FEM-10-2-08 2009-10-10 Static steel pallet racks under seismic conditions.pdf

pr-FEM 10.2.08 FEM 10.2.08 RECOMMENDATIONS FOR THE DESIGN OF STATIC STEEL PALLET RACKS UNDER SEISMIC CONDITIONS

October 2009

prFEM 10.2.08 FEM 10.2.08 RECOMMENDATIONS FOR THE DESIGN OF STATIC STEEL PALLET RACKS UNDER SEISMIC CONDITIONS Final REVIEW – October 2009

Editorial rules Updated or added parts Parts to be removed from the text Notes or editorial comments for discussion Format /editorial changes

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FEM 10.2.08 Seismic design Final Draft REVIEW 2009-10-10

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CONTENTS LIST

1

GENERAL .............................................................................................................7 1.1 1.2 1.3 1.4

2

Introduction................................................................................................................7 Scope ........................................................................................................................8 Reference Standards.................................................................................................9 Symbols ..................................................................................................................10

METHODS OF SEISMIC ANALYSIS ..................................................................13 2.1 2.2

Fundamental requirements and compliance criteria.................................................13 Description of the seismic action .............................................................................14

2.2.1 2.2.2 2.2.3 2.2.4 2.2.5 2.2.6

2.3

Design parameters for the seismic analysis.............................................................22

2.3.1 2.3.2 2.3.3 2.3.4 2.3.5 2.3.6 2.3.7

2.4

Definition of the intensity of the seismic action................................................................ 14 Earthquake design return period and importance factor γI .............................................. 15 Horizontal design spectrum for elastic analysis............................................................... 16 Vertical component of the seismic action ........................................................................ 19 Structural regularity criteria.............................................................................................. 21 Design ground displacement ........................................................................................... 21 Design spectrum modification factor................................................................................ 22 Pallet-beam friction coefficients ....................................................................................... 24 Design seismic pallet weight............................................................................................ 25 Pallet weight modification factor ...................................................................................... 26 Other seismic weights...................................................................................................... 26 Position of the center of gravity of the pallet.................................................................... 27 Accidental eccentricity ..................................................................................................... 28

Methods of analysis.................................................................................................29

2.4.1 Lateral force method of analysis...................................................................................... 30 2.4.1.1 General ........................................................................................................................ 30 2.4.1.2 Base shear force.......................................................................................................... 30 2.4.1.3 Vertical distribution of the horizontal seismic forces.................................................... 30 2.4.2 Modal response spectrum analysis ................................................................................. 31 2.4.2.1 General ........................................................................................................................ 31 2.4.2.2 Number of modes to be considered in the analysis..................................................... 31 2.4.2.3 Combination of modal responses ................................................................................ 32 2.4.3 Large displacements equivalent static analysis............................................................... 32 2.4.4 Combination of the horizontal components of the seismic action ................................... 33 2.4.5 Combination of the vertical component of the seismic action ......................................... 33 2.4.6 Displacements analysis ................................................................................................... 34

3

CRITERIA FOR THE SEISMIC DESIGN OF RACKS .........................................35 3.1

Design concepts......................................................................................................35

3.1.1 General ............................................................................................................................ 35 3.1.2 Materials .......................................................................................................................... 36 3.1.3 Structural types and behaviour factors ............................................................................ 37 3.1.4 Regularity criteria ............................................................................................................. 38 3.1.4.1 Cross aisle direction..................................................................................................... 38 3.1.4.2 Down aisle direction..................................................................................................... 38 3.1.5 Rules for the design of low dissipative structures............................................................ 39 3.1.6 Rules for the design of dissipative structures .................................................................. 40 3.1.7 Anchoring conditions ....................................................................................................... 40

3.2 3.3

Structural systems withstanding the seismic action .................................................41 Structural analysis ...................................................................................................42

3.3.1 3.3.2

Sub-modeling................................................................................................................... 42 Mass dispositions ............................................................................................................ 42


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3.3.3

3.4

3.4.1 3.4.2 3.4.3 3.4.4

4

Specific modeling requirements for the analysis ............................................................. 42

Structural types and maximum associated behavior factors ....................................44 Upright frames ................................................................................................................. 44 Moment resisting frames ................................................................................................. 45 Vertical bracings .............................................................................................................. 45 Horizontal bracings .......................................................................................................... 46

SEISMIC ANALYSIS AND DESIGN ...................................................................47 4.1 4.2

Actions ....................................................................................................................47 Safety Verifications..................................................................................................48

4.2.1 Ultimate limit state ........................................................................................................... 48 4.2.1.1 Combination rules ........................................................................................................ 48 4.2.1.2 Resistance condition.................................................................................................... 48 4.2.1.3 Material’s safety factor γM ............................................................................................ 48 4.2.1.4 Ductility condition ......................................................................................................... 49 4.2.1.5 Equilibrium condition.................................................................................................... 49 4.2.1.6 Resistance of horizontal bracings................................................................................ 49 4.2.1.7 Seismic joint condition ................................................................................................. 49 4.2.2 Serviceability limit state ................................................................................................... 49 4.2.2.1 Damage limitation requirement: assessment of the damage after an earthquake...... 49 4.2.2.2 Pallet sliding................................................................................................................. 49 4.2.3 Pallet falling...................................................................................................................... 50 4.2.3.1 Pallets fixed on the rack............................................................................................... 50 4.2.3.2 Pallet rocking ............................................................................................................... 50 4.2.4 Pallet beams .................................................................................................................... 52

5

DETAILING RULES FOR DISSIPATIVE ELEMENTS OF RACKS ....................53 5.1

Connections ............................................................................................................53

5.1.1 Connections of dissipative members ............................................................................... 53 5.1.1.1 Bolted connections....................................................................................................... 53 5.1.2 Connections participating to the energy dissipation ........................................................ 53

5.2

Detailing rules for concentric bracings .....................................................................54

5.2.1 5.2.2 5.2.3 5.2.4

5.3

Detailing rules for moment resisting frames .............................................................57

5.3.1 5.3.2

5.4 5.5

Design criteria .................................................................................................................. 57 Energy dissipation in beam to column connections......................................................... 57

Requirements for horizontal bracings ......................................................................58 Requirements for base plates and floor anchors......................................................59

5.5.1 5.5.2

1 2 3

Design criteria .................................................................................................................. 54 Analysis............................................................................................................................ 54 Design of diagonal members ........................................................................................... 54 Design of beams, horizontals and columns..................................................................... 56

Design criteria .................................................................................................................. 59 Energy dissipation in floor connections ........................................................................... 59

NUMERICAL TOOL ............................................................................................69 PARAMETER STUDY.........................................................................................70 DESIGN RECOMMENDATIONS ........................................................................74


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Annex 1

Structural types and maximum behavior factors (Extract from Table 6.2 of prEN 1998) (Extract from Chapter Table 6.3.1 of EN 1998-1:2005)

Annex 2

Design data to be provided by the Specifier/End User (Addendum to FEM 10.2.03 “Specifier Code” EN 15629 for racking installations in seismic areas)

Annex 3

Evaluation of the pallet-beam friction coefficient

Annex 4

Pallet rocking assessment criteria (FEMA 460)

Annex 5

Background on sliding problems

Annex 6

Design method to prevent pallet falling


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1 1.1

GENERAL Introduction

Racking systems are not “buildings” but very peculiar steel construction work. They are different from buildings for the use, for the loads to be supported, for the geometrical dimensions and for the steel components, mainly made of thin gauge profiles and continuously perforated uprights, which only can ensure the typical functionality, adaptability and flexibility needed for the huge variability of requirements in storing goods. Only the clad warehouse, where racking systems support goods but also mezzanines, roof and walls, shall be considered as very special “buildings”. For this reason it is necessary to explain how to consider the peculiarities of such kind of construction work when they are to be designed for seismic actions, because these peculiarities influence significantly the response against earthquakes and don’t allow a designer to follow exactly the same approach for “ordinary steel structures”, which is stated in the various National Building Regulations. While the basic technical description of earthquakes is obviously the same as of buildings, for racking systems it is of great importance to define whether or not it is possible to apply the “general design rules” which are enforced for ordinary steel structures, and how to modify correctly general principles and technical requirements, in order to take into consideration those peculiarities and to achieve the requested safety level at the end of the design procedure. In fact, many specific physical phenomena affect very much the structural behavior of a racking system during an earthquake, such as the energy dissipation in the deformation of stored goods, or the sliding effect that can occur between pallets (or other unit-loads) and their directly supporting components, like beams, when seismic forces exceed certain limits, depending on the intensity of the accelerations but also on the actual friction between the contact surfaces. Furthermore, it is to be considered that the variable loads, like pallets or other unit-loads, can result in more than 95% of the total mass, differently from buildings where dead weight and permanent loads sum generally in a significant percentage. Therefore their presence and distribution on racking systems affect very much the response of the structure under seismic actions. As far as the safety level is concerned, it is also of great importance to consider the potential movements of the stored goods, which can fall down accidentally from the supporting beams, regardless of the strength of the racking systems against the earthquake. Therefore, proper designed accessories should be placed on the seismic resistant racks, in order to reduce as much as possible the risk of fall and the consequent inducing risk of impacts, damages or even domino-collapse. Methods of seismic isolation can also be studied, with the aim to cut down the seismic forces and the rack oscillations, in such a way to prevent any accidental movements of the stored goods. Having said that, it is clear that for racking systems the achievable safety level cannot be only the result of a “standard” design procedure, as for common steel structures, but many other information and data are to be properly used. This is just the aim of this Code of Practice: to give to the designer all the well known information and data he may need in this specific field, trying to fill the existing gap between common steel structures and racking systems, considering the state of the art of the knowledge but also the on-going progress of various research projects in Europe, in the USA and in the world. This “Code of Practice”, consequently, is to be considered in a transition period, where it could be used as an experimental industry standard, waiting for a further improvement of specific knowledge. Nevertheless, it represents since now the best technical agreement on “the rules of the game” to be followed in seismic zones, that professional companies could follow with a voluntary approach in order to guarantee for their Clients a well defined safety level.


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This Code of Practice deals with all relevant and specific seismic design issues for racking systems, such as: 1) The seismic response could be significantly different in down-aisle direction and in cross-aisle direction, and could be considerably affected by the size and the distribution of the masses over the height. Reliable statistical evaluations are necessary to find the most probable mass distribution when the earthquake arises, depending on the racking system typology and dimensions. A most likely approach is given in this standard. 2) The natural damping of the “naked structure” is very little. But the real damping, measured in real condition, could be significantly more than that expected, because of the micro-movements in the stored goods and products and/or the sliding effects between pallets (or other unit-loads) and the supporting beams. 3) Cyclic forces due to earthquake can progressively damage connections and/or other components of a racking system. These changes could considerably affect the response of the structure and its way to react against seismic actions. A reliable modeling of the actual strength and stiffness is of fundamental importance in order to predict the structural behavior of the structure. 4) In case of seismic isolation, the effectiveness of the isolation devices must be guaranteed for all the loading conditions and during the whole expected life of the racking system

1.2

Scope

The design procedures given in this Code of Practice apply to all types of static pallet racks fabricated from steel members for the seismic load case, that are supported by floors laying on the ground. They do not apply to mobile storage systems. Indoor static pallet racks must be designed against earthquake in all seismic zones. For clad racks in very low seismic zones refer also to Eurocode 8, Art. 3.2.1, (5)P. The design for other loads shall comply with FEM 10.2.02 EN 15512. The approach to the seismic design is based upon the philosophy of prEN 1998-1 (Eurocode 8), however the peculiar dynamic behavior of racking structures and of the stored unit loads carried by them is included in this document. The reference to the design, tests and quality control of components and materials is based on FEM 10.2.02 EN 15512 to which reference is made. In case of clad racks, where the racking system is supporting roof and walls, this Code gives relevant information in addition to the National Building Regulation, concerning in particular: The interaction between pallets and structure, described by the coefficients ED1 and ED2 The figures for the behavior factors q when pertinent In case mechanical handling equipment is connected to the racking (e.g. crane racking), the supporting forces and/or guide forces under seismic conditions shall be specified by the designer of that equipment, in co-operation with the rack designer, because of the interactivity of dynamic systems. Special analysis is also required for racks supported by other structures, such as platforms, to take into account properly the effects of the amplification of the supporting structures.


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1.3

Reference Standards

• •

FEM 10.2.02 – “The design of static steel pallet racking“ – Ver. 1.02 - April 2001 edition EN 15512:2009 – “Steel storage static systems – Adjustable pallet racking systems – Principles for structural design”

•

EN 1993 - Eurocode 3 – “Design of steel structures” Part 1-1: “General rules and rules for buildings” ENV 1993-1-1:2005 Part 1-3: “Cold formed steel sheeting and members” ENV 1993-1-3:2007

•

prEN 1998-1 - Eurocode 8 - Doc. CEN/TC250/SC8/N269 - “Design of structures for earthquake resistance” – December, 2003 EN 1998-1:2005 - Eurocode 8 - Doc. CEN/TC250/SC8/N269 - “Design of structures for earthquake resistance”

• • • • • •

FEM 10.2.03 – “Guidelines for Specifier’s pf Static Steel Racking and Shelving - Specifier’s Code“ – January 2000 EN 15629:2008 – “Steel storage static systems – Specifications of storage equipment” FEM 10.3.01 – “Adjustable beam pallet racking (APR) - Tolerances, Deformations and Clearances” - 1997 EN 15620:2008 – “Steel storage static systems – Adjustable pallet racking systems – Tolerances, deformations and clearances” EN 15635:2008 – “Steel storage static systems – Application and maintenance of storage systems”


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1.4

Symbols

α β βA θ θp δ γi γµS ; γµH γov γpb γGA γM γM0 γM2 γQA µS λ

λ

ν

ψ2,i Ω

Ratio of the design ground acceleration ag to the acceleration of gravity g lower bound factor for the spectrum Section class coefficient Inter-storey drift sensitivity coefficient Rotation capacity parameter of the plastic hinge region Beam deflection at midspan Importance factor partial safety coefficients for pallet-beam friction coefficient Overstrength factor used in design Post buckling residual resistance coefficient Partial safety factor for permanent actions Material’s safety factor Material’s partial safety coefficient Connection partial safety coefficient Partial safety factor for variable actions Pallet – beam friction coefficient Slenderness ratio Non dimensional slenderness Reduction factor to take into account the lower return period of the seismic event associated with the serviceability limit state. Partial reduction coefficient for variable actions Overstrength coefficient

dg dr ds fu fy fy,max fy,act h g q qd si , sj zi , zj

Design ground acceleration Seismic horizontal acceleration at level i Design ground acceleration (EPA) for the reference return period of 475 years Displacement of a point of the structural system induced by the design seismic action as determined by a linear analysis based on the design response spectrum Design ground displacement Design inter-storey drift Displacement of a point of the structural system induced by the design seismic action Ultimate tensile strength of the material Nominal yield strength specified for the material Actual maximum yield strength of dissipative zones Actual yield strength of dissipative zones Inter-storey height Gravity acceleration behavior factor Displacement behavior factor Displacement of the masses mi , mj in the fundamental modal shape Heights of the masses mi , mj above the level of application of the seismic action

A Anet AE,d E Ed ED1 ED2 EE

Cross section gross area Net area of the member near the connection Design value of the seismic action for the reference return period Young modulus Design value of the action effect due to the design situation Design spectrum modification factor Pallet weight modification factor Seismic action effect

ag ag,i agR de


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EEd,G EEd,E EEi EEdx EEdy EEdz Fb Fi Gk L MEd MEd,G Mpl,Rd Npl,Rd NEd Nu,Rd NEd,G NEd,E Ptot Qk,i QP QP;rated Rd VEd VEd,G VEd,E Vpl,Rd VEd,M Vtot Rfy RF S Se(T) Sd(T) Sve(T) Sde(T) T T1 T B, T C TD Tk Vs,30 WE W E,tot Wi , Wj

Effect of the non-seismic actions included in the combination of actions for the seismic design situation Effect of the design seismic action Value of the seismic action effect due to the vibration mode i Action effects due to the application of the seismic action along the horizontal axis x Action effects due to the application of the seismic action along the horizontal axis y Action effects due to the application of the seismic action along the vertical axis z Seismic base shear force Horizontal force at level i Characteristic value of the permanent action (dead load) Beam’s lenght Design bending moment in seismic condition Design bending moment due to the non-seismic actions included in the combination of actions for the seismic design situation Design bending resistance Axial strength Axial stress under seismic load condition Net section axial strength at connection Axial force due to the non-seismic actions included in the combination of actions for the seismic design situation Axial force due to the design seismic action Total gravity load at and above the storey considered, in the seismic design situation Characteristic value of a typical variable action Design pallet load Rated pallet load Design resistance of the element Design shear in seismic condition Design shear due to the non-seismic actions included in the combination of actions for the seismic design situation Design shear due to the seismic actions Design shear resistance Design value of the shear force due to the application of the bending moments at the end sections of the beam Total seismic storey shear Plastic resistance of the connected dissipative member Rack filling grade reduction factor Soil parameter Ordinate of the elastic spectrum (normalized by g) Ordinate of the design spectrum (normalized by g) Ordinate of the vertical elastic response spectrum (normalized by g) Ordinate of the vertical design response spectrum (normalized by g) Vibration period of a linear single degree of freedom system Fundamental period of vibration Limits of the constant spectral acceleration branch value defining the beginning of the constant displacement range of the spectrum Period of vibration of mode k Average shear wave velocity in the soil Seismic mass of the pallet (unit load) Total seismic mass of the rack Weight of masses mi , mj (seismic weights)


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2

METHODS OF SEISMIC ANALYSIS

The seismic action is evaluated according to the methods of prEN 1998-1 - Eurocode 8, as specified hereafter.

2.1

Fundamental requirements and compliance criteria

(Reference to prEN1998-1, Chapter 2.1) Structures in seismic regions shall be designed and constructed in such a way that the following requirements are met, each with an adequate degree of reliability. 1) No collapse requirement The racking structure shall be designed and constructed to withstand the design seismic action without local or general collapse, thus retaining its structural integrity and a residual load bearing capacity after the seismic event Ultimate limit states are those associated with the collapse or with other forms of structural failure which may endanger the safety of people. The structural system shall be verified as having the specified resistance and ductility. 2) Damage limitation requirement No specific design requirement is prescribed in this Norm. After a seismic event of intensity greater than 0.30 agRS the control of the integrity of 100% of the racking structure and the assessment of the level of damage of the structural elements is mandatory before prosecute with usage. The movement of stored unit loads is not to be considered a damage. 3) Movement of pallets The seismic accelerations can cause the sliding of the pallet on the beams, when the dynamic horizontal force on the pallet exceeds the static friction force between pallet and beam. This effect has been demonstrated by full scale tests to occur also for small values ground accelerations (low intensity earthquake) for ordinary situations (wooden or plastic pallets on painted or zinc coated steel beams), because of the structural amplification of the seismic forces at the highest storage levels. The consequences of these phenomena are: • the reduction of the seismic action on the rack, due to the energy dissipation and the limitation of the horizontal action that can be transferred from the pallet to the rack’s structure • the risk of fall of the pallet, that can produce the local or global collapse of the rack, when the pallet falls inside the rack between the pallet beams, injury to people and damages to the equipment nearby the rack when the pallet falls out of the rack. The modification of the seismic response of the structure is deemed in this Norm by means of two coefficients that conventionally estimates the effects on the structure of phenomena typical of the racking structures, such as energy dissipation due to the pallet-beam friction pallet damping due to the movement of the stored product, pallet flexibility and others: ED1 = design spectrum modification factor ED2 = mass modification factor The ED1 coefficient is introduced in Chapter 2.2.3 and 2.3.1 The ED2 coefficient is introduced in Chapter 2.3.3 and 2.3.4 The designer must carefully assess the risks related to the pallet sliding and falling from the rack. The guidelines for this analysis are introduced in Chapters 4.2.2.4 and 4.2.3


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2.2

Description of the seismic action

The earthquake motion at a given point of the earth surface is described by an “elastic response spectrum” (refer to figure 2). The horizontal seismic action is described by two orthogonal components considered as independent and represented by the same response spectrum, and by a vertical component.

2.2.1

Definition of the intensity of the seismic action

In most of the seismic design Codes the seismic action is conventionally described by means of an elastic response spectrum with 10% probability to be exceeded in 50 years, corresponding to a return period of 475 years. This probability is assumed as reference for buildings. The seismic hazard is described by a single parameter ag that is the Peak Ground Acceleration (PGA). Two elastic spectra are those defined in EN1998-1 to describe the earthquake motion (called Type 1 and Type 2); reference should be made to the National Annexes for the use of the proper design spectrum. Design spectra based on EC8 approach defined in the National regulations may be used as well, according to National Norms in force. Guidance for the choice of the spectrum is also given in prEN 1998-1 Chapter 3.2.2.2 Clause (2)P . Figure 2.1 - Elastic Response Spectrum

EC8 Elastic Response Spectrum

Spectral Acceleration [g]

2,5agSη

2,5agSη[TC/T]

agS

2

2,5agSη[TCTD/T ]

TB

TC

Period T [sec]

TD

η = damping correction factor


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2.2.2

Earthquake design return period and importance factor γI

The return period of the design earthquake is governed by the coefficient γi; to the reference return period defined in the previous chapter the importance factor γi=1.0 is assigned. Unless otherwise specified on documents of contractual relevance, the reference importance factors reported in Table 2.1 should be used. For economical or strategic reasons the end-user may specify a higher importance factor; in any case the importance factor should be equal to the importance factor specified for the part of the building in which the racks are located.

Table 2.1 – Importance factors for racks Importance Class I II III IV

Description Warehouses with fully automated storage operations Low warehouse occupancy (1) Normal warehouse conditions, including picking areas Retail areas with public access Hazardous product storage

Importance factor reduced reference [Note (2)] 0.8

0.67

1.0 1.2 1.4

0.84 n. a. n. a.

(1) Warehouse conditions. In normal warehouse conditions only authorized and trained workers can access the storage area. In low warehouse occupancy no more than 5 authorized and trained workers can operate contemporarily within the storage area. For the purpose of the definition of the importance class the storage area is defined by the area included in the perimeter of the racks plus 2 times the maximum height from the warehouse floor level to the topmost height of the rack or the stored good, whichever is larger. (2) The reduced importance factor can only be used for racking systems not located on storey of a building and/or not used for retail areas or hazardous product storage. The reduced importance factor is based on design life of the rack of 30 years instead of 50.


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2.2.3

Horizontal design spectrum for elastic analysis

The capacity of structural systems to withstand seismic actions in the nonlinear range taking into account the nonlinear behavior of the structure itself and of the interaction with stored goods permits the structural design to be performed for horizontal forces actions smaller than those corresponding to a linear elastic response. The energy dissipation capacity of the structure and the interaction between the pallets and the racking structure is taken into account performing linear dynamic analysis based on a reduced response spectrum, called “design spectrum”, corrected by the modification factor ED1. The “design spectrum” is derived by the elastic spectrum scaled by the behavior factor q, that accounts for the ductility and damping of the racking structure. In case of racks installed on platforms the seismic design of the rack must be performed using the floor response spectrum; the owner of the building must provide such spectrum. For the reference return period, the design spectrum Sd(T) for the horizontal components of the seismic actions, normalized by the acceleration of gravity g, is defined by the following expressions:

0 ≤ T ≤ TB TB < T ≤ TC TC < T ≤ TD

TD < T

 2 T  2.5 2  S d (T ) = α ⋅ S ⋅  +  −   3 TB  q 3  2 .5 S d (T ) = α ⋅ S ⋅ q 2.5  TC  S d (T ) = α ⋅ S ⋅ ≥ β ⋅α q  T  S d (T ) = α ⋅ S ⋅

2.5  TC ⋅ TD  ≥ β ⋅α q  T 2 

where: Sd(T) ag = γi × agR agR γi α = ag/g T S T B, T C TD q β

ordinate of the design spectrum, which is normalized by g design ground acceleration design Peak Ground Acceleration (PGA) for the reference return period of 475 years importance factor ratio of the design ground acceleration ag to the acceleration of gravity g vibration period of a linear single degree of freedom system soil parameter limits of the constant spectral acceleration branch value defining the beginning of the constant displacement range of the spectrum behavior factor lower bound factor for the spectrum; the recommended value for β is β=0.2; the National Annexes to pr-EN 1998-1 may choose for other values of β

The design spectrum modification factor ED1 is defined in chapter 2.3.1


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Table 2.2: Values of the parameters describing the Type 1 elastic response spectrum (ref. Table 3.2 of prEN 1998-1) Ground type A B C D E

S 1.0 1.2 1.15 1.35 1.4

TB [sec] 0.15 0.15 0.20 0.20 0.15

TC [sec] 0.4 0.5 0.6 0.8 0.5

TD [sec] 2.0 2.0 2.0 2.0 2.0

Table 2.3: Values of the parameters describing the Type 2 elastic response spectrum (ref. Table 3.3 of prEN 1998-1) Ground type A B C D E

S 1.0 1.35 1.5 1.8 1.6

TB [sec] 0.05 0.05 0.10 0.10 0.05

TC [sec] 0.25 0.25 0.25 0.30 0.25

TD [sec] 1.2 1.2 1.2 1.2 1.2

The type of spectrum to be used in a country may be found in the National Annexes of prEN 1998-1. For sites with ground conditions matching either one of the two special ground types S1 or S2, special studies for the definition of the seismic action are required; refer to prEN 1998-1 Chapter 3. When soil properties are not known in sufficient detail to determine the site soil conditions, soil class D shall be used unless the building official or geotechnical determines that class E or F is likely to be presented at the site.


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Table 2.4: Classification of subsoil classes Subsoil class

Description of stratigraphic profile Rock or other rock-like geological formation, including at most 5 m of weaker material at the surface Deposits of very dense sand, gravel, or very stiff clay, at least several tens of meters in thickness, characterized by a gradual increase of mechanical properties with depth Deep deposits of dense or medium-dense sand, gravel or stiff clay with thickness from several tens to many hundreds of m Deposits of loose-to-medium cohesionless soil (with or without some soft cohesive layers), or of predominantly soft-to-firm cohesive soil A soil profile consisting of a surface alluvium layer with Vs,30 values of type C or D and thickness varying between about 5 m and 20 m, underlain by stiffer material with Vs,30 > 800 m/s Deposits consisting – or containing a layer at least 10 m thick – of soft clays/silts with high plasticity index (PI > 40) and high water content Deposits of liquefiable soils, of sensitive clays, or any other soil profile not included in classes A –E or S1

A

B

C D

E

S1 S2

Vs,30 (m/s)

Parameters NSPT (blows/30cm)

cu (kPa)

> 800

-

-

360 – 800

> 50

> 250

180 – 360

15 - 50

70 - 250

< 180

< 15

< 70

< 100 (indicative)

-

10 - 20

The average shear wave velocity Vs,30 is computed according to the following expression:

VS ,30 =

30 hj

∑V

j =1, N

j

where hi and Vi denote the thickness and shear-wave velocity (at low strain level) of the i-th formation or layer, in a total of N, existing in the top 30 meters. The site will be classified according to the value of Vs,30 if this is available, otherwise the value of NSPT will be used.


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2.2.4 Vertical component of the seismic action The vertical component of the seismic action is represented by an elastic response spectrum Sve(T) derived using the parameters defined in the previous chapter, in combination with the values of the control parameters presented in Table 2.5. The design spectrum Svd coincides with elastic spectrum Sve(T).

0 ≤ T ≤ TB TB < T ≤ TC

 T  S vd (T ) = α v 1 + 2 ⋅  TB   S d (T ) = α ⋅ 3

TC < T ≤ TD

T  S d (T ) = α ⋅ 3 ⋅  C  T 

TD < T ≤ 4 sec

T ⋅ T  S d (T ) = α ⋅ S ⋅ 3.0 ⋅  C 2 D   T 

where: Svd(T) avg αv T

ordinate of the vertical design spectrum, which is normalized by g design vertical ground acceleration (EPA) for the reference return period ratio of the design ground acceleration avg to the acceleration of gravity g vibration period of a linear single degree of freedom system

Table 2.5: Values of the parameters describing the vertical response spectrum Spectrum

av/ag

Type 1 Type 2

0.90 0.45

TB [sec] 0.05 0.05

TC [sec] 0.15 0.15

TD [sec] 1.0 1.0

The vertical component of the seismic action shall only be taken into account in the following relevant cases: 1) Cantilever components 2) Beams supporting columns (for example in order picking tunnels) The effect of the vertical component need only be considered for the elements under consideration and their directly associated supporting elements or substructures.


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2.2.5

Structural regularity criteria

For the purpose of the seismic design, the structures are distinguished as regular and non-regular. The concept of regularity is applied to both mass and stiffness distribution. This distinction has implications on the following aspects of the seismic design, as described in the following: • the structural model analysis, which can be carried out using either a simplified planar or a spatial one numerical model • the method of analysis, which can be either a simplified response spectrum analysis (lateral force procedure) or modal one • the value of the behavior factor q, which shall be decreased for non regularity in elevation • the regularity regard both the stiffness and the mass distribution, in plan and in elevation; the criteria for pallet racks are reported in chapter 3.1.4. • the decreased values of the behavior factors for pallet racks is set in chapter 3.1.3 Table 2.6: Consequences of structural regularity on seismic design Regularity plan

elevation

model

yes

yes

planar

yes

no

planar

no

yes

spatial

no

no

spatial

Allowed simplification linear elastic analysis method of linear analysis lateral force analysis Modal response spectrum analysis lateral force response spectrum analysis Modal response spectrum analysis

Behavior factor q nominal decreased (*) nominal decreased (*)

(*) see chapter 3.1.3 Note: when response spectrum analysis is performed for non regularity in plant the behavior factor must be decreased? The effects of torsion due to non regularity are considered by the analysis 2.2.6

Design ground displacement

The design ground displacement dg can be estimated by means of the following expression: dg = 0.025⋅ag⋅S⋅TC⋅TD.


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2.3 2.3.1

Design parameters for the seismic analysis Design spectrum modification factor

The design spectrum modification factor ED1 takes into account the effects that affect the design seismic action in terms of modification of the ordinate of the design spectrum and cut-off of the seismic action. ED1 is affected by the following parameters: • intensity of the seismic action, represented in terms of PGA • number of load levels, total mass and flexibility of the racking structure, expressed in terms of period of vibration (dominating period in the considered direction) • maximum horizontal force that can be transmitted by the pallet to the pallet beams, expressed in terms of friction coefficient When pallet are blocked on the pallet beams by means of any special system (for example materials increasing the friction between pallet and beam) ED,1 = 1.0 shall be assumed. If the pallets are likely to slide, a modified design spectrum may be used:

S d ,red (T ) = ED1 S d (T ) where Sd(T) is the reference design spectrum given in 2.2.3 ED1 can be estimated by the formula:

  µ + 0.15  ≤ 1.0 ED1 = max  0.4;0.25 Sd (T )   ED1 = max [ 0.4 ; µ/Sd(T1) +0.2 ] < 1.0 where

µ is the friction coefficient given in 2.3.2 T1 is the fundamental period of vibration of the structure in the considered direction

Background information on the derivation of ED1 are provided in Annex 5. COMMENTS The formula proposed for ED1 is based on a limited number of numerical simulations performed during the project SEISRACKS. These simulations have been made according to the following assumptions: -

Linear behaviour of the structure; Coulomb friction law; Pallets considered as point masses; Only down-aisle behaviour is considered without bracings; Racking structure with 1 to 3 load levels; PGA ranging from 0.05g to 0.15g; Friction coefficient ranging from 0.25 to 1.0.

On these assumptions, 315 simulations have been made. The following figure shows the reduction coefficient obtained from the numerical simulations plotted in function of the ratio µ/Sd(T) for each configuration and compares these results to the proposal for FEM


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and to the current RMI value. In these figure, numerical dots are sorted according to the 3 typical structures considered. 1.20

1.00

0.80

Ed1 0.60 Frame 1 0.40

Frame 2 Frame 3

0.20

Proposal FEM 10-2-08 RMI

0.00 0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

16.00

18.00

20.00

µ / Sd

The horizontal cut-off at a level of 0.4 is proposed because the resulting sliding displacements for lower values are considered as non admissible. It is clear that, due to the number of assumptions made to derive the current proposal, the values of the coefficients in the formula for ED1 should be assessed on additional configurations, in particular as regards cross-aisle behaviour. But on the other hand, it is felt that the simple structure of the formula could reasonably be extended to these other configurations.


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2.3.2

Pallet-beam friction coefficients

The reference pallet-beam friction coefficient to be considered in the analysis to define ED1 are reported in the following table Table 2.7 – Range Of Recommended values for the pallet-beam friction coefficient Materials in contact Steel beams – all finishing Wooden pallet Steel beams – all finishing Plastic and steel pallet Steel beams – all finishing Wooden pallet Steel beams – all finishing Plastic and steel pallet Steel beams – all finishing Wooden pallet

Friction coefficient µS Lower bound Upper bound

Environment Warehouse conditions

0.25

0.5

Warehouse conditions

0.1

0.2

Cold store

0.2

0.4

Cold store

0.05

0.15

Wet cold store Wet pallets

0.05

0.15

Materials in contact Steel beams – all finishing Wooden pallet Steel beams – all finishing Plastic and steel pallet Steel beams – all finishing Wooden pallet Steel beams – all finishing Plastic and steel pallet Steel beams – all finishing Wooden pallet

Environment

Friction coefficient µS


0.37


0.15

Cold store

0.30

Cold store

0.10

Wet cold store Wet pallets

0.10

The friction coefficient is strongly affected by the nature of the materials in contact and the type of coating of the beams, and researches have demonstrated that static and dynamic friction coefficients are very similar. The friction coefficient to be used in the design may be determined by tests, according to Annex 3 ED1 must be evaluated using the upper bound values of the friction coefficient. The friction coefficient is strongly affected by the nature of the materials in contact and the type of coating of the beams. Researches have demonstrated that static and dynamic friction coefficients are very similar. The reference values of the friction coefficients reported in Table 2.7are an approximation of the average values obtained from tests in literature; the values to be used in the design may be determined by tests, according to Annex 3 ED1 must be evaluated using the nominal values of the friction coefficient.


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The assessment of the occurrence of pallet sliding (4.2.2.2) may be performed considering the acceleration at each level, and using the reduced value of friction coefficient γµSµ with γµS = 0.67. The local check for the effects of the seismic actions on pallet beams in the horizontal plane (4.2.4) may be performed considering the horizontal action not greater than γµHµ times the weight of the design pallet weight, with γµH = 1.5. 2.3.3

Design seismic pallet weight

The design pallet weight W E to be considered in the seismic analysis for the evaluation of the horizontal seismic action, is determined by means of the following formula: W E = RF×ED2× QP;rated where: RF = rack filling grade reduction factor ED2 = Pallet weight modification factor (see 2.3.4) QP;rated = rated (specified) pallet load for the compartment, upright frame or global down aisle design (see FEM 10.2.02 EN 15512). ED2 modifies the period and the horizontal action If not otherwise specified by the Specifier/User, through reliable statistical evaluation with contractual relevance, the following values of the coefficients should be considered: RF = 1.0 QP;rated = QP = design pallet load For the analysis in the down aisle direction RF≥0.8 must be used in any case. For the analysis in the cross aisle direction RF=1.0 and QP;rated must be used in any case.


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2.3.4

Pallet weight modification factor

(1) The pallet weight modification factor ED2 represents conventionally the effects related to the interaction between pallet and racking structure that affect the response to earthquake in terms of participating mass and modification of the period of vibration. (2) Unless otherwise specified, the values for ED2 reported in Table 2.8 shall be considered, depending on the nature of the pallet and of the stored goods.

Table 2.8 – Pallet weight modification factors ED2

Stored goods class

1.0

COMPACT CONSTRAINED

0.8

WEAK

0.7 1.0

2.3.5

LOOSE AND UNCONSTRAINED LIQUID

Example Frozen goods (cold storage) Steel sheet package Coils and paper rolls Big number of pieces stored on the pallet whose size is small in comparison to the pallet size, INCLUDING GOODS STABILIZED BY STRETCH WRAPPING

Liquid in partially filled drums

Other seismic weights

All the permanent and live loads other than the pallet weight, must be properly considered in the seismic analysis. Reference to FEM 10.2.02 EN 15512 for the definition of: 1) Dead Loads (chapter 2.4.1): • weights of materials and constructions • weights of fixed service equipment 2) Floor and walkway loads (chapter 2.4.8): 2 • 1.0 kN/m on walkways and access floors not for storage, intended as global load 2 • 3.5 kN/m on floors for storage If not otherwise specified by the Specifier/User the following occupancy factors should be considered for the seismic analysis for the evaluation of the horizontal action: 0.8 floors for storage 0.3 walkways and access floors


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2.3.6

Position of the center of gravity of the pallet

The elevation of the center of gravity of the pallet referred to the support beams (vertical eccentricity) must in general be considered. 1) Cross aisle direction: the masses of the pallets must be placed at the pertinent level over the support beam (center of gravity levels) for the evaluation of the period of vibration and of the seismic action.

2) Down aisle direction: In the down aisle direction the eccentricity of the mass to the load level can in general be neglected for long racks, and it is not significant for the local check of the pallet beams and their connections.


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2.3.7

Accidental eccentricity

In order to cover irregularities in the placement of the pallets in the load cells, the calculated center of mass at each load level i shall be considered as specified. Refer to FEM 10.2.02 – Chapter 2.5.4 The accidental eccentricity due to the placement of the pallets can be neglected for the purpose of the seismic design


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2.4

Methods of analysis

The reference method for determining the seismic effects is the modal response spectrum analysis, using a linear-elastic model of the structure and the design spectrum defined in Chapter 2.2.3 multiplied by the modification factor ED1, and 2.2.4 for the vertical component when applicable. The reference methods above specified can be used if θ = (Ptot Dr) / (Vtot H) ≤ 0.50 θ = (Ptot dr) / (Vtot h) ≤ 0.50 where: θ = inter-storey drift sensitivity coefficient Ptot = total gravity load at and above the considered storey, in the seismic design situation dr = design inter-storey drift, evaluated as the difference of the average lateral displacements at the top and bottom of the storey under consideration and calculated st according to 2.4.5 by means of linear elastic 1 order analysis Vtot = total seismic storey shear h = inter-storey height (a) When θ < 0.1 the second order effects can be neglected in the analysis and in the structural checks (b) When 0.1 ≤ θ ≤ 0.3 a first order structural analysis can be performed and the effects of second order can be considered in the checks increasing the effects of the horizontal seismic action by a factor equal to 1/(1-θ). If multimodal analysis is performed, the stiffness matrix of the model must include the terms that reduce the stiffness of the system due to the vertical loads (geometric matrix). (c) When θ > 0.3 the second order effects must be explicitly considered in the analysis. Pushover analysis according to prEN 1998 Annex B must be performed. when the lateral force method is used. or the large displacement analysis presented in chapter 2.4.3 (large displacements equivalent analysis). If multimodal analysis is performed, the stiffness matrix of the model must include the terms that reduce the stiffness of the system due to the vertical loads (geometric matrix). If θ is greater than 0.5, a time history analysis including large displacements and nonlinear behavior of the materials and connections is required. Other methods of analysis can be used according to prEN 1998-1. In particular the analysis based on ground acceleration time-history representation of the seismic action can be performed, explicitly considering the effects of large displacements, the nonlinear behavior and plasticity of the materials and of the connections, and the other specific phenomena typical of the racking systems, such as the sliding of the pallets on the beams, the damping of the stored product, the flexibility of the load. The modeling assumptions and the parameters related to the dynamic behavior of the pallets and the interaction between pallets and the racking structure shall be properly demonstrated by tests or by rational analysis. The description of the ground motion shall be according to the guidelines of the prEN 1998-1.


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2.4.1

Lateral force method of analysis

2.4.1.1 General This type of analysis can be applied with regular structures that when the structure can be analyzed by two independent planar models in two orthogonal directions and whose response is not significantly affected by contribution of higher modes of vibration. The fundamental period of vibration T1 in the two main directions must be less than the following values: T1 ≤ 4×TC T1 ≤ 2 sec where TC is given in Table 2.2 and 2.3. 2.4.1.2 Base shear force The seismic base shear force Fb for each main direction is determined as follows: Fb = ED1× Sd(T1)×W E,tot where: ED1 spectrum modification factor Sd(T1) ordinate of the elastic design spectrum T1 fundamental period of vibration for translational motion in the considered direction W E,tot total seismic mass The fundamental period of vibration of the rack must be evaluated by means of modal analysis; simplified formulas proposed by various Norms and Standards for the evaluation of T1, which are typical for buildings, are not allowed for racks. If the fundamental period is not evaluated, with a simplified approach the maximum value of the design spectrum shall be assumed. The method for global analysis shall be according to chapter 4 of FEM 10.2.02 EN 15512 when θ ≤ 0.3.

2.4.1.3 Vertical distribution of the horizontal seismic forces The effects of the seismic action shall be determined by applying to each planar model a set of horizontal forces Fi to all the masses at load levels. (a) The forces shall be determined by assuming the entire mass as substitute mass of the fundamental mode of vibration, hence: s i × Wi Fi = Fb ∑ s j × Wj where Fi horizontal force at level i Fb seismic base shear si , sj displacement of the masses mi , mj in the fundamental modal shape Wi , Wj weight of masses mi , mj (seismic weights) (b) With a simplified approach, the fundamental mode shape can be approximated by horizontal displacements increasing linearly along the height; hence the horizontal forces Fi are given by: z i × Wi Fi = Fb ∑ z j × Wj where


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zi , zj

heights of the masses mi , mj above the level of application of the seismic action

The reference level of application of the seismic action should be usually regarded as the floor level

2.4.2

Modal response spectrum analysis

2.4.2.1

General

This method of analysis can be applied in all cases when θ ≤ 0.3. For structures complying with the criteria for regularity in plan the analysis can be performed using two planar models, one for each main direction. Structures not complying with these criteria shall be analyzed by using a spatial model. Whenever a spatial model is used, the design seismic action shall be applied along all the relevant horizontal directions.

2.4.2.2

Number of modes to be considered in the analysis

The response of all modes of vibration contributing significantly to the global response must be considered. At least one torsional mode must be taken into account The number of modes to be considered for the analysis in each direction is such that: 1) the sum of the effective modal masses for the considered modes amounts at least 90% of the total mass of the structure or 2) all modes with effective modal masses greater than 5% of the total mass are considered When using a spatial model the above conditions have to be fulfilled for each relevant direction. If none of the above conditions 1 and 2 can be fulfilled (for example when the global torsional behavior is relevant, such as in case of racks with vertical spine bracings only), the minimum number k of modes to be considered in a spatial analysis should satisfy the following conditions: k ≥ 3×n and Tk ≤ 0.20 s 1/2

where k = number of modes considered n = number of load levels Tk = period of vibration of mode k


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2.4.2.3

Combination of modal responses

(1) The response in two vibration modes i and j (including both translational and torsional modes) may be taken as independent of each other, if their periods Ti and Tj satisfy (with Tj ≤ Ti) the following condition: Tj ≤ 0.9 Ti (2) Whenever all relevant modal responses may be regarded as independent of each other, the maximum value EE of a seismic action effect may be taken as: 2 1/2 EE = [Σ(EEi )] where: EE = seismic action effect under consideration (force, displacement, etc) EEi = value of the seismic action effect due to the vibration mode i (3) If (1) is not satisfied, more accurate procedures for the combination of the modal maxima, such as the "Complete Quadratic Combination" shall be adopted.

2.4.3

Large displacements equivalent static analysis

This method of analysis can be applied in all cases when θ ≤ 0.5. nd

A 2 order large displacements analysis must be performed with a load history defined as follows: a) horizontal actions are determined according to lateral forces method analysis as per chapter 2.4.1.3 (a) with increasing values of the load multiplier varying from 0 to K. K may be assumed equal to q b) constant vertical loads, equal to the design values in the seismic load condition At the end of the analysis: •

the system must be stable

•

the components and the connections must be checked with the actions calculated with K=1.0

The nonlinear behavior of the elements and of the connections may be taken into account. Combinations of the seismic action according to 2.4.3 must be considered in the same analysis when the structure is non regular in plant (i.e. superimposition of the effects not permitted).


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2.4.4

Combination of the horizontal components of the seismic action

In general the components of the seismic action shall be considered as acting simultaneously, and their combination components may be accounted for as follows. Method 1 •

the structural response to each horizontal component shall be evaluated separately

•

the maximum value of the effect of each action on the structure due to the two horizontal components of the seismic action is estimated by the square root of the squared responses to each horizontal component.

Method 2 As an alternative to the above method, the action effect on the structure due to the two horizontal components of the seismic action may be computed using the two following combinations: The action effect on the structure due to the two horizontal components of the seismic action may be computed using the two following combinations: a) EEdx “+” 0.30×EEdy b) 0.30×EEdx “+” EEdy where “+” implies “to be combined with” EEdx = action effects due to the application of the seismic action along the horizontal axis x of the structure EEdy = action effects due to the application of the same seismic action along the orthogonal horizontal axis y of the structure The sign of each component in the above combinations shall be taken as the most unfavorable for the effect under consideration. When the regularity criteria are fulfilled and the lateral resisting systems are separated for the two principal directions, the seismic action may be assumed to act separately along the two main orthogonal horizontal axes of the structure.

2.4.5

Combination of the vertical component of the seismic action

In case the horizontal components of the seismic action are also relevant for those elements that are affected by the vertical seismic action, the following three combinations may be used for the computation of the action effects: a) 0.30×EEdx “+” 0.30×EEdy “+” EEdz b) EEdx “+” 0.30×EEdy “+” 0.30×EEdz


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c) 0.30×EEdx “+” EEdy ”+” 0.30×EEdz where: EEdx and EEdy have been defined previously EEdz = action effects due to the application of the vertical component of the design seismic action 2.4.6 Displacements analysis The displacements induced by the design seismic action shall be calculated on the basis of the elastic deformation of the system obtained by the analysis by means of the following simplified expression: ds = qd de where ds = qd = de =

displacement of a point of the structural system induced by the design seismic action displacement behavior factor, assumed equal to q displacement of the same point of the structural system, as determined by a linear analysis based on the design response spectrum


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3

CRITERIA FOR THE SEISMIC DESIGN OF RACKS

3.1 3.1.1

Design concepts General

Earthquake resistant steel racks shall be designed according to one of the following concepts: a) Low dissipative structural behaviour The effects of the seismic action are calculated on the basis of elastic global analysis without taking into account relevant non-linear material behaviour. b) Dissipative structural behaviour The capability of parts of the structure (dissipative zones) to withstand seismic actions out of their elastic range is taken into account. This capacity is defined by the behaviour factor q. The value of q depends on the structural type and on the member’s cross section classification (refer to EN 1993-1 for member’s cross sections).

Table 3.1.

Design concepts, and upper limit reference values of the behaviour factor

Design Concept

Range of the reference values of the behaviour factor q

Concept a) Low dissipative structure

q≤ 2

Concept b) Dissipative structural behaviour

q>2


according to chapter 3.4

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3.1.2

Materials

1) Structural steel should conform to the requirements of FEM 10.2.02 – section 1.8 EN 15512 chapter 8. 2) In bolted connections of the earthquake resisting structure, high strength bolts in category 8.8 or 10.9 shall be used. 3) When dissipative structural behavior concept is used, the distribution of material properties, such as yield strength and toughness, in the structure shall be such that dissipative zones form where they are intended to in the design; dissipative zones are expected to yield before other zones leave the elastic range during the earthquake. Such requirement may be satisfied if the yield strength of the steel of dissipative zones and the design of the structure conform to the conditions reported in prEN 1998-1 chapter 6.2; in particular for industrial racks conditions a) and c) from prEN1998-1 are recommended as reported in the following. Condition a) the actual maximum yield strength fy,max of the steel of dissipative zones satisfies the following expression: fy,max ≤ 1,1 γov fy where: is the overstrength factor used in design; and γov fy is the nominal yield strength specified for the steel grade. If not otherwise specified γov = 1.25 must be assumed Condition c) The actual yield strength fy,act of the steel of each dissipative zone is determined from measurements and the overstrength factor is computed for each dissipative zone as γov=fy,act/fy fy being the nominal yield strength of the steel of dissipative zones. This condition is applicable when known steels are taken from stock with certified measurements performed before fabrication. In case condition a) is used, the quality control of the materials used for construction of dissipative components must ensure that the maximum yield strength fy,max is not larger than 1.25 times the specified nominal yield strength fy. In case condition c) is used, fy,act is the average value of the yield strength resulting from the certified measurements of the materials used for the dissipative components, weighted on the used quantities of material from each batch or coil. The certified measurements are either: - the ones reported in the specific material’s certificates of the used batch or coil, - the certificates of the internal quality controls performed on the used batch or coil performed according to FEM 10.2.02 EN 15512 4) In the project specification the design shall specify the required fracture toughness of steel and welds and the lowest service temperature adopted in combination with earthquake action. Reference must be made to prEN 1998. 5) The designer must control the strength and ductility of the components where the ductility is expected to be developed. 6) Cold reduced steel and cold formed profiles cannot be used in dissipative zones when design concept b (dissipative structural behaviour) is used


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3.1.3

Structural types and behaviour factors

For the purpose of this Norm, the following structural systems are considered, according to their behaviour under seismic actions. a) Moment resisting frames: the horizontal seismic forces are withstood by members and connections flexural behaviour. In these structures, the dissipative zones are mainly located in plastic hinges near or in the beamcolumn joints, and energy is dissipated by means of cyclic bending. b) Frames with concentric bracings, in which members subject to axial forces withstand the horizontal seismic action. In these structures, the dissipative zones are mainly located in the tensile diagonals. Other mechanisms for energy dissipation may be considered and they are described in the prEN 1998-1. The behaviour factor q accounts for the energy dissipation capacity of the structure. The reference values of q are reported in the following sections, provided that the regularity requirements and the detailing rules are met. For structural non-regular assemblies in elevation the values of q is reduced by 20% (see chapter 3.1.4 for regularity criteria); in all cases in which the reference value of q is greater or equal to 1.5, the reduced value of q need not to be assumed less than 1.5. Seismic resisting structures connected to the rack (such as independent bracings, frames or shear walls) must be designed according to the rules of prEN 1998-1.


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3.1.4 Regularity criteria The regularity criteria for the racks regard both the stiffness and the mass distributions, in plan and in elevation; for a regular configuration all the criteria must be met. The consequences of the regularity of the rack are summarized in Chapter 2.2.5. In the storage racks the seismic weight is quite completely determined by the stored pallets, so in principle it is not possible to control the mass regularity for all the possible pallet configurations. Nevertheless the mass regularity condition in plan and in elevation can be assumed for the conditions which are relevant for the seismic design, when the pallet beams are placed with a regular pattern. 3.1.4.1 Cross aisle direction Regularity in plan • The upright frames not connected to the elements of a non-regular lateral resisting system (horizontal and vertical bracing) are stiffness regular. Regularity in elevation • The upright frame can be regarded as regular if: the diagonal bracings are without interruptions from the floor to the top load level (stiffness regularity) AND the ratio between the maximum and the minimum distance in elevation between the pallet st beams, and between floor and 1 level pallet beam, is less than 2; the first beam level near to the floor with a distance to the floor less than 1000 mm is allowed to be excluded from checking this criteria 3.1.4.2 Down aisle direction Regularity in plant • Racks not braced or symmetrically braced in the down aisle direction in the front and rear planes are stiffness regular in plan • Racks braced on the rear plane only in the down aisle direction are not stiffness regular in plan Regularity in elevation • Position of the pallet beams The rack can be regarded as mass regular if: the pallet beams are on the same level for the entire length of the block AND the ratio between the maximum and the minimum distance in elevation between the pallet st beams, and between floor and 1 level pallet beam, is less than 2; the first beam level near to the floor with a distance to the floor less than 1000 mm is allowed to be excluded from checking this criteria •

Type of vertical bracings Racks with vertical bracing continuous from the floor to the top load level are stiffness regular in elevation. Racks partially braced are not stiffness regular in elevation


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3.1.5

Rules for the design of low dissipative structures

1) For members which are part of the earthquake resisting structure, the rules on materials, given in 3.1.2 (1) and (2), apply. 2) The strength of the members and of the connections shall be evaluated according to the rules for elastic or plastic resistances of EN1993 and FEM 10.2.02 EN 15512. 3) The bolts must be fastened in order to prevent the loosening of the nuts under cycling loads. 4) Behaviour factor q > 1.5 may be assumed when members that contribute to the seismic resistance of the structure by working in compression or bending are of class 1, 2 or 3. 5) If the structure is not regular in plant or elevation q shall be taken equal to maximum 1.50. 6) K, X, D and Z bracings in which the resistance to the horizontal actions is provided by diagonals working in compression, can be used with q=1.5, provided that an overstrength a safety factor of 1.5 is applied to all bracing members and their connections; higher values of q may be used if demonstrated by tests. 7) For bolted shear connections the shear strength of the bolts should be higher than 1.20 times the bearing resistance. This requirement need not to be applied when the bearing strength of the bolted connection is greater than q times the calculated seismic action. 8) The strength of the connections is not required to exceed the design action obtained by multiplying by q the design seismic action.


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3.1.6 Rules for the design of dissipative structures Structures with dissipative zones shall be designed so that these zones develop in those parts of the structure where yielding or local buckling or other phenomena due to hysteretic behaviour do not affect the overall stability of the structure. Structural parts of dissipative zones shall have controlled ductility and strength. The strength shall be verified according to FEM 10.2.02 EN 15512 and EN1993. Non-dissipative parts of dissipative structures and the connections of the dissipative parts to the rest of the structure shall have sufficient overstrength to allow the development of cyclic yielding of the dissipative parts. For general design criteria of dissipative structural elements and connection reference must be made to the relevant parts of prEN1998. Specific rules applicable to racking structures are reported in Chapter 5.

3.1.7

Anchoring conditions

Cracked concrete conditions must be considered in the design when the anchors are installed in cracked concrete or in tension zones of the slab under service loads. The designer of the slab shall specify the cracked or uncracked conditions for the anchors in the concrete. Reference must be made to the following: ETAG No 001 - Edition 1997 “GUIDELINE FOR EUROPEAN TECHNICAL APPROVAL OF METAL ANCHORS FOR USE IN CONCRETE – Annex C: DESIGN METHODS FOR ANCHORAGES” – Chapter 4.1 In any case it is compulsory to consider cracked concrete conditions when: 2.5 α S ≥ 0.33 or when 2.5 α S TC ≥ 0.133.


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3.2

Structural systems withstanding the seismic action

The seismic action can in general be studied separately in the down aisle direction and in the cross aisle direction, and the lateral forces resisting systems can be considered separately. For the purpose of this Norm only self-supporting racks are considered with regular layout in plant. If not otherwise specified, the relevant load condition for the seismic design of the rack is the rack fully loaded, as the horizontal seismic action is maximized. In case of a structural system other than the rack is provided to withstand the seismic action, it should be designed with the criteria of prEN 1998-1. The rack’s structural systems withstanding the seismic actions are: 1) in the cross aisle direction, the upright frames 2) in the down aisle direction, one of the following. a) The unbraced frames The stability is provided by the beam – to – column joints of the rack, and no vertical bracings are provided; horizontal bracings are provided connecting the front and the rear frames. b) The rear bracing. The bracing system, made of the following elements: • a rear bracing placed behind the rear frame, which can be an independent structure connected to the rack, or bracing elements connected to the elements of the rack itself • horizontal bracings connecting the front unbraced frame to the rear braced frame The vertical bracing withstand the horizontal seismic action. The horizontal bracings and the upright frames connected to the horizontal bracings withstand the eccentricity of the seismic action to the vertical bracing, and transmit the action to the vertical bracing and to the connected horizontal bracing. The system must be regarded as non-regular in plant. The vertical bracing should be continuos from the floor to the top load level; in this case the system may be regarded as regular in elevation, otherwise it must be regarded also as non regular in elevation. Vertical bracings distributed among full rack height are STRONGLY RECOMMENDED. Interrupted vertical bracings should be avoided c) Symmetrical vertical bracings (each row of the rack is braced). Vertical bracings withstanding the seismic action are installed in a limited number of bays, in the front and in the rear frames. Horizontal bracings connecting the front and the rear frames are also provided to share the seismic force between the two bracings. The horizontal seismic forces can be equally divided between the front and the rear frames. The rack can be regarded as regular in plant, and also in elevation when the vertical bracing is continuos from the floor to the top level of the rack. Unbraced and symmetrically braced racks in down aisle direction can be assumed as regular in down aisle direction if horizontal bracings are provided in order to ensure the uniform distribution of the seismic actions between the lateral resisting systems on the front and on the back frames. In those cases the horizontal bracings must be conventionally designed to withstand the total seismic action acting on one row of uprights, with no additional requirements. Unbraced and symmetrically braced racks without horizontal bracings shall be regarded as nonregular in plant (see chapter 3.1.4).


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3.3

Structural analysis

3.3.1

Sub-modeling

1) Each lateral resisting system must be analyzed individually, subject to the pertinent seismic action, by means of sub-models (i.e. upright frames, vertical bracings) 2) Each subsystem must be analyzed considering all the elements participating to withstand the seismic action with the proper tributary masses (i.e. rear bracing, horizontal bracing and connected upright frames).

3.3.2

Mass dispositions

The most unfavorable loading configurations must be considered for the seismic analysis. The following could be considered to find the relevant ones: 1) The analysis in the cross aisle direction could be regarded as a local analysis, and the most severe local loading configuration must be found for the elements of the upright frame. Consequently the following loading configurations should be analyzed, in order to maximize the action in the upright, in the diagonals and in the floor anchors: - rack fully loaded - first load level from floor unloaded - first and second load levels from floor unloaded - …. - only top level loaded Almost the configurations fully loaded and the top level loaded conditions must be analyzed. 2) The analysis in the down aisle direction is a global analysis, and the most relevant action is obtained when the rack is completely loaded; nevertheless, the mass distributions that maximize the seismic action on single elements should be properly considered (typically the ones involving the uplift at the upright’s bases in the braced racks). The fully loaded rack configuration must be considered in any case.

3.3.3

Specific modeling requirements for the analysis

1) The modeling and analysis rules must be according to FEM 10.2.02 chapter 4 EN 15512 chapter 10. 2) In down aisle direction for beam-to-column connection and for floor connections (baseplates) the initial stiffness obtained from tests according to FEM 10.2.02 chapter 5 EN 15512 chapter A.2.4 for static load must be used. The single pallet beam must be checked under pallet load with pinned ends and load factor γL = 1.0 (moved to 4.2.4) 3) The shear stiffness of the upright frame must be evaluated according to FEM 10.2.02 chapter 5.9 EN 15512 chapter A.2.8


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4) When tension only diagonals are provided, the bracing’s elements must be modeled in order to take into account the proper stiffness of the bracing considering the effect of the active component only. When bracings with tension only elements are designed, only the active element must be considered in the numerical model. The elements that are put in the numerical model must be coherent with the path of the horizontal forces 5) Bracings a) the vertical bracings must be properly modeled with their eccentricity to the rack’s elements; also the elements connecting the vertical bracings to the rack must be modeled b) the horizontal bracings must be properly modeled when present, with their proper stiffness, using the same criteria described in the previous clause.


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3.4

Structural types and maximum associated behavior factors

3.4.1

Upright frames

(a) tension braced frame

Frame type

(b) battened (vierendeel) frame

(c) partially braced frame

Structural type

(d) Z- form braced frame

(e) D - form braced frame

Detailing rules for dissipative elements

tension diagonal 5.2 a

b c d-e-f d1

diagonal connections 5.1.1

(d1) Z-form dissipative braced frame

MAXIMUM q factor Regular Not regular Rack rack 2 or 4 (Note 1)

diagonal bracing with tension diagonals

diagonal bracing with tension and compression diagonals

(f) K - form braced frame

2.5 (sections of class 1-2)

1.6 or 3.2 (Note 1)

2.0

2.0 (sections of 1.6 class 1-2-3) (Note 2) dissipative battened frame can be used, provided that the requirements of moment resisting frames are met; otherwise q = 1.0 must be assumed 1.0 1.0 1.0 or 1.5 1.0 or 1.5 low dissipative (Note 3) (Note 3) Eccentric braced frame with energy dissipation in the 4 3.2 horizontals - Design according to prEN 1998-1 Chapter 6.8


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Note (1) q=4 can be assumed for X bracings with diagonal elements working only in tension when the ductility requirements of Chapter 5.2 are met. The requirement for dissipative homogeneous behavior described in chapter 5.2.3 for the upright frame is necessary to permit the lattice structure to behave as a bracing. When this requirement is not met, the plasticity is concentrated in a limited part of the frame, generally at the base, and the behavior of the upright frame can be assimilated to an “inverted pendulum” cantilever, and for this scheme q=2 is assumed according to EN1998. Note (2) See Point 4) of 3.1.5 Note (3) See Point 6) of 3.1.5 Note (4) Eccentricities of the connections must be consistent with the rules of FEM 10.2.02 EN 15512

3.4.2 Moment resisting frames In moment resisting frames the dissipative zones are located in the beams or in the beam to column connections, and columns bases. For low dissipative concept q=1.5 may be considered for moment resisting frames. When at least one bolt must be provided to secure the beam end connector to the upright in the beam-upright connections placed on the side of the upright above the beam, behavior factor q=2 may be assumed. Dissipative behavior (q>2) may be assumed when the requirements of chapter 5.3 are fulfilled.

3.4.3 Vertical bracings The type of vertical bracings considered in this Norm is the “concentric diagonal bracing” with energy dissipation in the tension diagonals. Refer to Table 6.2 of prEN 1998-1 reported in Attachment 1. Other types of vertical bracing can be used, and they must be analyzed with the methods of prEN 1998-1. The vertical bracing can be placed in the rear plane of the rack, or symmetrically positioned in the front and in the rear plane to allow structural regularity in plant. In the first case the connection of the rack to the vertical bracing must be properly designed and considered in the structural analysis. In particular the eccentricity of the vertical bracing to the rear uprights, that is necessary to allow the pallets overhang, must be properly modeled in the analysis, and the connection elements considered with their stiffness. The connections to the bracings shall be designed in order to avoid unproper behavior of the rack’s elements; in particular the torsion of the upright must be avoided. The eccentricities of the bracings shall be modeled and properly considered, according to FEM 10.2.02 Chapter 1.13.2 EN 15512 chapter 8.6 The elements connecting the rack to the bracings shall be designed with the overstrength requirements specified for the connections of dissipative members in Chapter 5.1.1.


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Bracings with tension diagonals For this typology the behavior factor q=1.5 is applicable for low dissipative structures; the requirements for the connections are given in Chapter 3.1.5. The behavior factor q=4 is applicable for ductile bracings meeting the requirements of chapter 5.2. Bracings with diagonals working in tension and compression For this typology the applicable behavior factors are: q=2.5 for bracing elements belonging to class 1 and 2 q=2.0 for bracing elements belonging to class 1, 2 and 3. Diagonal bracings made with steel strips are allowed, provided that turnbuckles are used to put them in tension, and their tightness is periodically checked. 3.4.4 Horizontal bracings The horizontal bracings designed to transmit the horizontal actions to the lateral load resisting system in ductile design shall fulfill the requirements of chapter 5.4. No energy dissipation is allowed in the horizontal bracings.


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4 4.1

SEISMIC ANALYSIS AND DESIGN Actions

Actions to be considered acting simultaneously with earthquake The following loads as defined in FEM 10.2.02 EN 15512 must be considered concurrently with the seismic loads: 1) Dead Loads (permanent actions) a) weights of materials and constructions b) weight of fixed equipment 2) Pallet loads (variable actions) 3) Live loads (variable actions) 4) Floor and walkways loads (variable actions) The characteristic vertical static load must be considered; no dynamic increment should be taken into account 5) Global imperfections, when αS > 0.05 Note (only for discussion) with initial imperfection 1/200 = 0.005, the design horizontal action is 1.4*0.005=0.007 if we consider a seismic action 7 times higher, the global shear is 0.05 → we assume that for an earthquake with maximum global shear 7 times larger than equivalent forces system used to describe the global imperfections, the global imperfections need not to be considered Actions not to be considered acting simultaneously with earthquake The following loads as defined in FEM 10.2.02 EN 15512 not be considered concurrently with the seismic loads: 1) 2) 3) 4) 5) 6) 7) 8)

Wind loads Vertical placement loads Horizontal placement loads Horizontal operational loads caused by rack-guided equipment Thrusts on handrails Temperature loads Global imperfections, when αS > 0.05 Impact loads


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4.2

Safety Verifications

4.2.1 Ultimate limit state The safety against collapse (ultimate limit state) under the seismic design situation is considered to be fulfilled if the following are met.

4.2.1.1 Combination rules The design values of actions shall be combined using the following formula: Σ γGA Gk “+” γQAΣ ψ2,i Qk,i “+” γI AE,d where “+” implies “to be combined with” Σ implies “the combined effects of” Gk = characteristic value of the permanent action (dead load) Qk,i = characteristic value of a typical variable action AE,d = design value of the seismic action for the reference return period γGA = partial safety factor for permanent actions = 1.0 γQA = partial safety factor for variable actions = 1.0 ψ2,i = partial reduction coefficient for variable actions: ψ2,1 = 1.0 for the pallet load for floor loads on storage areas ψ2,2 = 1.0 ψ2,3 = 0.5 for passage floor and walkways γI = importance factor 4.2.1.2 Resistance condition The following condition shall be satisfied for all structural elements, including connections: Ed ≤ Rd where Ed = design value of the action effect, due to the design seismic situation, obtained by combining the actions according to Chapter 4.2.1.1 Rd = R{fk/γM} = corresponding design resistance of the element

4.2.1.3

Material’s safety factor γM

If not otherwise specified, the material’s partial safety factors γM shall be according to FEM 10.2.02 Chapter 2.7.4. EN 15512 chapter 7.5


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4.2.1.4 Ductility condition It shall be verified that both the structural elements and the structure as a whole possess adequate ductility taking into account the expected exploitation of ductility, which depends on the selected system and the behavior factor. The behavior factor and the ductility of the structural elements shall be assessed.

4.2.1.5 Equilibrium condition The rack shall be stable under the set of actions given by the combination rules of Chapter 4.2.1.1, including effects such as overturning and sliding. This requirement must be fulfilled by means of an appropriate design of the floor connections.

4.2.1.6 Resistance of horizontal bracings The horizontal bracings shall be able to transmit with sufficient overstrength the effects of the design seismic action to the various lateral load resisting systems to which they are connected. The design concept and overstrength criteria are presented in Chapter 3.4.4 and 5.4 respectively.

4.2.1.7 Seismic joint condition To avoid collisions with adjacent structures induced by earthquake the distance from the boundary line to the potential points of impact is not less than the maximum horizontal displacement calculated according to Chapter 2.4.5. The following situations shall be checked: • the collision between unconnected racks • the collision between racks and adjacent building structures; this must be evaluated taking into account the displacement of the building; the owner of the building must provide the buiding’s displacements of the building for the analysis. 4.2.2

Serviceability limit state

4.2.2.1 Damage limitation requirement: assessment of the damage after an earthquake After a seismic event the damage caused by the earthquake to the structural elements must be assessed before continue the usage of the rack. In case of loss of capacity of the rack immediate action must be taken. The criteria for the evaluation of the damage and the actions to be taken are those prescribed in FEM 10.2.03 “User’s Code” EN 15635 4.2.2.2 Pallet sliding The sliding of the pallet on a rack is not to be considered as a damage. The initiation of relevant sliding occurs when γµSµ/Sd(T1) is lower than 1; in this case pallet falling occurrence must be assessed (4.2.3). When pallets are found after a seismic event in a position on the beams which is outside the range of acceptance according to FEM 10.3.01 “Tolerances, clearances, deformations” EN15620, those pallets must be repositioned.


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4.2.3

Pallet falling

The falling of the pallet inside or outside the rack could cause the local or global collapse of the structure, injury to persons and damage to the stored goods, especially in case of high racks and narrow aisles. It must be prevented by providing special components such as pallet support bars, third beam, nets or others. A design method is to provide a slope between the front and the rear beam at each load level, of at least 1%, in order to direct the movement of the pallets in the backward direction; safety pallet stops must be provided in the rear. A design method to prevent pallet falling outside the rack is presented in Annex 6 A design method is to provide a slope between the front and the rear beam at each load level, of at least 1%, in order to direct the movement of the pallets in the backward direction; safety pallet stops must be provided in the rear. The permitted displacement of the pallet in cross-aisle direction shall not be less than 75 mm from nominal position, but sufficient support of the pallet must be guaranteed on both sides. The single beam must be designed for the maximum weight due to the eccentricity of the pallet with respect to the initial position; the weight to be considered is the rated pallet weight. A “sliding stop” must be installed in order to avoid falling of the pallet from the rack. The “sliding stop” and its connections to the racking structures shall be designed for an horizontal force equal to 10% of the compartment load, acting as a uniform distributed load, at the ULS (the load factor for the design of the component and its connection is 1.0). NOTES: 1) The 1% of the slope must take into account the production and erection tolerances (1% must be the “as built” slope) 2) The real displacement due to sliding is quite unpredictable because of the random nature of the earthquake and also for the number of parameters which can affect the behavior of the pallet (relative friction coefficients, etc.). For this reason in seismic zones is recommended to install additional components in order to support pallets while displacement occurs. 4.2.3.1 Pallets fixed on the rack When the movement of the pallets on the beams is neglected by means of any special system (for example materials increasing the friction between pallet and beam) the spectrum modification coefficient ED,1 defined in 2.3.1 shall be assumed equal to 1.0 4.2.3.2 Pallet rocking The designer shall assess the risk related to the stability of the pallet with load against seismic action. In fact, depending on the ratio between the height and he width of the pallet and on the seismic acceleration at each load level, rocking phenomena con occur and overturning shall be prevented by means of proper choice of geometrical dimensions of the pallet with load. Guidelines are reported in ANNEX 4.


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4.2.4

Pallet beams

Pallet beams must be checked under the actions derived from the analysis. The horizontal seismic action in the cross aisle direction may be assumed to be equally absorbed by the beams of each bay, and limited by the capacity of the pallet-beam friction. In addition the single pallet beam must be checked under the pallet load only with pinned ends and load factor γL = 1.0 Pallet beams working as horizontal element of the vertical bracing should be checked for bending due to pallet weight and compression due to seismic action. The stabilizing effect of friction between the pallets and the pallet beams cannot be accounted for in the checks of the pallet beams working in compression due to the seismic load. For the purpose of the component check of the pallet beam, including the evaluation of the buckling length, the designer should assess the axial strength of the beam considering: •

in the horizontal plane: the presence of horizontal bracings, if any, with beam-ends pinned in the horizontal plane

•

in the vertical plane: a reduced value of the stiffness of the beam-to-upright connection, unless it is demonstrated by tests or by rational analysis that the connections maintain their efficiency under the design earthquake, the value of the beam-to-upright stiffness shall be reduced to 1/3 of the stiffness obtained from static tests performed according to FEM 10.2.02.EN 15512

To assume the beam’s buckling length in both the vertical and horizontal planes equal to the distance between upright’s axes (pinned beam ends) is on the conservative side.


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5

DETAILING RULES FOR DISSIPATIVE ELEMENTS OF RACKS

The design of dissipative components or sub-structures the seismic action using the concept of structural ductility through cyclic plasticity, shall be performed according to the rules of prEN 1998, including all the overstrength requirements and connections detailing. In the following some specific consideration about design of racking components are explained.

5.1

Connections

5.1.1 Connections of dissipative members Connections of dissipative members should have an adequate design and sufficient overstrength to allow for yielding of the connected members. The following overstrength condition should be met for fillet weld and bolted connections: Rd ≥ 1.1 γov Rfy where: Rd Resistance of the connection according to clause 6.6 of ENV 1993-1-1 Rfy plastic resistance of the connected dissipative member γov overstrength factor defined in 3.1.2 5.1.1.1 Bolted connections For bolted connections, Rd is the resistance of the connection according to clause 6.5 ENV 1993-1-1. High strength bolts 8.8 or 10.9 shall be used The bolts should be tightened in order to prevent the loosening of the nuts. For bolted shear connections, the shear resistance of the bolts should be higher than 1.2 times the bearing resistance; the design shall avoid the bending of the bolt.

5.1.2

Connections participating to the energy dissipation

The overstrength condition for connections need not apply if the connections are designed to contribute significantly to the energy dissipation capability inherent to the chosen q-factor and if the effects of such connections on the behavior of the structure are assessed. The strength and ductility of connections under cycling loading should be supported by experimental evidence, in order to comply with specific requirements defined for each structural type and structural ductility classes (see chapter 5.3 for beam-upright connections and 5.5 for baseplates). This applies to all types of connections in dissipative zones.


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5.2

Detailing rules for concentric bracings

5.2.1 Design criteria The following criteria are applicable to the design of: • upright frame bracings with X scheme • vertical bracings Concentric braced frames shall be designed so that yielding of the diagonals in tension will take place before failure of the connections and before yielding or buckling of the beams or columns. The diagonal elements of bracings shall be placed in such a way that the structure exhibits similar load deflection characteristic at each level and in every braced direction under load reversals. 5.2.2

Analysis

The diagonals shall be taken into account as follows in an elastic analysis of the structure for the seismic action: - in frames with X diagonal bracings working in tension, only the tension diagonals shall be taken into account; - in frames with V bracings and X diagonal bracings working in tension and compression, both the tension and compression diagonals shall be taken into account.

5.2.3

Design of diagonal members

Frames with tension diagonals In frames with X diagonal bracings, the non-dimensional slenderness should be limited to: 1,3 ≤

λ

as defined in EN 1993-1-1

λ ≤ 2,0

where:

λ=

β A Af y N cr

=

λ λ1

λ = slenderness

λ1 = π

E fy

E = Young modulus fy = yield strength of the material Ncr = Euler buckling load The upper limit to the non-dimensional slenderness made with pre-loaded elements by turnbuckles.

λ ≤ 2,0 can be not applied to tension diagonals

The effect of unbalanced vertical seismic action applied by the diagonals after buckling of the compression diagonal is calculated using γpb Npl,Rd for the element in compression. The factor γpb is used for the estimation of the post buckling resistance of diagonals in compression; the recommended value is 0.3.


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(1) Frames with diagonals in tension and compression In frames with bracing diagonals in tension and compression, the non-dimensional slenderness

λ should be limited to: λ ≤ 2,0 The compression diagonals should be designed for the compression resistance according to FEM 10.2.02. EN 15512

(2) Resistance of the tension element The yield resistance Npl,Rd of the gross cross-section of the diagonals should be such that: Npl,Rd ≥ NEd where:

N pl , Rd =

Af y

γM0

A = area of the gross section fy = yield strength of the material γM0 = 1.10 (3) Ductility requirement of the element The ultimate strength of the net section of the diagonal shall fulfill the ductility requirement of Clause 5.4.3(4) of prEN 1993-1-1:

N u , Rd ≥ N pl , Rd where: Nu,Rd = 0.9×Anet×fu/γM2 Anet = net area of the member near the connection fu = ultimate tensile strength of the material γM2 = 1.25 (4) Requirement for dissipative homogeneous behavior In order to satisfy a homogeneous dissipative behavior of the diagonals, it should be checked that the maximum overstrength Ωi defined in the following section does not differ from the minimum value Ω by more than 25%: [max(Ωi) - Ω ] / Ω ≤ 0.25 (5) Dissipative connections Dissipative semi-rigid and/or partial strength connections are permitted provided that: a) the connections have an elongation capacity consistent with global deformations and b) the effect of connections deformation on global drift is taken into account using nonlinear static (pushover) global analysis according to Eurocode 8 or non-linear time history analysis.


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5.2.4

Design of beams, horizontals and columns

Beams and columns with axial forces should meet the following minimum resistance requirements: Npl,Rd(MEd) ≥ NEd,G + 1.1×γov×ΩNEd,E where: Npl,Rd(MSd) NEd,G = NEd,E = Ω=

design buckling resistance of the beam or the column according to FEM 10.2.02 EN 15512, taking into account the interaction of the buckling resistance with the bending moment MEd defined as its design value in the seismic design situation. axial force in the beam or in the column due to the non-seismic actions included in the combination of actions for the seismic design situation axial force in the beam or in the column due to the design seismic action minimum value of Ωi = Npl,Rd,i/ NEd,i over all the diagonals of the braced frame system, where Npl,Rd,i design resistance of diagonal i NEd,i design value of the axial force in the same diagonal i in the seismic design situation

In frames with V bracings, the beams should be designed to resist: •

all non-seismic actions without considering the intermediate support given by the diagonals;

•

the effect of the unbalanced vertical seismic action applied to the beams and its connections by the diagonals after buckling of the compression diagonal. This action effect is calculated using Npl,Rd for the diagonal in tension and γpb Npl,Rd for the element in compression; the factor γpb is used for the estimation of the post buckling resistance of diagonals in compression; the recommended value is 0,3.


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5.3

Detailing rules for moment resisting frames

5.3.1 Design criteria Moment resisting frames shall be designed so that plastic hinges form in the beams or in the connections of the beams to the columns, but not in the columns, except at the base and at the top level. When dissipative zones are located in the members, the non-dissipative parts and the connections of the dissipative parts to the rest of the structure shall have sufficient overstrength to allow the development of cyclic yielding in the dissipative parts. When dissipative zones are located in the connections, the members shall have sufficient overstrength to allow the development of cyclic yielding in the connections, according to 5.3.2.

5.3.2 Energy dissipation in beam to column connections Dissipative semi-rigid and/or partial strength connections are permitted provided the all of the following conditions are satisfied: a) the connections have a rotation capacity consistent with global deformations and requested behavior factor q; b) members framing into the connections are demonstrated to be stable at ultimate limit state; c) the effect of connections deformation on global drift is taken into account using nonlinear static (pushover) global analysis according to Eurocode 8 or nonlinear time history analysis


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5.4

Requirements for horizontal bracings

The following requirements apply to the horizontal bracings that are designed as part of the earthquake resisting system, in particular to the horizontal bracings of the racks braced in the rear plane, including their links and connections to the vertical bracing, in addition to the criteria reported in chapter 3.4.4. The elements and the connections of the horizontal bracings should be verified considering the horizontal action transmitted to the rear plane VEd computed as: VEd = VEd,G + 1.1×γov×Ω×VEd,E where VEd,G

shear due to the non-seismic actions included in the combination of actions for the seismic design situation (usually null)

VEd,E

shear due to the design seismic action,

γov

overstrength factor defined in 3.1.2

Ω

minimum value of Ωi = Npl,Rdi/ NSdi over all the diagonals of the vertical bracing, where Npl,Rdi design resistance of diagonal i NSdi design value of the axial force in the same diagonal i in the seismic design situation


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5.5

Requirements for base plates and floor anchors

5.5.1 Design criteria The anchor bolts and base plates shall be designed considering the action calculated with the following overstrength criteria. The tension in the anchor bolts, the bending in the base plate and the connection to the upright’s base should be checked for the following action: EEd = EEd,G+1.1×γov×Ω×EEd,E where γov

overstrength factor defined in 3.1.2

EEd,G

effect of the non-seismic actions included in the combination of actions for the seismic design situation

EEd,E

effect of the design seismic action

Ω

value of (Rdi/Sdi) ≤ q of the dissipative zone or element i of the structure which has the highest influence on the effect EF under consideration, where

Rdi

design resistance of the zone or element i,

Sdi

design value of the effect on the zone or element i for the design seismic action.

For floor connections of uprights of moment-resisting frames, where the dissipative zones are located in the beam-upright connections, Ω is the minimum value of the ratio MRd/MEd at the beam to upright connection of the upright under consideration For floor connections of uprights of concentrically braced frames, Ω is the minimum value of the ratio Npl,Rd/NEd over all tensile diagonals of the braced frame. Anchor bolts specifically designed and certified for seismic load application should be selected. The cracked/uncracked conditions of the concrete must be assessed according to chapter 3.1.7.

5.5.2 Energy dissipation in floor connections Dissipative semi-rigid and/or partial strength connections floor connections are permitted in down aisle direction moment resisting frames, provided the all of the following conditions are satisfied: a) the connections have a rotation capacity consistent with global deformations and requested behavior factor q; b) members framing into the connections are demonstrated to be stable at ultimate limit state; c) the effect of connections deformation on global drift is taken into account using nonlinear static (pushover) global analysis or nonlinear time history analysis


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Annex 1 – Informative

Structural types and maximum behavior factors (Extract from Table 6.2 of prEN 1998) (Extract from Chapter Table 6.3.1 of EN 1998-1:2005)


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Refer to Chapter 6 of prEN 1998


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Annex 2 - Informative

Design data to be provided by the Specifier/End User (Addendum to FEM 10.2.03 “Specifier Code” EN 15629 for racking installations in seismic areas) The Specifier/End User should provide the following information. 1) Basic conditions a) Design standard or code to comply with, if no national standard exists b) Exact location of the site of the installation (preferably postal code or geographic coordinates) c) Seismic Zone or mapped spectral response accelerations d) Sub soil characteristics – Ground type (Chapter 2.2.3 Table 2.4) e) Importance class of the installation – Importance factor γi (Chapter 2.2.2) f) In case of racks installed on platforms the seismic design of the rack must be performed using the floor response spectrum; the Specifier/End User must provide such spectrum. 2) Interaction with the building floor The compression and/or uplift action at the location of uprights and anchorages shall be determined by the Supplier of the storage equipment. The final design of the foundation of the storage equipment (in general the building floor) shall be executed after Supplier specification of the actions at upright’s bases concerned. 3) Pallets and product specifications a) Maximum pallet load b) Rated pallet load (Chapter 2.3.3) For single-product storage rack the average pallet load is equal to the maximum (design) pallet load c) Rack filling grade reduction factor RF (Chapter 2.3.3) d) Stored good class and pallet weight modification factor ED2 (Chapter 2.3.4 Table 2.8) e) Pallet type or, alternatively, pallet-beam friction coefficient µS (Chapter 2.3.2 Table 2.7) 4) Building clearances Storage equipment installations shall accommodate the seismic displacement of storage racks and their contents relative to adjacent or attached components and elements. The assumed total relative rack interface with the building shall not be less than 5% of the height above the base, unless a shorter value is justified by test data or analysis. The Specifier/End User shall provide the displacements of the building for the displacement analysis (horizontal displacements at the height of the top of the uprights)


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Annex 3 - Normative

Guideline for the evaluation of the pallet-beam friction coefficient The preparation of the test procedure is in progress.


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Pallet rocking assessment criteria (FEMA 460 – Chapter 8) 8.3.5 End bay Uprights. It is recommended that the ends of a longitudinal row of racks have upright frames or frame extenders that extend high enough above the topmost shelf to provide sliding and overturning restraint for palletized or individually stored merchandise on the upper-most level. This is to prevent the merchandise from toppling into the main aisle-ways generally located at the end of a row of storage racks. If one end of the row abuts a wall, this frame need not have the frame extension.

8.3.6 Maximum height to Width Ratios for Uniformly Loaded pallets. To reduce the possibility of loaded pallets overturning, it is suggested that the height to least width ratio generally be limited to 2.0 or less for pallets placed higher than 8 feet (2.44 m) above the floor when SDS ≥ 1.1g (2.5⋅α⋅S ≥ 1.1) and generally be limited to 2.5 or less when SDS ≥ 0.75g (2.5⋅α⋅S ≥ 0.75) but less than 1.1 g (the pallet load is assumed to have a uniform weight distribution). These aspect ratio recommendations are derived from some recent theoretical studies by Saho and Tung (1999), who studied overturning and sliding of rigid bodies subjected to 75 real earthquake timehistory records. Using the data summarized in Table 1 of their work, it can be shown that rigid bodies, restrained against sliding and with a height-to-width ratio (H/D) of 2 to 1, have a 16 percent chance of overturning when subject to motions with peak shelf accelerations around 0.70g. If one assumes the amplification of motion from the floor to top shelf in the cross aisle direction is on the order of 1.5 tp 2.0, then earthquake motions with a peak ground acceleration (PGA) in the range of 0.35g to 0.50g may result in 16 percent chance of overturning. These PGA values correspond to and SDS of approximately 1.1g. Similarly, when H/D is 2.5 or greater, motions with PGA in the 0.3g to 0.4g range may create a 16 percent overturning hazard. Motions in this range, using the amplifications assumed above, correspond to an SDS of approximately 0.75g. It should be noted that when a pallet slides, its tendency to overturn may be reduced, provided that it does not slide sufficiently to topple off the shelf.

8.6.1 Pallet Tilt Test. The pallet tilt test involved “proof” testing the bidding (i.e., blocking) methods used to secure the merchandise to the pallet. The purpose of the test is to ensure that the means used to secure the merchandise to the pallet are sufficiently strong to keep the merchandise from sliding during earthquake shaking. The test is intended to establish the general adequacy of a particular binding method using a representative sample pallet load. …. Care must be taken in doing the tests so as to not cause the loaded pallet to overturn and damage the merchandise or injure the personnel. The basic test procedure is as follows: Step 1 – The merchandise is bound to the pallet with an approved securing method


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Step 2 – The pallet is lofted on one side to a height that produces an angle of 20 degrees between the ground and the bottom surface of the pallet Step 3 – If the merchandise remains restrained in place for at least 5 minutes without appreciable movement, the load secured to the pallet is considered to have adequate confinement and passes tilt test. Step 4 – If the merchandise shifts appreciably or the securing material breaks, the merchandise must be resecured using an industry- approved method and retested.


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Backgrounds on sliding problems in prFEM 10.2.08 FEM 10.2.08 H. Degée – 5 June 2009 The present note summarizes investigations carried out on the sliding behavior in the perspective of deriving design recommendations.

1

NUMERICAL TOOL

The investigations presented here are based on the use of a specifically developed numerical tool. The main features and assumptions of the model can be summarized as follows: • The sliding pallet model has been developed in the numerical tool FinelG (See Ref. [3]) and can be used in combination with any kind of non linear structure (geometrically as well as materially non linear). • The model is based on the concept of "mathematical deck". Pallet and structure are considered as two separate systems and an interface element (i.e. the so-called "mathematical deck") is used to restore equilibrium of forces and compatibility of displacements between pallet and supporting beams (See fig. 1 and Ref. [4], [5], [8]). • The pallet behavior with respect to the supporting beams is assumed to exhibit a stickslip motion with a Coulomb friction law (See Ref. [1], [6], [8]). • The model has been validated on simple semi-analytical examples and has showed its accuracy and efficiency (See Ref. [6], [8]). • The pallet is considered as a point mass located at the gravity centre of the pallet. This assumption has been compared with experimental data and is showed accurate enough for assessing the longitudinal down-aisle behavior of the rack, even if less accurate for the transverse cross-aisle behavior because of neglecting the rotational inertia of the pallets (see Ref. [1]). More precisely, the model is able to capture correctly the experimental sliding phases and to estimate in a proper way their impact on the structural behavior, while it tends to overestimate the local displacement of the pallet with respect to its support. The model is currently being extended to include the rotational inertia and to improve the accuracy of the local displacement prediction.


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Fh

-Fh Ustr = Upallet

Rh,dyn - Rh,dyn

Ustr ≠ Upallet

Figure 1: Principles of the stick-slip model - (a) "stick" phase - (b) "slip" phase

2

PARAMETER STUDY

As a consequence of the coupled pallet-structure dynamic behavior, it can easily be stressed that if the amplitude of the relative displacement is not too important, in such a way that pallets remain on the supporting beams, or if a third beam is used to prevent falling, the sliding effect can benefit to the structure since it is limiting the horizontal seismic forces transferred to the rack to a maximal value equal to the friction force at the interface between pallet and beam. Following this reasoning, recommendations of RMI (See Ref. [9]) propose to apply a reduction factor on the seismic forces calculated under the assumption of fixed pallets. This reduction factor is proposed equal to 0.67 whatever the friction conditions and the level of seismic action, which can be considered as a rough and questionable approach. Following a similar approach, a reduction coefficient ED1 has also been introduced in the European pre-standard for storage racks in seismic areas (See Ref. [2]). In order to propose values of this coefficient based on a rational background, a parameter study has been performed with the above-described numerical tool and is presented hereby. The parameter study is based on numerical simulations of the longitudinal behavior of a typical rack structure, corresponding to the specimen tested on shaking table during the Seisracks research (See Ref. [1] and Fig. 2). Three loading situations are considered: (i) 4 pallets of 750 kg on the lowest level only, (ii) 4 pallets on the lowest level + 4 pallets on the intermediate level, (iii) 4 pallets on each of the three levels. This leads to the 3 following values of the fundamental vibration period of the structure: Ti = 0,55s, Tii = 1,13s and Tiii = 1,64s. In this study, only the longitudinal behavior has been considered since the sliding model is essentially validated in this direction. Complementary studies in the transverse direction should be performed after improvement of the model performances.


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Figure 2: test specimen and corresponding numerical model

A set of linear time-history analyses are then performed. Each of the three structures are subjected to 7 artificial accelerograms generated with the software GOSCA (see Ref. [7]) in order to fit with an EC8 type 1 reference spectrum (soil C) with a value of agS equal to 0,15g, 0,30g and 0,45g. For each structure and each level of acceleration, the friction coefficient of the pallets is varied from 2, which is not physically possible but corresponds to the situation of pallets fixed on the structure, to 0,25, which corresponds to a lower bound obtained from experiments (see Ref. [1]) for plastic pallets put on beams with a very good coating quality. For each set of 7 accelerograms, mean values of the maximum structural displacement are recorded, according to the procedure suggested by Eurocode 8. Maximum relative displacements of the pallets with respect to the beams are also recorded, even if these values must be considered as overestimated as already mentioned previously. These results are plotted in figures 3 and 4. It can be seen that the reduction coefficient that can be applied with respect to a fully fixed situation is highly varying in the different situations. It ranges from no reduction even for very low friction coefficient (e.g. agS = 0,15g for a structure loaded on all three levels) to less than 0,2 (agS = 0,45g, structure loaded only on the lowest storey and friction coefficient equal to 0,25). This shows that the value of 0,67 proposed by RMI seems to be a good average value, but that it could be really unsafe in particular for moderate seismicity level. Moreover, the relative displacement of the pallets can be rather high (up to 30 cm), leading to the necessity of designing a system likely to avoid the fall of the pallet. However the amplitude of the sliding displacement of pallets is poorly reliable due to the non validated numerical model behaviour.


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0.16 PGA = 0.15g 0.14

PGA = 0.30g PGA = 0.45g Maximum displacement [m]

0.12 0.10 0.08 0.06 0.04 0.02 0.00 2.5

2

1.5

1

0.5

0

Friction coefficient (one loaded level) 0.35

Maximum displacement [m]

0.30 PGA = 0.15g (L1)

PGA = 0.30g (L1)

PGA = 0.45g (L1)

PGA = 0.15g (L2)

PGA = 0.30g (L2)

PGA = 0.45g (L2)

0.25

0.20

0.15

0.10

0.05

0.00 2.5

2

1.5

1

0.5

0

Friction coefficient (two loaded levels)

0.50


0.45 PGA = 0.15g (L1)

PGA = 0.30g (L1)

PGA = 0.45g (L1)

PGA = 0.15g (L2)

PGA = 0.30g (L2)

PGA = 0.45g (L2)

PGA = 0.15g (L3)

PGA = 0.30g (L3)

PGA = 0.45g (L3)

0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00

2.5

2

1.5

1

0.5

0

Friction coefficient (3 loaded levels)

Figure 3: Maximum structural displacement - (a) one loaded level - (b) two loaded levels - (c) three loaded levels


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0.16 PGA = 0.15g 0.14

PGA = 0.30g PGA = 0.45g Maximum displacement [m]

0.12 0.10 0.08 0.06 0.04 0.02 0.00

2.5

2

1.5

1

0.5

0

Friction coefficient 0.25 PGA = 0.30g (L1)

PGA = 045g (L1)

PGA = 0.15g (L2)

PGA = 0.30g (L2)

PGA = 0.45g (L2)

0.20


PGA = 0.15g (L1)

0.15

0.10

0.05

0.00 2.5

2

1.5

1

0.5

0

Friction coefficient

PGA = 0.30g (L1)

PGA = 0.45g (L1)

PGA = 0.15g (L2)

PGA = 0.30g (L2)

PGA = 0.45g (L2)

PGA = 0.15g (L3)

PGA = 0.30g (L3)

PGA = 0.45g (L3)

0.35

0.30


PGA = 0.15g (L1)

0.25

0.20

0.15

0.10

0.05

0.00 2.5

2

1.5

1

0.5

0

Friction coefficient

Figure 4: Maximum relative displacement of the pallets


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3

DESIGN RECOMMENDATIONS

In the simple case of a single pallet having a mass M moving on a structure that can be considered as a SDOF structure without mass, the derivation of the reduction coefficient is straightforward. The inertial force in case of a fully fixed pallet is given by: Finertia = M Sd (T )

(1)

where Sd(T) is the spectral acceleration corresponding to the period of the structure, while the maximum force that can be transferred to the structure in case of sliding is given by: Fmax = g M µ

(2)

where g is the acceleration of gravity and µ is the friction coefficient. The reduction factor is thus given by: E D1 =

Fmax µ = Finertia α

(3)

where α is the spectral acceleration of the structure expressed in terms of a fraction of acceleration of gravity for the structure considered as fully loaded. In the case of a real structure loaded with many masses at different levels, Equation (3) is for sure too simple, since the masses are not sliding altogether and since the inertial forces are different according to the considered structural level. However, Eq. (3) is felt as a good indicator of the actual reduction factor. Figure 5 is thus plotting the reduction factor obtained from the full set of numerical results as a function of the corresponding ratio µ/α, together with the theoretical formula given by Eq. (3) [blue curve]. It can be seen that the theoretical approach provides a lower bound of the actual situation. However, since the main goal of this contribution is to provide a conservative expression of ED1, and thus an upper bound of the cloud of numerical results, the following expression is finally proposed and also plotted on Figure 5 [red curve]: µ  ED1 = max  + 0, 2;0, 4  , not greater than 1.0 α 


(4)

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1.200

Reduction Factor Ed1

1.000

0.800

0.600

0.400

0.200

0.000 0.000

0.200

0.400

0.600

0.800

1L - 0.15g

1L - 0.30g

1L - 0.45g

2L - 0.15g

2L - 0.30g

2L - 0.45g

3L - 0.15g

3L - 0.30g

3L - 0.45g

Eq. (3)

Eq. (4)

RMI

1.000

1.200

1.400

1.600

1.800

2.000

mu / Sd

Figure 5: Reduction factor ED1 0.350

Sliding displacement

0.300

S1-a1

S1-a2

S1-a3

S2-a1

S2-a2

S2-a3

S3-a1

S3-a2

S3-a3

0.250

0.200

0.150

0.100

0.050

0.000 0.000

0.200

0.400

0.600

0.800

1.000

1.200

1.400

1.600

1.800

2.000

mu / Sd

Figure 6: Sliding displacement

As complementary information, Figure 6 shows the maximum displacement of the pallet with respect to the supporting beams for the different cases considered in the study. The local displacement is plotted as a function of the ratio µ /α. Even if has been stated previously that the numerical model tends to overestimate the sliding displacement in comparison with experimental values, some conclusions can nevertheless be drawn: • For a given value of the ratio µ /α, the local sliding displacement can vary significantly according to the number of storeys; • Small local displacements are identified even for values of the ratio µ /α higher than 1.0. However the amplitude of motion remains rather limited (up to 2 mm).


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•

According to the conservative character of the model, these could be reasonably neglected; For values of the ratio µ /α smaller than 1.0, sliding should always be considered and technological measures preventing the fall of pallets should be used.

REFERENCES [1] I. Rosin and al., Storage racks in seismic areas (Seisracks), Research program of the European Commission RFS-CR-04045, Final Report (2007). [2] Pr FEM 10.2.08 – Recommendations for the design of static steel pallet racks under seismic conditions – Fédération Européenne de la Manutention (2005). [3] FineLg User’s Manual, V9.2. Greisch Info – Department ArGEnCo – ULg (2003). [4] YANG Fuheng, Vibrations of cable-stayed bridges under moving vehicles, Ph. D. Thesis, ULg (1996). [5] A. Jennings, Matrix computation for engineers and scientists, Wiley and sons (1977). [6] V. Denoël, H. Degée, Cas particulier d’étude analytique de l’élément à frottement, Internal report 2005-1, Department M&S (2005). [7] V. Denoël, Calcul sismique des ouvrages d’art, Master Thesis, ULg (2001). [8] H. Degée, V. Denoël, C. Castiglioni, Seismic behaviour of storage racks made of thinwalled steel members, Proc. of the 7th European Conference on Structural Dynamics Eurodyn 2008, Southampton (2008) [9] RMI, Specification for the Design, Testing and Utilization of Industrial Steel Storage Racks, Rack Manufacturers Institute, Charlotte (2002)


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Design method to prevent pallet falling A design method is to provide a slope between the front and the rear beam at each load level, of at least 1%, in order to direct the movement of the pallets in the backward direction; safety pallet stops must be provided in the rear. The permitted displacement of the pallet in cross-aisle direction shall not be less than 75 mm from nominal position, but sufficient support of the pallet must be guaranteed on both sides. The single beam must be designed for the maximum weight due to the eccentricity of the pallet with respect to the initial position; the weight to be considered is the rated pallet weight. A “sliding stop” must be installed in order to avoid falling of the pallet from the rack. The “sliding stop” and its connections to the racking structures shall be designed for an horizontal force equal to 10% of the compartment load, acting as a uniform distributed load, at the ULS (the load factor for the design of the component and its connection is 1.0). NOTES: 1) The 1% of the slope must take into account the production and erection tolerances (1% must be the “as built” slope) 2) The real displacement due to sliding is quite unpredictable because of the random nature of the earthquake and also for the number of parameters which can affect the behavior of the pallet (relative friction coefficients, etc.). For this reason in seismic zones is recommended to install additional components in order to support pallets while displacement occurs.


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Commentary to the provisions of FEM 10.2.08 (3.2) Structural systems withstanding the seismic action Representation of the unbraced frame


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Representation of the rear bracing and the bracing system

The eccentricity of the rear bracing causes a global torsional behavior that affects the upright frames. In this case the rack must be considered not stiffness-regular in plant.

GLOBAL TORSIONAL EFFECTS !!


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In case of double entry rack the unsymmetry in plant is caused by the mass disposition as both the entries are in general not equally loaded. NO GLOBAL TORSIONAL EFFECTS !!

GLOBAL TORSIONAL EFFECTS !!


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Representation of the frame symmetrically braced in the down aisle direction


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(3.3.1) Sub-modelling Example of representation of sub-models for the analysis of a spine-braced rack.


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(3.3.2) Regularity criteria - (3.3.2.1) Down aisle direction Representation of the regularity criteria in the down aisle direction

hi/hj ≤ 2 ; with hi and hj heights between load levels 

Regular

hi/hj ≥ 2 ; with hi and hj height between load levels 

Not regular




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Typical occurrences in the seismic analysis of racks (informative) Sub-structure analysis

Occurrence a) b)

Upright frame 1

c) cross aisle direction

d)

single entry rack double entry rack – the connection between the upright frames is strong and allows the global cantilever scheme for both the upright frames double entry rack – the connection between the upright frames is weak and does not allows the global cantilever scheme for both the upright frames racks connected at top by crane racking top ties

Model

Method of analysis

Minimum loads configurations for seismic analysis Notes

planar

no modal simplified multimodal

All loading configurations, starting from fully loaded, unloading from bottom to top (1) a)

planar

multimodal b) a)

Frame 2

3

down aisle direction

Vertical bracing of single entry rack symmetrically braced

rack unbraced in the down aisle direction

rack symmetrically braced on front and rear planes

b)

All upright frames equally loaded All loading configurations, starting from fully loaded, unloading from bottom to top (1) One upright frame fully loaded, the others unloaded Fully loaded rack must be considered Other load configurations defined for the analysis under gravity loads on FEM 10.2.02 EN 15512 can be considered (2)

planar


planar


Rack fully loaded

spatial

no modal multimodal

Rack fully loaded for the analysis in the down aisle direction Same loading criteria for cases 1a) and 1b) for the analysis in the cross aisle direction

planar (3)



the horizontal bracings are placed in the bays where the vertical bracing is present, or in the adjacent ones

4

Vertical bracing of single entry rack braced on the back frame only down aisle and cross aisle directions

Note: analysis of the vertical bracing only

Rack fully loaded for the analysis in the down aisle direction Same loading criteria for cases 1a) and 1b) for the analysis in the cross aisle direction

the horizontal bracings are not placed in the bays where the vertical bracing is present, or in the adjacent ones spatial


Rack fully loaded

simplified multimodal

Note: the spatial model is necessary to consider the effect of the “twisting moment” and must include the upright frames connected by the horizontal bracings

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Sub-structure analysis

5

Vertical bracing of double entry rack symmetrically braced

Occurrence

6

Vertical bracing of double entry rack braced on the back frame only down aisle and cross aisle directions

…

……………….

Method of analysis

planar spatial


Both racks fully loaded

spatial

no modal multimodal

One rack only fully loaded

planar spatial


rack symmetrically braced on front and back frames


the horizontal bracings are placed in the bays where the vertical bracing is present, or in the adjacent ones the horizontal bracings are not placed in the bays where the vertical bracing is present, or in the adjacent ones

Minimum loads configurations for seismic analysis Notes

Model

Both racks fully loaded Note: analysis of the vertical bracing

Rack fully loaded for the analysis in the down aisle direction Same loading criteria for cases 1a) and 1b) for the analysis in the cross aisle direction spatial

simplified multimodal

Note: the spatial model is necessary to consider the effect of the “twisting moment” and must include the upright frames connected by the horizontal bracings

…………..

Notes (1)

(2)

(3)

Generally the rack fully loaded is relevant for the upright’s compression. The uplift force must be checked considering the topmost level loaded, and, successively, the n upper levels loaded, with n=2, 3, …, until the maximum uplift force is found. With a conservative approach, the horizontal seismic action calculated for rack fully loaded can be considered, with the different load configurations defined for the check under gravity loads by FEM 10.2.02 EN 15512 that must be checked in any case also under the seismic action. the matter should be analyzed with attention to consider the eccentricity of the bracing against the back frame, which affects the connected upright frames.


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FEM-10-2-08 2009-10-10 Static steel pallet racks under seismic conditions.pdf

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