school of ciVil engineering
reseArCH rePort r914MArCH 2011
issn 1833-2781
static friction coefficient BetWeen Pallets and Beam rail and Pallet shear stiffness tests
Vinh huaKim Jr rasmussen
STATIC FSHEAR ST RESEARC VINH HUA KIM RASMU MARCH 201 ISSN 1833-2
RICTION TIFFNESS
H REPORT
USSEN
11
2781
COEFFICIS TESTS
T R914
IENT BETWWEEN PA
SC
ALLETS AN
CHOOL OF
ND BEAM
F CIVIL ENG
RAIL AND
GINEERING
D PALLET
G
T
Static Friction Coefficient Between Pallets and Beam Rail and Pallet Shear Stiffness Tests
School of Civil Engineering Research Report R914 Page 2 The University of Sydney
Copyright Notice School of Civil Engineering, Research Report R914 Static Friction Coefficient Between Pallets and Beam Rail and Pallet Shear Stiffness Tests Vinh Hua & Kim Rasmussen March 2011 ISSN 1833-2781 This publication may be redistributed freely in its entirety and in its original form without the consent of the copyright owner. Use of material contained in this publication in any other published works must be appropriately referenced, and, if necessary, permission sought from the author. Published by: School of Civil Engineering The University of Sydney Sydney NSW 2006 Australia This report and other Research Reports published by the School of Civil Engineering are available at http://sydney.edu.au/civil
Static Friction Coefficient Between Pallets and Beam Rail and Pallet Shear Stiffness Tests
School of Civil Engineering Research Report R914 Page 3 The University of Sydney
ABSTRACT An experimental program was established at the University of Sydney to determine the coefficient of friction between various types of timber pallets and a typical Dematic beam rail. In addition, another test series was also carried out to measure the shear stiffness of those timber pallets. The outcome of the study can be used as a guideline for further design enhancement of the drive-in rack system. This report summarizes the test results and their possible implementations.
KEYWORDS Drive-in racks, steel storage racks, steel structures, finite element analysis, friction coefficient, shear stiffness.
Static Friction Coefficient Between Pallets and Beam Rail and Pallet Shear Stiffness Tests
School of Civil Engineering Research Report R914 Page 4 The University of Sydney
TABLE OF CONTENTS ABSTRACT .......................................................................................................................................................... 3 KEYWORDS ........................................................................................................................................................ 3 TABLE OF CONTENTS....................................................................................................................................... 4 1 INTRODUCTION .......................................................................................................................................... 5 2 EXPERIMENTAL SETUP ............................................................................................................................. 5
2.1 Test series ........................................................................................................................................... 5 2.2 Pallet friction test setup ........................................................................................................................ 8 2.3 Pallet shear stiffness test set up ........................................................................................................ 10
3 EXPERIMENTAL RESULTS ...................................................................................................................... 12 3.1 Pallet friction results ........................................................................................................................... 12 3.2 Pallet shear stiffness results .............................................................................................................. 13
4 IMPLEMENTATION OF THE RESULTS.................................................................................................... 15 4.1 Revised dynamic FE analysis with updated static coefficient of friction ............................................ 15 4.2 Study on friction forces from the dynamic FE analysis ...................................................................... 17
5 CONCLUSIONS ......................................................................................................................................... 22 6 REFERENCES ........................................................................................................................................... 22 APPENDIX A ..................................................................................................................................................... 23 APPENDIX B ..................................................................................................................................................... 45
School of CiviThe University
1 INT The static anthe down-aisfriction betwsystem undemay substanin the designfriction betwinterface has An experimebetween varalso carried as a guideliresults and t
2 EXP
2.1 TES The experimdeterminatioseries were Sydney. All displacemen
A total of 20given in tabDCR7 – T (fpallets variepurpose of tbeing left ou
Pallet
No.
1
2
Stati
il Engineeringy of Sydney
TRODUCT
nd dynamic bsle direction
ween the paller horizontalntially increasn of the drive
ween the palls been sugge
ental programrious types oout to measne for furthetheir possible
PERIMENT
ST SERIES
mental progon of the fric
conducted tests were
nt control mo
0 timber pallble 1. The mfigure 1) at 2ed from nearthe experime
utside of the l
D
Width
(mm)
1170
1165
ic Friction Co
ION
behaviour ofhas been stuets and the impact loadse the laterae-in rack sysets and the ested in the
m was estabof timber palsure the sheaer design ene implementa
TAL SETU
ram comprisction coefficie
in the J. We performed ode.
ets were avamoisture cont2 locations anrly new to qents to inclulaboratory, s
imension
Height
(mm)
1170
1163
oefficient Bet
Rese
f a standard dudied and resupporting b
d. The frictioal stiffness of stems by thebeam rail. Trange 0.4 to
blished at thelets and a ty
ar stiffness ohancement oations.
UP
sed a total ent and one
W. Roderick Lusing a 15
ailable for tetent of the pnd taking thequite badly dude a wide ruch that the
WDepth
(mm)
145
145
tween Pallet
earch Report
drive-in rackeported in [1]beam rails hanal resistancf the system.e industry duTypical value 0.6 in [3] an
e University ypical Demaof those timbof the drive-
of 40 testsfor the mea
Laboratory f50kN capac
esting and thpallet was me average vadamaged as range of palresults can b
Weight
(kg)
A
M
C
34
37
ts and Beam
R914
k structure su and [2]. It isas a significace together w This benefic
ue to the lack of coefficien
nd between 0
of Sydney ttic beam raier pallets. Th-in rack syst
s which incasurement offor Materialscity servo-co
heir dimensiomeasured usialue. It should
indicated inlet conditionbe reasonab
Average
oisture
Content
(%)
13
12
Rail and Pa
ubjected to a s indicated froant influencewith the shecial effect, hok of reliable dnt of friction 0.45 to 0.55 i
o determine l. In additionhe outcome em. This rep
luded two tf the pallet sand Structu
ontrolled hyd
ons, weight aing the Timbd be noted thn the associans, from beinly generalize
Desc
allet Shear St
a horizontal imom these stue on the behar stiffness oowever, is nodata on the between won [4].
the coefficien, another teof the study port summar
test series, shear stiffneures at the draulic ram
and moistureber Moisturehat the condated picturesng stored uned.
cription
tiffness Tests
Page 5
mpact load inudies that thehaviour of theof the palletsot consideredcoefficient o
ood and stee
ent of frictionst setup wascan be used
rizes the tes
one for thess. Both tesUniversity ooperated in
e content aree Meter Typeition of thoses. It was the
nder cover to
s
5
n e e s d
of el
n s d st
e st of n
e e e e o
School of CiviThe University
3
4
5
6
7
8
9
Stati
il Engineeringy of Sydney
1165
1165
1165
1164
1163
1162
1160
ic Friction Co
1161
1160
1160
1162
1166
1162
1170
oefficient Bet
Rese
145
145
145
145
145
145
145
tween Pallet
earch Report
37
37
37
33
32
34
44
ts and Beam
R914
13.5
11
11
13
16.5
11
15
Rail and Paallet Shear Sttiffness Tests
Page 6
s
6
School of CiviThe University
10
11
12
13
14
15
16
Stati
il Engineeringy of Sydney
1160
1165
1162
1160
1162
1160
1165
ic Friction Co
1170
1165
1165
1168
1160
1160
1165
oefficient Bet
Rese
145
145
145
145
145
145
145
tween Pallet
earch Report
21
40
35
40
42
37
35
ts and Beam
R914
10
12
13
10
12
11
12.5
Rail and Paallet Shear Sttiffness Tests
Page 7
s
7
School of CiviThe University
17
18
19
20
2.2 PAL A diagram oframes spacsupport at t
Stati
il Engineeringy of Sydney
1162
1163
1163
1163
LLET FRICT
of the pallet fced at 1250mhe base. Th
ic Friction Co
1155
1165
1160
1163
Tab
Figu
ION TEST S
friction test smm apart. The right hand
oefficient Bet
Rese
145
145
145
145
ble 1. Pallet D
ure 1. Timbe
SETUP
etup is showThe left handd side uprig
tween Pallet
earch Report
41
35
35
37
Dimensions a
er Moisture M
wn in figures d side uprighght frame wa
ts and Beam
R914
13
12
12
16
and Descript
Meter Type D
2a and 2b. ht frame wasas mounted
Rail and Pa
tions
CR7 – T
The test rig s attached toon a C cha
allet Shear St
comprised oo a rigid framannel connec
tiffness Tests
Page 8
of two uprighme with fixedcted to a pin
s
8
ht d n
School of CiviThe University
support at ethe beam raattached to was connecaffect the loa
The loading correspondindistance of transducers tests.
Stati
il Engineeringy of Sydney
ach end. Thails with 70mthe right han
cted to the mading ram an
ram was setng displacem40mm from were also i
ic Friction Co
is upright comm bearing nd side uprig
mid point of tnd vice versa
t up to run inment of the rleft to right nstalled at t
Figure
Fig
oefficient Bet
Rese
ould thereforewidth and l
ght frame at he SHS via
a.
n displacemeram were rewas preset he four corn
e 2a. Pallet f
ure 2b. Palle
tween Pallet
earch Report
e pivot freelyloaded by a395 mm aba half round
ent control mecorded usinfor the load
ners of the p
friction test s
et friction tes
ts and Beam
R914
y at the basea 1014 kg cobove the leved so that the
ode at constg Strainsmaing ram withpallet to reco
etup – Eleva
t setup – Pla
Rail and Pa
e. The test paoncrete blocel of the bea rotation of t
tant speed. Tart software dh an applied ord the palle
ation View
an View
allet Shear St
allet was plack. A 40x40xam rails. Thethe upright f
The applied fduring the te rate at 10m
et movemen
tiffness Tests
Page 9
aced betweenx4 SHS was
e loading ramframe did no
force and theests. A trave
mm/min. Fouts during the
s
9
n s
m ot
e el r e
School of CiviThe University
2.3 PAL The setup foend by mean10mm thick the pallet’s v
Similarly to speed, and using Strainsapplied rate
Stati
il Engineeringy of Sydney
Figure
LLET SHEAR
or the pallet ns of fabricasteel plate w
vertical studs
the friction tthe applied fsmart softwaat 20mm/mi
ic Friction Co
Figure 2c
2d. Pallet fr
R STIFFNES
shear stiffneted steel angwas inserteds when the lo
tests, the loforce and thare. A travel n.
oefficient Bet
Rese
c. Pallet frictio
iction test se
SS TEST SE
ess tests is ilgle clamps, w between th
oad is applied
ading ram we corresponddistance of 6
tween Pallet
earch Report
on test setup
etup – Front e
T UP
llustrated in which also pe pallet bottod at the top.
was set up tding displac60mm from r
ts and Beam
R914
p – Front elev
elevation pic
figure 3a. Threvent the paom and the
to run in disement of theright to left w
Rail and Pa
vation picture
ture – bottom
he test palletallets from lifbase H beam
placement ce ram were rwas preset fo
allet Shear St
e
m supports
t was fixed afting off. A 90m to allow th
control moderecorded dur
or the loading
tiffness Tests
Page 10
at the bottom0mm wide byhe rotation o
e at constanring the testsg ram with an
s
0
m y
of
nt s n
School of CiviThe University
Stati
il Engineeringy of Sydney
ic Friction Co
Figure 3
Figure 3b
oefficient Bet
Rese
3a. Pallet She
b. Pallet She
tween Pallet
earch Report
ear Stiffness
ar Stiffness S
ts and Beam
R914
s Setup – Ele
Setup – Elev
Rail and Pa
evation View
vation Picture
allet Shear St
e
tiffness Tests
Page 11
s
1
School of CiviThe University
3 EXP 3.1 PAL
Diagrams of23 in Appenuntil it becastarted to slat that point
(s N
where Fr is mp)g) basedapplied at th
rF8
12
where Fa is t
The resulting
Stati
il Engineeringy of Sydney
PERIMENT
LLET FRICT
f the applied ndix A for theme larger thip and the awas used to
)2w
r
N
F
the maximumd on the weihe pallet / rail
aF60
255
the maximum
g static frictio
ic Friction Co
Figure 3c.
TAL RESU
ION RESUL
load and dise 20 test palhan the statipplied load d
o determine t
m applied foght of the cl beam level
m load applie
on coefficien
oefficient Bet
Rese
. Pallet Shea
ULTS
TS
splacement olets respectic friction bedropped slighe static frict
orce at the poncrete blocwas determi
ed by the jac
ts for the 20
tween Pallet
earch Report
ar Stiffness S
of the transdively. As exptween the phtly to its dytion coefficie
allet/ rail beack (mcb) andined as;
ck when the s
tested pallet
ts and Beam
R914
Setup – botto
ducers versupected, the apallet and theynamic frictioent between t
am level andthe pallet s
slip occurred
ts are tabula
Rail and Pa
m clamp view
s time are shapplied load e rail beam n value. Ththe pallet an
d Nw is the tself weight (m
.
ted in table 2
allet Shear St
ew
hown in figuincreased nat which po
he maximum d the rail bea
total normal mp). The ma
2.
tiffness Tests
Page 12
re 4 to figureearly linearly
oint the palleapplied load
am, i.e.
(1)
force ((mcb +aximum force
(2)
s
2
e y
et d
+ e
Static Friction Coefficient Between Pallets and Beam Rail and Pallet Shear Stiffness Tests
School of Civil Engineering Research Report R914 Page 13 The University of Sydney
Pallet
Pallet self
weight (kg)
Total applied weight
(kg)
Max. applied lateral load
Fa (kN)
Max. applied lateral load at
pallet/rail level Fr
(kN)
Static Friction Coefficient
µs Pallet Condition
1 34 1048 1.934 2.822 0.549 Good
2 37 1051 1.779 2.596 0.504 Good
3 37 1051 1.514 2.209 0.429 Good
4 37 1051 1.691 2.468 0.479 Good
5 37 1051 1.903 2.777 0.539 Good
6 33 1047 1.923 2.806 0.546 Missing Board
7 32 1046 1.865 2.722 0.530 Good
8 34 1048 2.057 3.002 0.584 Missing Board
9 44 1058 2.428 3.543 0.683 Good
10 21 1035 2.036 2.971 0.585 Light weight
11 40 1054 2.01 2.933 0.567 Rotten one side
12 35 1049 2.263 3.302 0.642 Good
13 40 1054 1.853 2.704 0.523 Good
14 42 1056 1.903 2.777 0.536 Missing Board
15 37 1051 1.961 2.862 0.555 Missing Board
16 35 1049 2.33 3.400 0.661 Good
17 41 1055 2.367 3.454 0.668 Good
18 35 1049 2.388 3.485 0.677 Good
19 35 1049 2.204 3.216 0.625 Good
20 37 1051 2.228 3.251 0.631 Good
Table 2. Summary of static friction coefficients
From the above results, we can obtain the mean value of static coefficient of friction of 0.576 and a standard deviation of 0.068. The minimum and maximum were 0.429 and 0.683 respectively. A characteristic design value of static coefficient of friction can be determined by subtracting 2 times the standard deviation from the mean value, producing a 95% probability the sample value will be higher than characteristic value. For the above 20 test results, one can calculate the characteristic design static friction coefficient between the pallet and rail beam as 0.439. 3.2 PALLET SHEAR STIFFNESS RESULTS
The applied horizontal force versus lateral displacement of the pallets is shown in figure 24 and figure 25 in Appendix A for the good condition pallets and poor condition pallets respectively. It can be noted that for the shear stiffness tests, the condition of the pallet has significant influence on the stiffness value, unlike the friction test, where the pallet condition has little impact on the results.
Static Friction Coefficient Between Pallets and Beam Rail and Pallet Shear Stiffness Tests
School of Civil Engineering Research Report R914 Page 14 The University of Sydney
In addition, it can be seen from the diagrams that the force versus displacement behaviour for most of the pallets are nearly linear. Hence it has been assumed the shear stiffness can be determined as
minmax
minmax
FF
S (3)
where (�min, Fmin) and (�max, Fmax) are appropriate points defining the linear range of the force-displacement diagram.
The shear stiffness results are summarized in table 3, which also summarizes the pallet condition.
Pallet Shear Stiffness
(N/mm) Pallet Condition
1 12.43 Good
2 20.74 Good
3 31.41 Good
4 27.67 Good
5 14.79 Good
6 9.08 Missing board
7 16.55 Good
8 5.45 Missing board
9 17.89 Good
10 9.59 Light weight
11 5.13 Rotten one side
12 18.03 Good
13 17.56 Good
14 8.13 Missing board
15 10.41 Missing board
16 18.18 Good
17 18.72 Good
18 15.57 Good
19 17.57 Good
20 11.81 Good
Table 3. Summary of pallet shear stiffness
From the above results, for the good condition pallets, one can obtain the mean value of 18.5 N/mm and standard deviation of 5.1 N/mm. Similarly for the poor condition pallets, the mean value and standard deviation are 8.0 N/mm and 2.0 N/mm respectively. The characteristic design shear stiffness value for the good pallets can be calculated as 8.3 N/mm and for the poor condition pallets as 3.9 N/mm.
Static Friction Coefficient Between Pallets and Beam Rail and Pallet Shear Stiffness Tests
School of Civil Engineering Research Report R914 Page 15 The University of Sydney
4 IMPLEMENTATION OF THE RESULTS
4.1 REVISED DYNAMIC FE ANALYSIS WITH UPDATED STATIC COEFFICIENT OF FRICTION The finite element model for the loaded rack case 4 reported in [2] with pallets placed at the front bay of the rack was modified to incorporate the above test results. In order to accurately represent the characteristic shear stiffness (8.3 N/mm for a good pallet) of the pallets, a simple finite element model of the pallet was constructed to determine the appropriate properties (E, G) to be used to obtain the characteristic shear stiffness value. Figure 26 in Appendix B shows the single pallet model and the relevant parameters.
The model of the pallets was then incorporated into the rack model as shown in figure 27a and 27b. With a pallet length of 1050mm, seven pallets can be allocated to one fully loaded row. To keep the loaded mass the same as in the original case, each pallet was assigned a loaded mass of 2143 kg. The friction coefficient between the pallets and the rail beam has also been modified to the characteristic value of 0.44 for this revised study.
The deflection responses at the front face of the revised model are given in figures 28a to 28f for the six load duration cases with 1%, 3% and 5% damping considered in [2]. Similarly, the displacement gap response at the top pallet level and the down aisle bending moment at the base of the impacted upright are plotted in figures 28g to 28l and 28m to 28r in Appendix B respectively.
The peak response of the front face deflection, the displacement gap at the top pallet level and the bending moment at the base for the revised model as compared to the original model are summarized in tables 4a to 4c respectively.
Load Duration
(second)
Damping Ratio Static Result
5% 3% 1%
Original
Model
0.086 18.6 18.8 19.0
33.3
0.172 23.3 23.6 24.1
0.258 27.7 28.1 28.7
0.428 36.2 36.2 36.2
0.856 49.5 49.9 50.2
5.000 52.8 53.3 54.1
Revised
Model
0.086 18.1 18.2 18.4
34.9
0.172 22.1 22.2 22.4
0.258 25.9 26.0 26.1
0.428 34.0 34.3 34.5
0.856 48.4 48.8 49.2
5.000 54.1 54.4 54.8
Table 4a. Summary of peak response of the front face displacement
Static Friction Coefficient Between Pallets and Beam Rail and Pallet Shear Stiffness Tests
School of Civil Engineering Research Report R914 Page 16 The University of Sydney
Load Duration
(second)
Damping Ratio Static Result
5% 3% 1%
Original
Model
0.086 6.2 6.2 6.3
7.7
0.172 6.5 6.6 6.6
0.258 6.8 6.9 7.0
0.428 7.5 7.6 7.7
0.856 8.7 8.8 9.0
5.000 10.4 10.5 10.7
Revised
Model
0.086 3.7 3.7 3.8
4.1
0.172 3.7 3.7 3.8
0.258 3.9 4.0 4.2
0.428 4.5 4.7 4.9
0.856 5.5 5.8 6.1
5.000 5.1 5.1 5.2
Table 4b. Summary of peak response of the displacement gap at the top pallet level
Load Duration
(second)
Damping Ratio Static Result
5% 3% 1%
Original
Model
0.086 202 206 216
677
0.172 305 316 339
0.258 400 421 449
0.428 582 614 658
0.856 1009 1022 1017
5.000 1151 1164 1180
Revised
Model
0.086 265 272 277
727
0.172 287 294 319
0.258 372 386 414
0.428 549 558 577
0.856 914 929 948
5.000 1182 1193 1211
Table 4c. Summary of peak response of the bending moment at the base of the front upright
It can be observed from the above results that the peak response of the front face displacements and the bending moment at the base of the front upright are quite similar for the original and the revised model. The maximum difference is approximately 10%. On the other hand, the peak response of the displacement gap at the top pallet level is reduced significantly for the revised model when compared to the original case.
Static Friction Coefficient Between Pallets and Beam Rail and Pallet Shear Stiffness Tests
School of Civil Engineering Research Report R914 Page 17 The University of Sydney
The effect of load duration and damping ratio on the peak response is similar to that in the original study with longer load durations resulting in higher peak responses.
As noticed in [2], the dynamic impact load of 1000 N in this case results in shear forces less than the static friction force between the pallets and the rail beams for the obtained characteristic static friction coefficient of 0.44. The effect of the pallets is to enhance the overall lateral stiffness of the system in which they act as extra bracing at those pallet levels. As a result, the peak responses of the system are generally less than the static analysis results, especially at load durations of less than 0.5 second.
4.2 STUDY ON FRICTION FORCES FROM THE DYNAMIC FE ANALYSIS Given the importance of friction between the pallets and the supporting rail beam to the behaviour of the system from the above study, it would be interesting to investigate further on the response of the friction forces obtained from the FE model. It has been observed that the damping ratio did not have a significant impact on the rack response, hence for this study only the results for the case with 3% critical damping ratio were examined. As described previously, there were seven pallets along each rail beam and the associated masses are modeled at both the top and bottom pallet levels. Each pallet was supported by rail beams on the “front” side and “rear” side as illustrated in figure 27b. The friction force responses, which include the components in the down-aisle and cross-aisle directions, between pallets and rail beams can be obtained from the FE model for the duration of 10 seconds after the impact. The pallets are identified by a number with pallet 1 being closest to the front face of the rack and pallet 7 being closest to the back of the rack. The down-aisle friction force responses are shown in figures 29a to 29x and cross- aisle friction force responses are given in figures 30a to 30x for the top and bottom level pallets, front and rear sides when subjected to six different impact load durations. The peak down-aisle friction forces for each case have been extracted from the FE results and tabulated in tables 5a to 5d for the top pallet level front side, top pallet level rear side, bottom pallet level front side and bottom pallet level rear side respectively.
Load Duration (second)
Pallet 1 Pallet 2 Pallet 3 Pallet 4 Pallet 5 Pallet 6 Pallet 7
0.086 522 184 45 26 23 30 192
Max Value
0.172 522 184 65 51 40 60 387
0.258 522 184 47 73 58 89 583
0.428 522 184 66 110 89 148 1002
0.856 522 184 126 128 104 225 1666
5.000 522 184 45 75 91 78 448
0.086 -96 -117 -46 -33 -23 -27 -238
Min Value
0.172 -83 -84 -51 -61 -44 -55 -466
0.258 -135 -107 -72 -87 -63 -82 -671
0.428 -195 -101 -97 -129 -94 -144 -1033
0.856 -244 -219 -152 -123 -103 -273 -1425
5.000 -143 -110 -114 -125 -83 -165 -1016
Static Result 301 9 -39 -20 3 -45 -357
Table 5a. Summary of peak response of down aisle friction force (N) at top pallet level – front side
Static Friction Coefficient Between Pallets and Beam Rail and Pallet Shear Stiffness Tests
School of Civil Engineering Research Report R914 Page 18 The University of Sydney
Load Duration (second)
Pallet 1 Pallet 2 Pallet 3 Pallet 4 Pallet 5 Pallet 6 Pallet 7
0.086 102 170 133 76 40 40 246
Max Value
0.172 82 170 133 76 52 79 482
0.258 105 170 133 93 75 117 694
0.428 173 170 133 122 110 193 1060
0.856 290 180 133 128 101 325 1454
5.000 87 170 133 122 77 159 949
0.086 -281 -147 -58 -41 -31 -39 -192
Min Value
0.172 -281 -104 -56 -80 -60 -76 -385
0.258 -281 -134 -81 -114 -87 -110 -578
0.428 -313 -119 -114 -168 -129 -172 -988
0.856 -347 -237 -168 -157 -124 -252 -1665
5.000 -431 -104 -45 -74 -75 -77 -434
Static Result -301 -9 39 20 -3 51 357
Table 5b. Summary of peak response of down aisle friction force (N) at top pallet level - rear side
Load Duration (second)
Pallet 1 Pallet 2 Pallet 3 Pallet 4 Pallet 5 Pallet 6 Pallet 7
0.086 523 121 20 16 14 14 61
Max Value
0.172 523 121 32 32 27 26 117
0.258 523 121 39 48 40 37 165
0.428 523 121 65 77 66 61 245
0.856 523 121 122 130 107 91 286
5.000 523 121 35 57 56 54 282
0.086 -112 -67 -34 -35 -18 -13 -72
Min Value
0.172 -95 -60 -29 -35 -20 -25 -147
0.258 -152 -85 -37 -35 -30 -37 -226
0.428 -161 -86 -64 -55 -48 -62 -400
0.856 -221 -114 -112 -105 -84 -116 -752
5.000 -98 -45 -72 -77 -49 -115 -705
Static Result 359 35 -29 -19 6 -7 -452
Table 5c. Summary of peak response of down aisle friction force (N) at bottom pallet level - front side
Static Friction Coefficient Between Pallets and Beam Rail and Pallet Shear Stiffness Tests
School of Civil Engineering Research Report R914 Page 19 The University of Sydney
Load Duration (second)
Pallet 1 Pallet 2 Pallet 3 Pallet 4 Pallet 5 Pallet 6 Pallet 7
0.086 98 87 96 59 27 17 70
Max Value
0.172 74 87 96 59 27 34 145
0.258 78 87 96 66 34 51 222
0.428 122 87 96 76 54 85 399
0.856 149 88 96 76 64 137 765
5.000 134 87 96 76 40 100 697
0.086 -364 -92 -37 -19 -18 -18 -63
Min Value
0.172 -364 -74 -33 -33 -29 -34 -121
0.258 -364 -102 -41 -48 -41 -48 -172
0.428 -375 -98 -61 -71 -60 -71 -252
0.856 -389 -131 -84 -82 -70 -69 -300
5.000 -456 -102 -50 -61 -56 -52 -292
Static Result -359 -34 29 19 -6 10 451
Table 5d. Summary of peak response of down aisle friction force (N) at bottom pallet level - rear side
Similarly, the peak cross-aisle friction forces for each case are tabulated in tables 6a to 6d for the top pallet level front side, top pallet level rear side, bottom pallet level front side and bottom pallet level rear side respectively.
Load Duration (second)
Pallet 1 Pallet 2 Pallet 3 Pallet 4 Pallet 5 Pallet 6 Pallet 7
0.086 24 13 37 41 57 78 92
Max Value
0.172 25 24 37 41 57 78 92
0.258 35 35 37 41 57 79 104
0.428 56 52 37 41 57 88 121
0.856 85 52 37 41 57 88 123
5.000 11 24 37 41 57 88 123
0.086 -119 -43 -38 -14 -6 -17 -26
Min Value
0.172 -119 -45 -27 -14 -12 -34 -50
0.258 -119 -57 -37 -20 -18 -49 -72
0.428 -119 -69 -54 -32 -28 -75 -106
0.856 -119 -79 -48 -44 -46 -84 -106
5.000 -119 -79 -51 -26 -28 -41 -51
Static Result -73 -48 -16 10 29 40 61
Table 6a. Summary of peak response of cross aisle friction force (N) at top pallet level – front side
Static Friction Coefficient Between Pallets and Beam Rail and Pallet Shear Stiffness Tests
School of Civil Engineering Research Report R914 Page 20 The University of Sydney
Load Duration (second)
Pallet 1 Pallet 2 Pallet 3 Pallet 4 Pallet 5 Pallet 6 Pallet 7
0.086 124 54 41 17 9 18 26
Max Value
0.172 124 58 24 17 17 37 51
0.258 124 68 38 24 24 54 73
0.428 125 81 62 38 38 80 107
0.856 125 83 63 56 55 80 96
5.000 125 83 53 18 14 27 40
0.086 -19 -13 -25 -27 -43 -61 -79
Min Value
0.172 -34 -25 -25 -27 -43 -61 -79
0.258 -48 -35 -33 -32 -43 -70 -95
0.428 -77 -55 -55 -54 -54 -78 -110
0.856 -91 -51 -89 -88 -89 -89 -112
5.000 -40 -36 -25 -41 -60 -96 -125
Static Result 73 48 16 -10 -29 -40 -61
Table 6b. Summary of peak response of cross aisle friction force (N) at top pallet level – rear side
Load Duration (second)
Pallet 1 Pallet 2 Pallet 3 Pallet 4 Pallet 5 Pallet 6 Pallet 7
0.086 13 9 15 21 37 48 61
Max Value
0.172 15 18 16 21 37 48 61
0.258 22 26 24 21 37 54 74
0.428 37 38 34 24 37 59 84
0.856 63 44 35 30 37 59 86
5.000 37 36 35 35 46 60 86
0.086 -100 -46 -25 -7 -4 -9 -13
Min Value
0.172 -100 -46 -21 -11 -7 -16 -26
0.258 -100 -54 -31 -16 -11 -23 -37
0.428 -100 -59 -34 -25 -18 -35 -54
0.856 -100 -60 -43 -39 -34 -33 -47
5.000 -113 -76 -38 -31 -32 -42 -51
Static Result -71 -44 -8 11 25 35 50
Table 6c. Summary of peak response of cross aisle friction force (N) at bottom pallet level – front side
Static Friction Coefficient Between Pallets and Beam Rail and Pallet Shear Stiffness Tests
School of Civil Engineering Research Report R914 Page 21 The University of Sydney
Load Duration (second)
Pallet 1 Pallet 2 Pallet 3 Pallet 4 Pallet 5 Pallet 6 Pallet 7
0.086 100 51 25 6 5 10 14
Max Value
0.172 100 51 23 8 9 19 27
0.258 100 59 33 12 14 28 40
0.428 102 67 38 19 21 39 58
0.856 102 67 27 26 30 38 50
5.000 102 67 31 28 28 32 36
0.086 -17 -10 -12 -17 -32 -43 -57
Min Value
0.172 -17 -16 -14 -17 -32 -43 -57
0.258 -25 -22 -19 -17 -32 -48 -68
0.428 -41 -34 -30 -24 -34 -54 -80
0.856 -51 -30 -37 -43 -48 -54 -80
5.000 -38 -41 -43 -39 -51 -70 -93
Static Result 71 44 8 -11 -25 -35 -50
Table 6d. Summary of peak response of cross aisle friction force (N) at bottom pallet level – rear side The above friction forces do not include the friction forces occurring at the pallet interface due displacements induced by gravity loading. The friction forces resulting from gravity loading are tabulated in tables 7a and 7b for the down-aisle and cross-aisle directions respectively.
Location Pallet 1 Pallet 2 Pallet 3 Pallet 4 Pallet 5 Pallet 6 Pallet 7
Top Pallet Front -76 878 623 302 641 650 -2491
Top Pallet Rear 76 -878 -623 -302 -641 -653 2491
Bottom Pallet Front -663 270 -182 -822 -324 384 -181
Bottom Pallet Rear 663 -270 182 822 324 -384 181
Table 7a. Down-aisle friction force (N) from gravity loading
Location Pallet 1 Pallet 2 Pallet 3 Pallet 4 Pallet 5 Pallet 6 Pallet 7
Top Pallet Front 34 22 19 11 -4 -35 -77
Top Pallet Rear -34 -22 -19 -11 4 35 77
Bottom Pallet Front 40 21 14 1 -15 -24 -43
Bottom Pallet Rear -40 -21 -14 -1 15 24 43
Table 7b. Cross-aisle friction force (N) from gravity loading
It can be observed from the above results that the largest friction force occurs at the pallet closest to the back of the rack and the pallets closest to the impacted upright which in this case are the pallets closest to the front.
Static Friction Coefficient Between Pallets and Beam Rail and Pallet Shear Stiffness Tests
School of Civil Engineering Research Report R914 Page 22 The University of Sydney
In addition, the friction between pallets and rail beams engage the shear stiffness of the pallets to provide shear and axial forces in the cross-aisle direction. However, the magnitudes of the cross-aisle friction forces are fairly small which is probably because of the low shear stiffness of the pallets.
Considering both the cross-aisle and down-aisle components, the maximum friction forces are 536N and 1670 N, and occur at pallets 1 and 7 at the top and bottom pallet levels respectively, when the load duration is 0.856 second for the applied 1000 N impact load. If friction forces from gravity loading are also taken into account, the maximum friction forces increase to 1200 N and 4162 N at the pallet 1 and pallet 7 interfaces respectively. For a pallet mass of 2143 kg and a static friction coefficient of 0.44, the maximum possible friction force before sliding is 4625 N. Therefore, it is possible for pallet 7 to be sliding when the impact load is approximately 1100 N. Similarly, pallet 1 may start to slide when the impact load in the order of 3850 N. It can be noted that while pallet 7 may start to loose its grip at a low impact load, its location at the back of the rack means it is not subjected to a large displacement of the rail beam as in the case of pallet 1 at the front face of the rack.
It should be noticed that the above study has assumed that the gravity load is supported evenly at the front and rear sides of the pallet. It is entirely possible in practice that the load is shared unevenly depending on the location of the mass on the pallet and hence that uneven reaction forces may cause the pallet to slide at a much lower impact load. Therefore, it should be recommended in practice that (i) pallets should be positioned evenly between the supports and (ii) the minimum bearing width of pallets on the rail beam must be adhered to.
5 CONCLUSIONS
A series of experiments were carried out to determine the static friction coefficient between a typical pallet and the supporting rail beam in a standard drive-in rack system. A characteristic design static friction coefficient of 0.44 was obtained from the test results. In addition, a second series of tests was undertaken to evaluate the shear stiffness of a standard pallet. For pallets in poor and good conditions, characteristic design shear stiffness values of 3.9 N/mm and 8.3 N/mm were obtained respectively, which may be applicable for design purposes as appropriate. The effects of the characteristic design values obtained from the tests on the dynamic behaviour of a drive-in rack were then investigated using FEA for the case where the front bay is loaded. The finite element model, which was developed in [2], was revised to incorporate the new characteristic values of static friction and pallet shear stiffness. The results from the revised analysis indicated a similar behaviour of the rack under dynamic impact load as in the original model even though the magnitudes of the peak responses were a little smaller because of the assumed large coefficient of friction. Further investigations were also carried out to determine the friction force occurring at the interface between pallets and rail beams when subjected to an impact force of 1000 N. The results indicated that the friction forces are largest at the pallets closest to the back of the rack and the impacted upright. With the given pallet arrangement in this study, it is possible for the pallet closest to the back of the system to start loosing its grip at an impact load of 1100 N. Further study may be required to investigate the behaviour of the system when the impact load exceeds the above value and whether the sliding of the pallet has an effect on the friction forces at other pallet to rail beam interfaces.
6 REFERENCES 1. Vinh, H. and Rasmussen, K. The behaviour of drive-in racks under horizontal impact load, Research Report R871, 2006. University of Sydney. 2. Vinh, H. and Rasmussen, K. The dynamic study of drive-in racks under horizontal impact load, Research Report R915, 2011. University of Sydney. 3. Gregory, P. T. Port Engineering: planning, construction, maintenance and security, p.120, 2004, John Wiley & Sons. 4. Paulo, C. F. E. Design of hydraulic gates, p.226, 2004, Swets & Zeitlinger B.V., Lisse, The Netherlands.
Static Friction Coefficient Between Pallets and Beam Rail and Pallet Shear Stiffness Tests
School of Civil Engineering Research Report R914 Page 23 The University of Sydney
APPENDIX A
TEST RESULTS
School of CiviThe University
Stati
il Engineeringy of Sydney
F
ic Friction Co
Fig
igure 4b. Tra
oefficient Bet
Rese
ure 4a. Load
ansducer Dis
tween Pallet
earch Report
d vs Time Dia
splacement v
ts and Beam
R914
agram – Pall
vs Time Diag
Rail and Pa
let 1
gram – Pallet
allet Shear St
t 1
tiffness Tests
Page 24
s
4
School of CiviThe University
Stati
il Engineeringy of Sydney
F
ic Friction Co
Fig
igure 5b. Tra
oefficient Bet
Rese
ure 5a. Load
ansducer Dis
tween Pallet
earch Report
d vs Time Dia
splacement v
ts and Beam
R914
agram – Pall
vs Time Diag
Rail and Pa
let 2
gram – Pallet
allet Shear St
t 2
tiffness Tests
Page 25
s
5
School of CiviThe University
Stati
il Engineeringy of Sydney
F
ic Friction Co
Fig
igure 6b. Tra
oefficient Bet
Rese
ure 6a. Load
ansducer Dis
tween Pallet
earch Report
d vs Time Dia
splacement v
ts and Beam
R914
agram – Pall
vs Time Diag
Rail and Pa
let 3
gram – Pallet
allet Shear St
t 3
tiffness Tests
Page 26
s
6
School of CiviThe University
Stati
il Engineeringy of Sydney
ic Friction Co
F
Figure 7b. T
oefficient Bet
Rese
Figure 7a. Lo
Transducer D
tween Pallet
earch Report
oad vs Time D
Displacemen
ts and Beam
R914
Diagram – P
nt vs Time Di
Rail and Pa
allet 4
agram – Pal
allet Shear St
let 4
tiffness Tests
Page 27
s
7
School of CiviThe University
Stati
il Engineeringy of Sydney
ic Friction Co
Fig
Figure 8b. T
oefficient Bet
Rese
ure 8a. Load
Transducer D
tween Pallet
earch Report
d vs Time Dia
Displacemen
ts and Beam
R914
agram – Pall
nt vs Time Di
Rail and Pa
let 5
agram – Pal
allet Shear St
let 5
tiffness Tests
Page 28
s
8
School of CiviThe University
Stati
il Engineeringy of Sydney
ic Friction Co
F
Figure 9b. T
oefficient Bet
Rese
Figure 9a. Lo
Transducer D
tween Pallet
earch Report
oad vs Time D
Displacemen
ts and Beam
R914
Diagram – P
nt vs Time Di
Rail and Pa
allet 6
agram – Pal
allet Shear St
let 6
tiffness Tests
Page 29
s
9
School of CiviThe University
Stati
il Engineeringy of Sydney
ic Friction Co
Fi
Figure 10b.
oefficient Bet
Rese
gure 10a. Lo
Transducer
tween Pallet
earch Report
oad vs Time
Displacemen
ts and Beam
R914
Diagram – P
nt vs Time D
Rail and Pa
Pallet 7
iagram – Pa
allet Shear St
allet 7
tiffness Tests
Page 30
s
0
School of CiviThe University
Stati
il Engineeringy of Sydney
ic Friction Co
Fi
Figure 11b.
oefficient Bet
Rese
gure 11a. Lo
Transducer
tween Pallet
earch Report
oad vs Time
Displacemen
ts and Beam
R914
Diagram – P
nt vs Time D
Rail and Pa
Pallet 8
iagram – Pa
allet Shear St
allet 8
tiffness Tests
Page 31
s
1
School of CiviThe University
Stati
il Engineeringy of Sydney
ic Friction Co
Fi
Figure 12b.
oefficient Bet
Rese
gure 12a. Lo
Transducer
tween Pallet
earch Report
oad vs Time
Displacemen
ts and Beam
R914
Diagram – P
nt vs Time D
Rail and Pa
Pallet 9
iagram – Pa
allet Shear St
allet 9
tiffness Tests
Page 32
s
2
School of CiviThe University
Stati
il Engineeringy of Sydney
F
ic Friction Co
Fig
Figure 13b. T
oefficient Bet
Rese
gure 13a. Lo
Transducer D
tween Pallet
earch Report
oad vs Time D
Displacemen
ts and Beam
R914
Diagram – P
nt vs Time Di
Rail and Pa
allet 10
agram – Pal
allet Shear St
let 10
tiffness Tests
Page 33
s
3
School of CiviThe University
Stati
il Engineeringy of Sydney
F
ic Friction Co
Fig
Figure 14b. T
oefficient Bet
Rese
gure 14a. Lo
Transducer D
tween Pallet
earch Report
oad vs Time D
Displacemen
ts and Beam
R914
Diagram – P
nt vs Time Di
Rail and Pa
allet 11
agram – Pal
allet Shear St
let 11
tiffness Tests
Page 34
s
4
School of CiviThe University
Stati
il Engineeringy of Sydney
F
ic Friction Co
Fig
Figure 15b. T
oefficient Bet
Rese
gure 15a. Lo
Transducer D
tween Pallet
earch Report
oad vs Time D
Displacemen
ts and Beam
R914
Diagram – P
nt vs Time Di
Rail and Pa
allet 12
agram – Pal
allet Shear St
let 12
tiffness Tests
Page 35
s
5
School of CiviThe University
Stati
il Engineeringy of Sydney
F
ic Friction Co
Fig
Figure 16b. T
oefficient Bet
Rese
gure 16a. Lo
Transducer D
tween Pallet
earch Report
oad vs Time D
Displacemen
ts and Beam
R914
Diagram – P
nt vs Time Di
Rail and Pa
allet 13
agram – Pal
allet Shear St
let 13
tiffness Tests
Page 36
s
6
School of CiviThe University
Stati
il Engineeringy of Sydney
F
ic Friction Co
Fig
Figure 17b. T
oefficient Bet
Rese
gure 17a. Lo
Transducer D
tween Pallet
earch Report
oad vs Time D
Displacemen
ts and Beam
R914
Diagram – P
nt vs Time Di
Rail and Pa
allet 14
agram – Pal
allet Shear St
let 14
tiffness Tests
Page 37
s
7
School of CiviThe University
Stati
il Engineeringy of Sydney
F
ic Friction Co
Fig
Figure 18b. T
oefficient Bet
Rese
gure 18a. Lo
Transducer D
tween Pallet
earch Report
oad vs Time D
Displacemen
ts and Beam
R914
Diagram – P
nt vs Time Di
Rail and Pa
allet 15
agram – Pal
allet Shear St
let 15
tiffness Tests
Page 38
s
8
School of CiviThe University
Stati
il Engineeringy of Sydney
F
ic Friction Co
Fig
Figure 19b. T
oefficient Bet
Rese
gure 19a. Lo
Transducer D
tween Pallet
earch Report
oad vs Time D
Displacemen
ts and Beam
R914
Diagram – P
nt vs Time Di
Rail and Pa
allet 16
agram – Pal
allet Shear St
let 16
tiffness Tests
Page 39
s
9
School of CiviThe University
Stati
il Engineeringy of Sydney
F
ic Friction Co
Fig
Figure 20b. T
oefficient Bet
Rese
gure 20a. Lo
Transducer D
tween Pallet
earch Report
oad vs Time D
Displacemen
ts and Beam
R914
Diagram – P
nt vs Time Di
Rail and Pa
allet 17
agram – Pal
allet Shear St
let 17
tiffness Tests
Page 40
s
0
School of CiviThe University
Stati
il Engineeringy of Sydney
F
ic Friction Co
Fig
Figure 21b. T
oefficient Bet
Rese
gure 21a. Lo
Transducer D
tween Pallet
earch Report
oad vs Time D
Displacemen
ts and Beam
R914
Diagram – P
nt vs Time Di
Rail and Pa
allet 18
agram – Pal
allet Shear St
let 18
tiffness Tests
Page 41
s
1
School of CiviThe University
Stati
il Engineeringy of Sydney
F
ic Friction Co
Fig
Figure 22b. T
oefficient Bet
Rese
gure 22a. Lo
Transducer D
tween Pallet
earch Report
oad vs Time D
Displacemen
ts and Beam
R914
Diagram – P
nt vs Time Di
Rail and Pa
allet 19
agram – Pal
allet Shear St
let 19
tiffness Tests
Page 42
s
2
School of CiviThe University
Stati
il Engineeringy of Sydney
F
ic Friction Co
Fig
Figure 23b. T
oefficient Bet
Rese
gure 23a. Lo
Transducer D
tween Pallet
earch Report
oad vs Time D
Displacemen
ts and Beam
R914
Diagram – P
nt vs Time Di
Rail and Pa
allet 20
agram – Pal
allet Shear St
let 20
tiffness Tests
Page 43
s
3
School of CiviThe University
Stati
il Engineeringy of Sydney
ic Friction Co
Figure 2
Figure 2
oefficient Bet
Rese
24. Pallet She
25. Pallet Sh
tween Pallet
earch Report
ear Stiffness
hear Stiffness
ts and Beam
R914
s – Good con
s – Poor con
Rail and Pa
ndition pallets
dition pallets
allet Shear St
s
s
tiffness Tests
Page 44
s
4
Static Friction Coefficient Between Pallets and Beam Rail and Pallet Shear Stiffness Tests
School of Civil Engineering Research Report R914 Page 45 The University of Sydney
APPENDIX B
REVISED FINITE ELEMENT ANALYSIS RESULTS
School of CiviThe University
Stati
il Engineeringy of Sydney
ic Friction Co
Figu
Figure
oefficient Bet
Rese
ure 26. Single
27a. Revise
tween Pallet
earch Report
1050 mm
e Pallet Finit
ed Rack mod
ts and Beam
R914
te Element M
del with pallet
Rail and Pa
Model
ts modelled
allet Shear St
tiffness Tests
Page 46
s
6
School of CiviThe University
Front sidsupport
Friction Coefficie
Timber Pallet Beams
Stati
il Engineeringy of Sydney
de of
ent 0.44
ic Friction Co
Close up v
oefficient Bet
Rese
view of the re
tween Pallet
earch Report
evised rack m
ts and Beam
R914
model with p
Rail and Pa
allets modell
allet Shear St
led
tiffness Tests
Page 47
Figure 27b.
Rear side ofsupport
s
7
f
School of CiviThe University
Figure 28
Figure 28
Stati
il Engineeringy of Sydney
8a. Deflectio
8b. Deflectio
ic Friction Co
on Response
on Response
oefficient Bet
Rese
at the front fDuration
at the front fDuration
tween Pallet
earch Report
face of the ran ∆T = 0.086
face of the ran ∆T = 0.172
ts and Beam
R914
ack – Revise6 second
ack – Revise2 second
Rail and Pa
ed Front Bay
ed Front Bay
allet Shear St
y Loaded Rac
y Loaded Rac
tiffness Tests
Page 48
ck – Load
ck – Load
s
8
School of CiviThe University
Figure 28
Figure 28
Stati
il Engineeringy of Sydney
8c. Deflectio
8d. Deflectio
ic Friction Co
on Response
on Response
oefficient Bet
Rese
at the front fDuration
at the front fDuration
tween Pallet
earch Report
face of the ran ∆T = 0.258
face of the ran ∆T = 0.428
ts and Beam
R914
ack – Revise8 second
ack – Revise8 second
Rail and Pa
ed Front Bay
ed Front Bay
allet Shear St
y Loaded Rac
y Loaded Rac
tiffness Tests
Page 49
ck – Load
ck – Load
s
9
School of CiviThe University
Figure 2
Figure 2
Stati
il Engineeringy of Sydney
8e. Deflectio
8f. Deflectio
ic Friction Co
on Response
n Response
oefficient Bet
Rese
e at the front Duration
at the front fDuratio
tween Pallet
earch Report
face of the rn ∆T = 0.856
face of the raon ∆T = 5.0 s
ts and Beam
R914
rack - Revise6 second
ack – Revisesecond
Rail and Pa
ed Front Bay
ed Front Bay
allet Shear St
Loaded Rac
Loaded Rac
tiffness Tests
Page 50
ck – Load
ck – Load
s
0
School of CiviThe University
Figure 28
Figure 28
Stati
il Engineeringy of Sydney
8g. Displacem
8h. Displacem
ic Friction Co
ment Gap Re
Ra
ment Gap Re
Ra
oefficient Bet
Rese
esponse at th
ack – Load D
esponse at th
ack – Load D
tween Pallet
earch Report
he front face
Duration ∆T =
he front face
Duration ∆T =
ts and Beam
R914
of top pallet
= 0.086 seco
of top pallet
= 0.172 seco
Rail and Pa
level – Revi
ond
level – Revi
ond
allet Shear St
ised Front Ba
ised Front Ba
tiffness Tests
Page 51
ay Loaded
ay Loaded
s
1
School of CiviThe University
Figure 28i. D
Figure 28j. D
Stati
il Engineeringy of Sydney
Displacemen
Displacemen
ic Friction Co
nt Gap Respo
nt Gap Respo
oefficient Bet
Rese
onse at the f
– Load Dura
onse at the f
– Load Dura
tween Pallet
earch Report
front face of t
ation ∆T = 0
front face of t
ation ∆T = 0
ts and Beam
R914
top pallet lev
.258 second
top pallet lev
.428 second
Rail and Pa
vel – Revised
vel – Revised
allet Shear St
d Front Bay L
d Front Bay L
tiffness Tests
Page 52
Loaded Rack
Loaded Rack
s
2
k
k
School of CiviThe University
Figure 28
Figure 28l. D
Stati
il Engineeringy of Sydney
8k. Displacem
Displacemen
ic Friction Co
ment Gap Re
Ra
nt Gap Respo
oefficient Bet
Rese
esponse at th
ack – Load D
onse at the f
– Load Du
tween Pallet
earch Report
he front face
Duration ∆T =
front face of t
uration ∆T =
ts and Beam
R914
of top pallet
= 0.856 seco
top pallet lev
5.0 second
Rail and Pa
level – Revi
ond
vel – Revised
allet Shear St
ised Front Ba
d Front Bay L
tiffness Tests
Page 53
ay Loaded
Loaded Rack
s
3
k
School of CiviThe University
Figure 28m
Figure 28n.
Stati
il Engineeringy of Sydney
. Bending Mo
Bending Mo
ic Friction Co
oment Respo
oment Respo
oefficient Bet
Rese
onse at the b
Load Dura
onse at the b
Load Dura
tween Pallet
earch Report
base of impa
ation ∆T = 0.0
base of impa
ation ∆T = 0.1
ts and Beam
R914
acted upright
086 second
cted upright
172 second
Rail and Pa
– Revised F
– Revised F
allet Shear St
Front Bay Loa
Front Bay Loa
tiffness Tests
Page 54
aded Rack –
aded Rack –
s
4
–
–
School of CiviThe University
Figure 28o.
Figure 28p.
Stati
il Engineeringy of Sydney
Bending Mo
Bending Mo
ic Friction Co
oment Respo
oment Respo
oefficient Bet
Rese
onse at the b
Load Dura
onse at the b
Load Dura
tween Pallet
earch Report
base of impa
ation ∆T = 0.2
base of impa
ation ∆T = 0.4
ts and Beam
R914
cted upright
258 second
cted upright
428 second
Rail and Pa
– Revised F
– Revised F
allet Shear St
Front Bay Loa
Front Bay Loa
tiffness Tests
Page 55
aded Rack –
aded Rack –
s
5
–
–
School of CiviThe University
Figure 28q.
Figure 28r.
Stati
il Engineeringy of Sydney
Bending Mo
Bending Mo
ic Friction Co
oment Respo
oment Respo
oefficient Bet
Rese
onse at the b
Load Dura
onse at the b
Load Dur
tween Pallet
earch Report
base of impa
ation ∆T = 0.8
base of impac
ration ∆T = 5
ts and Beam
R914
cted upright
856 second
cted upright –
5.0 second
Rail and Pa
– Revised F
– Revised Fr
allet Shear St
Front Bay Loa
ront Bay Loa
tiffness Tests
Page 56
aded Rack –
aded Rack –
s
6
–
School of CiviThe University
Figure 29a.
Figure 29b.
Stati
il Engineeringy of Sydney
Down aisle f
Down aisle
ic Friction Co
friction force
friction force
oefficient Bet
Rese
response to
e response to
tween Pallet
earch Report
op pallet leve
second
op pallet leve
second
ts and Beam
R914
el – front side
el – rear side
Rail and Pa
e support – L
support – Lo
allet Shear St
Load Duration
oad Duration
tiffness Tests
Page 57
n ∆T = 0.086
n ∆T = 0.086
s
7
6
6
School of CiviThe University
Figure 29c
Figure 29d
Stati
il Engineeringy of Sydney
c. Down aisle
d. Down aisle
ic Friction Co
e friction forc
e friction forc
oefficient Bet
Rese
e response b0
ce response 0
tween Pallet
earch Report
bottom pallet0.086 secon
bottom palle0.086 secon
ts and Beam
R914
t level – frond
et level – reard
Rail and Pa
t side suppo
r side suppor
allet Shear St
rt – Load Du
rt – Load Du
tiffness Tests
Page 58
uration ∆T =
ration ∆T =
s
8
School of CiviThe University
Figure 29e.
Figure 29f.
Stati
il Engineeringy of Sydney
Down aisle f
Down aisle f
ic Friction Co
friction force
friction force
oefficient Bet
Rese
response to
response to
tween Pallet
earch Report
op pallet leve
second
op pallet levesecond
ts and Beam
R914
el – front side
el – rear side
Rail and Pa
e support – L
support – Lo
allet Shear St
Load Duration
oad Duration
tiffness Tests
Page 59
n ∆T = 0.172
n ∆T = 0.172
s
9
2
School of CiviThe University
Figure 29g
Figure 29h
Stati
il Engineeringy of Sydney
g. Down aisle
h. Down aisle
ic Friction Co
e friction forc
e friction forc
oefficient Bet
Rese
e response b0
ce response 0
tween Pallet
earch Report
bottom pallet0.172 secon
bottom palle0.172 secon
ts and Beam
R914
t level – frond
et level – reard
Rail and Pa
t side suppo
r side suppor
allet Shear St
ort – Load Du
rt – Load Du
tiffness Tests
Page 60
uration ∆T =
ration ∆T =
s
0
School of CiviThe University
Figure 29i.
Figure 29j.
Stati
il Engineeringy of Sydney
Down aisle f
Down aisle f
ic Friction Co
friction force
friction force
oefficient Bet
Rese
response to
response to
tween Pallet
earch Report
p pallet leve
second
op pallet leve
second
ts and Beam
R914
l – front side
el – rear side
Rail and Pa
support – Lo
support – Lo
allet Shear St
oad Duration
oad Duration
tiffness Tests
Page 61
n ∆T = 0.258
n ∆T = 0.258
s
1
8
School of CiviThe University
Figure 29k
Figure 29l
Stati
il Engineeringy of Sydney
k. Down aisle
l. Down aisle
ic Friction Co
e friction forc
e friction forc
oefficient Bet
Rese
e response b0
e response b0
tween Pallet
earch Report
bottom pallet0.258 secon
bottom pallet0.258 secon
ts and Beam
R914
t level – frond
t level – reard
Rail and Pa
t side suppo
side suppor
allet Shear St
rt – Load Du
rt – Load Dur
tiffness Tests
Page 62
uration ∆T =
ration ∆T =
s
2
School of CiviThe University
Figure 29m.
Figure 29n.
Stati
il Engineeringy of Sydney
Down aisle
Down aisle
ic Friction Co
friction force
friction force
oefficient Bet
Rese
e response to
e response to
tween Pallet
earch Report
op pallet leve
second
op pallet levesecond
ts and Beam
R914
el – front side
el – rear side
Rail and Pa
e support – L
support – Lo
allet Shear St
Load Duratio
oad Duration
tiffness Tests
Page 63
n ∆T = 0.428
n ∆T = 0.428
s
3
8
8
School of CiviThe University
Figure 29o
Figure 29p
Stati
il Engineeringy of Sydney
o. Down aisle
p. Down aisle
ic Friction Co
e friction forc
e friction forc
oefficient Bet
Rese
e response b0
ce response 0
tween Pallet
earch Report
bottom pallet0.428 secon
bottom palle0.428 secon
ts and Beam
R914
t level – frond
et level – reard
Rail and Pa
t side suppo
r side suppor
allet Shear St
ort – Load Du
rt – Load Du
tiffness Tests
Page 64
uration ∆T =
ration ∆T =
s
4
School of CiviThe University
Figure 29q.
Figure 29r.
Stati
il Engineeringy of Sydney
Down aisle f
Down aisle f
ic Friction Co
friction force
friction force
oefficient Bet
Rese
response to
response to
tween Pallet
earch Report
op pallet leve
second
op pallet levesecond
ts and Beam
R914
el – front side
el – rear side
Rail and Pa
e support – L
support – Lo
allet Shear St
Load Duration
oad Duration
tiffness Tests
Page 65
n ∆T = 0.856
n ∆T = 0.856
s
5
6
School of CiviThe University
Figure 29s
Figure 29t
Stati
il Engineeringy of Sydney
s. Down aisle
t. Down aisle
ic Friction Co
e friction forc
e friction forc
oefficient Bet
Rese
e response b0
e response b0
tween Pallet
earch Report
bottom pallet0.856 secon
bottom pallet0.856 secon
ts and Beam
R914
t level – frond
t level – reard
Rail and Pa
t side suppo
r side suppor
allet Shear St
rt – Load Du
rt – Load Du
tiffness Tests
Page 66
uration ∆T =
ration ∆T =
s
6
School of CiviThe University
Figure 29u
Figure 29v
Stati
il Engineeringy of Sydney
u. Down aisle
v. Down aisle
ic Friction Co
e friction forc
e friction forc
oefficient Bet
Rese
e response t
ce response t
tween Pallet
earch Report
top pallet lev
second
top pallet levsecond
ts and Beam
R914
vel – front sid
vel – rear sid
Rail and Pa
de support –
e support – L
allet Shear St
Load Duratio
Load Duratio
tiffness Tests
Page 67
on ∆T = 5.0
on ∆T = 5.0
s
7
School of CiviThe University
Figure 29w
Figure 29x.
Stati
il Engineeringy of Sydney
w. Down aisle
Down aisle f
ic Friction Co
e friction forc
friction force
oefficient Bet
Rese
ce response b
response bo
tween Pallet
earch Report
bottom palle5.0 second
ottom pallet lsecond
ts and Beam
R914
t level – fron
evel – rear s
Rail and Pa
t side suppo
side support –
allet Shear St
ort – Load Du
– Load Dura
tiffness Tests
Page 68
uration ∆T =
ation ∆T = 5.0
s
8
0
School of CiviThe University
Figure 30a.
Figure 30b.
Stati
il Engineeringy of Sydney
Cross aisle f
Cross aisle
ic Friction Co
friction force
friction force
oefficient Bet
Rese
response to
e response to
tween Pallet
earch Report
op pallet leve
second
op pallet levesecond
ts and Beam
R914
el – front side
el – rear side
Rail and Pa
e support – L
e support – Lo
allet Shear St
Load Duratio
oad Duration
tiffness Tests
Page 69
n ∆T = 0.086
n ∆T = 0.086
s
9
6
6
School of CiviThe University
Figure 30c
Figure 30d
Stati
il Engineeringy of Sydney
c. Cross aisle
d. Cross aisle
ic Friction Co
e friction forc
e friction forc
oefficient Bet
Rese
e response b0
ce response 0
tween Pallet
earch Report
bottom pallet0.086 secon
bottom palle0.086 secon
ts and Beam
R914
t level – frond
et level – reard
Rail and Pa
t side suppo
r side suppor
allet Shear St
ort – Load Du
rt – Load Du
tiffness Tests
Page 70
uration ∆T =
uration ∆T =
s
0
School of CiviThe University
Figure 30e.
Figure 30f.
Stati
il Engineeringy of Sydney
Cross aisle f
Cross aisle f
ic Friction Co
friction force
friction force
oefficient Bet
Rese
response to
response to
tween Pallet
earch Report
op pallet leve
second
op pallet levesecond
ts and Beam
R914
el – front side
el – rear side
Rail and Pa
e support – L
support – Lo
allet Shear St
Load Duratio
oad Duration
tiffness Tests
Page 71
n ∆T = 0.172
n ∆T = 0.172
s
1
2
School of CiviThe University
Figure 30g
Figure 30h
Stati
il Engineeringy of Sydney
g. Cross aisle
h. Cross aisle
ic Friction Co
e friction forc
e friction forc
oefficient Bet
Rese
ce response b0
ce response 0
tween Pallet
earch Report
bottom palle0.172 secon
bottom palle0.172 secon
ts and Beam
R914
t level – frond
et level – reard
Rail and Pa
t side suppo
r side suppor
allet Shear St
ort – Load Du
rt – Load Du
tiffness Tests
Page 72
uration ∆T =
uration ∆T =
s
2
School of CiviThe University
Figure 30i.
Figure 30j.
Stati
il Engineeringy of Sydney
Cross aisle f
Cross aisle f
ic Friction Co
friction force
friction force
oefficient Bet
Rese
response to
response to
tween Pallet
earch Report
p pallet leve
second
op pallet levesecond
ts and Beam
R914
l – front side
el – rear side
Rail and Pa
support – Lo
support – Lo
allet Shear St
oad Duration
oad Duration
tiffness Tests
Page 73
n ∆T = 0.258
n ∆T = 0.258
s
3
8
School of CiviThe University
Figure 30k
Figure 30l
Stati
il Engineeringy of Sydney
k. Cross aisle
l. Cross aisle
ic Friction Co
e friction forc
e friction forc
oefficient Bet
Rese
e response b0
e response b0
tween Pallet
earch Report
bottom pallet0.258 secon
bottom pallet0.258 secon
ts and Beam
R914
t level – frond
t level – reard
Rail and Pa
t side suppo
r side suppor
allet Shear St
ort – Load Du
rt – Load Du
tiffness Tests
Page 74
uration ∆T =
ration ∆T =
s
4
School of CiviThe University
Figure 30m.
Figure 30n.
Stati
il Engineeringy of Sydney
Cross aisle
Cross aisle
ic Friction Co
friction force
friction force
oefficient Bet
Rese
e response to
e response to
tween Pallet
earch Report
op pallet leve
second
op pallet levesecond
ts and Beam
R914
el – front side
el – rear side
Rail and Pa
e support – L
e support – Lo
allet Shear St
Load Duratio
oad Duration
tiffness Tests
Page 75
on ∆T = 0.428
n ∆T = 0.428
s
5
8
8
School of CiviThe University
Figure 30o
Figure 30p
Stati
il Engineeringy of Sydney
o. Cross aisle
p. Cross aisle
ic Friction Co
e friction forc
e friction forc
oefficient Bet
Rese
ce response b0
ce response 0
tween Pallet
earch Report
bottom palle0.428 secon
bottom palle0.428 secon
ts and Beam
R914
t level – frond
et level – reard
Rail and Pa
t side suppo
r side suppor
allet Shear St
ort – Load Du
rt – Load Du
tiffness Tests
Page 76
uration ∆T =
uration ∆T =
s
6
School of CiviThe University
Figure 30q.
Figure 30r.
Stati
il Engineeringy of Sydney
Cross aisle f
Cross aisle f
ic Friction Co
friction force
friction force
oefficient Bet
Rese
response to
response to
tween Pallet
earch Report
op pallet leve
second
op pallet levesecond
ts and Beam
R914
el – front side
el – rear side
Rail and Pa
e support – L
support – Lo
allet Shear St
Load Duratio
oad Duration
tiffness Tests
Page 77
n ∆T = 0.856
n ∆T = 0.856
s
7
6
School of CiviThe University
Figure 30s
Figure 30t
Stati
il Engineeringy of Sydney
s. Cross aisle
t. Cross aisle
ic Friction Co
e friction forc
e friction forc
oefficient Bet
Rese
e response b0
e response b0
tween Pallet
earch Report
bottom pallet0.856 secon
bottom pallet0.856 secon
ts and Beam
R914
t level – frond
t level – reard
Rail and Pa
t side suppo
r side suppor
allet Shear St
ort – Load Du
rt – Load Du
tiffness Tests
Page 78
uration ∆T =
ration ∆T =
s
8
School of CiviThe University
Figure 30u
Figure 30v
Stati
il Engineeringy of Sydney
u. Cross aisle
v. Cross aisle
ic Friction Co
e friction forc
e friction forc
oefficient Bet
Rese
ce response t
ce response t
tween Pallet
earch Report
top pallet levsecond
top pallet levsecond
ts and Beam
R914
vel – front sid
vel – rear sid
Rail and Pa
de support –
e support –
allet Shear St
Load Duratio
Load Duratio
tiffness Tests
Page 79
on ∆T = 5.0
on ∆T = 5.0
s
9
School of CiviThe University
Figure 30w
Figure 30x. C
Stati
il Engineeringy of Sydney
w. Cross aisle
Cross aisle f
ic Friction Co
e friction forc
friction force
oefficient Bet
Rese
ce response
response bo
tween Pallet
earch Report
bottom palle5.0 second
ottom pallet lsecond
ts and Beam
R914
et level – fron
evel – rear s
Rail and Pa
nt side suppo
side support –
allet Shear St
ort – Load Du
– Load Dura
tiffness Tests
Page 80
uration ∆T =
ation ∆T = 5.0
s
0
0