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FEM 10.2.07Comparison of methods of global analysis

Option 2 and Option 6

Working group FEM 10.2.072nd Meeting in Amsterdam, 02/2009

D. mdek, K. Tilburgs

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Contents

1. Geometry

2. Loading

3. Results

4. Conclusions

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1. Geometry

Main dimensions

- net channel width 1 340 mm- no. of lanes 20 lanes- frame height 11 350 mm- no. of levels 4 levels- spacing of levels 2 250 mm- frame depth 1 300 mm- spacing between frames 1 250 mm- channel depth 9 000 mm

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4 examples of bracing configuration

Example B- min. bracing acc. to Option 6 (numbers, shape ratios)- profiles designed for sway imperfection 1/100

Example B2- min. bracing acc. to Option 6 (numbers, shape ratios)- profiles designed for sway imperfection 1/100- without full-length plan bracing

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4 examples of bracing configuration (pg. 2)

Example B3- min. bracing acc. to Option 6 (numbers, shape ratios)- profiles designed for sway imperfection 1/50

Example A- bracing configuration corresponding to daily practise

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Derivation of geometry of individual examples

See following pages.

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Example B - Global view

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Example B - Down-lane direction

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Example B - Down-lane direction

FEM 10.2.07 - Option 6 - requires

- max. 1 mono post

Here in Example B- 1 mono post

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Example B - Cross-lane direction

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Example B - Spine bracing

FEM 10.2.07 - Option 6 - requires- min. 1 lane in 5 braced- max. Height / Width = 4 : 1- minimum profiles

Here in Example B- 1 lane in 5 braced- Height / Width = 3.83 : 1- minimum profiles

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Example B - Top view

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Example B - Top view

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Example B2 - Top view

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Example B - Plan bracing

FEM 10.2.07 - Option 6 - requires- min. 1 lane in 5 braced- max. Depth / Width = 3 : 1- minimum profiles

Here in Example B- 1 lane in 3.33 braced- Depth / Width = 2.03 : 1- minimum profiles

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Example A - Global view

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Example A - Down-lane direction

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Example A - Cross-lane direction

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Example A - Spine bracing

FEM 10.2.07 - Option 6 - requires- min. 1 lane in 5 braced- max. Height / Width = 4 : 1- minimum profiles

Here in Example A- 1 lane in 1.67 braced- Height / Width = 1.92 : 1- larger profiles

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Example A - Top view

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Example A - Top view

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Example A - Plan bracing

FEM 10.2.07 - Option 6 - requires- min. 1 lane in 5 braced- max. Depth / Width = 3 : 1- minimum profiles

Here in Example A- 1 lane in 1 braced- Depth / Width = 0.87 : 1- larger profiles

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Structural model remarks

- modeling for geometric linear vs. non-linear analysis

- non-uniform upright loads (multi-span factor, kms):

Upright kms

1 1.02 - 1.052 0.98 - 0.993 1.004 1.005 1.006 1.007 0.95 - 0.988 0.91 - 1.06

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Structural model remarks (pg. 2)

- torsional stiffness of uprights was for test purposes reduced 10x, 100x, 1000x in order to prove, that behaviour and stability of the model is not favourably influenced by upright torsional rigidity or by applied torsional restraints.

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2. Loading

1. Selfweight

2. Product load

- mpal = 1 000 kg- pallet depth 800 + 2*50 mm, 10 pcs in channel depth

3. Imperfection in cross-lane direction

- installation imperfection 1/350- design imperfection (20 lanes) 1/236

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Combinations

Geom. non-linear analysis (2nd order)

1.3 * G + 1.4 * Q (incl. Imperfections in c.-l. dir.)

Geom. linear analysis (1st order)

1.3 * G + 1.4 * Q (incl. Imperfections in c.-l. dir.)

Stability (Eulerian load)

1.3 * G + 1.4 * Q

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3. Results

Reminder - Studied issues

1. Comparison of results according to Option 2 and 6

2. Requirements for bracing systems acc. to Option 6

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3.1 Side sway

Option 2

- at 2nd line of uprights- ULS combination

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3.1 Side sway

Example Option Side sway k2nd Side swaymm %

B Option 2 - 2nd order 80.8 3.44 308Option 2 - 1st order 23.5Option 6 ---

B3 Option 2 - 2nd order 51.3 2.93 196Option 2 - 1st order 17.5Option 6 ---

A Option 2 - 2nd order 26.2 2.36 100Option 2 - 1st order 11.1Option 6 ---

Example B2 was not stable.

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Example B

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Example B2

NOT STABLE !!!

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Example A

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Example B

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Example A

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Example B

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Example A

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3.2 Normal force in standard upright

Standard upright- upright is part of plan bracing (effect of glob. tors. considered)- not part of vertical bracing; not mono post

Option 2- usually 3rd to 4th line of uprights (high NSd, My.Sd)

Option 6- hand calculated- including multi-span factor (1.143)- calculation method of global torsion effect is conservative- including 2nd order in frame direction (App. G4; prEN 15512)

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3.2 Normal force in standard upright

Example Option NSd k2nd NSdkN %

B Option 2 - 2nd order 90.867 1.06 69Option 2 - 1st order 85.655Option 6 131.083 100

B3 Option 2 - 2nd order 89.288 1.04 68Option 2 - 1st order 85.602Option 6 131.083 100

A Option 2 - 2nd order 82.799 1.01 82Option 2 - 1st order 82.005Option 6 100.929 100

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3.3 Bending moment at base of standard upright

Option 2- the same upright as upright with maximum normal force

Option 6- higher cbase due to higher normal force

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3.3 Bending moment at base of standard upright

Example Option MSd k2nd MSdkNm %

B Option 2 - 2nd order 1.957 3.16 392Option 2 - 1st order 0.620Option 6 0.499 100

B3 Option 2 - 2nd order 1.470 2.65 295Option 2 - 1st order 0.555Option 6 0.499 100

A Option 2 - 2nd order 1.165 2.24 247Option 2 - 1st order 0.520Option 6 0.471 100

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Example B

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Example A

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3.4 Buckling length in cross-lane direction

Option 2- 3D model with restricted sway of top plane- anti-symmetric modes only

Option 6- single upright with restricted sway at the top- anti-symmetric modes only

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3.4 Buckling length in cross-lane direction

Example Option Lcr.y Lcr.yBeta*Lsys %

B Option 2 0.445 101Option 6 0.441 100

B3 Option 2 0.445 101Option 6 0.441 100

A Option 2 0.442 98Option 6 0.449 100

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Example B

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Example B

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Example A

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Example A

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3.5 Unity check of standard upright

General

- including flexural-torsional buckling- one Lcr.y, My.Sd, bMy (i.e. ky)- checked at least on two levels (variable Lcr.z and NSd)

Note

- My.Sd also for Option 6 calculated using design imperfection (1/236)

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3.5 Unity check of standard upright

Example Option Check Check%

B Option 2 - 2nd order 1.03 87Option 6 1.18 100

B3 Option 2 - 2nd order 0.95 81Option 6 1.18 100

A Option 2 - 2nd order 0.85 90Option 6 0.94 100

Option 6 is conservative with regard to unity check of upright.

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3.6 Axial force in spine bracing

Option 2- 2nd (and 1st) order

Option 6- calculated by hand, 1st order- mass of total block considered- share to top calculated using model with upright

restricted at the top against translation

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3.6 Axial force in spine bracing

Example Option NSd k2nd NSdkN %

B Option 2 - 2nd order 41.48 2.74 218Option 2 - 1st order 15.147Option 6 19.051 100

B3 Option 2 - 2nd order 35.793 2.17 188Option 2 - 1st order 16.479Option 6 19.051 100

A Option 2 - 2nd order 30.822 1.78 177Option 2 - 1st order 17.347Option 6 17.435 100

Opt. 6 is very unconservative with regard to bracing sys. stiffness.

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4. Conclusions

a. Structures designed acc. to Option 6 are excessively flexible (high influence of 2nd order).

b. Upright design to Option 6 is conservative (assuming the use of multi-span factor and the effect of GT).

c. Spine bracing design to Option 6 is not conservative.

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Further remarks

d. The specification of min. ammount of bracing systems in Option 6 should be rephrased to avoid confusion.

e. Additional requirements (use of multi-span factor, effects of global torsion, 2nd order in frame dir.) must be added.

f. Requirement for design of min. bracing should be applicable for gross cross-sections only.

g. Upright check procedure might be further discussed (concerns all analysis options).