses some oil, therefore the pressure in the system is reduced, which leads to a small loss in
post-tensioning force.
−1 −0.5 0 0.50
100
200
300
400
500
600
Displacement [mm]
P [k
N]
WLOWL1WL2WL3
−1 −0.5 0 0.50
100
200
300
400
500
600
Displacement [mm]
P [k
N]
WROWR1WR2WR3WR4
Fig. 5.1: Initial compression test 13
The initial compression for the left beam is:
24 Chapter 5. Experimental analyis - test evaluation
wcomp,left = 0.31mm (5.1)
For the right beam this value is slightly higher:
wcomp,right = 0.34mm (5.2)
These values are approximations, as the LVDTs measure the initial compression at the outer
perimeter of the beam.
The theoretical compression can also be calculated using the symmetry of the system:
wcomp,calc =P0/A
E90· bs
2=
518000/(600 · 400)
860· 280
2= 0.35mm (5.3)
The value is slightly higher than the estimated ones, especially for the left interface.
5.1.2 Rotation
The rotations have to be checked for errors, since all the parameters are expressed according to
the rotations at the interfaces. The procedure to check the rotations is described in section 4.2.2.
The procedure is very simple, the rotations are multiplied with the beam length. This value
should then correspond to the measured deflection of the beam, taking into account the elastic
deformation of the beam. The results for the two beams are shown in figure 5.2. The calculated
- both from the linear regression of the LVDTs and the inclinometers - rotations correspond well
to the measured ones, the results are basically identical.
0 1 2 3 4 5 6 7 8 9 100
20
40
60
80
100
120
Deflection beam [mm]
M [k
Nm
]
regression leftinclinometer leftmeasured
0 1 2 3 4 5 6 7 8 9 100
20
40
60
80
100
120
Deflection beam [mm]
M [k
Nm
]
regression rightinclinometer rightmeasured
Fig. 5.2: Deflection beams test 13
5.1. Test 13 25
5.1.3 Evaluation symmetrical loading
All the key variables are plotted as a function of the rotation in figure 5.3.
0 1 2 3 4 5 6 7 8
x 10−3
0
20
40
60
80
100
120
θ [−]
M [k
Nm
]
leftright
0 1 2 3 4 5 6 7 8
x 10−3
0
100
200
300
400
500
600
700
θ [−]
P [k
N]
leftright
0 1 2 3 4 5 6 7 8
x 10−3
0
100
200
300
400
500
600
θ [−]
x [m
m]
leftrightFSR
0 1 2 3 4 5 6 7 8
x 10−3
0
2
4
6
8
10
θ [−]
σ inf [N
/mm
2 ]
leftright
Fig. 5.3: Evaluation test 13
The moment-rotation diagram shows, that the two connections behave similar until the moment
in the interface reaches a value of approximately 70 kNm. The two sides behave differently after
that; the right connection shows a stiffer behaviour, whereas the left connection softens with
increasing moment.
The tendon force (P) remains constant during the test. The beginning of an increase is noticeable
at a rotation of 5 mrad, which would lead to the conclusion, that the gap has reached the position
of the tendon.
The neutral axis depth (x) is constant at a value of 600 mm up to a rotation of 1.2 mrad. Then
it starts to decrease, which means that the moment of decompression is at 1.2 mrad or at a
moment of approximately 45 kNm. During the test a feeler gauge was used to check whether
a gap has opened or not. A gap could be noticed at a load of 40 kN, which corresponds to a
26 Chapter 5. Experimental analyis - test evaluation
moment of 50 kNm. The circle in the diagram shows the moment of decompression according
to the pressure sensor (FSR). The neutral axis depth gets smaller than 300 mm, which means
that the gap reaches the position of the tendon. This observation could also be made with the
tendon force.
The compressive stresses go up to 9 MPa, which is outside the expected elastic range. However,
no plastic deformations where observed after the test. A measurement value leap is noticeable at
a rotation of 1.2 mrad (moment of decompression) for the left interface. This is due to the way
the stresses are calculated: before decompression, equation (4.17) is used, after decompression
equation (4.16). If the initial compression is chosen poorly, a leap will occur, since the stresses
at decompression have different values for the two equations.
By increasing the initial compression for the left interface, the leap can be reduced (see figure
5.4).
0 1 2 3 4 5 6 7 8
x 10−3
0
20
40
60
80
100
120
θ [−]
M [k
Nm
]
leftright
0 1 2 3 4 5 6 7 8
x 10−3
0
100
200
300
400
500
600
700
θ [−]
P [k
N]
leftright
0 1 2 3 4 5 6 7 8
x 10−3
0
100
200
300
400
500
600
θ [−]
x [m
m]
leftrightFSR
0 1 2 3 4 5 6 7 8
x 10−3
0
2
4
6
8
10
θ [−]
σ inf [N
/mm
2 ]
leftright
Fig. 5.4: Modified evaluation test 13
5.1. Test 13 27
5.1.4 Evaluation asymmetrical loading - constant load on right beam
Figure 5.5 shows the deflections under the left beam during the test with a constant load on the
right beam. It is noticeable, that the rotation calculated from the LVDTs leads to better results
than using the rotations calculated from the inclinometers.
0 1 2 3 4 5 60
10
20
30
40
50
60
70
80
Displacement [mm]
M [k
Nm
]
regressionmeasured
0 1 2 3 4 5 60
10
20
30
40
50
60
70
80
Displacement [mm]
M [k
Nm
]
inclinometermeasured
Fig. 5.5: Deflection beam test 13, constant load on the right beam
The test evaluation focuses on the moment-rotation behaviour and the compressive zone (figure
5.6). The force in the tendon and the stresses are not of interest, since the applied load for the
asymmetrical loading is always smaller as the load applied for the symmetrical loading.
The moment-rotation-diagram shows a reduction of the initial stiffness of the connection with
decreasing load on the left beam. This effect is due to shear deformations in the column, which
only occur during asymmetrical loading.
The moment of decompression occurs basically at the same rotation compared with the sym-
metric loading.
0 1 2 3 4 5 6 7 8
x 10−3
0
20
40
60
80
100
120
θ [−]
M [k
Nm
]
symmetricr=20kNr=40kNr=0kN
0 1 2 3 4 5 6 7 8
x 10−3
0
100
200
300
400
500
600
θ [−]
x [m
m]
symmetricr=20kNr=40kNr=0kN
Fig. 5.6: Evaluation test 13, constant load on the right beam
28 Chapter 5. Experimental analyis - test evaluation
5.1.5 Evaluation asymmetrical loading - constant load on left beam
Figure 5.7 shows the deflections of the right beam during the test with a constant load on the left
beam. The rotation calculated from the LVDTs leads to better results than using the rotations
calculated from the inclinometers.
0 1 2 3 4 5 60
10
20
30
40
50
60
70
80
Displacement [mm]
M [k
Nm
]
regressionmeasured
0 1 2 3 4 5 60
10
20
30
40
50
60
70
80
Displacement [mm]
M [k
Nm
]
inclinometermeasured
Fig. 5.7: Deflection beam test 13, constant load on the left beam
The moment-rotation-diagram (figure 5.8) shows a reduction of the initial stiffness of the con-
nection with decreasing load on the right beam. This effect is due to shear deformations in the
column, which only occur during asymmetrical loading.
The moment of decompression occurs basically at the same rotation compared with the sym-
metric loading. However, this could not be verified with the feeler gauge during the tests. The
gap opened later compared to the symmetric loading. i.e. for the case where there is not load
on the right beam (r=0 kN) gap opening occurred at 44-45 kN, which is slightly later than for
the symmetric loading.
0 1 2 3 4 5 6 7 8
x 10−3
0
20
40
60
80
100
120
θ [−]
M [k
Nm
]
symmetricl=20kNl=40kNl=0kN
0 1 2 3 4 5 6 7 8
x 10−3
0
100
200
300
400
500
600
θ [−]
x [m
m]
symmetricl=20kNl=40kNl=0kN
Fig. 5.8: Evaluation test 13, constant load on the left beam
5.2. Test 14 29
5.2 Test 14
5.2.1 Initial compression
The initial compression is estimated according to section 4.1.
−1 −0.5 0 0.50
100
200
300
400
500
600
Displacement [mm]
P [k
N]
WLOWL1WL2WL3
−1 −0.5 0 0.50
100
200
300
400
500
600
Displacement [mm]
P [k
N]
WROWR1WR2WR3WR4
Fig. 5.9: Initial compression test 14
The initial compression for the left beam is:
wcomp,left = 0.27mm (5.4)
For the right beam this value is slightly higher:
wcomp,right = 0.28mm (5.5)
The theoretical compression is calculated as follows:
wcomp,calc =P0/A
E90· bs
2=
416000/(600 · 400)
860· 280
2= 0.28mm (5.6)
The value corresponds to the estimated ones for the two beams.
5.2.2 Rotation
The result for the verification of the rotation for the two beams is shown in figure 5.10. The
calculated - both from the linear regression of the LVDTs and the inclinometers - rotations
correspond well to the measured ones.
30 Chapter 5. Experimental analyis - test evaluation
0 1 2 3 4 5 6 7 8 9 100
20
40
60
80
100
120
Deflection beam [mm]
M [k
Nm
]
regression leftinclinometer leftmeasured
0 1 2 3 4 5 6 7 8 9 100
20
40
60
80
100
120
Deflection beam [mm]
M [k
Nm
]
regression rightinclinometer rightmeasured
Fig. 5.10: Deflection beams test 14
5.2.3 Evaluation symmetrical loading
0 1 2 3 4 5 6 7 8
x 10−3
0
20
40
60
80
100
120
θ [−]
M [k
Nm
]
leftright
0 1 2 3 4 5 6 7 8
x 10−3
0
100
200
300
400
500
600
700
θ [−]
P [k
N]
leftright
0 1 2 3 4 5 6 7 8
x 10−3
0
100
200
300
400
500
600
θ [−]
x [m
m]
leftrightFSR
0 1 2 3 4 5 6 7 8
x 10−3
0
2
4
6
8
10
θ [−]
σ inf [N
/mm
2 ]
leftright
Fig. 5.11: Evaluation test 14
5.2. Test 14 31
All the key variables are plotted in figure 5.11. The moment-rotation diagram shows that the
two connections behave similar until the moment in the interface reaches a value of approxi-
mately 50 kNm. The two sides behave differently after that; the right connection shows a stiffer
behaviour, whereas the left connection softens with increasing moment.
The tendon force (P) remains constant during the test. The beginning of an increase is notice-
able at a rotation of 4 mrad, which would lead to the conclusion, that the gap has reached the
position of the tendon.
The neutral axis depth (x) is constant at a value of 600 mm up to a rotation of 1.0 mrad. Then
it starts to decrease, which means that the moment of decompression is at 1.0 mrad or at a
moment of approximately 40 kNm. During the test a feeler gauge was used to check whether
a gap has opened or not. A gap could be noticed at a load of 32 kN, which corresponds to a
moment of 40 kNm. The circle in the diagram shows the moment of decompression according
to the pressure sensor (FSR). The neutral axis depth gets smaller than 300 mm, which means
that the gap reaches the position of the tendon.
The stresses reach 8 MPa, which is still in the expected elastic range.
5.2.4 Evaluation symmetrical loading - constant load on right beam
0 1 2 3 4 5 6 7 80
10
20
30
40
50
60
70
80
Displacement [mm]
M [k
Nm
]
regressionmeasured
0 1 2 3 4 5 6 7 80
10
20
30
40
50
60
70
80
Displacement [mm]
M [k
Nm
]
inclinometermeasured
Fig. 5.12: Deflection beam test 14, constant load on the right beam
Figure 5.12 shows the deflections of the left beam during the test with a constant load on the
right beam. The rotations calculated from the LVDTs lead to better results than using the
rotations calculated from the inclinometers.
It can be seen from the moment-rotation-diagram (figure 5.13), that the initial stiffness of the
connection reduces with decreasing load on the right beam.
The moment of decompression occurs at the same rotation compared with the symmetric loading.
32 Chapter 5. Experimental analyis - test evaluation
0 1 2 3 4 5 6 7 8
x 10−3
0
20
40
60
80
100
120
θ [−]
M [k
Nm
]
symmetricr=20kNr=40kNr=0kN
0 1 2 3 4 5 6 7 8
x 10−3
0
100
200
300
400
500
600
θ [−]
x [m
m]
symmetricr=20kNr=40kNr=0kN
Fig. 5.13: Evaluation test 14, constant load on the right beam
5.2.5 Evaluation asymmetrical loading - constant load on left beam
Figure 5.14 shows the deflections of the right beam during the test with a constant load on
the left beam. The rotation calculated from the LVDTs leads to better results than using the
rotations calculated from the inclinometers.
0 1 2 3 4 5 6 7 80
10
20
30
40
50
60
70
80
Displacement [mm]
M [k
Nm
]
regressionmeasured
0 1 2 3 4 5 6 7 80
10
20
30
40
50
60
70
80
Displacement [mm]
M [k
Nm
]
inclinometermeasured
Fig. 5.14: Deflection beam test 14, constant load on the left beam
The moment-rotation-diagram (figure 5.15) shows a reduction of the initial stiffness of the con-
nection with decreasing load on the left beam). This effect is due to shear deformations in the
column, which only occur during asymmetrical loading.
The moment of decompression occurs basically at the same rotation compared with the sym-
metric loading. This could however not be verified with the feeler gauge during the tests. The
gap opened later compared to the symmetric loading. I.e. for the case where there is not load
on the right beam (r=0 kN) gap opening occurred at 35 kN, which is slightly later than for the
symmetric loading.
5.3. Test 15 33
0 1 2 3 4 5 6 7 8
x 10−3
0
20
40
60
80
100
120
θ [−]
M [k
Nm
]
symmetricl=20kNl=40kNl=0kN
0 1 2 3 4 5 6 7 8
x 10−3
0
100
200
300
400
500
600
θ [−]
x [m
m]
symmetricl=20kNl=40kNl=0kN
Fig. 5.15: Evaluation test 14, constant load on the left beam
5.3 Test 15
5.3.1 Initial compression
The initial compression is estimated according to section 4.1. The procedure is performed for
both beams separately (see figure 5.16).
−1 −0.5 0 0.50
100
200
300
400
500
600
Displacement [mm]
P [k
N]
WLOWL1WL2WL3
−1 −0.5 0 0.50
100
200
300
400
500
600
Displacement [mm]
P [k
N]
WROWR1WR2WR3WR4
Fig. 5.16: Initial compression test 15
The initial compression for the left beam is:
wcomp,left = 0.33mm (5.7)
For the right beam this value is slightly higher:
wcomp,right = 0.38mm (5.8)
34 Chapter 5. Experimental analyis - test evaluation
The theoretical compression can also be calculated:
wcomp,calc =P0/A
E90· bs
2=
612000/(600 · 400)
860· 280
2= 0.42mm (5.9)
The value is higher than the estimated ones for the two beams.
5.3.2 Rotation test 15
The result of the verification of the rotation for the two beams is shown in figure 5.17. The
calculated - both from the linear regression of the LVDTs and the inclinometers - rotations
correspond well to the measured ones, the results are basically identical.
0 1 2 3 4 5 6 7 8 9 100
20
40
60
80
100
120
Deflection beam [mm]
M [k
Nm
]
regression leftinclinometer leftmeasured
0 1 2 3 4 5 6 7 8 9 100
20
40
60
80
100
120
Deflection beam [mm]
M [k
Nm
]
regression rightinclinometer rightmeasured
Fig. 5.17: Deflection beams test 15
5.3.3 Evaluation symmetrical loading
All the key variables are plotted in figure 5.18. The moment-rotation diagram shows that the
two connections behave similar. The right connection shows a bit a stiffer behaviour than the
left one, but the difference is smaller than for the previous tests. This could be due to the higher
force in the tendon.
The tendon force (P) remains constant during the test.
The neutral axis depth (x) is constant at a value of 600 mm up to a rotation of 1.3 mrad. Then it
starts to decrease, which means that the moment of decompression is at 1.3 mrad or at a moment
of approximately 60 kNm. The circle in the diagram shows the moment of decompression
according to the pressure sensor (FSR). The comparison shows, that the decompression probably
occurs slightly later than estimated with the LVDTs. The neutral axis depth does not get
smaller than 300 mm, which means that the gap does not reach the position of the tendon. This
observation could also be made with the tendon force.
The stresses go up to 8 MPa, which is still in the expected elastic range.
5.3. Test 15 35
0 1 2 3 4 5 6 7 8
x 10−3
0
20
40
60
80
100
120
θ [−]
M [k
Nm
]
leftright
0 1 2 3 4 5 6 7 8
x 10−3
0
100
200
300
400
500
600
700
θ [−]
P [k
N]
leftright
0 1 2 3 4 5 6 7 8
x 10−3
0
100
200
300
400
500
600
θ [−]
x [m
m]
leftrightFSR
0 1 2 3 4 5 6 7 8
x 10−3
0
2
4
6
8
10
θ [−]
σ inf [N
/mm
2 ]
leftright
Fig. 5.18: Evaluation test 15
5.3.4 Evaluation asymmetrical loading - constant load on right beam
0 1 2 3 4 5 6 7 80
10
20
30
40
50
60
70
80
90
100
Displacement [mm]
M [k
Nm
]
regressionmeasured
0 1 2 3 4 5 6 7 80
10
20
30
40
50
60
70
80
90
100
Displacement [mm]
M [k
Nm
]
inclinometermeasured
Fig. 5.19: Deflection beam test 15, constant load on the right beam
36 Chapter 5. Experimental analyis - test evaluation
Figure 5.19 shows the deflections of the left beam during the test with a constant load on the
right beam. The rotation calculated from the LVDTs leads to better results than using the
rotations calculated from the inclinometers.
The moment-rotation-diagram shows a reduction of the initial stiffness with decreasing load on
the right beam. This effect is due to shear deformations in the column, which only occur during
asymmetrical loading.
The moment of decompression happens at the same rotation compared with the symmetric
loading.
0 1 2 3 4 5 6 7 8
x 10−3
0
20
40
60
80
100
120
θ [−]
M [k
Nm
]
symmetricr=20kNr=40kNr=0kN
0 1 2 3 4 5 6 7 8
x 10−3
0
100
200
300
400
500
600
θ [−]
x [m
m]
symmetricr=20kNr=40kNr=0kN
Fig. 5.20: Evaluation test 15, constant load on the right beam
5.3.5 Evaluation asymmetrical loading - constant load on left beam
Figure 5.21 shows the deflections of the right beam during the test with a constant load on the
left beam.
0 1 2 3 4 5 6 7 80
10
20
30
40
50
60
70
80
90
100
Displacement [mm]
M [k
Nm
]
regressionmeasured
0 1 2 3 4 5 6 7 80
10
20
30
40
50
60
70
80
90
100
Displacement [mm]
M [k
Nm
]
inclinometermeasured
Fig. 5.21: Deflection beam test 15, constant load on the left beam
5.4. Test 17 37
The initial stiffness of the connection reduces with decreasing load on the right beam, as can be
seen in the moment-rotation-diagram (figure 5.22).
The moment of decompression occurs at the same rotation compared with the symmetric loading.
0 1 2 3 4 5 6 7 8
x 10−3
0
20
40
60
80
100
120
θ [−]
M [k
Nm
]
symmetricl=20kNl=40kNl=0kN
0 1 2 3 4 5 6 7 8
x 10−3
0
100
200
300
400
500
600
θ [−]x
[mm
]
symmetricl=20kNl=40kNl=0kN
Fig. 5.22: Evaluation test 15, constant load on the left beam
5.4 Test 17
5.4.1 Initial compression
The initial compression is estimated according to section 4.1.
−1 −0.5 0 0.50
100
200
300
400
500
600
700
Displacement [mm]
P [k
N]
WLOWL1WL2WL3
−1 −0.5 0 0.50
100
200
300
400
500
600
700
Displacement [mm]
P [k
N]
WROWR1WR2WR3WR4
Fig. 5.23: Initial compression test 17
The initial compression for the left beam is:
wcomp,left = 0.35mm (5.10)
For the right beam this value is slightly higher:
38 Chapter 5. Experimental analyis - test evaluation
wcomp,right = 0.41mm (5.11)
These values are approximations, also since the LVDTs measure the initial compression at the
outer perimeter of the beam.
The theoretical compression can be calculated as follows:
wcomp,calc =P0/A
E90· bs
2=
683000/(600 · 400)
860· 280
2= 0.46mm (5.12)
The value is higher than the estimated ones for the two beams.
5.4.2 Rotation test 17
The result for the two beams is shown in figure 5.24. The calculated - both from the linear
regression of the LVDTs and the inclinometers - rotations are slightly underestimating the
measured deflections. The results for the LVDTs and inclinometers are identical though.
0 1 2 3 4 5 6 7 8 9 100
20
40
60
80
100
120
Deflection beam [mm]
M [k
Nm
]
regression leftinclinometer leftmeasured
0 1 2 3 4 5 6 7 8 9 100
20
40
60
80
100
120
Deflection beam [mm]
M [k
Nm
]
regression rightinclinometer rightmeasured
Fig. 5.24: Deflection beams test 17
5.4. Test 17 39
5.4.3 Evaluation symmetrical loading
0 1 2 3 4 5 6 7 8
x 10−3
0
20
40
60
80
100
120
θ [−]
M [k
Nm
]
leftright
0 1 2 3 4 5 6 7 8
x 10−3
0
100
200
300
400
500
600
700
θ [−]P
[kN
]
leftright
0 1 2 3 4 5 6 7 8
x 10−3
0
100
200
300
400
500
600
θ [−]
x [m
m]
leftrightFSR
0 1 2 3 4 5 6 7 8
x 10−3
0
2
4
6
8
10
θ [−]
σ inf [N
/mm
2 ]
leftright
Fig. 5.25: Evaluation test 17
All the key variables are plotted as a function of the rotation in figure 5.25. The moment-rotation
diagram shows that the two connections behave similar, no difference is noticeable. It seems,
that with increasing force in the tendon the two connection behave more similar.
The tendon force (P) remains constant during the test. No elongation of the tendon can be
noticed.
The neutral axis depth (x) is constant at a value of 600 mm up to a rotation of 1.5 mrad. Then
it starts to decrease, which means that the moment of decompression is at 1.5 mrad or at a
moment of approximately 70 kNm. During the test a feeler gauge was used to check whether
a gap has opened or not. A gap could be noticed at a load of 55 kN, which corresponds to a
moment of 68 kNm. The circle in the diagram shows the moment of decompression according
to the pressure sensor (FSR).
The stresses go up to 7 MPa, which is still in the expected elastic range.
40 Chapter 5. Experimental analyis - test evaluation
5.4.4 Evaluation asymmetrical loading - constant load on right beam
Figure 5.26 shows the deflections of the left beam during the test with a constant load on the
right beam. It is noticeable, that the rotation calculated from the LVDTs seem to lead to slightly
smaller displacements than measured.
0 1 2 3 4 5 6 7 80
10
20
30
40
50
60
70
80
Displacement [mm]
M [k
Nm
]
regressionmeasured
0 1 2 3 4 5 6 7 80
10
20
30
40
50
60
70
80
Displacement [mm]
M [k
Nm
]
inclinometermeasured
Fig. 5.26: Deflection beam test 17, constant load on the right beam
It is noticeable from the moment-rotation-diagram (figure 5.27), that the initial stiffness of the
connection gets smaller with decreasing load on the right beam. This effect is due to shear
deformations in the beam, which only occur during asymmetrical loading.
The moment of decompression happens basically at the same time compared with the symmetric
loading.
0 1 2 3 4 5 6 7 8
x 10−3
0
20
40
60
80
100
120
θ [−]
M [k
Nm
]
symmetricr=20kNr=40kNr=0kN
0 1 2 3 4 5 6 7 8
x 10−3
0
100
200
300
400
500
600
θ [−]
x [m
m]
symmetricr=20kNr=40kNr=0kN
Fig. 5.27: Evaluation test 14, constant load on the right beam
5.4.5 Evaluation asymmetrical loading - constant load on left beam
The moment-rotation-diagram (figure 5.29) shows a reduction of the initial stiffness of the con-
nection with decreasing load on the left beam. This effect is due to shear deformations in the
column, which only occur during asymmetrical loading.
5.4. Test 17 41
0 1 2 3 4 5 6 7 80
10
20
30
40
50
60
70
80
Displacement [mm]
M [k
Nm
]
regressionmeasured
0 1 2 3 4 5 6 7 80
10
20
30
40
50
60
70
80
Displacement [mm]
M [k
Nm
]
inclinometermeasured
Fig. 5.28: Deflection beam test 17, constant load on the left beam
The moment of decompression occurs at the same rotation compared with the symmetric load-
ing. This could however not be verified with the feeler gauge during the tests. The gap opened
later compared to the symmetric loading. I.e. for the case where there is not load on the right
beam (r=0 kN) gap opening occurred at 49 kN, which is a bit later than for the symmetric
loading.
0 1 2 3 4 5 6 7 8
x 10−3
0
20
40
60
80
100
120
θ [−]
M [k
Nm
]
symmetricl=20kNl=40kNl=0kN
0 1 2 3 4 5 6 7 8
x 10−3
0
100
200
300
400
500
600
θ [−]
x [m
m]
symmetricl=20kNl=40kNl=0kN
Fig. 5.29: Evaluation test 17, constant load on the left beam
42 Chapter 5. Experimental analyis - test evaluation
5.5 Test 21
5.5.1 Initial compression
−1 −0.5 0 0.50
100
200
300
400
500
600
Displacement [mm]
P [k
N]
WLOWL1WL2WL3
−1 −0.5 0 0.50
100
200
300
400
500
600
Displacement [mm]
P [k
N]
WROWR1WR2WR3WR4
Fig. 5.30: Initial compression test 21
The decompression for both beams can be estimating with a linear regression as described in
section 4.1. The initial compression for the left beam is:
wcomp,left = 0.32mm (5.13)
For the right beam this value is slightly higher:
wcomp,right = 0.3mm (5.14)
The theoretical compression can be calculated as follows:
wcomp,calc =P0/A
E90· bs
2=
554000/(600 · 400)
800· 280
2= 0.38mm (5.15)
The value is slightly higher than the estimated ones for the two beams.
5.5.2 Rotation
The rotations have to be checked for errors, since all the parameters are expressed according to
the rotation of the interface. The procedure to check the rotations is described in section 4.2.2.
The calculated - both from the linear regression of the LVDTs and the inclinometers - rotations
correspond well to the measured ones, the results are basically identical.
5.5. Test 21 43
0 1 2 3 4 5 6 7 8 9 100
20
40
60
80
100
120
Deflection beam [mm]
M [k
Nm
]
regression leftinclinometer leftmeasured
0 1 2 3 4 5 6 7 8 9 100
20
40
60
80
100
120
Deflection beam [mm]
M [k
Nm
]
regression rightinclinometer rightmeasured
Fig. 5.31: Deflection beams test 21
5.5.3 Evaluation symmetrical loading
0 1 2 3 4 5 6 7 8
x 10−3
0
20
40
60
80
100
120
θ [−]
M [k
Nm
]
leftright
0 1 2 3 4 5 6 7 8
x 10−3
0
100
200
300
400
500
600
700
θ [−]
P [k
N]
leftright
0 1 2 3 4 5 6 7 8
x 10−3
0
100
200
300
400
500
600
θ [−]
x [m
m]
leftrightFSR
0 1 2 3 4 5 6 7 8
x 10−3
0
2
4
6
8
10
12
θ [−]
σ inf [N
/mm
2 ]
leftright
Fig. 5.32: Evaluation test 21
44 Chapter 5. Experimental analyis - test evaluation
All the key variables are plotted in figure 5.32. The moment-rotation diagram shows, that the
two connections behave similar until the moment in the interface reaches a value of approxi-
mately 80 kNm. The two sides behave differently after that; the right connection shows a stiffer
behaviour, whereas the left connection is softer.
The tendon force (P) remains constant during the test. The beginning of an increase is notice-
able at a rotation of 5 mrad, which would lead to the conclusion, that the gap has reached the
position of the tendon.
The neutral axis depth (x) is constant at a value of 600 mm up to a rotation of 1.1 mrad. Then
it starts to decrease, which means that the moment of decompression is at 1.1 mrad or at a
moment of approximately 50 kNm. During the test a feeler gauge was used to check whether
a gap has opened or not. A gap could be noticed at a load of 48 kN, which corresponds to a
moment of 60 kNm. The circle in the diagram shows the moment of decompression according
to the pressure sensor (FSR). The comparison shows, that the decompression happens a later
than estimated with the LVDTs.
The stresses go up to 11 MPa, which is outside the estimated elastic range. However, no residual
deformations could be observed after the test. A measurement leap occurred at a rotation of
1.1 mrad (moment of decompression). This is due to the way the stresses are calculated: Before
decompression, equation 4.12 is used, after decompression equation 4.11.
5.5.4 Evaluation asymmetrical loading - constant load on right beam
0 1 2 3 4 5 6 7 80
10
20
30
40
50
60
70
80
90
100
Displacement [mm]
M [k
Nm
]
regressionmeasured
0 1 2 3 4 5 6 7 80
10
20
30
40
50
60
70
80
90
100
Displacement [mm]
M [k
Nm
]
inclinometermeasured
Fig. 5.33: Deflection beam test 21, constant load on the right beam
Figure 5.33 shows the deflections of the left beam during the test with a constant load on the
right beam. It is noticeable, that the rotation calculated from the LVDTs leads to better results
than using the rotations calculated from the inclinometers.
It is noticeable from the moment-rotation-diagram, that the initial stiffness of the connection
reduces with decreasing load on the right beam.
The moment of decompression occurs basically at the same roatation compared with the sym-
metric loading.
5.5. Test 21 45
0 1 2 3 4 5 6 7 8
x 10−3
0
20
40
60
80
100
120
θ [−]
M [k
Nm
]
symmetricr=0kNr=20kNr=40kN
0 1 2 3 4 5 6 7 8
x 10−3
0
100
200
300
400
500
600
θ [−]
x [m
m]
symmetricr=0kNr=20kNr=40kN
Fig. 5.34: Evaluation test 21, constant load on the right beam
5.5.5 Evaluation asymmetrical loading - constant load on left beam
Figure 5.35 shows the deflections of the right beam during the test with a constant load on the
left beam. It is noticeable, that the rotation calculated from the LVDTs leads to better results
than using the rotations calculated from the inclinometers.
0 1 2 3 4 5 6 7 80
10
20
30
40
50
60
70
80
90
100
Displacement [mm]
M [k
Nm
]
regressionmeasured
0 1 2 3 4 5 6 7 80
10
20
30
40
50
60
70
80
90
100
Displacement [mm]
M [k
Nm
]
inclinometermeasured
Fig. 5.35: Deflection beam test 21, constant load on the left beam
The moment-rotation-diagram (figure 5.36) shows a reduction of the initial stiffness of the con-
nection with decreasing load on the left beam. This effect is due to shear deformations in the
column, which only occur during asymmetrical loading.
The moment of decompression occurs at the same rotation compared with the symmetric load-
ing. This could however not be verified with the feeler gauge during the tests. The gap opened
later compared to the symmetric loading. I.e. for the case where there is not load on the right
beam (r=0 kN) gap opening occurred at 42 kN, which is a bit earlier than for the symmetric
loading.
46 Chapter 5. Experimental analyis - test evaluation
0 1 2 3 4 5 6 7 8
x 10−3
0
20
40
60
80
100
120
θ [−]
M [k
Nm
]
symmetricl=0kNl=20kNl=40kN
0 1 2 3 4 5 6 7 8
x 10−3
0
100
200
300
400
500
600
θ [−]
x [m
m]
symmetricl=0kNl=20kNl=40kN
Fig. 5.36: Evaluation test 21, constant load on the left beam
5.6 Test 22
5.6.1 Initial compression
−1 −0.5 0 0.50
100
200
300
400
500
600
Displacement [mm]
P [k
N]
WLOWL1WL2WL3
−1 −0.5 0 0.50
100
200
300
400
500
600
Displacement [mm]
P [k
N]
WROWR1WR2WR3WR4
Fig. 5.37: Initial compression test 21
The decompression for both beams can be estimating with a linear regression as described in
section 4.1. The initial compression for the left beam is:
wcomp,left = 0.33mm (5.16)
For the right beam this value is slightly higher:
wcomp,right = 0.34mm (5.17)
The theoretical compression can also be calculated as follows:
5.6. Test 22 47
wcomp,calc =P0/A
E90· bs
2=
557000/(600 · 400)
860· 280
2= 0.38mm (5.18)
The value is slightly higher than the estimated ones for the two beams.
5.6.2 Rotation
The rotations during test 22 reached very large values compared to all other tests. The LVDTs
at the beam-column interface had to be re-adjusted and some of them reached their measuring
range. This was not noticed during the test, which means that the rotations can not be estimated
from the LVDTs. The rotations for test 22 are estimated from the inclinometers, according to
section 4.2.2.
The LVDTs being out of range also caused a problem with the neutral axis depth and the
compressive stresses, which are all calculated based on the measured values of the LVDTs (see
section 4.2.2 and 4.2.6). To get reasonable values for the missing measurements of the defor-
mations in the connection interfaces, the values are re-constructed with the rotations from the
inclinometer:
WRO = θinclinometer · dWRO−WR3 + |WR3| (5.19)
By using equation (5.19) it is assumed that the cross-sections remain plain. It has to be men-
tioned, that this correction only had to be applied on the left beam and only for moments greater
than 130 kNm. The amount of modified data is therefore small.
The rotations have to be checked for errors, since all the parameters are expressed according to
the rotation of the interface. The procedure to check the rotations is described in section 4.2.2.
The result for the two beams is shown in figure 5.38. The calculated rotations correspond well
to the measured ones, the results are identical.
0 10 20 30 40 50 600
25
50
75
100
125
150
175
200
Deflection [mm]
M [k
Nm
]
inclinometer leftmeasured
0 10 20 30 40 50 600
25
50
75
100
125
150
175
200
Deflection [mm]
M [k
Nm
]
inclinometer rightmeasured
Fig. 5.38: Deflection beams test 22
48 Chapter 5. Experimental analyis - test evaluation
By plotting the displacements under the beams in one diagram (figure 5.39), it can be seen
that the two sides behave similar. The right connection shows a slightly softer tendency with
increasing moment.
0 10 20 30 40 50 600
25
50
75
100
125
150
175
200
Deflection [mm]
M [k
Nm
]
leftright
Fig. 5.39: Deflection beams test 22
5.6.3 Evaluation
All the key variables are plotted in figure 5.40.
The two beams seem to show a hysteretic behaviour in the moment-rotation-diagram (different
loading and unloading path). Since nearly no plastic deformations occurred during the test (the
residual deformation under the beams after the test was 2 mm), nearly no energy was dissipated.
The hysteretic behaviour is mainly due to loss in post-tensioning force during the test. Due to
elongation of the tendon the post-tensioning force increases, which also leads to an increase in
oil pressure in the hydraulic system. This leads to an increase of loss in hydraulic fluids, so that
the pressure and therefore the tendon force are deteriorating. The tendon force at the beginning
of the test is 557 kN, at the end 510 kN.
The tendon force (P) increases at a rotation of 6 mrad. The gap reaches the position of the
tendon and therefore elongates it as the load is increased. This elongation leads to an increase
in the tendon force. The force climbs up to 750 kN, where the tests had to be stopped in order
to prevent the tendon from failing.
The neutral axis depth (x) is constant at a value of 600 mm up to a rotation of 1.2 mrad. Then
it starts to decrease, which means that the moment of decompression is at 1.2 mrad or at a
moment of approximately 50 kNm. The neutral axis depth gets smaller than 300 mm, which
means that the gap reaches the position of the tendon. This observation could also be made
with the tendon force. For the right beam the range of altered data is visible; a discontinuity is
clearly visible at approximately 20 mrad. The left beam also shows a behaviour, which is not
correct. The height x starts to increase from a rotation of 30 mrad, which is not possible. This
5.6. Test 22 49
0 0.01 0.02 0.03 0.04 0.050
50
100
150
200
θ [−]
M [k
Nm
]
leftright
0 0.01 0.02 0.03 0.04 0.050
200
400
600
800
θ [−]
P [k
N]
0 0.01 0.02 0.03 0.04 0.050
100
200
300
400
500
600
θ [−]
x [m
m]
leftrightFSR
0 0.01 0.02 0.03 0.04 0.050
5
10
15
20
25
θ [−]
σ inf [N
/mm
2 ]
leftright
Fig. 5.40: Evaluation test 22
phenomena is due to the error in the LVDTs (out of range).
The stresses exceed 20 MPa, which is not in the expected elastic range any more. The plastic
deformations measured after the test are very small though, each beam had residual deformations
of 2 mm. Large leaps are noticeable for both interfaces. For the left interface it is due some
LVDTs being out of their measuring range, at the right interface it is due to the alteration of
the data, which is very sensitive regarding the stresses.
To have a better overview the same diagrams are plotted in figure 5.41, but only for one load
cycle.
50 Chapter 5. Experimental analyis - test evaluation
0 0.01 0.02 0.03 0.04 0.050
50
100
150
200
θ [−]
M [k
Nm
]
leftright
0 0.01 0.02 0.03 0.04 0.050
200
400
600
800
θ [−]
P [k
N]
0 0.01 0.02 0.03 0.04 0.050
100
200
300
400
500
600
θ [−]
x [m
m]
leftrightFSR
0 0.01 0.02 0.03 0.04 0.050
5
10
15
20
25
θ [−]
σ inf [N
/mm
2 ]
leftright
Fig. 5.41: Evaluation test 22 one load cycle
Chapter 6
Test summary
The moment-rotation-behaviour of a post-tensioned beam-column timber joint has been anal-
ysed extensively with a series of static bending tests. The timber joint was loaded at the end
of the beams in order to apply a moment to the connection. The tests were conducted with
various forces in the tendon, from 300 kN up to 700 kN. The experimental analysis showed, that
the connection stiffness increases with increasing tendon force.
The tests were conducted with different load cases; a series of test was conducted with an
symmetrical loading, so that the column is only loaded in compression perpendicular to the
grain. An asymmetrical load case was applied in order to load the column in compression and
shear, leading to significantly softer behaviour due to shear deformations in the column.
A final bending test was conducted in order to study the failure mode of the post-tensioned
timber joint. The vertical load on the beams was increased until the tendon elongation got so
high that the test had to be aborted. Therefore, an actual failure did not occur during the test.
However, the estimated strength in the column perpendicular to the grain was exceeded mas-
sively (at least by a factor of two) but only minor damage could be observed after disassembling
the specimen.
The performed tests showed, that a very simple semi-rigid connection can be built with post-
tensioning a timber specimen. Furthermore, the failure mode is not brittle but plastic. The
timber fails due to embedment failure perpendicular to the grain, which only leads to very small
damage in the connection.
52 Chapter 6. Test summary
Appendix A
Drawings
A.1 Specimen and instrumentation
54 Chapter A. Drawings
A.1. Specimen and instrumentation 55
0.04
0.28
0.04
WLV
3
WLO
2
WLV
1
WLV
2
WR
V3
WR
O2
WR
V1
WR
V4
WR
V2
1.25
1.25
0.70.60.7
0.06
1.6
0.36
0.025
0.301
0.437
0.571
0.644
0.622
0.574
0.2990.029
Dur
ch L
Dur
ch R
IL2
IL1
IR1
IR2
1.6
0.06
LVD
T
Incl
inom
eter
Test
spe
cim
en w
ith in
stru
men
tatio
nFr
ont v
iew
1:20
[m]
56 Chapter A. Drawings
A.1. Specimen and instrumentation 57
1.25
1.25
0.70.60.7
WR
V3
WR
O2
WR
V1
WR
V4
WR
V2
0.644
0.571
0.437
0.3010.025
Dur
ch R
Dur
ch L
0.299
0.029
0.574
0.622
IR1
IR2
IL1
IL2
WLV
3
WLO
2
WLV
1
WLV
2
LVD
T
Incl
inom
eter
Test
spe
cim
en w
ith in
stru
men
tatio
nB
ack
view
1:20
[m]
58 Chapter A. Drawings
A.1. Specimen and instrumentation 59
0.7
0.6
0.7
0.1 0.4 0.1
Test Specimen 1:20 [m]
60 Chapter A. Drawings
A.2. Specimen and test setup 61
A.2 Specimen and test setup
62 Chapter A. Drawings
A.2. Specimen and test setup 63
Test
set
up
1:25
21 1
2
64 Chapter A. Drawings
A.2. Specimen and test setup 65
1-1
2-2
66 Chapter A. Drawings
Appendix B
Test protocols
68 Chapter B. Test protocols
B.1 Test 13
Tab. B.1: Protocol test 13
Load cycle Load application Notes
No. 0 Tendon to 518 kN FSR connected at 300 kN
No. 1 symmetric 0 → 20 kN
No. 2 symmetric 0 → 40 kN
No. 3 symmetric 0 → 60 kN Gap opening at 39 kN
No. 4 symmetric 0 → 80 kN Gap opening at 41 kN
No. 5 right constant to 10 kN, left 0 → 40 kN
No. 6 right constant to 10 kN, left 0 → 60 kN
No. 7 right constant to 20 kN, left 0 → 40 kN
No. 8 right constant to 20 kN, left 0 → 60 kN
No. 9 right constant to 30 kN, left 0 → 40 kN
No. 10 right constant to 30 kN, left 0 → 60 kN
No. 11 right constant to 40 kN, left 0 → 60 kN
No. 12 right constant to 0 kN, left 0 → 40 kN
No. 13 right constant to 0 kN, left 0 → 60 kN
No. 14 left constant to 10 kN, right 0 → 40 kN Gap opening at 40 kN
No. 15 left constant to 10 kN, right 0 → 60 kN Gap opening at 40 kN
No. 16 left constant to 20 kN, right 0 → 40 kN
No. 17 left constant to 20 kN, right 0 → 60 kN Gap opening at 42 kN
No. 18 left constant to 30 kN, right 0 → 40 kN
No. 19 left constant to 30 kN, right 0 → 60 kN Gap opening at 44 kN
No. 20 left constant to 40 kN, right 0 → 40 kN Gap opening at 40 kN
No. 21 left constant to 0 kN, right 0 → 40 kN Gap opening at 45 kN
No. 22 left constant to 0 kN, right 0 → 60 kN Gap opening at 45 kN
B.2. Test 14 69
B.2 Test 14
Tab. B.2: Protocol test 14
Load cycle Load application Notes
No. 0 Tendon to 416 kN FSR connected at 200 kN
No. 1 symmetric 0 → 20 kN
No. 2 symmetric 0 → 40 kN
No. 3 symmetric 0 → 60 kN Gap opening at 33 kN
No. 4 symmetric 0 → 60 kN Gap opening at 33 kN
No. 5 right constant to 10 kN, left 0 → 40 kN
No. 6 right constant to 10 kN, left 0 → 60 kN
No. 7 right constant to 20 kN, left 0 → 40 kN
No. 8 right constant to 20 kN, left 0 → 60 kN
No. 9 right constant to 30 kN, left 0 → 40 kN
No. 10 right constant to 30 kN, left 0 → 60 kN
No. 11 right constant to 40 kN, left 0 → 60 kN
No. 12 right constant to 0 kN, left 0 → 40 kN
No. 13 right constant to 0 kN, left 0 → 60 kN
No. 14 left constant to 10 kN, right 0 → 40 kN Gap opening at 36 kN
No. 15 left constant to 10 kN, right 0 → 60 kN Gap opening at 35 kN
No. 16 left constant to 20 kN, right 0 → 40 kN Gap opening at 36 kN
No. 17 left constant to 20 kN, right 0 → 60 kN Gap opening at 36 kN
No. 18 left constant to 30 kN, right 0 → 40 kN
No. 19 left constant to 30 kN, right 0 → 60 kN Gap opening at 38 kN
No. 20 left constant to 40 kN, right 0 → 60 kN Gap opening at 40 kN
No. 21 left constant to 0 kN, right 0 → 40 kN Gap opening at 35 kN
No. 22 left constant to 0 kN, right 0 → 60 kN Gap opening at 36 kN
70 Chapter B. Test protocols
B.3 Test 15
Tab. B.3: Protocol test 15
Load cycle Load application Notes
No. 0 Tendon to 612 kN FSR connected at 400 kN
No. 1 symmetric 0 → 20 kN
No. 2 symmetric 0 → 40 kN
No. 3 symmetric 0 → 60 kN (Gap opening at 55 kN)
No. 4 symmetric 0 → 80 kN (Gap opening at 55 kN)
No. 5 left constant to 10 kN, right 0 → 40 kN
No. 6 left constant to 10 kN, right 0 → 70 kN (Gap opening at 53 kN)
No. 7 left constant to 20 kN, right 0 → 40 kN
No. 8 left constant to 20 kN, right 0 → 70 kN Gap opening at 49 kN
No. 9 left constant to 30 kN, right 0 → 40 kN
No. 10 left constant to 30 kN, right 0 → 70 kN Gap opening at 48 kN
No. 11 left constant to 40 kN, right 0 → 70 kN Gap opening at 49 kN
No. 12 left constant to 0 kN, right 0 → 40 kN
No. 13 left constant to 0 kN, right 0 → 60 kN
No. 14 right constant to 10 kN, left 0 → 40 kN
No. 15 right constant to 10 kN, left 0 → 70 kN
No. 16 right constant to 20 kN, left 0 → 40 kN
No. 17 right constant to 20 kN, left 0 → 70 kN
No. 18 right constant to 30 kN, left 0 → 40 kN
No. 19 right constant to 30 kN, left 0 → 70 kN
No. 20 right constant to 40 kN, left 0 → 70 kN
No. 21 right constant to 0 kN, left 0 → 40 kN
No. 22 right constant to 0 kN, left 0 → 60 kN
No. 23 symmetric 0 → 20 kN
No. 24 symmetric 0 → 40 kN
No. 25 symmetric 0 → 60 kN
No. 26 symmetric 0 → 70 kN
No. 27 symmetric 0 → 80 kN noise (cracking)
B.4. Test 16 71
B.4 Test 16
Tab. B.4: Protocol test 16
Load cycle Load application Notes
No. 0 Tendon to 325 kN FSR connected at 150 kN
No. 1 symmetric 0 → 20 kN
No. 2 symmetric 0 → 40 kN
No. 3 symmetric 0 → 50 kN
No. 4 symmetric 0 → 40 kN Gap opening at 25 kN
No. 5 left constant to 10 kN, right 0 → 40 kN Gap opening at 22 kN
No. 6 left constant to 10 kN, right 0 → 45 kN Gap opening at 19 kN
No. 7 left constant to 20 kN, right 0 → 40 kN Gap opening at 22 kN
No. 8 left constant to 20 kN, right 0 → 45 kN Gap opening at 23 kN
No. 9 left constant to 30 kN, right 0 → 40 kN
No. 10 left constant to 30 kN, right 0 → 45 kN
No. 11 left constant to 0 kN, right 0 → 40 kN Gap opening at 19 kN
No. 12 left constant to 0 kN, right 0 → 40 kN Gap opening at 19 kN
No. 13 right constant to 10 kN, left 0 → 40 kN
No. 14 right constant to 10 kN, left 0 → 45 kN
No. 15 right constant to 20 kN, left 0 → 40 kN
No. 16 right constant to 20 kN, left 0 → 45 kN
No. 17 right constant to 30 kN, left 0 → 40 kN
No. 18 right constant to 30 kN, left 0 → 45 kN
No. 19 right constant to 0 kN, left 0 → 40 kN
No. 20 right constant to 0 kN, left 0 → 45 kN
No. 21 symmetric 0 → 40 kN Gap opening at 23 kN
No. 22 symmetric 0 → 50 kN Gap opening at 25 kN
72 Chapter B. Test protocols
B.5 Test 17
Tab. B.5: Protocol test 17
Load cycle Load application Notes
No. 0 Tendon to 683 kN FSR connected at 500 kN
No. 1 symmetric 0 → 20 kN
No. 2 symmetric 0 → 40 kN
No. 3 symmetric 0 → 70 kN Gap opening at 54 kN
No. 4 right constant to 10 kN, left 0 → 20 kN
No. 5 right constant to 10 kN, left 0 → 40 kN
No. 6 right constant to 10 kN, left 0 → 50 kN
No. 7 right constant to 20 kN, left 0 → 40 kN
No. 8 right constant to 20 kN, left 0 → 50 kN
No. 9 right constant to 30 kN, left 0 → 45 kN
No. 10 right constant to 30 kN, left 0 → 50 kN
No. 11 right constant to 40 kN, left 0 → 50 kN
No. 12 right constant to 40 kN, left 0 → 50 kN
No. 13 right constant to 0 kN, left 0 → 40 kN
No. 14 right constant to 0 kN, left 0 → 40 kN
No. 15 left constant to 10 kN, right 0 → 20 kN
No. 16 left constant to 10 kN, right 0 → 40 kN
No. 17 left constant to 10 kN, right 0 → 50 kN Gap opening at 48 kN
No. 18 left constant to 20 kN, right 0 → 40 kN
No. 19 left constant to 20 kN, right 0 → 50 kN Gap opening at 49 kN
No. 20 left constant to 30 kN, right 0 → 40 kN
No. 21 left constant to 30 kN, right 0 → 50 kN Gap opening at 51 kN
No. 22 left constant to 40 kN, right 0 → 50 kN Gap opening at 49 kN
No. 23 left constant to 40 kN, right 0 → 50 kN Gap opening at 50 kN
No. 24 left constant to 0 kN, right 0 → 40 kN
No. 25 left constant to 0 kN, right 0 → 40 kN
No. 26 symmetric 0 → 40 kN
No. 27 symmetric 0 → 70 kN Gap opening at 54 kN
B.6. Test 18 73
B.6 Test 18
Tab. B.6: Protocol test 18
Load cycle Load application Notes
No. 0 Tendon to 560 kN FSR connected at 400 kN
No. 1 symmetric 0 → 20 kN
No. 2 symmetric 0 → 40 kN
No. 3 symmetric 0 → 60 kN Gap opening at 45 kN
No. 4 symmetric 0 → 80 kN Gap opening at 45 kN
No. 5 left constant to 10 kN, right 0 → 40 kN
No. 6 left constant to 10 kN, right 0 → 60 kN
No. 7 left constant to 20 kN, right 0 → 40 kN
No. 8 left constant to 20 kN, right 0 → 60 kN Gap opening at 45 kN
No. 9 left constant to 30 kN, right 0 → 40 kN
No. 10 left constant to 30 kN, right 0 → 60 kN Gap opening at 47 kN
No. 11 left constant to 40 kN, right 0 → 60 kN
No. 12 left constant to 40 kN, right 0 → 60 kN
No. 13 left constant to 0 kN, right 0 → 40 kN
No. 14 left constant to 0 kN, right 0 → 60 kN
No. 15 right constant to 10 kN, left 0 → 40 kN
No. 16 right constant to 10 kN, left 0 → 60 kN
No. 17 right constant to 20 kN, left 0 → 40 kN
No. 18 right constant to 20 kN, left 0 → 60 kN
No. 19 right constant to 30 kN, left 0 → 40 kN
No. 20 right constant to 30 kN, left 0 → 60 kN
No. 21 right constant to 40 kN, left 0 → 40 kN
No. 22 right constant to 40 kN, left 0 → 60 kN
No. 23 right constant to 0 kN, left 0 → 40 kN
No. 24 right constant to 0 kN, left 0 → 60 kN
No. 25 symmetric 0 → 60 kN Gap opening at 44 kN
No. 26 symmetric 0 → 85 kN Gap opening at 44 kN
No. 27 symmetric 0 → 80 kN
74 Chapter B. Test protocols
B.7 Test 19
An error occured during the tests. One cylinder was not attached properly. The cylces 1 to 7
are therefore not suitable for analysis.
Tab. B.7: Protocol test 19
Load cycle Load application Notes
No. 0 Tendon to 596 kN FSR connected at 400 kN
No. 1 symmetric 0 → 20 kN
No. 2 symmetric 0 → 40 kN
No. 3 symmetric 0 → 40 kN
No. 4 symmetric 0 → 60 kN Gap opening at 51 kN
No. 5 symmetric 0 → 60 kN Gap opening at 53 kN
No. 6 symmetric 0 → 80 kN Gap opening at 52 kN
No. 7 symmetric 0 → 80 kN Gap opening at 56 kN
No. 8 symmetric 0 → 40 kN
No. 9 symmetric 0 → 40 kN
No. 10 symmetric 0 → 60 kN Gap opening at 48 kN
No. 11 symmetric 0 → 60 kN Gap opening at 48 kN
No. 12 symmetric 0 → 90 kN Gap opening at 48 kN
No. 13 symmetric 0 → 90 kN Gap opening at 47 kN
B.8. Test 20 75
B.8 Test 20
Tab. B.8: Protocol test 20
Load cycle Load application Notes
No. 0 Tendon to 462 kN FSR connected at 300 kN
No. 1 symmetric 0 → 20 kN
No. 2 symmetric 0 → 40 kN Gap opening at 32 kN
No. 3 symmetric 0 → 40 kN Gap opening at 35 kN
No. 4 symmetric 0 → 60 kN Gap opening at 37 kN
No. 5 symmetric 0 → 60 kN Gap opening at 36 kN
No. 6 symmetric 0 → 75 kN Gap opening at 35 kN
No. 7 left constant to 10 kN, right 0 → 40 kN
No. 8 left constant to 10 kN, right 0 → 60 kN Gap opening at 34 kN
No. 9 left constant to 20 kN, right 0 → 40 kN Gap opening at 35 kN
No. 10 left constant to 20 kN, right 0 → 60 kN Gap opening at 34 kN
No. 11 left constant to 30 kN, right 0 → 40 kN Gap opening at 35 kN
No. 12 left constant to 30 kN, right 0 → 60 kN Gap opening at 35 kN
No. 13 left constant to 40 kN, right 0 → 60 kN
No. 14 left constant to 0 kN, right 0 → 40 kN Gap opening at 34 kN
No. 15 left constant to 0 kN, right 0 → 60 kN Gap opening at 35 kN
No. 16 right constant to 10 kN, left 0 → 40 kN
No. 17 right constant to 10 kN, left 0 → 60 kN
No. 18 right constant to 20 kN, left 0 → 40 kN
No. 19 right constant to 20 kN, left 0 → 60 kN
No. 20 right constant to 30 kN, left 0 → 40 kN
No. 21 right constant to 30 kN, left 0 → 60 kN
No. 22 right constant to 40 kN, left 0 → 60 kN
No. 23 right constant to 0 kN, left 0 → 40 kN
No. 24 right constant to 0 kN, left 0 → 60 kN
No. 25 symmetric 0 → 40 kN Gap opening at 37 kN
No. 26 symmetric 0 → 60 kN Gap opening at 35 kN
No. 27 symmetric 0 → 75 kN Gap opening at 37 kN
76 Chapter B. Test protocols
B.9 Test 21
Tab. B.9: Protocol test 21
Load cycle Load application Notes
No. 0 Tendon to 554 kN FSR connected at 400 kN
No. 1 symmetric 0 → 20 kN
No. 2 symmetric 0 → 40 kN
No. 3 symmetric 0 → 60 kN Gap opening at 48 kN
No. 4 symmetric 0 → 80 kN Gap opening at 48 kN
No. 5 symmetric 0 → 85 kN
No. 6 right constant to 0 kN, left 0 → 40 kN
No. 7 right constant to 0 kN, left 0 → 70 kN
No. 8 right constant to 10 kN, left 0 → 40 kN
No. 9 right constant to 10 kN, left 0 → 70 kN
No. 10 right constant to 20 kN, left 0 → 40 kN
No. 11 right constant to 20 kN, left 0 → 70 kN
No. 12 right constant to 30 kN, left 0 → 40 kN
No. 13 right constant to 30 kN, left 0 → 70 kN
No. 14 right constant to 40 kN, left 0 → 70 kN
No. 15 left constant to 0 kN, right 0 → 40 kN
No. 16 left constant to 0 kN, right 0 → 70 kN Gap opening at 42 kN
No. 17 left constant to 10 kN, right 0 → 40 kN
No. 18 left constant to 10 kN, right 0 → 70 kN Gap opening at 41 kN
No. 19 left constant to 20 kN, right 0 → 40 kN
No. 20 left constant to 20 kN, right 0 → 70 kN Gap opening at 43 kN
No. 21 left constant to 30 kN, right 0 → 40 kN
No. 22 left constant to 30 kN, right 0 → 70 kN Gap opening at 43 kN
No. 23 left constant to 40 kN, right 0 → 70 kN
No. 24 symmetric 0 → 40 kN
No. 25 symmetric 0 → 60 kN Gap opening at 45 kN
No. 26 symmetric 0 → 90 kN Gap opening at 46 kN
B.10. Test 22 77
B.10 Test 22
Tab. B.10: Protocol test 22
Load cycle Load application Notes
No. 0 Tendon to 557 kN FSR connected at 400 kN
No. 1 symmetric 0 → 40 kN
No. 2 symmetric 0 → 60 kN
No. 3 symmetric 0 → 80 kN
No. 4 symmetric 0 → 100 kN
No. 5 symmetric 0 → 120 kN
No. 6 symmetric 0 → 135 kN WLO1 and WLO2 re-adjusted
No. 7 symmetric 0 → 140 kN
No. 8 symmetric 0 → 142 kN Durch L and Durch R re-adjusted
No. 9 symmetric 0 → 143 kN
No. 10 symmetric 0 → 146 kN
No. 11 symmetric 0 → 150 kN
No. 12 symmetric 0 → 156 kN
No. 13 symmetric 0 → 150 kN
No. 14 symmetric 0 → 151 kN P = 514 kN
No. 15 symmetric 0 → 130 kN
No. 16 symmetric 0 → 133 kN
No. 17 symmetric 0 → 130 kN
No. 18 symmetric 0 → 150 kN
No. 19 symmetric 0 → 157 kN P = 510 kN
78 Chapter B. Test protocols
Appendix C
Test evaluation
80 Chapter C. Test evaluation
C.1 Test 16
C.1.1 Initial compression
The initial compression is estimated according to section 4.1.
−1 −0.5 0 0.50
100
200
300
400
500
600
Displacement [mm]
P [k
N]
WLOWL1WL2WL3
−1 −0.5 0 0.50
100
200
300
400
500
600
Displacement [mm]
P [k
N]
WROWR1WR2WR3WR4
Fig. C.1: Initial compression test 16
The initial compression is the same for both interfaces :
wcomp,left = wcomp,right = 0.23mm (C.1)
C.1.2 Rotation test 16
The procedure to check the rotations is described in section 4.2.2.
0 1 2 3 4 5 6 7 8 9 100
20
40
60
80
100
120
Deflection beam [mm]
M [k
Nm
]
regression leftinclinometer leftmeasured
0 1 2 3 4 5 6 7 8 9 100
20
40
60
80
100
120
Deflection beam [mm]
M [k
Nm
]
regression rightinclinometer rightmeasured
Fig. C.2: Deflection beams test 16
C.1. Test 16 81
C.1.3 Evaluation symmetrical loading
The moment-rotation diagram shows, that the two connections behave similar, again with a
different stiffness for higher moments.
The tendon force (P) remains constant during the test. No elongation of the tendon can be
noticed.
The neutral axis depth (x) is constant at a value of 600 mm up to a rotation of 0.8 mrad. Then
it starts to decrease, which means that the moment of decompression is at 0.8 mrad or at a
moment of approximately 20 kNm.
The stresses go up to 7 MPa, which is still in the expected elastic range.
0 1 2 3 4 5 6 7 8
x 10−3
0
20
40
60
80
100
120
θ [−]
M [k
Nm
]
leftright
0 1 2 3 4 5 6 7 8
x 10−3
0
100
200
300
400
500
600
700
θ [−]
P [k
N]
leftright
0 1 2 3 4 5 6 7 8
x 10−3
0
100
200
300
400
500
600
θ [−]
x [m
m]
leftrightFSR
0 1 2 3 4 5 6 7 8
x 10−3
0
2
4
6
8
10
θ [−]
σ inf [N
/mm
2 ]
leftright
Fig. C.3: Evaluation test 16
82 Chapter C. Test evaluation
C.1.4 Evaluation asymmetrical loading
The same observations can be made for both tests, with a constant load on the right beam or
the left beam, respectively.
The rotations calculated from the LVDTs lead to more accurate results than the rotations
calculated from the inclinometers. The moment-rotation-diagram shows a reduction of the
initial stiffness of the connection with decreasing load on the other beam.
The moment of decompression happens basically at the same time compared with the symmetric
loading.
0 1 2 3 4 5 6 7 80
10
20
30
40
50
60
70
80
Displacement [mm]
M [k
Nm
]
regressionmeasured
0 1 2 3 4 5 6 7 80
10
20
30
40
50
60
70
80
Displacement [mm]
M [k
Nm
]
inclinometermeasured
Fig. C.4: Deflection beam test 16, constant load on the right beam
0 1 2 3 4 5 6 7 8
x 10−3
0
20
40
60
80
100
120
θ [−]
M [k
Nm
]
symmetricr=20kNr=40kNr=0kN
0 1 2 3 4 5 6 7 8
x 10−3
0
100
200
300
400
500
600
θ [−]
x [m
m]
symmetricr=20kNr=40kNr=0kN
Fig. C.5: Evaluation test 16, constant load on the right beam
C.1. Test 16 83
0 1 2 3 4 5 6 7 80
10
20
30
40
50
60
70
80
Displacement [mm]
M [k
Nm
]
regressionmeasured
0 1 2 3 4 5 6 7 80
10
20
30
40
50
60
70
80
Displacement [mm]
M [k
Nm
]
inclinometermeasured
Fig. C.6: Deflection beam test 16, constant load on the left beam
0 1 2 3 4 5 6 7 8
x 10−3
0
20
40
60
80
100
120
θ [−]
M [k
Nm
]
symmetricl=20kNl=40kNl=0kN
0 1 2 3 4 5 6 7 8
x 10−3
0
100
200
300
400
500
600
θ [−]
x [m
m]
symmetricl=20kNl=40kNl=0kN
Fig. C.7: Evaluation test 16, constant load on the left beam
84 Chapter C. Test evaluation
C.2 Test 18
C.2.1 Initial Compression
−1 −0.5 0 0.50
100
200
300
400
500
600
Displacement [mm]
P [k
N]
WLOWL1WL2WL3
−1 −0.5 0 0.50
100
200
300
400
500
600
Displacement [mm]
P [k
N]
WROWR1WR2WR3WR4
Fig. C.8: Initial compression test 18
The initial compression for the left beam is:
wcomp,left = 0.32mm (C.2)
For the right beam this value is slightly higher:
wcomp,right = 0.35mm (C.3)
C.2.2 Rotation
0 1 2 3 4 5 6 7 8 9 100
20
40
60
80
100
120
Deflection beam [mm]
M [k
Nm
]
regression leftinclinometer leftmeasured
0 1 2 3 4 5 6 7 8 9 100
20
40
60
80
100
120
Deflection beam [mm]
M [k
Nm
]
regression rightinclinometer rightmeasured
Fig. C.9: Deflection beams test 18
C.2. Test 18 85
C.2.3 Evaluation symmetrical loading
The moment-rotation diagram shows, that the two connections behave similar, again with a
different stiffness for higher moments.
The tendon force (P) remains constant during the test. No elongation of the tendon can be
noticed.
The neutral axis depth (x) is constant at a value of 600 mm up to a rotation of 1.2 mrad. Then
it starts to decrease, which means that the moment of decompression is at 1.2 mrad or at a
moment of approximately 50 kNm.
The stresses go up to 7 MPa, which is still in the expected elastic range.
0 1 2 3 4 5 6 7 8
x 10−3
0
20
40
60
80
100
120
θ [−]
M [k
Nm
]
leftright
0 1 2 3 4 5 6 7 8
x 10−3
0
100
200
300
400
500
600
700
θ [−]
P [k
N]
leftright
0 1 2 3 4 5 6 7 8
x 10−3
0
100
200
300
400
500
600
θ [−]
x [m
m]
leftrightFSR
0 1 2 3 4 5 6 7 8
x 10−3
0
2
4
6
8
10
θ [−]
σ inf [N
/mm
2 ]
leftright
Fig. C.10: Evaluation test 18
86 Chapter C. Test evaluation
C.2.4 Evaluation asymmetrical loading
The same observations can be made for both tests, with a constant load on the right beam or
the left beam, respectively.
The rotations calculated from the LVDTs lead to more accurate results than the rotations cal-
cualted from the inclinometers. The moment-rotation-diagram show a reduction of the initial
stiffness of the connection with decreasing load on the other beam.
The moment of decompression happens basically at the same rotation compared with the sym-
metric loading.
0 1 2 3 4 5 6 7 80
10
20
30
40
50
60
70
80
Displacement [mm]
M [k
Nm
]
regressionmeasured
0 1 2 3 4 5 6 7 80
10
20
30
40
50
60
70
80
Displacement [mm]
M [k
Nm
]
inclinometermeasured
Fig. C.11: Deflection beam test 18, constant load on the right beam
0 1 2 3 4 5 6 7 8
x 10−3
0
20
40
60
80
100
120
θ [−]
M [k
Nm
]
symmetricr=20kNr=40kNr=0kN
0 1 2 3 4 5 6 7 8
x 10−3
0
100
200
300
400
500
600
θ [−]
x [m
m]
symmetricr=20kNr=40kNr=0kN
Fig. C.12: Evaluation test 18, constant load on the right beam
C.2. Test 18 87
0 1 2 3 4 5 6 7 80
10
20
30
40
50
60
70
80
Displacement [mm]
M [k
Nm
]
regressionmeasured
0 1 2 3 4 5 6 7 80
10
20
30
40
50
60
70
80
Displacement [mm]
M [k
Nm
]
inclinometermeasured
Fig. C.13: Deflection beam test 18, constant load on the left beam
0 1 2 3 4 5 6 7 8
x 10−3
0
20
40
60
80
100
120
θ [−]
M [k
Nm
]
symmetricl=20kNl=40kNl=0kN
0 1 2 3 4 5 6 7 8
x 10−3
0
100
200
300
400
500
600
θ [−]
x [m
m]
symmetricl=20kNl=40kNl=0kN
Fig. C.14: Evaluation test 18, constant load on the left beam
88 Chapter C. Test evaluation
C.3 Test 20
C.3.1 Initial compression
−1 −0.5 0 0.50
100
200
300
400
500
600
Displacement [mm]
P [k
N]
WLOWL1WL2WL3
−1 −0.5 0 0.50
100
200
300
400
500
600
Displacement [mm]
P [k
N]
WROWR1WR2WR3WR4
Fig. C.15: Initial compression test 20
The initial compression for the left beam is:
wcomp,left = 0.29mm (C.4)
For the right beam this value is slightly higher:
wcomp,right = 0.3mm (C.5)
C.3.2 Rotation
0 1 2 3 4 5 6 7 8 9 100
20
40
60
80
100
120
Deflection beam [mm]
M [k
Nm
]
regression leftinclinometer leftmeasured
0 1 2 3 4 5 6 7 8 9 100
20
40
60
80
100
120
Deflection beam [mm]
M [k
Nm
]
regression rightinclinometer rightmeasured
Fig. C.16: Deflection beams test 20
C.3. Test 20 89
C.3.3 Evaluation symmetrical loading
The moment-rotation plot shows, that the two connections behave similar, again with a different
stiffness for higher moments.
The tendon force (P) remains constant during the test. No elongation of the tendon can be
noticed.
The neutral axis depth (x) is constant at a value of 600 mm up to a rotation of 1.0 mrad. Then
it starts to decrease, which means that the moment of decompression is at 1.0 mrad or at a
moment of approximately 40 kNm.
The stresses go up to 9 MPa, which is outside the expected elastic range (no plastic deformations
where observed after the test).
0 1 2 3 4 5 6 7 8
x 10−3
0
20
40
60
80
100
120
θ [−]
M [k
Nm
]
leftright
0 1 2 3 4 5 6 7 8
x 10−3
0
100
200
300
400
500
600
700
θ [−]
P [k
N]
leftright
0 1 2 3 4 5 6 7 8
x 10−3
0
100
200
300
400
500
600
θ [−]
x [m
m]
leftrightFSR
0 1 2 3 4 5 6 7 8
x 10−3
0
2
4
6
8
10
θ [−]
σ inf [N
/mm
2 ]
leftright
Fig. C.17: Evaluation test 20
90 Chapter C. Test evaluation
C.3.4 Evaluation asymmetrical loading
The same observations can be made for both tests, with a constant load on the right beam or
the left beam, respectively.
The rotations calculated from the LVDTs lead to more accurate results than the rotations cal-
culated from the inclinometers. The moment-rotation-diagram shows a reduction of the initial
stiffness of the connection with decreasing load on the right beam.
The moment of decompression happens basically at the same rotation compared with the sym-
metric loading.
0 1 2 3 4 5 6 7 80
10
20
30
40
50
60
70
80
Displacement [mm]
M [k
Nm
]
regressionmeasured
0 1 2 3 4 5 6 7 80
10
20
30
40
50
60
70
80
Displacement [mm]
M [k
Nm
]
inclinometermeasured
Fig. C.18: Deflection beam test 20, constant load on the right beam
0 1 2 3 4 5 6 7 8
x 10−3
0
20
40
60
80
100
120
θ [−]
M [k
Nm
]
symmetricr=20kNr=40kNr=0kN
0 1 2 3 4 5 6 7 8
x 10−3
0
100
200
300
400
500
600
θ [−]
x [m
m]
symmetricr=20kNr=40kNr=0kN
Fig. C.19: Evaluation test 20, constant load on the right beam
C.3. Test 20 91
0 1 2 3 4 5 6 7 80
10
20
30
40
50
60
70
80
Displacement [mm]
M [k
Nm
]
regressionmeasured
0 1 2 3 4 5 6 7 80
10
20
30
40
50
60
70
80
Displacement [mm]
M [k
Nm
]
inclinometermeasured
Fig. C.20: Deflection beam test 20, constant load the on left beam
0 1 2 3 4 5 6 7 8
x 10−3
0
20
40
60
80
100
120
θ [−]
M [k
Nm
]
symmetricl=20kNl=40kNl=0kN
0 1 2 3 4 5 6 7 8
x 10−3
0
100
200
300
400
500
600
θ [−]
x [m
m]
symmetricl=20kNl=40kNl=0kN
Fig. C.21: Evaluation test 20, constant load on the left beam
92 Chapter C. Test evaluation
Nomenclature
Abbreviations
DurchL Deflection under the left beam
DurchR Deflection under the right beam
FSR Pressure sensors
IL... Inclination on the left beam
IR... Inclination on the right beam
KMD Load cell
LV DT Linear voltage displacement transducer
WL... Displacement at the left connection
WR... Displacement at the right connection
Upper-case Roman letters
A Cross section area beam
Ap Cross section area tendon
E Modulus of elasticity beam
E0,mean Modulus of elasticity parallel to the grain
E90,mean Modulus of elasticity perpendicular to the grain
Ep Modulus of elasticity tendon
F Applied load on the beam
Gmean Shear modulus
I Moment of inertia beam
Icol Moment of inertia column
Lcant Distance between interface and applied load F
94 Nomenclature
Lp Length tendon
M Moment at the interface
Masymmetric,col Moment in the column due to asymmetrical loading
N Number of strands
P Tendon force
P0 Initial tendon force
PFSR Tendon force when FSR-sensor is mounted
Pmax Applicable design load tendon
W Elastic section modulus beam
Lower-case Roman letters
b Width beam
bs Witdh column
f Distance between two LVDTs
fc,0,k Compressive strength parallel to the grain
fc,90,k Compressive strength perpendicular to the grain
fFSR Factor FSR
fp,k Tensile strength tendon
n Displacement at lower edge of the interface
w′ Inclination beam
wasymmetric Deflection beam due to asymmetric loading
wcalc Calculated deflection beam
wcomp,calc Calculated initial compression
wcomp,left Initial compression left interface
wcomp,right Initial compression right interface
wel,beam Elastic deflection beam
wmeasured Measured deflection beam
x Height compressive zone
xincl Position inclinometer measured from interface
y Displacement measured with LVDT
Nomenclature 95
Greek letters
σinf Stresses interface
θ Rotation
θasymmetric Rotation asymmetric load case
96 Nomenclature
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