ThesisPDF Available

Estimation of actuator parameters for a Reaction Wall through Pushover Analysis

Authors:
  • Ircon and partners

Abstract and Figures

A national seismic testing lab is to be built in Bulgaria. It will accommodate state of art seismic testing facilities one of which is a Reaction wall - Strong floor (RWSF). As a first step towards determining suitable actuators for it, an appropriate numerical simulation must be performed on a number of Prototypes made of different materials and composed of diverse lateral restraining systems (LRS). As part of the Thesis, the Prototype is chosen as a steel structure composed of two different LRS in both orthogonal directions - Moment Resisting Frame (MRF) and Concentrically Braced Frame (CBF). A linear seismic analysis is then carried out using the Modal Response Spectrum Analysis (MRSA) on a spatial computational model in Autodesk Robot. A brief sensitivity study is performed for determining the most conservative response spectra based on EC8. Both LRS are designed following the Capacity Design concept. The obtained results are validated and discussed. The SeismoStruct software is used to simulate a RWSF test by performing a planar nonlinear static (Pushover) analysis on the MRF and CBF. The non-linear response is verified and the necessary parameters for choosing an actuator are provided. The results are discussed with focus on uncertainties and the steps that follow.
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MSc Structural & Civil Engineering Aalborg University
MASTER’S THESIS
Estimation of actuator parameters for a Reaction Wall through
Pushover Analysis
Boris Minkov
bminko20@student.aau.dk
Aalborg University
Department of The Built Environment
Thomas Manns Vej 23
DK-9220 Aalborg Ø
www.build.aau.dk/
Title:
Master Thesis
Theme:
Seismic Analysis & Design
Thesis Period:
Spring Semester 2022
Author:
B.Eng., Boris Minkov
Supervisor, AAU:
Assoc. Prof. Lars Damkilde
Supervisor, External:
Assoc. Prof. Tzvetan Georgiev
Copies: 4
Pages: 163
Date of Completion:
09th of June 2022
Abstract:
A national seismic testing lab is to be built
in Bulgaria. It will accommodate state of
art seismic testing facilities one of which is
a Reaction wall - Strong floor (RWSF). As
a first step towards determining suitable ac-
tuators for it, an appropriate numerical sim-
ulation must be performed on a number of
Prototypes made of different materials and
composed of diverse lateral restraining sys-
tems (LRS).
As part of the Thesis, the Prototype is chosen
as a steel structure composed of two differ-
ent LRS in both orthogonal directions - Mo-
ment Resisting Frame (MRF) and Concentri-
cally Braced Frame (CBF). A linear seismic
analysis is then carried out using the Modal
Response Spectrum Analysis (MRSA) on
a spatial computational model in Autodesk
Robot. A brief sensitivity study is performed
for determining the most conservative re-
sponse spectra based on EC8. Both LRS are
designed following the Capacity Design con-
cept. The obtained results are validated and
discussed.
The SeismoStruct software is used to simu-
late a RWSF test by performing a planar non-
linear static (Pushover) analysis on the MRF
and CBF. The non-linear response is verified
and the necessary parameters for choosing
an actuator are provided. The results are dis-
cussed with focus on uncertainties and the
steps that follow.
iv
Preface
This report is created in relation to the final Master Thesis in the Master of Science program in
Structural and Civil Engineering at Aalborg University (AAU). This is a short type of thesis which
is worth 30 ECTS corresponding to 900 working hours distributed in the period between February
2022 and June 2022. The signed Thesis contract between all parties can be found in Appendix G.
Reading Guide
This document is formed of two parts:
Report, the purpose of which is to guide the reader through the process of completing the
project.
Appendix, accompanying the Report and providing an in-depth explanation in form of ad-
ditional description, formulae and supportive material.
An example of the way the Report (left) and Appendix (right) are structured is shown below:
I Part
1 Chapter
1.1 Section
1.1.1 Sub-section
Figure 1.1 Figure 1 in Section 1
Table 1.1 Table 1 in Section 1
(1.1) Equation 1 in Section 1
A Chapter
A.1 Section
A.1.1 Sub-section
Figure A.1 Figure 1 in Section A
Table A.1 Table 1 in Section A
(A.1) Equation 1 in Section A
Each chapter begins with a small synopsis which summarizes its content. The references to the
literature used in the report are provided using the Harvard-Method. If the project is wanted in
paper form, it is recommended to print in color.
v
Aalborg University
Boris Minkov
<bminko20@student.aau.dk>
vi
Contents
Preface ........................................................ 5
Acknowledgment ................................................ 5
ISetting the scene
1Experimental seismic testing ..................................... 11
1.1 Introduction 11
1.2 History 12
1.3 Facilities around the globe 12
1.4 Bulgaria’s needs 14
1.5 Problem statement 14
2Prototype ..................................................... 15
2.1 Introduction 15
2.2 Geometry 16
2.3 Sections and materials 18
2.4 Loads and actions 19
2.5 Load combinations 19
2.6 Structural systems and boundary conditions 20
2.6.1 Slab/diaphragm ....................................................21
2.6.2 Concentrically Braced Frame (CBF) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.6.3 MomentResistingFrame(MRF).........................................23
II Preliminaries
3RWSF test methods ............................................. 27
3.1 Introduction 27
3.2 Snap-back 28
3.3 Hybrid Testing 29
3.3.1 Pseudodynamic(PsD) ...............................................29
3.3.2 Realtime ........................................................30
3.3.3 Geographicallydistributed .............................................30
3.4 Pushover 31
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CONTENTS Aalborg University
3.5 Conclusion 31
4Seismic analysis & design methods ................................ 33
4.1 Introduction 33
4.2 Modal response spectrum (MRSA) 34
4.3 Pushover analysis (PA) 35
4.4 Earthquake design 36
4.4.1 Capacity design and influence of behaviour factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
III Prototype Linear Analysis & Design
5Modal Response Spectrum Analysis ............................... 41
5.1 Introduction 41
5.2 Linear computational model 42
5.3 Modal analysis parameters 43
5.4 Response spectrum 44
5.4.1 Behaviourfactor....................................................44
5.4.2 Designgroundacceleration ............................................45
5.4.3 Sensitivity study: ground and spectra types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
5.4.4 Conclusion .......................................................47
5.5 EC8 criteria and output quality assurance 48
5.5.1 Eigenperiods, mass participation and mode shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
5.5.2 Torsionaleffects....................................................50
5.5.3 Baseshear........................................................51
5.5.4 Displacements .....................................................52
5.5.5 Damagelimitation ..................................................53
5.5.6 Secondordereffects .................................................54
5.5.7 Bucklinganalysisofcolumns ...........................................55
6Capacity design ................................................ 57
6.1 CBF 57
6.1.1 Diagonals ........................................................58
6.1.2 Beams&columns ..................................................60
6.2 MRF 61
6.2.1 Beams ..........................................................61
6.2.2 Columns&connections...............................................65
7Seismic design situation ......................................... 71
7.1 Seismic load cases and combinations 71
7.1.1 Loadcases .......................................................71
7.1.2 Load combinations: dissipative elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
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Boris Minkov CONTENTS
7.1.3 Load combinations: non-dissipative elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
7.2 Member capacity check (ULS+SLS) 74
7.3 Conclusion 76
IV Prototype response assessment through Pushover analysis
8Pushover analysis .............................................. 79
8.1 Introduction 79
8.2 Non-linear computational models 80
8.2.1 Boundaryconditions.................................................81
8.2.2 Elementtypes .....................................................82
8.2.3 Modelverication ..................................................83
8.3 Constitutive model 84
8.4 Loads and mass 86
8.4.1 Massdenition ....................................................86
8.4.2 Vertical(gravity)load ................................................87
8.4.3 Lateral(incremental)load .............................................88
9Non-linear response ............................................ 89
9.1 Preliminaries 89
9.1.1 Choiceofcontrolnode ...............................................89
9.1.2 Choiceofcriteria ...................................................90
9.1.3 Choice of lateral load distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
9.2 MRF pushover curve 92
9.2.1 Yieldstages.......................................................93
9.2.2 Fracturestages.....................................................94
9.3 CBF pushover curve 95
9.3.1 Yieldandfracturestages ..............................................96
9.4 Conclusion 97
10 Discussion .................................................... 101
Bibliography ................................................. 111
VAppendix
APrototype .................................................... 115
A.1 Steel properties 115
A.1.1 Linearconstitutivemodel.............................................115
A.1.2 Non-linearconstitutivemodel..........................................115
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CONTENTS Aalborg University
A.2 Characteristic loads and actions 116
A.2.1 Trapezoidal sheet HI-BOND A55/P600 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
A.2.2 Permanentloads-kG ...............................................118
A.2.3 Imposedloads-kQ.................................................120
A.2.4 Variableactions-kS1 ...............................................121
BLinear computational model .................................... 123
B.1 Member and node numbers 123
B.2 Member definition - design parameters 126
B.3 Load cases and combinations 128
B.4 Quality assurance (QA) 129
CNon-linear computational model ................................. 135
C.1 Member and node numbers 135
C.2 Vertical (gravity) loads 137
C.2.1 MRF ..........................................................137
C.2.2 CBF...........................................................137
C.3 Lateral (incremental) loads 138
C.3.1 MRF ..........................................................138
C.3.2 CBF...........................................................139
C.4 Quality assurance (QA) 140
DModal Response Spectrum Analysis .............................. 141
D.1 Theory 141
D.1.1 Formingofaresponsespectrum ........................................141
D.1.2 Modalcombinationrules .............................................141
D.1.3 EN1998-1 [2004] response spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
D.2 Basic period check using the Rayleigh quotient 146
D.3 Sensitivity study: choice of response spectrum 147
D.4 Base shear quality assurance 149
D.5 Prototype sensitivity to second order effects 150
D.6 Prototype damage limitation 150
EPushover analysis ............................................. 151
E.1 Theory 151
FPrototype Capacity Design ...................................... 155
F.1 CBF 155
F.1.1 General ........................................................155
F.1.2 Calculation ......................................................156
F.2 MRF 157
F.2.1 General ........................................................157
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Boris Minkov CONTENTS
F.2.2 Beamplasticcapacity ...............................................158
F.2.3 Beamsegmentlateralstability..........................................159
F.2.4 SCWBconcept ...................................................159
F.2.5 Columnplasticshearcapacity..........................................159
F.2.6 Panelzone ......................................................160
F.2.7 Columnverication ................................................160
GThesis contract ................................................ 161
5
Acknowledgement
The preparation for my Master Thesis started more than a year ago during a practical placement
in the Bulgarian consultancy company - Ircon where I built a strong foundation on Earthquake
Engineering without which this work would not be possible. I would therefore want to thank once
again the entire structural engineering department of Ircon for their time and contribution during
my six months there.
I want to express my deep gratitude to Ircon’s manager, Associate Professor in the Steel structures
Division at UASG and company supervisor - Assoc. Prof. Tzvetan Georgiev. His guidance and
support helped me move in the right direction and bring sense of the confusion I was sometimes
in. I would also like to express my special gratitude to Assoc. Prof. Lars Damkilde for his
committed supervision from AAU side during the last one year of my MSc degree. I believe that
his unorthodox teaching methods and approach helped me improve significantly my research and
learning style. I am very thankful to the responsible for ELSA Reaction Wall - PhD. Pierre Pegon
for the short but very constructive and valuable conversations I had with him.
I wish to thank to my family and close friends for the support and motivation especially during the
last 2 months of my Thesis.
Last but not least I would like to extend my acknowledgement to all my Professors and teachers
who guided and helped me reach this consecrate point in my education. It is with great sense
of appreciation I wish to specially thank Prof. Pauli Andreasen for his dedicated approach to
Structural Engineering and the influence he had on me during my Bachelor’s degree in VIAUC.
7
I
1Experimental seismic testing ............ 11
1.1 Introduction
1.2 History
1.3 Facilities around the globe
1.4 Bulgaria’s needs
1.5 Problem statement
2Prototype ............................ 15
2.1 Introduction
2.2 Geometry
2.3 Sections and materials
2.4 Loads and actions
2.5 Load combinations
2.6 Structural systems and boundary conditions
Setting the scene
1Experimental seismic testing
The content in this chapter is meant to introduce the reader to what the different facilities used for
experimental seismic testing are and where the biggest of them are located worldwide. Bulgaria’s
need for such a facility is briefly discussed after which the Thesis’s problem statement is formed.
1.1 Introduction
The main challenge with seismic testing (similar to other experimental studies) is the scaling factor
which greatly impacts the structural response especially when dynamics are involved. Therefore,
it is understandable that experimental testing facilities grow in size with an aim of accommodating
as large as possible test specimens (prototypes). Furthermore, a growing amount of consulting
companies prefer to experimentally verify their numerical results on complex infrastructures such
as bridges. The two most common facility types used for experimental seismic testing are briefly
described below:
Reaction Wall Strong Floor (RWSF)
The reaction wall and strong floor are typically one structural system. The RWSF can be L
shaped (figure 1.1), rectangular or modular (re-configurable). Actuators which are anchored
to the wall gradually apply a load in very small increments on the prototype structure. This
is why this facility is used mainly for pseudo-dynamic testing (more is discussed in Chapter
3). It however allows for testing of large structures without scaling them down.
Shake table
A platform which is moved by actuators in up to its 6 DOF (see figure 1.2). This facility
allows for a fully dynamic seismic testing, simulation of accelerogram in real time, etc. The
main drawback of the shake tables is that the test specimens are very often scaled down.
Figure 1.1: RWSF concept at IIT Kanpur, India [Rai
et al., 2014]
Figure 1.2: 6 DOF shaking table concept Illustration
courtesy of MTS.
11
1. Experimental seismic testing Aalborg University
1.2 History
Earthquakes has always been one of the most destructive natural phenomenon known to hu-
mankind. Peru is known for being a highly seismic part of the world where people have adapted
their structures to resist earthquakes through trial and error. The ancient Peruvian civilization has
found that using dry-stone construction created more seismic resistant structure instead of using
mortar. It is visible in figure 1.3 how the Incas cut the stones to perfection so that they can tightly
fit and create what is known today as a shear wall.
Figure 1.3: Dry-stone walls of Machu Picchu, Peru
Today the seismic performance assessment in a laboratory has replaced (thank god) the ancient
trial and error approach used by our ancestors. It is well established methodology to calibrate pre-
dictive models and analytical formulas from experimental data since numerical studies have their
limitations. This methodology is used for developing of modern seismic codes such as EN1998-1
[2004]. Moreover, developing novel structural solutions require experimental validations in order
to ensure their safety.
In the last decades considerable advances have been achieved in the Earthquake Engineering
(EE) field. The research results have contributed to the preparation of modern design codes, to
the identification of several problems in the existing structures and to innovative solutions for the
structural assessment. [Marazzi et al., 2011]
1.3 Facilities around the globe
Some of the major labs for seismic performance assessment are shown in tables 1.1 and 1.2 on the
following page with figures 1.4 and 1.5 illustrating the largest of them.
12
Boris Minkov 1.3 Facilities around the globe
As seen in table 1.1 the capabilities of a shaking table are most often expressed using its dimen-
sions, maximum acceleration and shaking frequency it can provide. Other parameters are the
maximum velocity in the different DOF measured in mm/s, the available DOF and the maximum
weight it can accommodate.
Table 1.1: Major shaking tables around the world
Country Name Dimensions Max. acceleration Max. frequency
[mxm] [g] [Hz]
USA University of Nevada at Reno 4.3 x 4.5 1.0 50
USA University of California at San Diego 7.6 x 12.2 1.0 20
Japan E-Defense 20.0 x 15.0 1.5 50
China Tongji University in Shangai 4.0 x 6.0 1.5 50
Portugal LNEC - 6.0 -
As seen in table 1.2, the two most important parameters for a RWSF facility are the maximum force
it can apply on a prototype (actuator capacity) and the maximum distance it can push it (actuator
stroke). Its shape (U, L, rectangular), dimensions (especially heigth), RW and SF capacity are also
important factors.
Table 1.2: RWSF around the world
Country Name Max height Actuator capacity Actuator stroke
[m] [kN] [m]
Japan Building Research Institute (BRI) 25.0 1000 ±0,5
Taiwan NCREE 15.0 1000 ±0,25 to ±0,5
Italy ELSA 16.0 3000 ±0,25 to ±0,5
US NEES, Leigh University 15.2 2000 ±0,5
India IIT Kanpur 10.5 - -
Greece NTUA 6.0 500 -
Figure 1.4: ELSA RWSF in Italy [GA et al., 2014] Figure 1.5: E-Defence shake table in Japan. Photo cour-
tesy of Bosai.
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1. Experimental seismic testing Aalborg University
1.4 Bulgaria’s needs
Bulgaria is located on the Balkan Peninsula which is one of the most geodynamically active parts
not only in Europe but the whole world. It is understandable why a lot of resources has been
invested throughout the years for R&D in the Seismic Engineering field. The University of Archi-
tecture, Civil Engineering and Geodesy (UASG) in Sofia, Bulgaria has been a place where a big
part of the R&D has taken place not only on national but also on international levels. An example
of this is the EQUALJOINTS+ EU project with an aim of developing standardized seismically
qualified joints according to EN1998-1 [2004] [Landolfo, 2022] (see also figure 1.6).
Figure 1.6: Beam-to-column joints prequalified in the framework of EQUALJOINTS project: a) Bolted hunched joint
b) Bolted extended stiffened end-plate joint c) Bolted extended unstiffened end-plate joint d) Welded dog-bone joint
[ECCS, 2018]
An advanced seismic testing facility in Bulgaria is not only a good idea but rather a necessity if the
country wants to remain part of the international seismic R&D projects and community. Moreover,
this would represent a substantial advantage for the Seismic Engineering students in UASG since
it will impact the learning process by promoting and motivating the work in this field.
A project for seismic testing facility is currently being developed where both a large scale RWSF
and a shaking table are planned. Once the facility is completed it will become the largest of its
kind on the Balkan Peninsula. Currently the National Technical University of Athens hold this title
(see table 1.2). For confidentiality purposes more information on the project (drawings, location,
etc.) cannot be shared.
1.5 Problem statement
The following problem formulation is stated below:
Problem formulation
Choose, analyze & design an appropriate Prototype from steel. Perform a suitable numerical
simulation and find the necessary actuator capacity and stroke to accommodate it in the new
RWSF facility.
The following is not part of the problem formulation
The choice of the actual actuators (product).
The detail design of joints
Investigation of soil-structure interaction
Experimental validations and studies
14
2Prototype
A prototype is defined as the structure which is analyzed, designed and assessed as part of an-
swering the problem stated in section 1.5. The aim of this chapter is to introduce the reader to the
chosen structure for the Prototype. The choice of structural systems, loads and materials are all
discussed in details. Preliminary drawings/sketches of the structural joints are proposed.
2.1 Introduction
Before choosing the Prototype structure and its lateral restraining systems (LRS) a number of
consultation were made with Phd. Pierre Pegon (responsible for the largest RWSF facility in
Europe - ELSA) and Assoc. Prof. Tzvetan Georgiev (Company Supervisor and Professor in the
Steel Structures Division at UASG).
”...you have to deal with various scenario...You do not want to overestimate your needs, but at the
same time you would like to be prepared for the future!” -Pierre Pegon
Taking into consideration this feedback, it was decided to incorporate the two most common steel
lateral restraining systems (LRS) in the Prototype structure or namely the Concentrically Braced
Frame (CBF) and Moment Resisting Frame (MRF) - see figure 2.2. Having different LRS in
each orthogonal direction will yield more diverse results as their load-deflection characteristics are
different. It should be noted that the more scenarios for materials and LRS types are investigated
- the more diverse results will be obtained which will help choosing a suitable actuator for the
RWSF facility.
Figure 2.1: Members by type Figure 2.2: Investigated LRS: a) CBF b) MRF
15
2. Prototype Aalborg University
2.2 Geometry
The prototype structure is chosen to be regular in height and elevation so as not to introduce
torsional effects which would unnecessarily complicate a future experiment on it. It is part of a
three storey 10.5 m high steel office building with an inter-storey height of 3.5 m. It is composed
of three 6 m bays in both longitudinal xand transverse ydirections as shown in figure 2.3 below.
Figure 2.3: Stories and dimensions
The dimensions of the prototype structure are in accordance with the size of the future RWSF
facility. The XZ and Y Z elevation can be seen in figures 2.5 and 2.6. A plan view is provided in
figure 2.4.
16
Boris Minkov 2.2 Geometry
Figure 2.4: Plan in XY plane
Figure 2.5: Elevation in XZ plane
Figure 2.6: Elevation in Y Z plane
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2. Prototype Aalborg University
2.3 Sections and materials
The materials and steel sections are shown in table 2.1 and figure 2.7 below. The corresponding
steel properties can be seen in Appendix A.1. Please note that different properties are used for the
linear and non-linear constitutive models (see later in section 8.3).
Table 2.1: Used sections and materials by member type
Member type Section Material according to EC
Columns HEB 400 S460 N/NL
Diagonals (storey 3) CF SHS 100x3 S235 JR
Diagonals (storey 2) CF SHS 120x4 S235 JR
Diagonals (storey 1) CF SHS 140x4 S235 JR
Secondary beams IPE 270 S275 JR
MRF beams IPE 360 S275 JR
CBF beams IPE 400 S275 JR
Figure 2.7: Used sections
The shown steel sections and materials are later verified with the linear analysis and design in part
III of this report.
18
Boris Minkov 2.4 Loads and actions
2.4 Loads and actions
The applied loads and actions are discussed in detail with the company supervisor. This includes
conservative but realistic assumptions for their values and positioning. The non-seismic (vertical)
load cases are defined in table 2.2 below with reference to the corresponding tables in Appendix
A.2 where the values can be found.
Table 2.2: Non-seismic load cases as defined in Autodesk Robot [2021]
Number Name Load origin Reference
1 kG1/struct/ steel elements and slab/diaphragm tables A.3 and A.4
2 kG2/roof/ roof structure table A.5
3 kG3/floor/ floor and ceiling structure table A.6
4 kG4/wall/ external wall cladding table A.7
21 kS1/snow/ snow on the roof table A.10
22 kQ1/live/ imposed load on the roof table A.8
23 kQ2/live/ imposed load on the floors table A.9
Permanent loads kG include the structural and non-structural elements.
Variable actions kS1 of which only snow is considered. Wind actions are neglected assum-
ing that seismic actions are dominant.
Imposed loads kQ for the corresponding building category chosen for the prototype - office,
The seismic actions are applied as equivalent static forces using the Modal Response Spectrum
Method (MRSA) as described in section 4.2. This includes performing a sensitivity study in
section 5.4 for finding the most conservative spectra for the Prototype structure. The derived
seismic load cases are shown in subsection 7.1.1.
2.5 Load combinations
The SLS and ULS load combinations are defined according to EN1990 [2007] and can be seen in
Appendix B.3. Please note that the seismic load combinations are shown separately in subsections
7.1.2 and 7.1.3. The SLS criteria for the different members are defined in table 2.3 below where L
is their length/height.
Table 2.3: Defined SLS criteria for the members
Member Criteria
Beam/slab Maximum vertical deformation (final) L/200
Beam/slab Maximum vertical deformation (imposed loads) L/250
Column Maximum nodal displacement L/150
The maximum design vertical load on the slab used to choose a trapezoidal sheet product in sub-
section 2.6.1 is calculated in (2.1) below
qd=1.35kG1+1.35kG3+1.50kQ2=13.30 kN/m2(2.1)
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2. Prototype Aalborg University
2.6 Structural systems and boundary conditions
The Prototype’s structural systems alongside with the boundary conditions (BC) are summarized
in figure 2.8 below. The following subsections contain detailed description of each system and the
design measurements undertaken to ensure the chosen BC for the three main structural systems:
Slab/diaphragm - subsection 2.6.1
Concentrically Braced Frame (CBF) - subsection 2.6.2
Moment Resisting Frame (MRF) - subsection 2.6.3
Please note that the proposed design solutions are only supported with preliminary drawings/sketches
since the detailed design is not part of the Thesis’s delimitation.
The member definition parameters (example: buckling length) are shown in Appendix B.2 as
defined in Autodesk Robot [2021]. Their definition is based on the boundary conditions and
design choices discussed in the following sub sections.
Figure 2.8: Structural systems in 2 elevations and 1 plan
20
Boris Minkov 2.6 Structural systems and boundary conditions
2.6.1 Slab/diaphragm
The slab/diaphragm of the prototype is made of a com-
posite deck formed from structural trapezoidal sheeting
filled with reinforced concrete as shown in figure 2.9.
This is a widely used solution for steel structures since
it is cost effective, simple to execute and it provides ex-
cellent diaphragm behaviour in both orthogonal direc-
tion. Moreover, after a brief research it was found that
a similar solution was used in an seismic experiment
performed at ELSA’s RWSF facility [GA et al., 2014].
The TYPE A55/P600 trapezoidal sheeting solution by
METECNO [1961] is chosen. Its properties and load
bearing capacity can be found in Appendix A.2.1.
Figure 2.9: Composite slab made of trape-
zoidal sheeting and reinforced concrete
[Ganesh et al., 2005]
A reinforced concrete slab of t=95mm made of C25/30 concrete is casted on top of the 55mm
high TYPE A55/P600 steel sheeting driving the total slab thickness of t=150mm as shown in
figure 2.11. The maximum design vertical load on the trapezoidal sheet has been calculated to
qd=13.30kN/m2in (2.1). TYPE A55/P600 with t=1.2mm is able to withstand a load of
13.54kN/m2with a deflection less than L/200 (in agreement with table 2.3). The solution is
illustrated in figure 2.11 and can be seen in details in Appendix A.2.1.
As seen from figures 2.11 and 2.10 , the slab is spanning in one direction and supported on the
secondary and MRF beams. The secondary beams are hinged to the CBF beams. In this way only
1/3 of the vertical load is transferred to the MRF beams and the remaining 2/3 go to the CBF
beams. The load distribution is done in this way so as not to overload the dissipative MRF beams
with vertical load but rather have a leading lateral (seismic) combination for their design which is
a more economic solution.
Figure 2.10: Floor plan with slab span Figure 2.11: Chosen solution for supporting the
slab on the prototype structure
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2. Prototype Aalborg University
2.6.2 Concentrically Braced Frame (CBF)
The lateral stabilizing system in y-direction is formed of four identical CBFs as shown in figure
2.12. An elevation view is provided in figure 2.13 where the connection details are visible. Please
note that figure 2.14 is a preliminary sketch used for demonstrating the used connection concept -
the joints design is not in the thesis’s scope.
Figure 2.12: CBF in transverse ydirection Figure 2.13: Elevation, YZ plane, structure axis 1
Each beam-column connection is hinged
(moment released) leading to the CBF
cores (marked in figure 2.12) becoming the
stiffest system in the lateral ydirection.
This means that the largest amount of lateral
force is accumulated in the diagonals which
is desired as they are later designed as
dissipative elements. Figure 2.14 illustrates
a proposed connection design concept
where a low rotational stiffness is provided
by using a bolted joint between the CBF
beam and column. A traditional gusset plate
connection is used for connecting the di-
agonal struts and CBF beam to the column
with an emphasis on the center-lines of all
elements meeting in one point.
The base of the columns are moment
released around x(released Mx) i.e. they are
considered as pinned in the direction of the
CBF. In this way the development of the
plastic mechanism in the CBF is easier to
control. In practice this is done by reducing
the width of the base plate and keeping a
minimal ydistance between the bolts as
shown in figure 2.14.
Figure 2.14: Connection concept for detail 1.1 and 0.1 with
shown boundary conditions
22
Boris Minkov 2.6 Structural systems and boundary conditions
2.6.3 Moment Resisting Frame (MRF)
The structure is stabilized laterally by the four MRF provided in the x-direction as shown in figure
2.15. An elevation view is provided in figure 2.16 where the connection details are visible. Please
note that figure 2.17 is a preliminary sketch used for demonstrating the used connection concept -
the joints design is not in the thesis’s scope.
Figure 2.15: MRF in longitudinal xdirection Figure 2.16: Elevation, XZ plane, structure axis A
As seen in figure 2.17, the MRF beams are
fixed to the columns by means of a welded
connection. A compressible material with a
width of minimum 25mm must be placed
between the slab and column in order
to avoid the contact point between steel
and concrete. Moreover, shear connectors
(struts) are provided between the slab and
the top flange of the MRF beam which
restrict the in-plane movement of the
diaphragm. Note that this connection detail
is further examined in subsection 6.2.1.
The base of the columns is provided
with a fixed support (Mymoment is fixed).
For this purpose the rotational stiffness
around yis increased by adding a longitu-
dinal stiffener at the base plate by naturally
continuing the column’s web. Figure 2.17: Connection concept for detail 1.2 and 0.1 with
shown boundary conditions
23
II
3RWSF test methods .................... 27
3.1 Introduction
3.2 Snap-back
3.3 Hybrid Testing
3.4 Pushover
3.5 Conclusion
4Seismic analysis & design methods ....... 33
4.1 Introduction
4.2 Modal response spectrum (MRSA)
4.3 Pushover analysis (PA)
4.4 Earthquake design
Preliminaries
3RWSF test methods
The aim of this chapter is to present the most common test methods performed on a RWSF facility.
Each of them is briefly discussed after which the chapter is concluded with the most suitable one
that can be reproduced by a numerical simulation
3.1 Introduction
As previously mentioned, one of the substantial advantage of the RWSF facility is the possibility
to test large specimens without scaling them down. This, combined with the flexibility and the
wide range of test offered by a RWSF facility is often the reason for choosing it instead of a shake
table.
To show the possibilities of a RWSF test simulation, the results from DUAREM: Full-scale ex-
perimental validation of DUAl eccentrically braced frame with REMovable links performed at
ELSA’s RWSF facility (see table 1.2) are used as an example in the subsections to follow - see
figure 3.1.
Figure 3.1: Cover page of DUAREM report [GA et al., 2014]
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3. RWSF test methods Aalborg University
3.2 Snap-back
Almost all experimental studies on a RWSF be-
gin with this type of test since it provides vital
response parameters of a specimen such as its
natural frequency.
Actuators pull, with an increasing force, a ten-
sion bar which is attached to the prototype
structure. At a given point the bar fractures
(snaps) which results in an instant release of
energy causing the structure to freely vibrate.
Example for the set up of a snap-back test is
shown in figure 3.2 on the right where the ten-
sion bar can be seen marked with a red circle.
Figure 3.2: Snap-back test set up. Example from
DUAREM [GA et al., 2014]
Figures 3.3 and 3.4 below illustrate the obtained output from DUAREM snap-back test (figure
3.2). The results provide a number of important response parameters of the specimen which can
be used to obtain the damping of the structure, acquire the modal frequencies, identify the main
vibration modes, etc. This test method can also be utilized to apply an appropriate range of force
which will cause only the dissipative structural elements to yield.
Figure 3.3: Displacement time-history of a snap-back
test. Example from DUAREM [GA et al., 2014]
Figure 3.4: Load function time-history of a snap-back
test. Example from DUAREM [GA et al., 2014]
28
Boris Minkov 3.3 Hybrid Testing
3.3 Hybrid Testing
Hybrid testing (HT) is defined as one that uses a combination of numerical simulations and exper-
imental results to obtain the structural response. The different HT methods possible on a RWSF
facility depend on their execution time and location and are discussed in the following subsections.
According to Marazzi et al. [2011]: Specimen can be limited to a small substructure (the part that
is difficult to model numerically) and the remaining restoring and inertial forces can be simulated
numerically in the equation of motion. This means that for example, the part of a large bridge that
is difficult to accurately simulate numerically can first be experimentally tested. The test results
can then be used in a numerical model to simulate more precisely the non-linear behavior of the
bridge structure.
3.3.1 Pseudo dynamic (PsD)
The PsD test is a hybrid method for which the forces are applied quasi-statically (very slow).
Figure 3.5 shows an example of numerical integration of a discrete equation of motion containing
a theoretical mass matrix Mand seismic-equivalent external loads Fbut with a physical model
for the restoring forces R. This is rather smart since Ris hard to compute numerically when the
structure is within its inelastic range and influenced by material non-linearity. The physical model
can thus be reliably utilized to obtain the restoring force vector and fed back into the equation to
solve it numerically. The steps for performing a PsD test (figure 3.5) are briefly discussed below.
Figure 3.5: Hybrid testing principle: PsD MECHS [2018]
1. For each time-discrete state of an accelerogram, a target displacement uis computed from
the numerical model and applied to the physical one by means of actuators.
2. Load cells are used to record the structural response (in form of R(u)) and fed back to the
numerical model where the equation of motion can be solved since the inertial forces F(t)
are simulated numerically. In this way the non-linear and inelastic behaviour of the structure
is captured more accurately.
3. The process is repeated for every time-discrete state of the chosen accelerogram. The time
it takes to run the test depends on how the accelerogram is scaled and it may range from 1
to 5 hours until it has been completely simulated. Since the experiment is much longer than
in real time, the simulation is controlled more accurately, non-desirable results are easily
avoided and the necessary hydraulic power for the actuators can be reduced. The response
is then plotted using the time of the original accelerogram as shown in figure 3.6.
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3. RWSF test methods Aalborg University
Figure 3.6: ULS equivalent PsD test - reference displacements at each storey plotted for the time of the original
accelerogram. Example from DUAREM [GA et al., 2014]
3.3.2 Real time
The real time (also called fast) is a hybrid test during which an accelerogram is simulated in real
time. It usually takes from a couple of seconds to minutes. According to Marazzi et al. [2011],
this test is associated with many difficulties and are feasible only for relatively simple tests. Some
of the problem include, amongst all:
Time delay and response time of actuators
Influence of measurement noise on the control action
Short required computation time implying that numerical substructures with only a few
degrees of freedom can be considered since the computation must be done in real time.
Alternatively, special computational techniques should be adopted to increase computational
efficiency.
3.3.3 Geographically distributed
This type of hybrid testing involves coupling of numerical or physical models in different labo-
ratories while simultaneously performing an experiment. This testing technique is fairly new and
used rarely but continuous research is being done on the topic. The main difficulties are connected
with the high demand in networking technology and the lack of collaboration standards.
European seismic engineering research suffers from extreme fragmentation of research infras-
tructures (RI) between countries and limited access to them by the S/T community of earthquake
engineering, especially that of Europe’s most seismic regions. [SERIES, 2013]
The method has the potential to further develop the international collaboration and strengthen the
relations between laboratories. Countries that cannot meet their testing needs with the experimen-
tal infrastructure they currently own would benefit the most out of this test type.
30
Boris Minkov 3.4 Pushover
3.4 Pushover
The pushover is both a RWSF testing method and a non-linear static analysis type (section 4.3).
Actuators push the test specimen with a certain speed most often measured in mm/min (i.e. dis-
placement control) in order to avoid torsional effects that would otherwise alter the structural
response. One of the main purposes of this type of experiment is to bring the prototype to its
failure state and determine its plastic mechanism. Since the objective of the pushover analysis is
precisely the same, numerical and experimental results can be easily compared - formation and
location of plastic hinges, maximum roof displacements, damage limitations, capacity curves, etc.
(see figure 3.7)
Figure 3.7: Pushover analysis: Capacity Curve [Marabi, 2016]
A test example is shown in figure 3.8 below. It can be seen that it takes different frame shear
force (x-axis) for both frames to achieve similar frame drift displacement (y-axis). This shows the
importance of performing the test in displacement control if the lateral stabilizing systems (S and
N) have different properties (stiffness).
Figure 3.8: Pushover test results. S - south frame and N - north frame. Example from DUAREM [GA et al., 2014]
3.5 Conclusion
In order to numerically simulate a RWSF test on the Prototype discussed in in chapter 2 it is
reasonable to conclude that the most suitable one would be a Pushover simulation. This is because,
as previously mentioned, the Pushover is also a non-linear static seismic analysis method which is
further discussed in section 4.3.
31
4Seismic analysis & design methods
The aim of this chapter is to briefly describe the seismic analysis & design methods in EN1998-1
[2004] used to study the prototype. Some of the methods were previously studied in depth by the
author and presented in the form of a case study [Minkov, 2022]. For the sake of avoiding repeti-
tion, reference to the aforementioned is made whenever a more in-depth explanation is required.
4.1 Introduction
There are many seismic analysis methods available, it is however decided to delimit the choice
to what EN1998-1 [2004] can offer. Figure 4.1 below illustrate the four main seismic analysis
methods proposed by EN1998-1 [2004].
Figure 4.1: Analysis methods in EC8 [Minkov, 2022]
The Modal response spectrum analysis (MRSA) is the most preferred methods by earthquake
engineers. This is because it is one of the most well established and researched analysis methods
in EN1998-1 [2004]. Moreover, it is based on modal analysis which provides transparency of the
output that helps understand the structural response. This is the reason for choosing the MRSA to
analyse the Prototype structure (see later in chapter 5). The method is further discussed in details
in the following section 4.2.
The Pushover analysis is most often used as a tool to evaluate the structural behaviour. Its most
common use is in retrofitting and numerical assessment of old structures. As mentioned in section
3.4, it is also a RWSF test method. This makes it ideal to use as numerical tool for simulating and
assessing the response of the Prototype structure during a RWSF test (see later in part IV). The
method is further discussed in details in the following section 4.3.
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4. Seismic analysis & design methods Aalborg University
4.2 Modal response spectrum (MRSA)
The MRSA is a pseudo dynamic linear analysis method. The method takes into account the
dynamic characteristics of a structure (eigenperiod, damping, etc.) via a Modal analysis. Its
equation of motion is stated in modal form in (4.1) where ηiare the modal coordinates with i
being the investigated eigenmode.
¯mi¨
ηi+¯ci˙
ηi+¯
kiηi=¯pi(4.1)
An equivalent static load is derived from a response spectrum (Appendix D.1.1) and it simulates
the maximum response (i.e. displacement) the structure will exhibit. The method is covered in the
following five steps:
1. Perform a Modal Analysis and obtain the eigenperiod Tiof the different mode shapes i.
According to EN1998-1 [2004] at least 90% of the modal mass must be activated - this
dictates the minimum number of mode shapes ithat must be investigated.
2. Choose a suitable elastic response spectrum Sefrom EN1998-1 [2004] (figure 4.2) which
best describes the expected geodynamical environment at the location of the structure - soil
conditions, ground acceleration ag, etc.
3. Based on how ductile the structure is (dictated by the behaviour factor q) obtain the design
response spectrum Sd. Higher qcorresponds to high ductility which lowers the Sd. However,
aq>2 requires undertaking special design measurements (capacity design concept) which
ensure sufficient ductility by establishing an adequate dissipative mechanism - see more in
section 4.4.1.
4. Use the response spectrum and modal analysis results to derive a design spectral acceleration
Sd(Ti)for each of the investigated mode shapes i. The Sd(Ti)provides an equivalent static
load Pin each DOF of a given mode shape i. The load Psimulates the maximum response
(i.e. displacement) the structure will exhibit in the given mode shape for the given response
spectrum.
5. Use a modal combination method (most often CQC) to combine the response from the
different mode shapes iand obtain the final response of the structure - see also Appendix
D.1.2.
Figure 4.2: Elastic response spectrum type 1 for soil types Ato Eand ξ=5 % [EN1998-1, 2004]
34
Boris Minkov 4.3 Pushover analysis (PA)
4.3 Pushover analysis (PA)
This is a non-linear static analysis method as seen in figure 4.2, therefore its equation of motion is
as stated in (4.2) below.
[M]{¨
D}+ [C]{˙
D}+ [K(D)]{D}= [P](4.2)
The Pushover analysis works by monotonically increasing a set of static lateral forces on a non-
linear numerical model with constant gravity loads. With increase of lateral loading, the response
of the structure can be visualized through a capacity curve (top displacement - base shear)
As a first step a lateral load distribution type must be chosen. According to EN1998-1 [2004] the
following two types must be studied and the one that yields the most conservative result for the
given investigation must be used (see also figure 4.3):
1. Mass proportional (uniform) load distribution. This distribution assumes constant acceler-
ation along the structure height which means that the lateral loads are proportional to the
mass on each storey i. The force is obtained as Fi
1=mi.
2. Modal load distribution assumes acceleration which is proportional to the fundamental mode
shape m. In this case the normalized displacement Φi
mfrom the modal analysis of mode
shape mis used to obtain the lateral force as Fi
2=miΦi
m.
Figure 4.3: Load distributions methods according to EN1998-1 [2004] and the corresponding pushover response curves
[Spacone et al., 2010]
For more details regarding the theory behind the Pushover analysis please refer to Appendix E.1.
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4. Seismic analysis & design methods Aalborg University
4.4 Earthquake design
Once earthquake waves reach the surface they carry large amount of seismic energy Eseismic which
causes the ground and the buildings attached to it to shake violently. Generally, buildings can
dissipitate this energy through elastic (strain) energy Eelastic, inelastic energy Einelastic, external
Edam ping and material Eξdamping as shown in (4.3).
Eseismic =Eelastic +Einel astic +Ed amping +Eξ(4.3)
As seen in figure 4.4, the maximum elastic en-
ergy is Eelastic =1/2fyεywhich is still very
low compared to the available inelastic energy
Einelastic . This is the reason why earthquake re-
sistant structures are very often designed to dis-
sipate the energy through inelastic behaviour.
This behaviour is ensured by providing suffi-
cient ductility in lateral restraining systems of
the structure. One way to do that is through ca-
pacity design, which is discussed in the follow-
ing section 4.4.1. Another option is to increase
Edam ping by employing an external damping
mechanism such as the viscous damper shown
in figures 4.5 and 4.6, however this can be very
expensive.
Figure 4.4: Elastic and inelastic energy on a typical
stress-strain curve for steel
Figure 4.5: Fluid viscous damper employed on a bridge.
Photo courtesy of roadjz.com.
Figure 4.6: Fluid viscous damper employed on a struc-
ture. Photo courtesy of roadjz.com.
36
Boris Minkov 4.4 Earthquake design
4.4.1 Capacity design and influence of behaviour factor
The capacity design is an eartquake design method which aims at providing non-dissipative (ND)
strutural members with sufficient overstrength compared to the dissipative (D) ones. In this way it
is ensured that when D members enter in inelastic stage (energy dissipation), the ND ones remain
within their elastic limit. This is a rather smart approach since one can design the D members to
be replaceable after they have accumulated too much plastic deformations. This method can be
illustrated with a rather simple example - a chain with many brittle links (non-dissipative elements)
and a ductile (dissipative element) as shown in figure 4.7
Figure 4.7: Capacity design principle: chain with brittle and ductile links [Khoso and Naqash, 2014]
In [EN1998-1, 2004] the use of this method is required if a ductility class medium DCM or high
DCH is chosen i.e. when a behaviour factor of q>2 is selected as shown in figure 4.8. Choosing
q<4 allows for working in the linear-elastic range which does not require employing special
earthquake design procedures. However this can result in very large structural members since the
seismic energy is dissipated only through Eelastic .
However, the behaviour influences the size of the seismic loads through the response spectra: the
higher the q- the lower the spectral acceleration Sand therefore applied seismic forces - see figure
4.9. Reducing the response spectra through qis how EN1998-1 [2004] indirectly exploits the
non-linear proprieties of structures in DCM and DCH.
Figure 4.8: Influence of qon the design concepts
[EN1998-1, 2004]
Figure 4.9: Influence of qon the response spectra [Peres
et al., 2016]
37
III
5Modal Response Spectrum Analysis ...... 41
5.1 Introduction
5.2 Linear computational model
5.3 Modal analysis parameters
5.4 Response spectrum
5.5 EC8 criteria and output quality assurance
6Capacity design ....................... 57
6.1 CBF
6.2 MRF
7Seismic design situation ................ 71
7.1 Seismic load cases and combinations
7.2 Member capacity check (ULS+SLS)
7.3 Conclusion
Prototype Linear Analysis &
Design
5Modal Response Spectrum Analy-
sis
This chapter contains the documentation of the linear analysis performed on the Prototype struc-
ture (section 2) using the MRSA method previously discussed in section 4.2. The output from the
used computational model is verified and described. The criteria posed by EN1998-1 [2004] in
relation to MRSA are discussed in details.
5.1 Introduction
The three main aspects for performing the Modal Response Spectrum Analysis (MRSA) are:
Choice of computational model - section 5.2
Choice of modal analysis parameters - section 5.3
Choice of response spectrum - section 5.4
Section 5.5 contain the quality assurance of the output from the analysis and the verification of the
criteria posed by EN1998-1 [2004] in relation to MRSA. The following is part of it:
Eigenperiods, mass participation and mode shapes - subsection 5.5.1
Application of torsional effects - subsection 5.5.2
Quality assurance of base shear - subsection 5.5.3
Seismic displacements - subsection 5.5.4
Damage limitation - subsection 5.5.5
Sensitivity to second order effects - subsection 5.5.6
Buckling analysis of columns - subsection 5.5.7
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5. Modal Response Spectrum Analysis Aalborg University
5.2 Linear computational model
The well known numerical tool Autodesk Robot [2021] is used to create the computational model
(see figure 5.1) on which the MRSA is performed. The origin (0,0,0) is the crossing point of grid
A and 1 at level +0.00. The output is verified via a quality check which can be seen in Appendix
B.4. For the node and member numbers please refer to Appendix B.1.
Figure 5.1: Computational model with shown support conditions and diaphragms
The most important modelling choices and assumptions are briefly summarized in the points be-
low:
A spatial model has been used with UX UY U Z termed as translational degrees of freedom
(DOF) and RX,RY and RZ termed as rotational DOF.
A linear elastic model is used with Peffects ignored (see section 5.5.6)
The floor diaphragm is simulated by fixing only the UX,UY and RZ DOF i.e. its vertical
stiffness is neglected. In this way the MRF beams are loaded with seismic internal forces
(primarily bending moment) instead of the diaphragm.
The facade elements are modelled as cladding with no stiffness since they are non-load-
bearing part of the structure.
The foundation is modelled as rigid i.e. the soil-structure interaction is not considered as
stated in the Thesis delimitation in section 1.5.
The boundary conditions discussed in section 2.6 are simulated by fully releasing or fixing
the appropriate DOF.
42
Boris Minkov 5.3 Modal analysis parameters
5.3 Modal analysis parameters
Figure 5.2: Modal analysis parameters in Autodesk Robot [2021]
The mass is defined following EN1998-1 [2004] as shown in (5.1). Table 5.1 shows how it
is split along each storey.
The mass is lumped without rotations (diagonal mass matrix) i.e. mass rotational DoF are
neglected. According to Autodesk Robot [2021] using this type of mass matrix requires
minimum computational efforts and provides sufficiently accurate results.
The mass is activated only in Xand Ydirections i.e vertical seismic actions (Z-direction)
are not considered since it is not required by EN1998-1 [2004] and it is not a common
design practise. Moreover, in some cases activating the mass in Z-direction can lead to net
reduction in the downward action.
The accidental torsional effects are generated through mass shifting option in Autodesk
Robot [2021] (see section 5.5.2)
The rest of the parameters can be seen in figure 5.2 and are based either on recommendations
from Autodesk Robot [2021] or practical experience.
mdyn =1.0kG +0.4kS1+0.24kQ2=775t (5.1)
Table 5.1: Dynamic mass on each storey (rounded)
Storey Dynamic mass according to EC8-1
i mdyn,i
-[t]
1 265
2 265
3 245
775
43
5. Modal Response Spectrum Analysis