The use of Fuse Connectors in Cold-Formed Steel Drive-In Racks, Thesis by C.J Wodzinski, 2014

Faculty of Engineering and Information Sciences
The use of Fuse Connectors in Cold-Formed Steel Drive-In Racks
Christopher John Wodzinski
This thesis is presented as part of the requirements for the
award of the Degree of Bachelor of Engineering (Civil) of the
University of Wollongong
November 2014

For Helena Wodzinski who held indescribable pride
for her grandsons and their studies.

i
ABSTRACT
Steel pallet racking technology accommodates the demand for cost effective and space
efficient storage solutions. Due to the industrial environment inherently attracting
heavy machinery, accidental loading forces through impacts can induce a variety of
collapse mechanisms. Progressive collapse can result in severe economic and logistical
losses, the prevention of which has significant implications in terms of reducing these
losses.
This thesis focuses on the prevention of progressive collapse in the event of local
upright failure through the inclusion of fuse connectors. Fuse connectors are designed
to fail sacrificially such that the failure mechanism is inhibited and localised to the
immediate area. A fuse connector can be feasibly incorporated if capacities are reliably
defined to provide functionality throughout operational conditions and fail consistently
upon increased loads due to a local failure. Linear and nonlinear analysis are
undertaken to determine the feasibility of fuse connectors to act as a medium to prevent
the progressive failure mechanism in cold-formed steel drive-in racks.
The findings of this research suggest the feasibility of applying fuse connectors in
cold-formed steel drive-in racks is strongly dependent on the topology of the structure
and the operational conditions. Additionally, the feasibility has been found to be
strongly influenced by the modelling of structural aspects such as Rayleigh Damping
and the residual capacity of uprights following failure.

ii
ACKNOWLEDGEMENTS
I would like to extend my gratitude to my supervisor Dr. Lip Teh for his guidance
throughout the course of this thesis in addition to the later portion of my university
career. His motivation and support have proved invaluable. In addition to Dr. Teh, I
would like to thank Dr. Martin Liu and Dr. Alex Remennikov for their support in
developing the skills and knowledge of finite element analysis.
Thank you to my father Tom Wodzinski who has provided assistance throughout the
entire process and who worked to push me to maintain motivation. Thank you to my
mother and brother Sally and Nicholas Wodzinski who have been there to help me
through whenever I needed. I would like to thank my grandparents, Dr. John and
Frances Tregellas-Williams for their support across my university career.
I would like to thank Georgia Broderick for her unwavering support throughout this
past year and throughout my studies. Additionally, I would like to thank Peter Marshall
and Georgia Lyons for the support they provided throughout the past year. I really
appreciate the little thing you all have done for me to keep me pressing forward.
Special thanks must go to Christian Treloar for providing me the technical support
required to efficiently develop large numbers of finite element models. I would again
like to thank Peter Marshall for his invaluable contribution to this development
process. Without their enthusiasm to help, the analysis could not have been completed
so comprehensively.
Finally, I would like to thank and congratulate my friends who have undertaken this
journey over the past year. Specifically I’d like to thank Josiah Strong and James
Birchall for their help throughout. The support everyone has provided to each other
has been amazing and I’m glad I was able to share the time with you all.

iii
TABLE OF CONTENTS
ABSTRACT..................................................................................................................i
ACKNOWLEDGEMENTS.........................................................................................ii
TABLE OF CONTENTS............................................................................................iii
LIST OF FIGURES ....................................................................................................vi
LIST OF TABLES......................................................................................................ix
NOTATION................................................................................................................xi
1 INTRODUCTION ............................................................................................... 1
1. 1 BACKGROUND ......................................................................................... 1
1. 2 PROBLEMS ASSOCIATED WITH DRIVE-IN RACKS .......................... 3
1. 3 AIM.............................................................................................................. 4
1. 4 OBJECTIVES .............................................................................................. 4
1. 5 THESIS OUTLINE...................................................................................... 5
2 LITERATURE REVIEW..................................................................................... 6
2. 1 DESIGN SPECIFICATIONS ...................................................................... 6
2. 2 BEHAVIOUR OF DIR STRUCTURAL COMPONENTS......................... 7
2.2.1 EFFECT OF TORSION ON STRUCTURAL COMPONENTS............. 7
2.2.2 BASE PLATE CONNECTION............................................................... 7
2.2.3 BEAM END CONNECTOR ................................................................. 10
2.2.4 UPRIGHT MEMBERS.......................................................................... 12
2.2.5 RESIDUAL CAPACITY....................................................................... 13
2.2.6 BRACING.............................................................................................. 14
2.2.7 STRUCTURAL DAMPING.................................................................. 14
2.2.8 EFFECT OF LOADED PALLETS........................................................ 15
2. 3 FUSE CONNECTORS .............................................................................. 16
2. 4 BEHAVIOUR OF DRIVE-IN RACKING................................................ 17
2.4.1 OPERATIONAL CONDITIONS .......................................................... 17
2.4.2 DYNAMIC CONDITIONS ................................................................... 20
3 METHODOLOGY............................................................................................. 26
3. 1 FINITE ELEMENT MODEL .................................................................... 26
3.1.1 ANALYSIS SOFTWARE ..................................................................... 26
3.1.2 DIR TOPOLOGY .................................................................................. 26
3.1.3 STRUCTURAL MEMBERS................................................................. 29

iv
3.1.4 MEMBER MATERIAL......................................................................... 30
3.1.5 CONNECTIONS ................................................................................... 31
3.1.6 BOUNDARY CONDITIONS................................................................ 35
3.1.7 STRUCTURAL DAMPING.................................................................. 36
3.1.8 SOLVER, TIME STEP AND FREQUENCY ....................................... 37
3.1.9 MODELLING FORCES........................................................................ 38
3. 2 OPERATIONAL CONDITIONS .............................................................. 40
3.2.1 DESIGN LOADS................................................................................... 40
3.2.2 ACCIDENTAL IMPACT LOADING................................................... 41
3.2.3 INFLUENCE OF PALLETS/OSCILLATION/SWAY......................... 43
3. 3 LOCAL AND PROGRESSIVE COLLAPSE SIMULATION.................. 44
3.3.1 INITIAL UPRIGHT FAILURE............................................................. 44
3.3.3 MEMBER FAILURE PROPAGATION ............................................... 54
4 RESULTS .......................................................................................................... 56
4.1.1 ACCIDENTAL IMPACT LOADING................................................... 56
4.1.2 EFFECT OF PALLETS......................................................................... 59
4.1.3 EFFECT OF RAYLEIGH DAMPING.................................................. 61
4.1.4 FUSE CONNECTOR LOWER LIMIT ................................................. 62
4. 2 LOCAL AND PROGRESSIVE FAILURE SIMULATION..................... 63
4.2.1 REMOVALS.......................................................................................... 63
4.2.2 EFFECT OF VARIED RESIDUAL CAPACITY ON PORTAL BEAM
FORCES............................................................................................................. 65
4.2.3 SENSITIVITY OF COLLAPSE TO VARYING RESIDUAL
CAPACITY........................................................................................................ 66
4.2.4 FUSE CONNECTOR UPPER LIMIT................................................... 67
4. 3 FUSE CONNECTOR DEFINITION......................................................... 68
5 DISCUSSION .................................................................................................... 70
5.1.1 IMPACT LOCATION ........................................................................... 70
5.1.2 DIR2....................................................................................................... 71
5.1.3 EFFECT OF PALLETS......................................................................... 71
5.1.4 RAYLEIGH DAMPING........................................................................ 75

v
5. 2 FAILURE SIMULATION......................................................................... 77
5.2.1 ZERO AND LOCAL FAILURE ........................................................... 77
5.2.2 PROGRESSIVE FAILURE................................................................... 78
5.2.4 RAYLEIGH DAMPING........................................................................ 81
5. 3 FUSE CONNECTOR FEASIBILITY ....................................................... 81
5. 4 COMPARISON OF RESULTS................................................................. 83
5.4.1 CONCLUSIONS.................................................................................... 83
5.4.2 DIFFERENCES ..................................................................................... 84
6 CONCLUSIONS AND RECOMMENDATIONS ............................................ 86
6. 1 CONCLUSIONS........................................................................................ 86
6.1.1 PORTAL BEAMS UNDER IMPACT LOADING ............................... 86
6.1.2 PORTAL BEAMS FOLLOWING UPRIGHT FAILURE .................... 87
6.1.3 FUSE CONNECTOR FEASIBILITY ................................................... 88
6. 2 RECOMMENDATIONS FOR FURTHER RESEARCH......................... 89
REFERENCES..............................................................................................................I
APPENDIX A: MEMBER DETAILS.......................................................................IV
APPENDIX B: DRIVE-IN RACK DETAILS............................................................ V
APPENDIX C: RESIDUAL CAPACITY VISCOUS DAMPING TESTING
RESULTS ..................................................................................................................VI
APPENDIX D: MAXIMUM PORTAL BEAM RESULTS (IMPACTS)................VII
APPENDIX E: MAXIMUM PORTAL BEAM RESULTS (EFFECT OF PALLETS)
................................................................................................................................. VIII
APPENDIX F: MAXIMUM PORTAL BEAM RESULTS (REMOVAL)...............IX
APPENDIX G: SENSITIVITY TO COLLAPSE ANALYSIS .................................. X

vi
LIST OF FIGURES
Figure 1-1: Comparison of storage rack arrangements, Selective racking (Left) and
Drive-In Racking (Right), Dexion Shelving, (2014). .......................................... 1
Figure 1-2: Typical Drive-In Rack Components, HR Largertechnik, (2010).............. 2
Figure 1-3: Depiction of a progressive collapse failure mechanism (Left), Bay
widening due to forklift impact (Right), Gilbert and Rasmussen (2011). ........... 3
Figure 2-1: Base plate deformation mechanisms proposed by Gilbert (2010). ........... 8
Figure 2-2: An example of a beam end connector, Gilbert (2010). ........................... 10
Figure 2-3: A failed upright demonstrating residual support..................................... 13
Figure 2-4: Expected behaviour of fuse connector component under loading, Yadwad
(2011)................................................................................................................. 17
Figure 2-5: Load configurations, Yadwad (2011)...................................................... 18
Figure 2-6: Joint rotation following upright failure, Yadwad (2011)........................ 21
Figure 2-7: Bay opening, Gilbert (2010).................................................................... 22
Figure 3-1: DIR topology notation conventions, Yadwad (2011). ............................ 27
Figure 3-2: DIR1 Topology, Yadwad (2011). ........................................................... 27
Figure 3-7: Connections between members, Gilbert (2010)...................................... 31
Figure 3-8: Connection between uprights and frame bracing, Gilbert (2010)........... 32
Figure 3-9: Upright to rail beam connection.............................................................. 32
Figure 3-10: Portal and rail beam end releases applied (Shown in black)................. 33
Figure 3-11: Upright to Portal Beam Connection, Gilbert (2010)............................. 33
Figure 3-12: Upright to Spine Bracing Connection, Gilbert (2010).......................... 34
Figure 3-13: Upright to Plan Bracing Connection, Gilbert (2010)............................ 35
Figure 3-14: DIR2 boundary rotational stiffness’ as determined by Yadwad (2011).
............................................................................................................................ 36
Figure 3-15: Strand7 Rayleigh Damping Definition.................................................. 37
Figure 3-16: Observed difference in sample rates, Yadwad (2011). ......................... 38
Figure 3-17: Original pallet loading on lowest rail beams......................................... 39
Figure 3-18: The Impact Impulse Function applied in Strand7................................. 39

vii
Figure 3-19: The removal function applied in Strand7.............................................. 40
Figure 3-20: DIR2 impact location. ........................................................................... 42
Figure 3-21: Modelling the influence of pallets on DIR4.......................................... 44
Figure 3-22: Application of supporting force (black) and moments (red)................. 46
Figure 3-23: Nonlinear transient dynamic loading options. ...................................... 46
Figure 3-24: Spring-Damper element, Strand7 (Strand7 2010)................................. 47
Figure 3-25: Example of the residual capacity’s effect on the axial force, Yadwad
(2011)................................................................................................................. 48
Figure 3-26: Comparison of nodal displacement between varying residual capacity
mechanisms........................................................................................................ 50
Figure 3-27: The effect of varied damping values on rate of nodal displacement..... 50
Figure 3-28: Residual support reaction...................................................................... 51
Figure 3-29: Oscillatory effects following removal of DIR2 1A............................... 52
Figure 3-30: Applied residual capacity mechanism................................................... 52
Figure 3-31: Residual capacity component properties............................................... 53
Figure 3-32: Swinging motion observed following removal, Yadwad (2011). ......... 54
Figure 5-1: Displacement at mid-span of upright 5A following impact.................... 72
Figure 5-2: Displacement at mid-span of upright 5A following impact, incorporating
the effect of pallets............................................................................................. 72
Figure 5-3: Front View of DIR4 following an impact on upright 5A showing bay
opening............................................................................................................... 73
Figure 5-4: Plan View of DIR4 following an impact on upright 5A showing bay
opening............................................................................................................... 73
Figure 5-5: Front View of DIR4 following an impact on upright 5A showing load
redistribution. ..................................................................................................... 73
Figure 5-6: Plan View of DIR4 following an impact on upright 5A showing load
redistribution. ..................................................................................................... 74
Figure 5-7: Front View of DIR4 following an impact on upright 3A showing portal
beam tensile force magnitudes (10kN, Pink to -20kN, Blue). ........................... 75
Figure 5-8: Front View of DIR4 following an impact on upright 3A showing portal
beam tensile force magnitudes (10kN, Pink to -20kN, Blue) including pallets
effects................................................................................................................. 75
Figure 5-9: Oscillation occurring in DIR3 following impact on upright 2A (0%
Rayleigh Damping)............................................................................................ 76

viii
Figure 5-10: Oscillation occurring in DIR3 following impact on upright 2A (5%
Rayleigh Damping)............................................................................................ 76
Figure 5-11: DIR2 zero collapse mechanism following 1A removal. ....................... 77
Figure 5-12: DIR3 local collapse mechanism following 9A removal. ...................... 78
Figure 5-13: Front View, DIR3 2A Removal ............................................................ 79
Figure 5-14: Plan View, DIR3 2A Removal.............................................................. 79
Figure 5-17: Plan View, DIR4 3A Removal.............................................................. 80
Figure 5-18: Disruption of load path continuity between low and high stiffness regions
due to upright failure, Yadwad (2011)............................................................... 84
Figure 6-1: Pallet model as presented by Gilbert (2010)........................................... 89

ix
LIST OF TABLES
Table 3-1: G450 Steel Material Properties................................................................. 30
Table 3-2: Member capacity and residual capacity values calculated for different
localised failure elevations, Yadwad (2011)...................................................... 48
Table 4-1: Maximum portal beam axial forces for all DIR topologies (Operational
Conditions)......................................................................................................... 56
Table 4-2: Maximum portal beam axial forces for DIR1 (Operational Conditions) . 57
Table 4-7: Effect of Pallets on Maximum portal beam axial forces in DIR4 (Original
Load) (0% Rayleigh Damping).......................................................................... 59
Table 4-8: Effect of Pallets on Maximum portal beam axial forces in DIR4 (Increased
Table 4-9: Effect of Pallets on Maximum portal beam axial forces in DIR4 (Original
Table 4-10: Effect of Pallets on Maximum portal beam axial forces in DIR4 (Increased
Table 4-11: Effect of Rayleigh Damping on Maximum portal beam axial forces in
DIR3 (Operational Conditions).......................................................................... 61
Table 4-12: Effect of Rayleigh Damping on Maximum portal beam axial forces in
DIR4 (Operational Conditions).......................................................................... 62
Table 4-13: Fuse Connector Lower Limits for all DIR Topologies........................... 62
Table 4-14: Maximum portal beam axial forces for all DIR topologies (Removal
Conditions)......................................................................................................... 63
Table 4-15: Maximum portal beam axial forces in DIR1 (Removal Conditions) ..... 63
Table 4-20: Maximum portal beam axial force in DIR4 following 2A removal for
varying residual capacities................................................................................. 66

x
Table 4-21: Maximum portal beam axial force in DIR4 following 2A removal for
varying residual capacities................................................................................. 66
Table 4-22: Sensitivity of collapse of 4B to varying residual capacities following 4A
removal. (0% Rayleigh Damping) ..................................................................... 66
Table 4-23: Sensitivity of collapse of 4B to varying residual capacities following 4A
removal. (5% Rayleigh Damping) ..................................................................... 67
Table 4-24: Fuse Connector Upper Limits for all DIR Topologies........................... 67
Table 4-25: Summary of fuse connector feasibility for all DIR topologies............... 68
Table 4-26: Maximum portal beam axial forces for all DIR topologies (Removal
Conditions)......................................................................................................... 69

xi
NOTATION
Latin symbols
b Base plate width mm
d Base plate depth mm
dcog Distance from forklift mast to pallet centre of gravity mm
Ec Elastic modulus of floor material MPa
Es Elastic modulus of the drive-in rack material MPa
Fimp Dynamic forklift impact force kN
Fout-of-plumb Force due to out-of-plumb kN
g Gravitational acceleration m·s-2
h Upright height mm
Hrack Height of drive-in rack mm
Himp Height of forklift impact mm
I Second moment of area of upright mm4
kh Limiting stiffness of the base plate kN·mm-1
krz Initial upright rotational stiffness about minor axis kN·mm-1
Effective upright length mm
m Mass of pallets kg
M Moment at base plate kN·m
Mbx Nominal member capacity (x-axis) kN·m
Mby Nominal member capacity (y-axis) kN·m
Mx
* Design bending moment (x-axis) kN·m
My
* Design bending moment (y-axis) kN·m
Mzu Ultimate moment about the cross-aisle axis of the upright kN·m
n Base plate moment rotation curve parameter
nb Number of interconnected bays
N Normal force kN
N* Design axial compression kN
Nc Nominal capacity of a member in compression kN
Ns Nominal capacity of a cross section in compression kN

xii
Noc Upright elastic buckling load kN
W Vertical load on drive-in rack component for out-of-
plumb
kN
Greek symbols
α Lateral forklift truck rotation Radians
αnx Moment amplification factor (x-axis)
αny Moment amplification factor (y-axis)
θ Out-of-plumb angle Radians
θb Base plate rotation Radians
ϕb Bending capacity reduction factor
ϕc Compression capacity reduction factor
Φ1 Initial connection looseness Radians
Ψ0 Initial out-of-plumb Radians

1
1 INTRODUCTION
1. 1 BACKGROUND
Steel storage racking is utilised throughout industry as a cost efficient storage solution
for the storage of goods. Structural designs range from small scale household
applications to larger scale projects such as pallet racking. Steel racks have been
identified as a cost efficient solution due to material costs constituting approximately
80% of the total cost of the rack structure (Ng, 2009). This is due to minimisations in
material and manufacturing costs associated with cold-formed steel sections. For
heavier loading conditions, hot-rolled sections may be utilised due to their increased
loading capacity although typically this will result in increased costs relative to cold-
formed sections. Due to the competitive nature of the industry the practice of reducing
costs result in racks being designed as close to capacity within standards.
Figure 1-1: Comparison of storage rack arrangements, Selective racking (Left) and
Drive-In Racking (Right), Dexion Shelving, (2014).
The two most common types of steel storage racking are ‘Selective Racks’ and ‘Drive-
in Racks’ (DIRs). Selective Racking feature one pallet deep storage capacity which
allows the retrieval of pallets as requested. These racks are utilised in applications
where a large variation of goods are required to be stored. Due to the depth of these
racks, bracing can be provided where required without compromising retrieval
efficiency. DIRs comparatively provide a more economical solution to selective
racking when storing uniform goods. DIRs provide high density storage of goods
though when compared with Selective Racking are limited in the retrieval as they
operate by a ‘First In Last Out’ principle. The high density of storage is due to the

2
arrangement of the system where rack depth can be anywhere from 3 to 7 pallets
resulting in reduced aisles and therefore increased storage space. This requires forklifts
to enter the racking structure in order to retrieve the pallets. Due to this, bracing options
are limited relative to selective racks. Additionally, accidental impacts are more likely
to occur during operation in DIR systems due to loading and loading processes
associated with DIR structures.
Figure 1-2: Typical Drive-In Rack Components, HR Largertechnik, (2010).
In DIR structures, frames are connected via portal beams in the down-aisle direction
and rail beams in the cross-aisle direction. Frames are constituted by two consecutive
uprights linked together by cross aisle bracing. Each upright is anchored to the ground
through the incorporation of base plate assemblies. The number of frames connected
is determined by the depth required for storage. As mentioned previously, rail beams
provide a linkage between frames in the cross aisle direction while they also support
and transfer pallet loads to the system. Spine bracing is included to provide stability in
down-aisle direction while plan bracing provides stability in both cross and down aisle
direction. Typically, spine bracing is located either at the back of the structure though
in alternate arrangements such as double-entry DIRs. This bracing is located in the
centre allowing accessibility from both sides. Cross-aisle bracing is provided in the
vertical plane between uprights in addition to rail beams.

3
1. 2 PROBLEMS ASSOCIATED WITH DRIVE-IN RACKS
The nature of cold formed steel racking presents an inherent risk of collapse due
application of slender uprights subject to complex loading situations. Specifications
until recently have omitted design considerations for DIRs, focusing specifically on
selective racking. These specifications can be utilised for the induction of accidental
loading although do not propose procedures to mitigate progressive collapse failure.
Literature must therefore be sought in order to perform such analysis. When
conducting analysis, impacts should be applied at the least favourable location in order
to produce the most critical response. It is commonly believed that selective racking
experiences the greatest response induced by an impact when the lowest part of
uprights are obstructed. DIRs respond differently when the impact forces is applied at
the span of upright sections bowing occurs (Figure 1-3) which may result in pallet drop
through causing overloading. Forklift loading due to accidental impacts have been
deemed to be the most likely cause of member failure and occur when forklift trucks
are entering/exiting or manoeuvering pallets within the aisles. (Zhang, Gilbert, &
Rasmussen 2012, Gilbert, Teh, Badet, & Rasmussen, 2014)
Figure 1-3: Depiction of a progressive collapse failure mechanism (Left), Bay
widening due to forklift impact (Right), Gilbert and Rasmussen (2011).
Progressive collapse is initiated typically by localised upright failure due to an impact
from a forklift truck. Redistribution of pallet load can occur either due to the opening
up of bays initiated by the bowing of an impacted upright, or by the failure of
supporting uprights. Bowing of uprights facilitates pallets to drop through rail beams
causing the propagation of failure thus overloading of the system. A limiting factor to
which propagation will occur in selective racks was discussed by McConnel and Kelly
(1983) in which the pull out strength of pallet beam to upright connections would
dictate the likelihood of the failure mechanism occurring. It was proposed that in cases

4
where these connections failed prior to propagation of local collapse, confinement of
the failure could be achieved.
Yadwad (2011) investigated the effect of fuse connectors in order to halt the
development of the progressive mechanism following local collapse. In the design of
these components, it is important to account for the typical operational conditions such
as out-of-plumb, accidental impact and seismic loading factors in addition to the
failure loads experienced due to collapse. Yadwad (2011) proposed the importance in
identifying the operational strength under such conditions and discussed the feasibility
of applying sacrificial connections in order to disengage under the increased loads
associated with propagation.
1. 3 AIM
The aim of this thesis is to investigate the feasibility of incorporating fuse connectors
into design in order to prevent the progressive collapse of a cold-formed steel drive-in
rack in the event of a local upright failure.
1. 4 OBJECTIVES
The following is a list of objectives that will contribute towards achieving the aim
presented in Section 1.3.
1. Conduct a literature review regarding the design and behaviour of cold-formed
steel drive-in storage racks under both static (operational) and dynamic
(impact) conditions.
2. Re-analyse maximum portal beam tensile forces and verify previous finite
element model results Yadwad (2011).
3. Investigate the response of pallet influence and Rayleigh Damping on portal
beam forces.
4. Refine residual capacity model to be applied in conjunction with a newly
developed model.
5. Develop finite element model for various arrangements of drive-in racks.
6. Apply both linear and nonlinear inelastic techniques to determine the
maximum and minimum portal beam tensile forces experienced during
operation and after local failure.

5
7. Provide recommendations regarding the feasibility of using fuse connectors to
prevent progressive collapse of cold-formed steel drive-in racks of various
arrangements.
1. 5 THESIS OUTLINE
This thesis is structured as follows:
• Chapter 1 provides an introduction to the general problem associated with
steel drive-in racks explored throughout this thesis and justification of research.
• Chapter 2 reviews literature relevant to design, analysis and behaviour of steel
drive-in racks and their components.
• Chapter 3 establishes the methodology applied in achieving the aim and
objectives of this thesis. Details of the finite element model and the processes
of analysis are included.
• Chapter 4 presents the results of the finite element analysis undertaken.
• Chapter 5 presents discussions of the analysis results in addition to the
implications and applicability.
• Chapter 6 establishes conclusions drawn from analysis addressing the aim and
objectives of this thesis. Additional information regarding improvements and
suggestions for further research has been presented.

6
2 LITERATURE REVIEW
This literature review presents an overview of the current standard principles for
structural design associated with steel storage racking. Following this overview, the
behaviour of key structural components is described. A description of the behaviour
of fuse connectors is then presented.
2. 1 DESIGN SPECIFICATIONS
The most commonly adopted design specifications throughout the industry for the
design of storage racking are the European Standard EN 15512 (2009), the Fédération
Européenne de la Manutention FEM 10.2.07 (2011), the Australian Standard AS 4084
(2012) and the American Rack Manufacturers Institute (RMI) Specification ANSI
MH16.1 (2012). Each standard examines the design of storage racking to varying
degrees. EN 15512 (2009) has been determined to contain the most advanced
modelling provisions by Rasmussen and Gilbert (2013). Limitations due to
peculiarities of DIR and DTRs do not allow the full application of this standard.
Further to this, AS 4084 (2012) and ANSI MH16.1 (2012) equally display insufficient
scope for the consideration of DIR and DTR design. The highly anticipated revision
of FEM 10.2.07 (2011) describes structural design principles and requirements
specifically applicable to DIR and DTR structures. These procedures though are
supplementary, and therefore additional design shall be undertaken in accordance with
EN 15512 (2009).
FEM 10.2.07 (2011) offers a standard including the principles of DIR and DTR
structures. The new code, based on the safety and design concept of the European
Standards Series “Steel Static Storage Systems”, now provides supplementary
guidance accepted by both AS 4084 (2012) and EN 15512 (2009). The procedure
instructed by FEM 10.2.07 (2011) states that design by calculation alone may not be
appropriate. Test procedures therefore have been specified for the situations where
current analytical methods are not given, or are not appropriate.
Although comparatively comprehensive, relative to previously adopted standards (EN
15512, 2009), FEM 10.2.07 (2011) does not consider the formation and effects of
progressive collapse failure mechanisms. It is important to consider the method in
which the DIR structure must be analysed in order to obtain an accurate response upon

7
loading. The structure of FEM 10.2.07 (2011) presents global analysis methods which
only consider static and reasonably simple dynamic response. Procedures to analyse
the dynamic conditions experienced by the removal of an upright have been explored
by many including Marjanishvili (2004) and Izzuddin, Vlassis, Elghazouli &
Nethercot (2008). Due to the limited guidance provided from design specifications,
additional literature will be explored on the dynamic conditions experienced by DIR
structures in Section 2. 4. (pg. 17).
2. 2 BEHAVIOUR OF DIR STRUCTURAL COMPONENTS
2.2.1 EFFECT OF TORSION ON STRUCTURAL COMPONENTS
FEM 10.2.07 (2011) outlines corrections dependant on the global analysis method
undertaken for open section components to incorporate the effects of torsional and
flexural torsional buckling. Corrections which have been proposed are based on
analytical calculations dependant on the shape of the upright profiles. Strand7 (Strand7
2010) considers Saint-Venant torsional while omitting warping torsional effects.
Additionally, FEM 10.2.07 (2011) allows corrections to be disregarded upon
demonstration that upright profiles are not susceptible to torsional effects.
2.2.2 BASE PLATE CONNECTION
Generally, storage racking is connected to the floor through base plate connections
which are bolted to the floor providing a semi-rigid restraint. The significance of base
plate stiffness in terms of the structural stiffness has been determined non negligible
(Baldassino & Bernuzzi, 2000) due to the reduction of upright buckling lengths
(Freitas, Souza & Freitas, 2010). Additionally, base plate stiffness has been found to
be an important factor in down-aisle stability while plate thickness has been found to
influence the rotational stiffness of the assembly (Freitas et. al. 2010). Due to these
findings, it is essential for the accurate representation of the global structure for the
connection stiffness to be correctly modelled.
Gilbert (2010) found that the deformation of the base plate connection can be divided
into four separate categories whereby each contribute towards the total
deformation/rotation of the connection, though all categories may not all be acting
simultaneously.

8
Each deformation mechanism has been presented by Gilbert (2010) in Figure 2-1. The
mechanisms are:
• the local deformation of concrete floor (Diagram a)
• bending of the base plate bracket (Diagram b)
• bending and local deformation of upright (Diagram c)
• combined flexure and yield line formation in the base plate resulting in plate
rotation (Diagram d).
Figure 2-1: Base plate deformation mechanisms proposed by Gilbert (2010).
The base plate uplift as shown in Figure 2-1 (d) has been determined by Gilbert (2010)
to be required during analysis and modelling if it has been incorporated into the
physical design, although models created in Strand7 (Strand7 2010) by Yadwad (2011)
have not considered this.
FEM 10.2.07 (2011) and EN 15512 (2009) both require physical testing in order to
determine base plate stiffness, however due to the scope of this thesis not allowing
experimental procedures to be undertaken, an analytical solution has been sought.
ANSI MH16.1 (2012) provides analytical methodology, though review undertaken of
previous version ANSI MH16.1 (2008) by Sajja, Beale and Godley (2008) determined
that the stiffness predicted by the RMI code is significantly higher than the
experimental stiffness. The inaccuracy in the equation determined by RMI has been
determined to omit effect base plate stiffness while focusing primarily on the
deformation of the floor beneath the base plate. A modified expression (Equation 2-1)
applied by Gilbert (2010) has accounted for this, allowing the determination of
moment-rotation relationship dependant of base plate geometry.

9
( =
7+,-
25
0123 Equation 2-1
Where M is the moment at the baseplate, b and d are the depth and width of the upright
sections, 01 is the Young’s modulus of the concrete floor.
The strength and initial rotational stiffness of the base plate to floor connection was
found to depend on the axial load in the upright, with increases in axial load resulting
in increases in rotational capacity (Godley, Beale & Feng, 1998). Additionally, it was
found that the stiffness of the floor material influences the rotational stiffness of the
assembly, though above a certain stiffness value, the capacity does not increase further
due to the buckling length associated with the upright member approaching fixed
conditions.
( = 4523 =
067
ℎ
23 → 45 =
067
ℎ Equation 2-2
Where 45 is the limiting stiffness of the base plate, E is the Young’s modulus, I is the
sectional second moment of area and h is the distance from plate to first horizontal
beam member.
A maximum stiffness value can been determined and justified through
experimentation. The behaviour displays nonlinearity between initial and maximum
capacity conditions. This was discussed by Freitas et al. (2010) where the base plate
behaviour was described to initially exhibit linear and high stiffness properties. At a
limiting moment, this stiffness decays to lower, nonlinear values. In order to account
accurately for this, a multi-linear rotational stiffness curve has been proposed through
experimental studies by Gilbert (2010). It was determined through comparison of full
scale tests, together with the idealised rotational stiffness curve, that this model
accurately captures the behaviour of the tested racks. Although this process allows the
modelling of loading response, Beale and Godley (2008) determined that under certain
loading combinations where an increased lateral load during operational conditions is
applied to the connection, the plate assembly will fail and rotational stiffness reduce
to zero thus being analysed as a pinned connection.

10
2.2.3 BEAM END CONNECTOR
Beam end connectors are located at portal and pallet beam/upright interfaces which
typically resemble an endplate welded to the ends of the beams. These end connectors
feature tabs which are inserted into the perforations within uprights, additionally,
locking pins may be installed to ensure greater security of the connection. Figure 2-2
shows the component as described.
Figure 2-2: An example of a beam end connector, Gilbert (2010).
While internal loads can be determined through procedures outlined in EN 15512
(2009), in order to determine the mechanical properties of beam end connectors, unlike
base plate connections, physical testing must be undertaken. Justification of this clause
has been explored (Baldassino & Bernuzzi, 2000) due to the variability of designs
implemented throughout the industry. Two beam end connector tests are proposed in
ANSI MH16.1 (2012) and AS 4084 (2012) while only one test set up is proposed in
EN 15512 (2009). The two tests which are proposed are the ‘cantilever test’ and the
‘portal frame test’. Each outline specific procedures in which conditions and
methodology vary between tests in order to produce connection rotational stiffness
values. Harris (2006) provided a comparison of results gathered between the two tests
and determined that the cantilever tests produce half the connector rotational stiffness
of those obtained from the portal beam test, due to these variations.

11
DIRs are in nature, slender structures and therefore are inherently sensitive to second
order effects. To accurately model their behaviour under P-Δ effects, connection
looseness must be accounted for. Under current specifications, these effects have been
introduced into analysis through geometric imperfections throughout the frame which
can be referred to as ‘out of plumb’. These imperfections are accounted for through
the application of the horizontal forces, ;<=>?<@?AB=C3.
;<=>?<@?AB=C3 = 2 ∙ F Equation 2-3
Where 2 is the ‘out-of-plumb’ angle and W is the weight of the vertical load. 2 is
determined following AS 4084 (2012) recommendations by the expression:
2 =
1
2
ψH I1 +
1
K3
L + ΦM Equation 2-4
Where ΨH is the initial ‘out-of-plumb’ angle equal to 0.007 radians for manually
operated braced DIRs, K3 is the number of bays which are interconnected and ΦM
specifies the connection looseness.
Beal and Godley (2008) recommended incorporating measured looseness of the
connection into ‘out-of-plumb’ and thus designing rack based on bolt stiffness in
bearing. This approach was found to produce conservative results for connections
which experience significant amounts of looseness (Gilbert & Rasmussen, 2010).
Locking pins have been replaced by bolts by Gilbert (2010) in order to provide an
improvement in stiffness and thus moment capacity of the connection. This is a
suggested alternative to the typical tab and slot type connection which are most
commonly found in DIR structures. Although the bolted connections allow for a much
stiffer connection alternative, looseness and therefore ‘out-of-plumb’ forces cannot be
eliminated. Through ensuring sufficient torque is applied to the connection during the
installation, it is possible to reduce the possibility of looseness developing under
operational conditions. This is possible due to the high capacity of the connection and
expected operational loads not achieving those required to induce significant moments
for the development of connection looseness.

12
The axial capacity of beam-end connections has been determined to influence the type
of collapse which occurs under the force by forklift impact (McConnel & Kelly, 1983).
If the capacity of the connector is relatively low, the expected mechanism would be
confined, while a high connector capacity would result in a progressive collapse
mechanism (Gilbert & Rasmussen, 2010).
Additionally, Baldassino and Bernuzzi (2000) investigated the behaviour of beam end
connections and determined that consideration should be taken when modelling such
hinged connections. Hinged connections were determined to provide a non-negligible
amount of stiffness and are therefore recommended to be modelled as such, even if
classified in accordance with design specifications. This information will help to
accurately predict and define finite element members and their appropriate parameters.
2.2.4 UPRIGHT MEMBERS
As previously mentioned, due to the slender nature of members, DIR structures are
susceptible to P-Δ. In addition to this, uprights are most susceptible to flexural-
torsional buckling failure mechanisms due to biaxial bending and axial compression
loading combinations and which has been discussed by Rasmussen and Gilbert (2013).
AS/NZS 4600 3.5.1 (2005) outlines processes for determining action-capacity ratios
for uprights. When analysing the members, torsion is not directly imposed through
factors influencing design factors (N∗
, (∗
), instead through factors which are used to
determine these design factors. Equation 2-5 and Equation 2-6 represent the design
checks required for member capacities and which take into account both down-aisle
and cross-aisle moments.
N∗
PQNQ
+
RCS(S
∗
P3(3STUS
+
RCV(V
∗
P3(3VTUV
W ≤ 1 Equation 2-5
N∗
PQN6
+
(S
∗
P3(3S
+
(V
∗
P3(3V
≤ 1 Equation 2-6
Through the application of the program ColdSteel (Dematic 2007), sections capacities
can be checked against limiting values provided by the relevant standard, in this case,
AS/NZS 4600 (2005). ColdSteel (Dematic 2007) utilises the elastic buckling load N<1
which is required to be determined through separate buckling analysis which has been
undertaken previously by Yadwad (2011). Additionally, Rasmussen and Gilbert

13
(2013) propose consideration be taken to include torsion-induced moment
amplification if this is expected to produce significant effects. The inclusion of an
amplification factor is determined by analysing flexural and torsional buckling stresses
present in the member. If torsional bucking stress is higher, amplification is not
expected to impact.
Additionally, Hancock (1998) and Pekoz (1988) investigated the effect of perforations
on the capacity of uprights, though this has already been considered in calculations by
the use of reduced cross section properties throughout standards
2.2.5 RESIDUAL CAPACITY
When considering the failure of a member, typically the member will continue to
provide a supporting reaction although this will only be a fraction of the original
capacity. As the member translates downwards, the effect of this damaged member
will continue to act as it is connected to the system. If the member is required to resist
horizontal movement as shown in Figure 2-3, the boundary conditions must be
maintained when modelling in order to simulate this restraint.
Figure 2-3: A failed upright demonstrating residual support, Bristol Storage.
McConnel and Kelly (1983) undertook their analysis without the inclusion of this
residual capacity in their progressive collapse analysis though may have still included
some restraining mechanism. Yadwad (2011) undertook analysis incorporating this
capacity throughout some analyses in which he conducted a parametric study with
varying values based on fractions of the ultimate member capacity in pure

14
compression, (1%, 2%, 5% and 10%). Yadwad (2011) showed that the inclusion of the
residual capacity resulted in a delay of the formation of portal beam tensile forces but
not prevention, additionally peak portal beam tensile forces were noted to reduce as
the residual capacity increased. Yadwad (2011) proposed that refinement of the
residual capacity mechanism incorporated into his models was required due to the
upward force applied not providing sufficient representation of member undergoing
oscillation.
2.2.6 BRACING
Bracing has been determined to provide significant stiffness to the overall structural
response of DIRs under lateral loading. Similar to previously discussed connections,
flexibility and looseness of the joints will result in a reduced stiffness and thus capacity
of the assembly. Due to this, it is required that physical testing must be undertaken in
order to determine the shear stiffness of the bracing (Rasmussen and Gilbert 2013).
Bracing is applied to the structure in the forms of spine and plan arrangements,
providing shear stiffness in the vertical (improving the down-aisle direction response)
and horizontal (improving cross-aisle direction response) planes respectively.
Additionally, Gilbert and Rasmussen (2009) suggest that the higher shear stiffness
imparted by these braces result in reduced rotation of the portal beams and base plates.
2.2.7 STRUCTURAL DAMPING
It is important to simulate the effect of structural damping throughout the considered
system in order to accurately reflect the physical behaviour and response of the
structure. The magnitude of the damping effort across the system when analysing
dynamic equilibrium (Equation 2-7) is defined as c and stiffness k. Rayleigh damping
is calculated through the assumption of damping characteristic as a linear combination
of mass and stiffness matrices defined in Equation 2-8.
YWZ + [W + 4W = ](_) Equation 2-7
aRb = Ta(b + cadb Equation 2-8
e =
1
2
f
T
g
+ cgh Equation 2-9

15
The relationship between the coefficients T and c and the damping ratio, e at a specific
frequency g is defined in Equation 2-9. This equation is often utilised through
application of two chosen damping ratios (eM and e-) at two chosen frequencies (gM
and g-) and solved simultaneously in order to give the coefficients T and c. The
disadvantage of this damping model as identified by Gilbert (2010) is the assumption
of the linear relationship between mass and stiffness tends to yield underdamped
values for frequencies within those defined (gMand g-) while values outside this
region tend to be overdamped. Although this has been identified as an issue, proper
defining of frequencies may negate potential structural inaccuracies and will provide
an effective accurate of modelling the damping.
Literature regarding the magnitude of the required damping effort in order to simulate
the physical behaviour is somewhat lacking with respect to current specifications with
no information being available in AS4084 (2012) or FEM 10.2.7 (2012). FEMA450
(2005) suggests damping ratios for varying ground accelerations for the design of
storage racks for seismic loading conditions. The damping ratio which is proposed is
5% for ground accelerations of 0.1g and below. Bangash (1993) proposed a suitable
ratio of structural damping to be applied within the range of 0.1% to 0.9%. Following
this, Gilbert (2010) determined a damping ratio of 0.7% to be sufficient in simulation
of structural behaviour from physical DIR testing.
2.2.8 EFFECT OF LOADED PALLETS
The concept of loaded pallets affecting the structural response of DIR structures was
initially proposed by Salmon, Welch and Longinow (1973) and later demonstrated
experimentally by Gilbert (2010). Early research by Salmon et. al. (1973) proposed
significant effects of pallet bracing on the structure. Gilbert (2010) performed a
comparison between DIR models both incorporating and omitting these restraining
actions. Following this, he worked to determine the requirement of consideration of
these actions in the overall analysis of DIR design. Upon further experimentation of
these effects, it was determined that under normal operating conditions the frictional
forces developed between pallet and rail beams are sufficient in resisting sliding thus
providing some degree of horizontal bracing. Results produced by Gilbert (2010)
compared to current industry standards, determined incorrect bending moment
distributions may be calculated and which may lead to a less conservative design. The

16
degree of conservativeness has been determined to be minor, with the overall detriment
of the action-to-capacity ratio for the critical upright being reduced only in the order
of 4%.
Although Gilbert et al. (2014) determined the effect of horizontal bracing restraint of
the pallets to be minor, it is worth noting the effect of loaded pallets in terms of upright
and base plate connection member forces. Due to the increase of load transferred
through from pallets via rail beams into the uprights, the increase in base plate axial
load, the rotational stiffness of these connections as previously discussed shall acquire
significant increases. Gilbert (2010) described that for similar bracing topologies the
stiffness of the loaded system will be greater than that compared to an unloaded
system, which is expected due to effects previously discussed. However, it was
proposed that the stiffness of a loaded rack without plan bracing would be greater than
that of an unloaded rack with bracing signifying the contribution offered by the loaded
pallets.
2. 3 FUSE CONNECTORS
Fuse connectors were proposed by Yadwad (2011) as a design consideration for DIRs
in order to prevent the propagation of collapse due to local failures and unexpected
loading conditions. These connectors resemble safety measures applied throughout
electrical and mechanical equipment such as electrical fuses and shear pins. These
components are designed to fail sacrificially upon experiencing their respective
predetermined parameters. Mechanical fuse connectors such as the ones proposed are
triggered to active in the event of overloading of the system.
Connectors adopted for the purposes of this thesis are strictly strength limited, and will
be modelled to disengage upon a predetermined axial load. Figure 2-4 represents the
expected behaviour expected upon loading of the fuse connector with severe plastic
extension occurring prior to failure associated with disengagement.
In order to determine the feasibility of the inclusion of fuse connectors to neutralise
the formation of progressive collapse mechanisms, forces prior to collapse and under
operational conditions must be analysed. The limits must be sufficient as not to
unexpectedly induce disengagement of connectors under operational conditions.

17
Figure 2-4: Expected behaviour of fuse connector component under loading, Yadwad
(2011).
2. 4 BEHAVIOUR OF DRIVE-IN RACKING
To determine both the upper and lower limits to define the fuse connection, analysis
must be undertaken for a number of conditions. The following section investigates
literature for both static and dynamic analysis of DIR operational conditions and those
following upright failure leading to progressive collapse.
2.4.1 OPERATIONAL CONDITIONS
This section analyses literature regarding the development of system forces under
static/operational conditions. Information of static, out-of-plumb and accidental
impact loading has been included. The maximum tensile forces determined in the
portal beams through these conditions are to help define the lower fuse connector limit.
2.4.1.1 STATIC LOADING
The stability of DIRs during their operational state has been determined to be
influenced by the rotational stiffness of portal beam to upright, in addition to baseplate
to floor connection (Freitas et al., 2010). As previously mentioned, the axial force
developed in the upright, influences the rotational stiffness of the baseplate to floor
connection. The stability may therefore be linked with the static loading. Yadwad
(2011) investigated the effects of four loading cases for which the largest tensile forces
were developed in the portal beams. A uniformly loaded configuration as presented in
Figure 2-5 (top right) was found to be the critical case.

18
FEM 10.2.07 (2012) defines a horizontal placement load of 0.5kN applied in the cross-
aisle direction at the level closest to the midpoint of the upright. This load is to be
considered on a single upright and any potential distribution by the bail rails neglected.
The minimum horizontal placement load is not intended to represent an impact load
arising from misuse.
Figure 2-5: Load configurations, Yadwad (2011).
In addition to static loading, out-of-plumb forces are present in the system under
operational conditions resulting from component misfit. AS4084 (2012) and FEM
10.2.7 (2012) define tolerances certain components and dimensions such as the
maximum out-of-plumb upright in both cross-aisle and down-aisle directions. Yadwad
(2011) undertook analysis as per methods prescribed in AS4084 (1993) from which he
determined the maximum tensile forces developed due to all ordinary design loading
cases in the DIR systems considered to be far less (0.68kN) than those developed due
to accidental impacts (7.14kN).
2.4.1.2 IMPACT LOADING
Due to the loading and unloading process associated with DIR structures the
susceptibility to accidental loading due to placement and impacts is much greater than
that of selective racking. In order to ensure stability, racking must be designed in order

19
to resist these additional loads without structural failures and which may result in either
a local or progressive collapse mechanism. A local collapse mechanism for this thesis
has been defined as the collapse of a bay without progression of failure throughout
(also defined as confined collapse by McConnel and Kelly (1983)).
EN15512 (2009) considers an impact due to a forklift counterweight striking an
upright 0.25m from the base of the structure. This force is applied at magnitudes of
1.5kN and 2.5kN in the down-aisle and cross-aisle directions respectively. FEM 10.2.7
(2012) applies similar methodology with magnitudes of 2.5kN and 1.25kN in the
down-aisle and cross-aisle directions respectively at a height of 0.4m. This load may
only be applied on the first two uprights in the down-aisle direction from the entry. In
addition to this, the loads may only be applied on one member at a time and shall be
treated as occurring separately in order to simulate impact behaviour and not inducing
unreasonable conditions. AS4084 (2012) defines the same magnitudes as FEM 10.2.7
(2012) at a distance from floor to 1m height on the aisle-side upright. The location at
which the impact force is placed has been taken to be at the most unfavourable location
although this does vary between standards.
While specifications do not include the theoretical basis for the impact magnitude for
specifications such as FEM 10.2.7 (2012), the loading method (eg manual or
automatic) is used to define a reduction in impact force as expected due to the accuracy
of the equipment. An alternative approach was first investigated by Ng, Beale, and
Godley (2009) to determine the equivalent static impact force developed by the
interaction between a forklift and the upright. Gilbert (2010) refined the model through
physical testing of the interaction between these components and determined the effect
of rotation of the forklift truck and impact height to effect the interaction. The impact
force has been defined by Gilbert (2010) as:
;iCA =
T
0.023
0.11;l Equation 2-10
;l =
4M
1 + 0.1
4M
4-
( M + -)
Equation 2-11

20
4M =
067mno1p
miCA
-
qmno1p − miCAs
- Equation 2-12
4- =
Yt
miCA + ,1<u
Equation 2-13
Through the application of these formulae Gilbert (2010) provided the background
from which a static equivalent force can be determined and applied for storage racks
of different topology. The magnitude of the impact force ;iCA as described before, is
directly proportional to the forklift truck rotation upon impact, T. Through parametric
testing Gilbert (2010) determined a rotational value of 0.046 radians to be suitable for
member and serviceability design. In order to provide the most unfavourable
conditions for analysis, Gilbert (2010) determined that loaded pallets placed either side
of the impact along the length of the rail beam would result in the greatest response
while excluding the pallet in the location at which impact is simulated.
2.4.2 DYNAMIC CONDITIONS
This section analyses literature regarding the development of system forces under
dynamic conditions. This includes the types of mechanisms of collapse and additional
details regarding the development and simulation of the progressive collapse
mechanism. The smallest peak tensile forces determined in the portal beams through
these conditions are to help define the upper fuse connector limit.
2.4.2.1 COLLAPSE MECHANISMS
The three most distinct types of collapse mechanisms which develop in racking
structures resulting from an initial upright failure are described by McConnel and
Kelly (1983) as:
1. zero collapse,
2. confined collapse,
3. progressive collapse.
Collapse has been identified by McConnel and Kelly (1983) to be typically initiated
by forklift impacts leading to the localised failure of upright members due to
overloading. Once the damage has been initiated, one of the collapse mechanisms will
begin to form. Initially, the adjacent bays are drawn inward. In a zero collapse

21
mechanism this movement is resisted from translating too far downwards. For the zero
collapse mechanism, static equilibrium is regained following the failure of the upright.
The rotation of the portal beams occurs due to the formation of a ‘join rotation’
mechanism. The formation is slightly obstructed by the bracing arrangements until
failure of these members. In order to eliminate the development of other mechanisms
through this manner, would require an increase in load capacity of the uprights by at
least 50% (McConnel and Kelly, 1983). Due to this competitive market for DIR
design, this increase would result in an increase in material and therefore a less
economical design. Prevention of collapse mechanisms through alternate methods
therefore needs to be considered.
Figure 2-6: Joint rotation following upright failure, Yadwad (2011).
Confined collapse has been defined as the collapse localised to the surrounding bays
of the damaged upright. Confined collapse has been identified by the separation of
members within the structure and which prevents the propagation of failure throughout
the system (McConnel and Kelly 1983). This collapse mechanism represents the main
idea behind prevention of progressive collapse through the application of fuse
connectors.
Finally, the progressive collapse mechanism. Defined by entire structural failure
initiated by a damaged impact, this mechanism is the focus of this thesis. Progressive
collapse has been conversely identified by the lack of separation of members within
the structure following damage. The pull-out characteristics of portal beam
connections has been identified to significantly affect the formation of this type of
collapse.

22
Joint rotational collapse has been identified by Gilbert (2010) as one of two collapse
situations. The other involves pallets falling through due to upright movement and
therefore bay opening upon impact or buckling of the upright displayed in Figure 2-7.
As the pallet begins to fall through it may overload the rail beam below, triggering
failure or failure of the upright. This behaviour is very variable and difficult to predict.
For the purposes of this thesis it has therefore not been considered.
Figure 2-7: Bay opening, Gilbert (2010).
2.4.2.2 INITIAL DAMAGE
As previously mentioned, the most likely cause of member failure due to localised
damage are due to forklift upright impacts. This interaction may be of the magnitude
that it causes the upright to fail and if the topology of the structure allows it,
progressive collapse will ensue. Determining the forces required for the failure of the
members while important, remain outside the scope of this thesis as upright failure will
be initiated regardless.
In order to simulate member failure, the approach adopted by McConnel and Kelly
(1983) and Ng (2009) requires the member to be removed from the analysis/structure
completely and assumes that no damage to surrounding components has occurred. The
advantage of this method is that the determination of the impact load required to induce
failure of the upright is not required. In addition to this, modelling the event prior to
collapse is not required as the impact magnitude is assumed sufficient to induce failure.
Therefore, with this approach the initial conditions of a finite element model will be

23
simply determined and analysis undertaken. Although this method has been utilised, it
neglects to incorporate the lateral effects due to an impact which may cause sway or
oscillatory effects varying the analysis. Analyses undertaken similar to those by
McConnel and Kelly (1983) do not consider the residual member capacity effects and
are therefore considered cause independent. These methods may provide conservative
results for the case of omitting residual capacity or alternately provide incorrect
behaviour such as sway and oscillation. Cause dependent methods allow the simulation
of the component following the event, and which may include the residual capacity
and system displacements due to impact. In order to accurately simulate the member
response, the initiating event must be modelled in addition to the likely behaviour of
the failed member (Marjanashvili, 2004).
2.4.2.3 ANALYSIS METHODS
Methods regarding the analysis of progressive collapse can be divided into the
following separate analysis methods:
1. linear-elastic static and dynamic analysis,
2. nonlinear static and dynamic analysis.
Literature regarding progressive collapse analysis of DIRs is limited, though guidance
can be found from other structural collapse processes such as steel and concrete framed
buildings.
Linear-elastic static analysis involved the removal of failed members, as previously
discussed. This process is undertaken assuming linear-elastic member properties, in
addition to assuming linear geometry responses. For this process, the damaged
member is removed from the model and the analysis is undertaken from which
members are examined for failure. If the member is determined to fail, the member is
removed and the analysis is performed again, repeating until equilibrium is attained
either through zero collapse or any other mechanism. Marjanashvili (2006) describes
this form of analysis as the simplest method for predicting and verifying a structures
response to damage. Additionally, the computational effort required for this form of
analysis is the least demanding. Limitations of this method may affect application due
to neglecting the inherent dynamic behaviour of DIR structures. Linear-elastic static
analysis omits the influence of inertial and structural damping effects following

24
removal which have been found to affect the formation of failure mechanisms in
storage racks (McConnel and Kelly, 1983). In addition to these dynamic effects,
nonlinear geometric behaviour will not be considered throughout the analysis although
will be somewhat represented through the iterative nature of this process. This may
have significant ramifications if the wrong mechanism of collapse (e.g. zero collapse)
is determined in the first iteration. The methodology does not incorporate the nonlinear
material behaviour of the members and therefore cannot be utilised for larger or
complex structures with great accuracy (Marjanashvili, 2006). Due to the relative
complexity of DIR structures this is acceptable as failure of this type of structure is
usually due to elastic instability (Ng et. al. 2009).
Non-linear static analysis involves the process of performing numerous static analyses
on the structure while incorporating either nonlinear geometry or material properties
of the members and applying incrementally higher loads until the initially loaded
condition is applied. This method however may result in early termination of the
analysis if the maximum allowable deflection limit is reached. Ng et al. (2009)
undertook analysis of selective racking using this approach with the primary goal to
establish the magnitude of force necessary to initiate the formation of plastic hinges in
uprights. The advantage of this method allows for the consideration of the change in
geometry and material properties however although being more complex and
computation requirements are increased it can only be effectively applied for the
verification for structures of predictable behaviour (Mohamed, 2006).
Dynamic analyses incorporate dynamic effects such as inertia and structural damping
into the solution unlike static analyses and therefore provide a much more accurate
result. Linear-elastic dynamic analysis is undertaken through the undertaking of an
initial static analysis in order to determine the internal member forces and global
deflections and to define the initial conditions for analysis. Removal of the damaged
element is made ensuring the deflections are maintained. Following this, a reaction
force is applied with magnitudes determined from the internal member forces
calculated previously. Estimation of a time step and the reduction of the reaction force
for each succeeding time step is undertaken prior to performing the dynamic analysis.
Finally, the results should be checked, validated and analysed. As per the linear-static
analysis, this method does not incorporate the nonlinear geometry and material

25
properties of the structure and would therefore not be effective to be applied while the
structure undergoes large deflections.
Finally, nonlinear-elastic dynamic analysis incorporates both the nonlinear geometric
and material effects throughout the analysis. This method follows the same procedure
providing the most accurate results, though it is the most time consuming and
computationally demanding of all the options. Following this, verification of the
results can be time consuming particularly for complex structures (Marjanashvili,
2006).

26
3 METHODOLOGY
This chapter describes the methodology applied in this thesis in order to achieve the
aims and objectives defined in Chapter 1. Detailed descriptions of the finite element
model are included followed by the processes which have been applied in order to
determine the lower and upper fuse connector limits.
3. 1 FINITE ELEMENT MODEL
This section describes the development of the finite element models utilised
throughout this thesis including the key details central to the methodology. As Finite
Element Analysis (FEA) is central to this thesis, an increased level of detail has been
produced in order to assist future replication and improvement. A description of the
software utilised is provided in addition to detailed descriptions of the topology of each
model and their components. This includes the modelling of sections, members and
connections in addition to the system wide details of boundary conditions, application
of forces, structural characteristics such as damping and finally solver methods.
3.1.1 ANALYSIS SOFTWARE
The software package primarily used for the creation and analysis of the DIR structures
was Strand7 (Strand7 2010). This software allows linear/nonlinear static and dynamic
analysis to be undertaken. Although the required forms of analysis can be undertaken,
as mentioned previously in Section 2.2.1 (pg. 7), Strand7 (Strand7 2010) considers
Saint-Venant torsional while omitting torsional warping effects.
ColdSteel (Dematic 2007) was used to determine the action-to-capacity ratios based
on AS/NZS 4600 (2005). ColdSteel (Dematic 2007) is able to utilise the elastic
buckling load NvQ determined in RAD (Dematic 2009).
3.1.2 DIR TOPOLOGY
Although DIR refers to a specific type of cold-formed steel structural system, there are
a large number of different topologies which constitute pallet racking. A total of five
arrangements have been analysed reflecting the designs assessed by both Gilbert
(2010) and Yadwad (2011). This section describes the notation for referring and
navigating specific elements in addition to different topologies considered in the
analysis.

27
The notation applied in order to locate certain elements of the DIR system have been
included in Figure 3-1. As previously discussed in Section 1. 1 (pg. 1), the convention
when referring to the global axes of DIR follows those displayed below. Uprights
within a particular plane in the down-aisle and cross-aisle directions are referred to as
so. In order to quickly differentiate between the two directions, members in the down-
aisle direction will be labelled with letters while cross-aisle members will be identified
with numbers. In order to identify individual uprights, such as the member highlighted
below, the cross and down-aisle notation has been considered as a grid with the
member below located at 3C. In order to identify portal beams a similar approach is
undertaken whereby the cross-aisle plane is displayed followed by the span which it
covers, e.g. B2-3.
Figure 3-1: DIR topology notation conventions, Yadwad (2011).
The first DIR topology considered, labelled as DIR1, is the same as that which was
considered by Gilbert (2010) and Yadwad (2011) and is displayed in Figure 3-2.
Figure 3-2: DIR1 Topology, Yadwad (2011).

28
DIR1 is a four bay wide rack which is four pallets deep and four pallets in elevation
resulting in the dimensions of a 5900mm wide, 5000mm high and 4800mm deep rack.
Spine bracing is applied across Bay 1 between D12 while plan bracing is applied in
across Bay 2. DIR2 similarly was analysed by both Gilbert (2010) and Yadwad (2011)
and has the exact dimensions as DIR1. The differences between the two DIRs is the
bracing arrangement, DIR2 provides spine bracing across the span D15 while plan
bracing is applied spanning Bay 2, 3 and 4. Additionally, two portal beam sections are
applied mid height across D34 and D35. This DIR was included by Gilbert (2010) in
order to observe the effect of difference bracing arrangements while also providing a
typical topology representative of a complete compact system, a topology expected in
storage facilities.
The third topology considered, DIR3, is an eight bay rack displayed in Figure 3-4.
Similar to DIR2 with its bracing arrangements though with the number of bays
extended. The total width of this DIR is 11800mm.

29
Similar to DIR3, DIR4 is an arrangement considered by Yadwad (2011) in order to
observe the effect of symmetrical bracing on the structural response during analysis.
This arrangement therefore considers the same spine and plan bracing spanning Bay 9
and 8 respectively, shown in Figure 3-5.
The final arrangement considered, which was analysed by Yadwad (2011), is DIR5,
displayed in Figure 3-6. This rack has 8 full bays available for storage with a similar
overall width of 11800mm. This rack is an example of a Drive-Through Rack in which
access is available from either side of the structure. Due to this, the storage capacity of
Bay 9 has been sacrificed in order to apply bracing throughout each down-aisle plane.
Plan bracing is applied across the top of Bay 9.
3.1.3 STRUCTURAL MEMBERS
Members and connections have been modelled as ‘Beam’ and ‘Link’ elements in
Strand7 (Strand7 2010) instead of an assembly of shell elements, although this would
allow an increase in accuracy of the structural response. This was decided due to the
increased accuracy of localised effects gained and was determined to be beyond the
scope of this thesis. In addition, the application of shell element members was deemed
to unacceptably increase both modelling and computational time. Modelling the

30
members as ‘Beam’ components increases the compatibility between Yadwad (2011)
and results determined in this thesis. Analysis has been undertaken previously by
Yadwad (2011) in which sectional properties have been determined in RAD (Dematic
2009). These details have been included in Appendix A and have been adopted
throughout this thesis.
Spine and plan bracing considered in the analysis has been applied in a similar fashion
to the structural members such that ‘Cable’ members span to connections with their
properties as defined in Appendix A. The major advantage of applying the bracing as
‘Cable’ members is unlike ‘Beam’ members which support compression loading, the
tensile capacity of these members is very low and can be neglected. During analysis
these members will remain throughout regardless of the nature of loading.
Alternatively, the utilisation of a ‘Cut-off Bar’ ‘Contact Element’ member has been
identified to be applied in certain models created by Yadwad (2011). This type of
member has been deemed unsuitable as the element may undergo compression after
experiencing tension, in which case they would have been removed from the model.
Due to the oscillation demonstrated in transient-dynamic analyses of the system, this
member type would provide inaccurate behaviour of the bracing.
All members have been modelled by ‘Beam2’ elements with the location of each
member being located through the centroid of the section.
3.1.4 MEMBER MATERIAL
The sections outlined previously have been assumed to be composed of G450 steel
which is associated with cold-formed steel structures. The following material
properties have been linearly adopted in static and transient-dynamic analyses:
Density (kg/m3
) 7850
Poisson’s Ratio 0.25
Elastic Modulus (GPa) 218
Table 3-1: G450 Steel Material Properties

31
3.1.5 CONNECTIONS
This section presents the detail of all connections modelled and applied in each model
as shown in Figure 3-7. The methodology utilised by Gilbert (2010) has been applied
for the design of connections in order to accurately replicate the behaviour and
interaction of the connections.
Figure 3-7: Connections between members, Gilbert (2010)
In order to model connections between members, links have been used, specifically
‘rigid links’ in order to simulate connection geometry. A rigid link provides an
infinitely stiff connection between two nodes while providing constraints on the nodal
rotation such that there is no relative rotation between the connected nodes. This
stiffness allows the structural behaviour to be modelled effectively while incorporating
the connection geometry.
3.1.5.1 UPRIGHT TO FRAME BRACING CONNECTION
In order to model the connection between the upright and the bracing, the nature of the
connection has been considered. Bracing members are inserted between the flanges of
the upright and attached through the application of two M12 bolts. This connection as
discussed by Gilbert (2010) behaves as though it was welded/fixed due to the increased
friction developed between the members. This behaviour consequently results in
coupled nodal translations and rotation. Links are located between the upright centroid
to the flange bolt centreline as shown in Figure 3-8.

32
Figure 3-8: Connection between uprights and frame bracing, Gilbert (2010).
3.1.5.2 UPRIGHT TO RAIL BEAM CONNECTION
Rail beams are connected to the uprights by the application of cantilever brackets
attached by one and two M12 bolts respectively. The rigid links in this case have been
applied between the upright centroid and the rail beam shear centre. The nature of the
single bolt connecting the bracket to the rail beam results in the possibility of rotation
about the bolt. In the model, in order to simulate free rotations about the bolt, the ends
of the rail beams have been released about the suitable axes. Free rotation occurs about
the axes 2 and 3 as displayed in Figure 3-9 while still resisting rotation about the
longitudinal axis to simulate the presence of the bolt.
Figure 3-9: Upright to rail beam connection

33
3.1.5.3 UPRIGHT TO PORTAL BEAM CONNECTION
The upright to portal beam connection has been modelled considering two M12 bolts
for connection. For the purpose of this thesis, connections implemented by Yadwad
(2011) have been adopted for which rigid links have been applied between the centroid
of the upright to the bolt centreline. Additionally, the connections implemented into
models created by Gilbert (2010) have been briefly examined in which the geometry
of the offset of the connection has been considered (Figure 3-11). Similar to the rail
beam configuration, the longitudinal axis has been restrained against rotation while the
others allow rotation through the end release of portal beams (Figure 3-10).
Figure 3-10: Portal and rail beam end releases applied (Shown in black).
Figure 3-11: Upright to Portal Beam Connection, Gilbert (2010).

34
3.1.5.4 UPRIGHT TO SPINE BRACING CONNECTION
The connection between spine bracing and uprights comprises of two different
members interacting with the upright. Firstly, horizontal bracing members identical to
portal beams were modelled and were connected by rigid links from the centroid to
the intersection between the centreline of the upright and the horizontal beam (see
Figure 3-12).
Secondly, between this connection, tension bracing has been applied. This was applied
through the application of cable elements, as previously mentioned. The members have
been modelled through the centroid of the bracing and connect to the same node at
which the horizontal bracing is located. As single bolts connect this bracing, the cable
is free to rotate while fixed to translation. Gilbert (2010) states the simplification of
bracing members being connected to the centreline of uprights is unlikely to affect the
load distribution of the rack upon loading.
Figure 3-12: Upright to Spine Bracing Connection, Gilbert (2010).
3.1.5.5 UPRIGHT TO PLAN BRACING CONNECTION
The final connection considered is the connection of the plan bracing to the structure.
For this, the plan bracing has been applied similar to spine bracing, where rigid link
connections are applied at the centreline of the upright while accounting for spacing
as displayed in Figure 3-13. Similarly, single bolts connect the bracing to the structure
allowing rotation and have been modelled as such. In addition to the plan bracing
struts, a section of upright is connected horizontally in order to restrain and connect
the bracing to the uprights via the inverted baseplate.

35
Figure 3-13: Upright to Plan Bracing Connection, Gilbert (2010)
In some cases, DIR plan bracing may be connected to portal beams without the use of
horizontal bracing members. This case has been discussed further in the context of
fuse connector feasibility and applicability for such members.
3.1.6 BOUNDARY CONDITIONS
Uprights are connected to the floor via bolted on base plates fastened to a concrete
floor. In modelling the DIRs, the most crucial boundary condition to consider is that
of the connection of uprights to the floor. As previously discussed in Section 2.2.2 (pg.
7), the rotational stiffness of the connection is influenced by the axial force
experienced in the upright. The rotational stiffness applied throughout the models has
been applied from values determined by Yadwad (2011) from analysis undertaken in
RAD (Dematic 2009). The stiffness values were determined through the use of a
nonlinear stiffness curve, as represented in Equation 3-1.
4nw1 =
4nw
I1 + f
4nw23
(w=
h
U
L
fMx
M
U
h Equation 3-1
For the models created in Strand7 (Strand7 2010), a nonlinear static analysis was
undertaken in order to determine the axial load experienced in the upright from which
a single rotational stiffness was applied to each baseplate. The baseplate assemblies
have been modelled in order to resist both rotation and translation in all directions bar
rotation about the down aisle direction.

36
Figure 3-14: DIR2 boundary rotational stiffness’ as determined by Yadwad (2011).
In addition to rotational stiffness characteristics, baseplate uplift has been identified as
a situation which occurs due to uprights developing tensile forces. This has been
investigated by Yadwad (2011) though in the models created in Strand7 (Strand7
2010) though has not been applied in order to limit the variations between models for
comparison.
3.1.7 STRUCTURAL DAMPING
Structural damping as described in Section 2.2.7 (pg. 14) has been applied across the
system for a couple of different scenarios in order to determine the most extreme portal
beam behaviour. Analysis undertaken in Strand7 (Strand7 2010) requires defining of
damping characteristics for which Rayleigh Damping has been applied.
Models were run with undamped conditions to provide a control value for which a
damping of 5% was compared. This value is based on the findings of FEMA450 (2005)
which is suitable for steel storage racks under seismic excitation for accelerations of
less than 0.1g. In order to define the damping characteristics, a Natural Frequency
Analysis must be undertaken to determine the first two modes of vibration for each
model and applied as the first two frequency values (Figure 3-15).

37
Figure 3-15: Strand7 Rayleigh Damping Definition
3.1.8 SOLVER, TIME STEP AND FREQUENCY
Analysis of the models required a number of solving options in Strand7 (Strand7 2010)
in order to determine specific results. Throughout analysis, only nonlinear geometric
conditions were explored due to having selected ColdSteel (Dematic 2007) as the
medium for which to determine member failure. Nonlinear Static Analysis and Natural
Frequency calculations were undertaken in addition to the Nonlinear Transient
Dynamic Analysis. For dynamic analysis, dynamic forces must be defined with respect
to time via Factor-Time tables as described in Section 3.2.2 (pg. 41).
For the Nonlinear Transient Dynamic Analysis, times steps for which the analysis
would be run have been defined as 60 steps every 0.1 seconds totalling to a 6 second
analysis. Yadwad (2011) analysed the sensitivity of the time step in terms of its effects
on member forces. In order to determine a suitable sample rate which will provide
sufficient data, numerous samples rates have been investigated.
A sample rate of 0.1 seconds provided accurate representation while minimising
computational effort. Figure 3-16 demonstrates the differences associated with each
sample rate and the accuracy gained.

38
Figure 3-16: Observed difference in sample rates, Yadwad (2011).
3.1.9 MODELLING FORCES
This section provides an overview of the process of how forces have been modelled in
the analysis. In order to simulate the behaviour of pallets, forklift impacts and the
behaviour of a failed upright the following methodology has been undertaken.
3.1.9.1 PALLET MASSES
In order to model the structural mass of the pallets, translational masses have been
adopted in order to account for the dynamic effects experienced throughout analysis
rather than the application of vertical forces which will omit inertial effects introduced
by the pallets themselves. As impacts can induce sideways motion and some degree of
oscillation, the inclusion of horizontal dynamic effects helps to achieve more accurate
simulation.
The pallet masses have been modelled as lumped masses located on the rail beam at
the point of intersection with the upright. The magnitudes of the masses have been
applied trough determination of the total pallet load on each rail beam and division of
this load over the length of the rail beam. This value is then multiplied by the tributary
length and applied to each connection point shown in Figure 3-17.

39
Figure 3-17: Original pallet loading on lowest rail beams.
3.1.9.2 IMPACTS
Accidental impact forces have been modelled in order to simulate the dynamic nature
of forklift impacts, with a theoretically derived impact force of 6.28kN applied at the
most critical location of 3.8m as determined by Yadwad (2011). The impact force has
been modelled as a global point force on the relevant member, to simulate the dynamic
nature this force must vary with time in order to strike the member and then unload as
the forklift withdraws. As the force is required to vary with time, a table must be
defined within Strand7 (Strand7 2010) to associate the static force with the required
transient dynamic behaviour. Figure 3-18 presents the table which defines the force as
a factor of the initially defined force magnitude applied with respect to time.
Figure 3-18: The Impact Impulse Function applied in Strand7.

40
This impact function is defined in the Nonlinear Transient Dynamic Solver along with
any other loading requirements. The initial peak has been defined at 0.6 seconds
increasing from 0.55 seconds and similarly decreasing between 1.0 and 1.05 seconds.
Additional details regarding the application are included in Section 3.2.2 (pg. 41).
3.1.9.3 UPRIGHT FAILURE
Similarly, the removal process undertaken adopts a dynamically defined force in order
to simulate the initial effect of a failing member. Supporting reactions are applied in
place of the failed member and are associated with the factor-time table displayed in
Figure 3-19. The factor is defined as 1.0 until 0.6 seconds from which it reduces to 0.0
across a time period of 0.4 seconds. Additional details regarding the application are
included in Section 3.3.1 (pg. 44) and Section 3.3.3 (pg. 54).
Figure 3-19: The removal function applied in Strand7.
3. 2 OPERATIONAL CONDITIONS
This section outlines the methods undertaken in order to determine the lower limit of
fuse connectors. This force is defined as the maximum force developed in the portal
beams during operational conditions.
3.2.1 DESIGN LOADS
As discussed in Section 2.4.1.1 (pg. 17), the loading cases, determined by Yadwad
(2011), that produced the most critical portal beam tensile forces under design loading
conditions defined by the specifications presented in 2. 1 (pg. 6), was a fully loaded

41
configuration. In addition to this, Yadwad (2011) discovered his original loading
magnitudes did not induce a progressive collapse mechanism and subsequently were
increased. Consequently, the same loading cases have been implemented for the sake
of comparison. The first loading arrangement consisted of 2000kg pallets placed at the
middle two rail beams while 1200kg pallets are placed on the upper most rail beams.
The second loading arrangement consisted of the same arrangement with pallet masses
being increased by 12% in order to enable the localised and progressive mechanisms
to form.
Of the design loading cases, the out-of-plumb condition considered by Yadwad (2011)
was shown to develop the largest portal beam tensile forces. These forces are applied
as per the method prescribed in AS 4084 (1993) and are applied concurrently with the
static loading. Analysis determined that the magnitude developed by out-of-plumb
were not particularly large (0.68kN) and relative to accidental impact loading should
not influence the determination of the lower bound of fuse connectors. Due to the
validity and the large difference between other operational portal beam forces, similar
analysis was not undertaken to determine a maximum portal beam force due to-out-of
plumb.
3.2.2 ACCIDENTAL IMPACT LOADING
As previously mentioned, impacts induced by forklifts is common and therefore is
considered an ordinary condition of use. In order to model this impact there are
numerous procedures from design specifications which define the loading magnitudes
and nature. Additionally, Gilbert (2010) proposed a secondary method from which a
theoretical dynamic accidental impact force can be determined. Both methods have
been adopted in order to determine which produced the most critical result.
The most recent DIR specification FEM 10.2.7 (2012) describes the process of
analysing forces due to minor impacts in restricted areas. In addition, EN15512 (2009)
provides similar guidance regarding both the location and magnitude of the impact
which has been undertaken by Yadwad (2011). FEM 10.2.7 (2012) suggests the
application of a horizontal load applied from the floor to a height of 0.4m, this load
may occur on the first two uprights in the down-aisle direction at the entry of the lane
but only shall be applied to one upright at a time. Although the specification allows

42
the impact on the first two uprights, analysis has been undertaken on the first upright.
The specification prescribed a load of 2.5kN in the down-aisle direction and a load of
1.25kN in the cross-aisle direction though these must be applied separately. For the
purpose of this thesis and to maintain conformity between Yadwad’s (2011) results,
the magnitudes have been adopted while the impact location has been applied at the
most unfavourable position. As such, the impact force has been applied at each upright
in the front row of each DIR to determine the most critical tensile forces. The forces
applied as per the specifications, have been assigned as global point forces onto the
suggested upright for both impact directions with the impact on upright 1A to the left
being displayed in Figure 3-20.
Figure 3-20: DIR2 impact location.
Yadwad (2011) undertook analysis through the application of the methodology
prescribed by Gilbert (2010) in order to determine the dynamic impact force. Applying
the model allowed the determination of impact force at each relevant rail beam
elevation. The impact force, unlike those defined in the design specifications, are to be
modelled as dynamic forces and therefore require the application of dynamic analysis.
A maximum force of 6.28kN was determined by Yadwad (2010) to be the critical force
and therefore this was applied similarly to each upright. This impact force was applied
as per the methodology provided in Section 3.1.9.2, (pg. 39) utilising a factor-time
table in Strand7 (Strand7 2010) to simulate the impact behaviour. The critical impact
height was determined to be 3800mm and was adopted for analysis in this thesis.
Analysis was undertaken in the nonlinear transient dynamic solver in order for the
effects of structural damping to be utilised and resulting in more accurate results. The

43
downside of this solving method is the increased computation time required. In order
to complete the numerous impacts the batch solver was utilised allowing the set up and
subsequent analysis of all impact cases.
While two separate procedures were followed in order to determine the maximum
tensile force, the larger value is to be utilised for the fuse connector lower limit.
3.2.3 INFLUENCE OF PALLETS/OSCILLATION/SWAY
Although Gilbert et al. (2014) determined the effect of horizontal bracing restraint of
the pallets to be minor, during analysis this effect was investigated with respect to the
portal beam tensile forces. Gilbert (2010) described that for similar bracing topologies
the stiffness of the loaded system will be greater than that compared to an unloaded
system, which is expected due to effects discussed in Section 2.2.8 (pg. 15). Analysis
of this effect was undertaken due to oscillatory behaviour produced during accidental
impact loading in both analyses undertaken in this thesis, in addition to results
discussed by Yadwad (2011).
Peak portal beam tensile forces has been determined through recording the highest
force experienced by the beam over the duration of the nonlinear transient dynamic
analysis. During this analysis, the behaviour of the DIR post impact produced
oscillation of the uprights and in some cases critical portal beam forces due to
superposition. These cases developed when the impacted upright initially displaced by
the force began to move back and forth to establish equilibrium, but in doing so became
in-phase with a surrounding upright. Due to the movement of each upright, the case
where two uprights were moving away from each other produced the largest portal
beam tensile force. Although pallet masses have been assigned on the rail beam at the
point of connection between rail beam and upright, this does not promote continuity
between each adjacent point as would be (to some degree) with the inclusion of pallets.
This load transfer mechanism was investigated through the use of ‘pinned’ links
provided between each set of rail beams shown in Figure 3-21. The pinned link allows
rotation while translations are dependent on the connected nodes. This model provides
an upper limit of restraint due to pallets and can be compared to the behaviour
modelled without the influence of this restraint. Within this range, the influence of

44
pallets may be determined but has been determined to be outside the scope of this
thesis.
Figure 3-21: Modelling the influence of pallets on DIR4.
3. 3 LOCAL AND PROGRESSIVE COLLAPSE SIMULATION
This section outlines the process in which collapse has been modelled in Strand7
(Strand7 2010) in order to determine the upper limit of the proposed fuse connectors.
As previously described in Section 2.4.2 (pg. 20), the nature of the analysis required
in order to accurately simulate the structural response requires dynamic analysis. Due
to the sudden disruption of equilibrium initiated by the removal of the damaged
member as proposed in Section 2.4.2.2 (pg. 22) the transient dynamic solver has been
utilised, see Section 3.1.8 (pg. 37). This section provides an outline of the process in
which initial upright failure has been modelled through the determination and
application of supporting reactions, removal of these reactions and the process of
determining the event of propagation of the failure. Additionally, details on the
determination and application of the residual capacity of damaged members has been
explored.
3.3.1 INITIAL UPRIGHT FAILURE
As discussed in Section 2.4.2.2 (pg. 22), the process of inducing failure due to a forklift
impact has been undertaken as per methods described in FEM 10.2.7 (2012). This
specification describes the impact occurring at a height of 400mm, Yadwad (2011)
considered this failure elevation at heights of 300mm and 1200mm. Impacts are to be
modelled in this case for failure elevations of 300mm in order to obtain a comparison

The use of Fuse Connectors in Cold-Formed Steel Drive-In Racks, Thesis by C.J Wodzinski, 2014

The use of Fuse Connectors in Cold-Formed Steel Drive-In Racks, Thesis by C.J Wodzinski, 2014

Recommended

Recommended

More Related Content

Similar to The use of Fuse Connectors in Cold-Formed Steel Drive-In Racks, Thesis by C.J Wodzinski, 2014

Similar to The use of Fuse Connectors in Cold-Formed Steel Drive-In Racks, Thesis by C.J Wodzinski, 2014 (20)

Recently uploaded

Recently uploaded (20)

The use of Fuse Connectors in Cold-Formed Steel Drive-In Racks, Thesis by C.J Wodzinski, 2014