Numerical simulation of the seismic behavior of steel storage pallet racking systems

Transcription

1 1 Numerical imulation of the eimic behavior of teel torage pallet racking ytem Gonçalo E. Novai Ribeiro Coutinho a a Intituto Superior Técnico, Liboa, Portugal 1. Introduction 1.1. Overview Depite their lightne, racking carry very high live load (many time larger than the dead load, oppoite of what happen for uual civil engineering tructure) and can raie a coniderable height. For thee reaon they have to be properly deigned. Many difficultie arie in the prediction of the tructural behaviour of pallet rack, like intability (global, local and ditortional) or modelling problem (beam-upright connection tiffne, bae plate anchoring). The behaviour of thee ytem i affected by the particular geometry of their tructural component, made by high lenderne element, by the non-linear behaviour of both the beam-tocolumn (Agatino, Bernuzzi and Catiglioni, 21) and by the bae-plate joint (Baldaino and Zandonini, 21). Therefore, thee tructure cannot be conidered a building, and reference cannot be made to uual Structural Deign Recommendation and Standard. The mot recent Deign Standard for teel torage rack (R.M.I. 22 a and b, FEM 21, RAL 199, A.S. 1993, FEM 25) provide a combined numerical/experimental approach in which the deign tructural analyi i upported by pecific tet to evaluate the performance of the key component (member and joint). The deign need particular attention for torage rack intalled in a eimic zone, where they mut be able to withtand dynamic force. Beide the uual global and local collape mechanim, an additional limit tate for the ytem i repreented by the fall of the pallet with ubequent damage to good, people and to the tructure itelf. In Europe, no official document i currently available for the eimic deign of pallet rack, and the deigner are compelled to operate with a total lack of reference and of commonly accepted deign rule. Very often they make reference to the Rack Manufacturer Intitute (R.M.I.) Specification (R.M.I. a and b, 22), while the European Federation of Maintenance (F.E.M.) i preently working in order to produce an official document (FEM, 25). It mut be pointed out that the eimic behaviour of teel torage rack i not only a very intereting and challenging problem from a cientific point of view, but it ha alo a very large economic impact. Rack, in fact, are widely adopted in warehoue where they are loaded with enormou weight of (more or le) valuable good. The lo of thee good during an earthquake may repreent for the owner a very large economic lo, much larger than the cot of the whole rack on which the good are tored, or of the cot for it eimic upgrade. Rack are alo more and more frequently adopted in upermarket and hopping centre, in area open to the public. The falling of the pallet, in thi cae, may endanger the life of the client a well a of the workmen and employee, involving not only Civil and Penal Right conideration about the liability of the owner, but alo economic conideration related to the inurance coverage. In fact, liding of the pallet on the rack and their conequent fall repreent a erviceability limit tate i.e. a ituation that might occur during a eimic event alo in the cae of a well deigned torage rack, the phenomenon depending only on the dynamic friction coefficient between the pallet and the teel beam of the rack. Many time, after an earthquake, lo of good wa reported, with or without contemporary failure of the teel rack tructural ytem. Mot probably, thee tructural failure are a conequence of the fall of the pallet and of the impact of the good on the tructure at the lower level, triggering a progreive dynamic collape. The uncertaintie aociated with a clear aement of the caue of uch failure (due to tructural deign fault or caued by fall of the pallet) may reult in long quarrel among contructor, uer and inurance companie.

2 2 Fig.2 Typical torage rack configuration (from FEMA 46). Fig. 1 Storage rack example (SEISRACKS, 27) The SEISRACKS Project The objective of thi project, initiated in December 24 and terminated in June 27, were: to increae knowledge on actual ervice condition of torage rack, to increae knowledge on rack actual tructural behaviour to ae deign rule for rack under earthquake condition. The reearch team i compoed by the following unit: ACAI the Italian Aociation of Steel Contructor (Coordinator), Intituto Superior Tecnico of Libon (P), National Technical Univerity of Athen (GR), Politecnico di Milano (I), Univerity of Liege (B) and the European Laboratory for Structural Aement (ELSA) of the Joint Reearch Center of Ipra (Subcontractor of Politecnico di Milano). Storage rack are compoed of pecially deigned teel element that permit eay intallation and reconfiguration conitent with the merchandiing need of a warehoue retail tore. Except where adjacent to wall, torage rack normally are configured a two row of rack that are interconnected. Pallet typically can have plan area of approximately one quare meter and can have a maximum loaded weight of approximately 1-15 kn. Storage rack bay are typically meter deep and meter wide and can accommodate two or three pallet. The overall height of pallet rack tructural frame found in retail warehoue tore varie between 5 and 6 meter. In indutrial warehoue facilitie, racking ytem can reach coniderable height, uch a meter or more. (SEISRACKS, 27) 1.3. Organization, cope and aim of thi work The racking ytem behavior and the liding of pallet with a commercial oftware package Perform 3D ha been imulated in thi work. The diviion of the work i made in five chapter: In chapter one it i explained the cope and aim of thi work, the numerical and experimental tate of art of the pallet racking ytem problem and all the SEISRACKS project explanation. In chapter two it i explained the entire experimental program, with the decription of the load and the material beam, column, connector characteritic. Some reult and concluion are given to undertand the ituation of the experimental tudy. In chapter three i given all the numerical imulation explanation. It i tarted to be decribed briefly the feature and characteritic of the ued program Perform 3D. Then, it i hown all the preliminary tudie and the cae that were ued to tart working with the program. Some reult analyi i done. The lat ub-chapter i the SEISRACKS numerical model decription. All the eimic device, beam, column, connector and the imulation tet are characterized. In chapter four, an accuracy of the numerical model i done, by the comparion between the numerical and experimental reult. Chapter five i the concluion, where general overview of the reult of thi work i approached. Generally, it i given an overview of the torage rack ituation, including all the needed reearche and the cope of the SEISRACKS project. It i explained all the experimental tet, it reult and analyi. The next tep i focued on the explanation of the numerical model

3 3 calibration and it pecific. Then, it i teted the accuracy of the model by the comparion between the numerical and the experimental model reult. Finally, concluion and new purpoe are given. 2. The mental Program 2.1. mental Structural Component Two different cro-ection for beam (S25GD and TG 13x45x1.5) were adopted with upright of identical croection (1/2b). The S25GD wa ued to the lateral beam and the TG 13x45x1.5 wa the configuration of the other beam. The member geometrical propertie are hown in Table 1. Table 1- Geometrical Propertie of the Member Table 2- Material characteritic Member f y [MPa] f u [MPa] ε u (%) Beam 13x45x Upright 1x82x Table 3- Bae column propertie Bae Axial load [KN] M y [KNm] φ y [mrad] concrete Table 4 - Beam-to-column connection propertie M y [KNm] φ y [mrad] M u [KNm] φ u [mrad] Member Propertie Section 1/2b TG 13x45x1.5 S25GD A [mm 2 ] t [mm] 2 I x [mm 4 ] 461 I y [mm 4 ] W x [mm 3 ] 833 W y [mm 3 ] A [mm 2 ] t [mm] 1.5 I x [mm 4 ] I y [mm 4 ] W x [mm 3 ] W y [mm 3 ] 5171 A [mm2] 141 t [mm] 1.5 I x [mm 4 ] I y [mm 4 ] 9636 W x [mm 3 ] 1965 W y [mm 3 ] Tet pecimen mentally, there were teted ix pecimen. In thi thei will be tudied the pecimen A1, A2 and A4. Specimen A1 Specimen A1 i made with beam type 13x45x1.5 mm and upright type 1/2b, i.e. of the ame type of profile adopted when characterizing the behaviour of beam-toupright a well a bae connection, in the teting campaign carried out at Intituto Superior Tecnico in Libon. Pallet were rigidly connected to the teel beam, in order to avoid any poible liding. Thi wa achieved by mean of wooden board, crewed on the beam, on which the wooden pallet were nailed Specimen A1 wa ubmitted along the down-aile direction (the Y main direction of hake table) to the tet hitory, where for each tet both the Peak Ground Acceleration (PGA) a well a the Effective Deign Acceleration 44 Chapter 6 (EDA) are reported. Thi parameter correpond to the peak acceleration value found after low-pa filtering the input time hitory with a cut-off frequency of 9 Hz (Benjamin, 1988). Specimen A2 The material ued for beam and upright i S275 teel, with actual value of yield and ultimate tre howed in Table 2. Specimen A2 i imilar to pecimen A1, but the pallet are free to lide on the teel beam, and wa ubmitted along the down-aile direction.

4 4 Specimen A4 Specimen A4 i imilar to pecimen A2 with the pallet free to lide and wa ubmitted, along the cro-aile direction.(seisracks, 27) Numerical SEISRACKS model It wa performed the three pecimen A1, A2 and A4 - in the PERFORM 3D. The bae of the tructure i very imilar between them. The tructure i in the Figure Numerical Simulation In thi chapter it i given a hort decription about the ued program, it i explained all the preliminary tudie and finally, the decription of the SEISRACKS numerical model. The information about the program wa kindly provided by CSI Computer and Structure The Software PERFORM 3D i a highly focued nonlinear oftware tool for earthquake reitant deign. Complex tructure, including thoe with intricate hear wall layout, can be analyzed nonlinearly uing a wide variety of deformationbaed and trength-baed limit tate. Model data can be imported directly from ETABS and SAP2. A wide variety of element type are upported, including beam (with panel zone), column, brace, hear wall (with opening), floor lab, damper, and iolator. Nonlinear analyi can be tatic and/or dynamic and can be run on the ame model. Load can be applied in any equence, uch a a dynamic earthquake load followed by a tatic puhover. PERFORM 3D provide powerful performance baed deign capabilitie, and can calculate demand/capacity (uage) ratio for all component and all limit tate. Performance aement baed on ATC-4, FEMA-356 or ATC-44 i fully automated. PERFORM 3D output include uage ratio plot, puhover diagram, energy balance diplay, a well a mode hape, deflected hape, and time hitory record of diplacement and force. (CSI Computer and Structure). The program include two phae: Modeling and Analyi. The Modeling i the building phae of the program. It ha variou function to improve a good modeling. The Analyi phae can be divided into Structural Analyi tak, Behavior Aement tak and Demand- Capacity tak. The tructural analyi tak are for defining load cae and running tructural analye. The behavior aement tak allow you to examine and check the behavior of the analyi model. The demand-capacity tak allow to calculate demand-capacity ratio, and hence make deciion about the performance of the tructure. Fig.3 SEISRACKS project numerical model (program diplay). Fig. 4 SEISRACKS experimental model.

5 5 Fig. 5 SEISRACKS experimental model. The ued beam were the TG13x45x1.5 and S25GD and the column wa the 1x2b all thoe characteritic decribed in chapter 2. Thee were the column and beam definition. All their propertie were baed in the experimental model beam and column, a it i poible to ee on table 1 and 2. The beam to column connection were defined with the experimental model propertie characteritic on the Table 3. The trilinear hape relationhip i ued and it i defined a ymmetric to both ide. It i very important to ay that thi beam to column connection i ued to the A1 and A2 model due to the unawarene of the cro aile direction propertie of the beam to column connection i.e., a it wa een in the next ub-chapter that the A1 and A2 model are teted in the down-aile direction all the device propertie are known- and in the cae of the A4 model it doen t happen. The column bae propertie were the ame to the three model. The characteritic are on table 4. Thee were the component ued to the experimental tet. Their propertie were ued to define the model in PERFORM 3D. Defining the propertie and the material it i poible to improve and get better reult. In the experimental tudie, everal tet were done to the pecimen, a it wa een before. In thi thei, it wa choen one PGA for each model and it wa improved the tet to it. The haking table tet were done baed in the accelerogram of the experimental tet. In the next figure are the accelerogram ued to each tet. Fig.6 A1 pecimen accelerogram (program diplay). Fig.7 A2 pecimen accelerogram (program diplay). Fig.8 A4 pecimen accelerogram (program diplay).

6 Diplacement (mm) Diplacement (mm) Diplacement (mm) 6 The figure correpond to the A1, A2 and A4 pecimen accelerogram, with a peak acceleration of 1.31g,.75g and.22g repectively. Thee tet were choen to tudy the model with a high and low PGA acceleration, being aware to the limit of the tructure. To define the analyi load cae, it wa choen the dynamic earthquake category. The tet were performed in the Q1 direction down aile direction with a total time of 3.48 econd, maximum of 2 tep and aving the reult for each tep.1 econd Second Floor Diplacement mental 4. Accuracy of the numerical model -15 In thi chapter a tudy of the accuracy of the numerical model i performed. To evaluate the overall accuracy of thi model, it wa neceary to do a tudy of the force, the tiffne and energy diipation. Due to the unawarene of information, it i tudied jut the diplacement reult and it i given the preciion of the model in thi area. Thi chapter i ub-divided in the three pecimen reult A1 Specimen Thee were the obtained reult in the pecimen A1. The reult are ub-divided by floor. -1 Fig.1 - A1 comparion between numerical and experimental diplacement econd floor Firt Floor Diplacement menta l Third Floor Diplacement Exper iment al Reul t Fig.9 - A1 comparion between numerical and experimental diplacement third floor. Fig.1 - A1 comparion between numerical and experimental diplacement firt floor. The graphic illutrate the diplacement of the third, econd and firt floor. Looking to the lat ten econd of the numerical reult, it i notable that the tructure ha platic deformation in thi period. In comparion with the experimental reult, it matche well. In thi tructure the reult are good. It i poible to ee that the agreement and the value of the reult of the firt level match very well. The econd and the third floor are le precie due to the maximum value are not matching o good; but the reult remain acceptable. Thi kind of tructure wa not the problematic one due to the fact of the pallet being fixed to the beam.

7 Diplacement (mm) Diplacement (mm) Diplacement (mm) A2 Specimen In thi pecimen the pallet i free to lide in the beam. Due to it, the reult were affected highly in the lat two floor Third Floor Diplacement Second Floor Diplacement mental Fig.12 A2 comparion between numerical and experimental diplacement third floor. mental Numeri cal Fig.13 - A2 comparion between numerical and experimental diplacement econd floor Firt Floor Diplacement men tal Numerical Fig.14 A2 comparion between numerical and experimental diplacement firt floor. In thi pecimen, it i notable that a difference between the final tate of the numerical and the experimental model exit. The numerical model ha elatic deformation, a it i poible to oberve. In the other hand, the experimental reult, how platic deformation in the tructure between the 23 and the 3 econd of the performed tet. Throughout a generically perpective, the reult of thi tructure are not a good a the A1 pecimen, but very acceptable. Once more, the firt floor diplacement contain the better reult. Comparing to the experimental model, it ha been obtained larger diplacement in the econd and third floor their maximum do not match. Thi wa a complicated pecimen, due to the calibration of the eimic device. To get thee reult it wa needed to calibrate preciely the μ dynamic factor - calibrating directly the FU of the eimic device. The μ dynamic factor i the friction factor. Friction i the tangential reaction force between two urface in contact. Phyically thee reaction force are the reult of many different mechanim, which depend on contact geometry and topology, propertie of the bulk and urface material of the bodie, diplacement and relative velocity of the bodie and preence of lubrication. In dry liding contact between flat urface, friction can be modeled a elatic and platic deformation force of microcopically aperitie in contact. To calibrate the μ, it wa ued the expreion, (eq.1) The ued ma round the 8 Kg (concrete block were ued in the experimental tet) o, each eimic device carrie a ma of 2 Kg, a it i poible to ee in Figure 76. The acceleration i the gravity acceleration, and the ued μ wa.3. So, the defined FU wa.6. Thi friction

8 Diplacement (mm) Diplacement (mm) Diplacement (mm) 8 factor correpond to a friction between the wood pallet and the beam A4 Specimen The A4 pecimen wa the mot difficult model to analyze. Thi model wa tudied in the cro-aile direction Third Floor Diplacement Second Floor Diplacement mental Fig. 15 A4 comparion between numerical and experimental diplacement third floor. Fig.16 A4 comparion between numerical and experimental diplacement econd floor. menta l Firt Floor Diplacement Fig.17 A4 comparion between numerical and experimental diplacement firt floor. Exper iment al Reul t A it i happening in the A2 pecimen, the numerical model i having elatic deformation. In the other hand, the experimental model finihe the tet with platic deformation. The value of the three floor generally match well. The higher value of the experimental model do not match. The agreement of thi pecimen i not the bet. Conequently the drift graphic are not the mot accurate. To improve the reult, the eimic device wa defined with a higher FU 1.2 KN and the tiffne of the beam-tocolumn connection, in the cro aile direction, were decreaed to 1/1. The reaon to thi i the fact of the pallet rack rigidity being much higher in the down aile direction than in the cro aile direction. All thee factor are being conidered to get the bet poible reult. The reult of thi pecimen are acceptable, taking in conideration all the experimental failure (analyzed in the chapter 2) and all the miing information about the connector in thi direction. It i important refer that the tiffne of the connection between the upright and the bracing member of the tranveral frame i not known, and wa imulated a a hinge. Thi i alo probably the caue for the dicrepancie between numerical and experimental reult. They are due to difficulty in calibration of the tiffne of the tranveral frame Concluion The A1 pecimen reult were atifactory, taking in conideration that thi wa the implet tructure, due to the analyi direction down-aile - and the fixed pallet-beam relation.

9 9 The A2 pecimen reult were very acceptable, but numerically peaking it wa the wort of the three. The liding pallet had an important influence and conequently the eimic device definition. The A4 pecimen wa, in the beginning, the problematic pecimen. The unawarene of the beam-to-upright connection propertie wa determinant. But, taking it into account, the reult were very good, conidering that wa the unique pecimen that had the numerical reult under the experimental one, that tranmit confidence to thi numerical tudy. Generally, the reult were atifactory, and it i concluive that the model had a good accuracy in the diplacement area. Force, tiffne and energy diipation are fundamental to the global accuracy of the model. It i a poibility of a future tudy in thi area. 5. Concluion The liding of the pallet on the rack and their conequent fall repreent a erviceability limit tate i.e. a ituation that might occur during a eimic event alo in the cae of a well deigned torage rack. The eimic action in thi kind of tructure i a topic of tudy that, nowaday, i in contant development. Thi diertation developed the tudy of the racking ytem in helping to avoid human and economical conequence, throughout the undertanding of the behavior of the pallet liding in the rack. The development of a numerical model wa leaded, with all the propertie of the experimental pecimen. An accuracy of thi model wa verified by the comparion of the diplacement of each model. Several trie and imulation were done in thi tudy in order to get the bet poible reult. Other problem wa the imulation of the pallet and it friction with the beam. Thi problem wa olved, by the tudy of the program eimic device. It i important to mention that a good accuracy of the model require a tudy of the force, tiffne, energy diipation and diplacement. In thi diertation only the diplacement reult were tudied due to the available information. The obtained reult were acceptable, taking in conideration all the factor that were mentioned before unawarene of ome device characteritic. The initial aim of thi work were accomplihed. The model could be calibrated and it reult improved. In the future, the tudy of the force, tiffne and energy diipation of the model, allowed that the tudy could be performed by computer oftware, dimiing the experimental project, giving a good economical and cientific improvement to thi tudy. 6. Reference A.S. 484 (1993), Steel Storage Racking, Autralian Standard Agatino, M.R., Bernuzzi C. and Catiglioni C.A. (21), Joint under cyclic reveral loading in teel torage pallet rack, Proc. of XVIII Conference C.T.A., Venezia, September 21, pp ATC-3 (1978), Tentative Proviion for the Development of Seimic Regulation for Building. Applied Technology Council, Redwood City, CA. Baldaino N. and Zandonini R. (21), Numerical and mental Analyi of Bae-plate Connection of Steel Storage Pallet Rack, Proc. of XVIII Conference C.T.A., Venezia, Catiglioni C.A., Panzeri N, Brecianini J.C. and Carydi P. (23) Shaking Table Tet on Steel Pallet Rack, Proceeding of the Conference on Behaviour of Steel Structure in Seimic Area-Stea 23, Naple, Italy, Catiglioni C.A. (23). Dynamic Tet on Steel Pallet Rack, Cotruzioni Metalliche, 55(3), CSI Computer and Structure, Perform Component and Element, verion 4, Augut 26 CSI Computer and Structure, Perform Uer Guide, verion 4, Augut 26 FEM (21) a, The Deign of Static Steel Pallet Rack, Federation Europeen de la Manutention, Ver. 1.2 FEM (21) b, Guideline fot the afe ue of tatic teel racking and helving, Federation Europeen de la Manutention, Ver. 1.2 FEM (25), The Seimic Deign of Static Steel Pallet Rack, Federation Europeen de la Manutention, final draft, December 25. FEMA (25), Seimic Conideration for Steel Storage Rack Located in Area Acceible to the Public, FEMA 46, September 25

10 1 Filiatrault A., Bachman R.E., Mahoney M.G. (26), Performance-Baed Seimic Deign of Pallet-Type Steel Storage Rack, Earthquake Spectra, 22 (1), RMI. (22) a, Specification for the deign teting and utilization of indutrial teel torage rack, Rack Manufacturer Intitute, Charlotte, NC., 22 edition RMI. (22) b, Commentary to Specification for the deign teting and utilization of indutrial teel torage rack, Rack Manufacturer Intitute, Charlotte NC. SEISRACKS (27), Storage Rack In Seimic Area (SEISRACKS), Reearch Programme of the Reearch Fund for Coal and Steel RTD, Final Report, May 27