static friction coefficient between pallets and beam rail

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



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.



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

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R914

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Page 12

re 4 to figureearly linearly

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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.



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


9 17.89 Good

10 9.59 Light weight

11 5.13 Rotten one side

12 18.03 Good

13 17.56 Good



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.



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



Load Duration

(second)


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)


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.



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





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



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





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.



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





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



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





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.



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.



APPENDIX A

TEST RESULTS


Stati


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


Stati


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


Stati


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


Stati


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


Stati


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


Stati


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


Stati


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


Stati


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


Stati


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


Stati


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


Stati


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


Stati


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


Stati


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


Stati


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


Stati


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


Stati


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


Stati


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


Stati


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


Stati


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


Stati


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


Stati


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



APPENDIX B

REVISED FINITE ELEMENT ANALYSIS RESULTS


Stati


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


Front sidsupport

Friction Coefficie

Timber Pallet Beams

Stati


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


Figure 28

Figure 28

Stati


8a. Deflectio

8b. Deflectio

ic Friction Co

on Response

on Response

oefficient Bet

Rese

at the front fDuration


tween Pallet

earch Report

face of the ran ∆T = 0.086


ts and Beam

R914

ack – Revise6 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


Figure 28

Figure 28

Stati


8c. Deflectio

8d. Deflectio

ic Friction Co

on Response

on Response

oefficient Bet

Rese



tween Pallet

earch Report



ts and Beam

R914



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


Figure 2

Figure 2

Stati


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


Figure 28

Figure 28

Stati


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


Figure 28i. D

Figure 28j. D

Stati


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


Figure 28

Figure 28l. D

Stati


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


Figure 28m

Figure 28n.

Stati


. 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

–

–


Figure 28o.

Figure 28p.

Stati


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

–

–


Figure 28q.

Figure 28r.

Stati


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

–


Figure 29a.

Figure 29b.

Stati


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


Figure 29c

Figure 29d

Stati


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


Figure 29e.

Figure 29f.

Stati


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


Figure 29g

Figure 29h

Stati


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



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


Figure 29i.

Figure 29j.

Stati


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


Figure 29k

Figure 29l

Stati


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



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


Figure 29m.

Figure 29n.

Stati


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


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


Figure 29o

Figure 29p

Stati


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



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


Figure 29q.

Figure 29r.

Stati


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


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


Figure 29s

Figure 29t

Stati


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



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


Figure 29u

Figure 29v

Stati


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


Figure 29w

Figure 29x.

Stati


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


Figure 30a.

Figure 30b.

Stati


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


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


Figure 30c

Figure 30d

Stati


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



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


Figure 30e.

Figure 30f.

Stati


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


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


Figure 30g

Figure 30h

Stati


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



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


Figure 30i.

Figure 30j.

Stati


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


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


Figure 30k

Figure 30l

Stati


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



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


Figure 30m.

Figure 30n.

Stati


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


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


Figure 30o

Figure 30p

Stati


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



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


Figure 30q.

Figure 30r.

Stati


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


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


Figure 30s

Figure 30t

Stati


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



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


Figure 30u

Figure 30v

Stati


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



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


Figure 30w

Figure 30x. C

Stati


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

static friction coefficient between pallets and beam rail

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