SEISMIC EVALUATION AND PERFORMANCE ENHANCEMENT OF INDUSTRIAL STORAGE RACKS YUAN GAO. Submitted in partial fulfillment of the requirements

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1 SEISMIC EVALUATION AND PERFORMANCE ENHANCEMENT OF INDUSTRIAL STORAGE RACKS by YUAN GAO Submitted in partial fulfillment of the requirements For the degree of Master of Science Thesis Adviser: Prof. Michael Pollino Civil Engineering Department Case Western Reserve University January, 2013

2 CASE WESTERN RESERVE UNIVERSITY SCHOOL OF GRADUATE STUDIES We hereby approve the thesis/dissertation of Yuan Gao candidate for the Master of Science degree*. Prof. Michael Pollino (chair of the committee) Prof. Arthur Huckelbridge Prof. Dario Gaspaini December 3 rd, 2012 *We also certify that written approval has been obtained for any proprietary material contained therein.

3 Table of Content 1. Introduction and purpose of study 1 2. Background Existing guidelines for seismic design of steel storage rack Ground motions used in the project Recent study on merchandise behavior Recent studies on elastomer damper and the damped structures under earthquakes.7 3. Investigation of merchandise flexibility on storage rack seismic response General Linear viscous modeling Rack/merchandise transient analysis model Results and discussion Linear viscous with sliding model Linear viscous with sliding model Results and discussion Failure conditions discussion Damper design General Elastomeric damper behavior Damper implementation to rack Damper design procedure Simplified iterative design procedure. 32 Page i

4 4.4.2 Time history analysis Results and discussion Impact of merchandise mass configuration on seismic response of damped racks General Parameters and analysis input Results Results with 5 kip merchandise Results with 3 kip merchandise Results with 1 kip merchandise Conclusions and future research. 77 Page ii

5 List of Figures Figure 2.1 Shear Modulus and Damping Ratio Strain Dependence.. 9 Figure Shelf Heavy-duty Retail Rack..18 Figure 3.2 Analytical Model for Linear-viscous Merchandise Behavior..19 Figure 3.3 Spectral Acceleration for DBE Motions..19 Figure 3.4 Spectral Acceleration for MCE Motions.20 Figure 3.5 Response for Linear-viscous Merchandise..21 Figure 3.6 Analytical Model for Behavior of Linear-viscous with Sliding..22 Figure 3.7 Fundamental of Linear-viscous with Sliding Merchandise.22 Figure 3.8 Response for Sliding Merchandise..23 Figure 3.9 Merchandise Deformation for Linear-viscous with Sliding 24 Figure 3.10 Failure Conditions..25 Figure 3.11 Merchandise Deformation for Linear-viscous with Sliding under DBE Motions...26 Figure 3.12 Merchandise Deformation for Linear-viscous with Sliding under MCE Motions...27 Figure 4.1 Sketch of Proposed Elastomeric Damper.37 Figure 4.2 Force-deformation curve for Elastomeric Damper...38 Figure 4.3 Shear Modulus and Damping Ratio Strain Dependence..39 Figure 4.4 Sketch of Rack with Damper 39 Figure 4.5 Response of Baseline Rack..40 Figure 4.6 Response of Damped Rack 41 Figure 4.7 Normalized Impulse...42 Page iii

6 Figure 5.1 Mass Configuration Conditions 50 Figure 5.2 Flowchart for ANSYS Program Input File...51 Figure 5.3 Peak Acceleration Comparison for 5 kip Merchandise 54 Figure 5.4 Median Value for Fourier Transform of DBE Motions 54 Figure 5.5 Peak Acceleration Comparison for 3 kip Merchandise.57 Figure 5.6 Peak Acceleration Comparison for 1 kip Merchandise.59 Figure 5.7 Peak Displacement Comparison for 5 kip Merchandise 62 Figure 5.8 Peak Displacement Comparison for 3 kip Merchandise 64 Figure 5.9 Peak Displacement Comparison for 1 kip Merchandise 67 Figure 5.10 Normalized Impulse for 5 kip Merchandise 69 Figure 5.11 Normalized Impulse for 3 kip Merchandise 72 Figure 5.12 Normalized Impulse for 1 kip Merchandise 74 Page iv

7 List of Tables Table 3.1 Merchandise Properties Considered for Linear-viscous Model..28 Table 3.2 Section Properties for Rack Members.28 Table 4.1 Values of Spectral Damping Coefficient (Adapted from ASCE 7-05) 43 Table 4.2 Resulting Damper Properties from Simplified Iterative Design Procedure.43 Table 4.3 Resulting Damper Properties from Time History Analysis.44 Table 5.1 Modal Properties of Baseline Rack..75 Table 5.2 Model Properties of Damped Rack..76 Page v

8 Seismic Evaluation and Performance Enhancement Of Industrial Storage Racks Abstract by YUAN GAO The use of industrial storage racks in large warehouse stores and the public s direct access to merchandise on these racks has significantly increased over the last twenty years. Such racks and their supported merchandise have in some cases performed poorly in past earthquakes as a result of rack failure or product shedding (palletized merchandise falling off shelves). While the warehouse buildings themselves may be adequately designed for seismic effect, the rack performance also significantly impacts the seismic risk to society both in terms of life-safety and economic losses. The seismic behavior of industrial storage racks is fundamentally different than typical civil engineering structures due to the high percentage of mass from the merchandise which is flexible and not fixed to the structural system, as opposed to buildings for example that have significant dead load from relatively rigid sources (floor slabs, members, fixed equipment, etc.). This research first explores the influence of merchandise dynamic characteristics on rack seismic performance. Behavior of the pallet merchandise varies significantly and is quite complex therefore bounding parametric analyses are performed for response assessment. A number of mechanical model increasing in complexity are considered for modeling of Page vi

9 the merchandise which includes linear-viscous, and linear-viscous with sliding. Secondly, a simple highly compressed elastomeric damper is proposed to enhance the seismic performance of industrial storage racks by decreasing merchandise damage and probability of merchandise shedding. Finally, the impact of merchandise mass variability on the effectiveness of damped rack is evaluated through parametric seismic analyses. Page vii

10 Section 1 Introduction and Purpose of Study The seismic risk associated with storage rack failure is increasing as publicly accessible warehouse shopping has grown across North America and Europe. Such stores often display merchandise directly on pallets on cold-formed steel storage racks. These steel storage racks effectively make use of the available space by combining storage and retail space but places customers close to large pallets of merchandise. The risk to public safety during an earthquake is significant and proper design, installation, and maintenance is required and should be considered as important as the warehouse building for evaluation of seismic design. In addition to the rack s design, the merchandise supported on the racks imposes a hazard to safety and can result in significant economic loss. Significant damage has been reported in past earthquakes since storage rack use has significantly increased. Investigating the seismic performance of industrial storage racks requires knowledge of both the rack and merchandise behavior since the merchandise constitutes nearly all of the rack seismic mass and failure could be a result of merchandise shedding or failure of the rack itself. Unlike conventional buildings, rack merchandise configuration is highly variable and seismic response and design must consider this significant mass variation. This research first explores the effect of merchandise flexibility on rack seismic response. Various analytical models are considered to model merchandise dynamic behavior and assess the impact of merchandise response on rack response and also to provide quantitative information to assess merchandise shedding. Note that common practice in rack seismic design is to consider the merchandise mass fixed to the rack with 10% damping. Then, an elastomer damping system is proposed to improve the rack seismic Page 1

11 performance in the cross-aisle direction since product shedding can only occur in this direction. The elastomeric dampers are intended to replace the diagonal steel braces in the cross-aisle direction, reduce rack shelf acceleration and cumulative impulse imparted on the merchandise without exceeding the rack s elastic design strength. Finally, a parametric analysis study is performed to further investigate the effect of mass variability on the seismic response of steel storage rack and its impact on design of the added damping system. Page 2

12 Section 2 Background Due to the large spread of public warehouse stores, the use of steel storage racks has become more popular. More rack and merchandise failures have been reported during earthquakes, which has drawn more attentions from researchers and the rack industry. In this section, previous work is reviewed to assess the current knowledge on seismic behavior of steel storage racks and its supported merchandise. The development of the damping system in partnses guidelines provided in structural building code provisions. The utilization of elastomeric dampers in place of the diagonal steel brace member has been considered in previous studies on improvement of seismic behavior of conventional buildings. 2.1 Existing guidelines for seismic design of steel storage racks FEMA 460 provides guidance for the seismic design of storage racks in areas accessible to the public. According to previous damage reports for storage racks, the failure mode of racks includes the global overturning and down-aisle beam to upright connection failure. Even in cases where rack damage does not occur, merchandise shedding could occur. In addition, the friction between the merchandise and the shelves has a significant influence on the seismic behavior of storage rack. Therefore, a lifesafety design to prevent the collapse or overturn of the rack and the shedding of contents is required per FEMA 460 for the rack which is higher than 8 feet. To prevent rack collapse and overturning, FEMA 460 recommends optional displacement-based and limit state design procedures developed in 2008 NEHRP Recommended Provisions (NEHRP, 2008) and ASCE 7-05 (ASCE, 2005) for the cross- Page 3

13 aisle direction. The choice of procedure depends on the level of seismicity. However, the recommendations do not account for merchandise flexibility or sliding relative to the rack. FEMA 460 also offers guidelines to prevent, or at least reduce the risk of falling merchandise during earthquakes. First, for merchandise stored on pallets, wire decking, spaced wood boards or metal channels with angles or plates, or perforated metal decking is recommended to prevent the lateral movement of the pallet in earthquakes. Also, several approaches are recommended to secure individual merchandise to pallets including stretch-wrapping, shrink-wrapping, banding, and integral box-pallet. For merchandise not stored on pallets, FEMA 460 provides approaches to protect merchandise shedding in earthquakes, including restraining bars, restraining chains or cables, or netting. To further improve merchandise behavior, pallet friction needs to be tested to determine whether pallets (wood, plastic, or metal) will slide off shelves in earthquake. FEMA 460 lists some previous research on seismic behavior of storage racks which includes both experimental and analytical studies. Experiments are performed on the rack and merchandise using with shake table testing methods. Two kinds of numerical rack models are presented in previous analytical research, which include linear and nonlinear models. By reviewing these past research, FEMA 460 gives future research needs related to the seismic response of steel storage racks. Experimental and analytical studies are needed for cross-aisle response since most failures are reported in the cross-aisle direction. The development analytical models are needed to predict the rack and merchandise seismic behavior under earthquakes. Experimental test results are needed for storage racks and merchandise preferably by shake-table testing. Page 4

14 This research focuses on analytical methods for investigating the seismic behavior of steel storage racks and the merchandise. Finite-element based models are developed to investigate the merchandise flexibility and quantitatively assess failure. Also, only crossaisle direction behavior is considered in this research. ASCE 7-05 (ASCE, 2005) specifies the design loads and analysis procedures for structures including added damping systems for seismic design. The elastomeric damper developed in this study is based on the response spectrum procedure provided by ASCE 7-05, in which design seismic forces are determined based on rack modal properties and the site response spectrum. The forces applied to each floor are distributed over the height of the structure based on dominant mode shape. The proposed elastomeric damper is designed for each cross-aisle panel to dissipate the rack energy through shear deformations on the elastomer. The seismic forces are calculated based on an equivalent linear viscous SDOF representation of the rack. 2.2 Ground motions used in the project FEMA 355C summarizes steel moment-frame buildings behavior under a range of different ground motions and was prepared under the SAC Joint Venture following the 1994 Northridge, CA earthquake. The ground motions used in FEMA 355C consists of both recorded ground motions and synthetically generated records scaled to represent seismic hazards with return periods of 475 years (10% probability of being exceeded in 50 years), and 2475 years (2% probability of being exceeded in 50 years) for the Los Angeles, California area. Ten ground motions from each hazard level are utilized in this study. Page 5

15 2.3 Recent study on merchandise behavior Sideris (2010) performed pull tests and shake table tests to investigate the seismic behavior of palletized merchandise stored on steel storage racks. The pull tests aimed to find the frictional properties of the pallet interface to rack and the relative velocity of the pallets relative to the rack shelf. The friction force between wooden pallets and rack shelves with wired decking varied from 37 and 45% of the merchandise weight during the pull test. A model with a linear spring and a coulomb spring connected in series is considered to describe the response of a loaded pallet. Sideris also performed a shaking table test for inclined shelving to investigate its effect to reduce merchandise shedding. The input motion is varied to simulate the behavior of different rack shelves. Sideris s study on seismic behavior of palletized merchandise focused more on the friction between the shelf and the pallet, which is important but not sufficient to describe the merchandise behavior under earthquakes. In the thesis project, a more complex numerical model for the merchandise is considered. 2.4 Recent studies on elastomer damper and the damped structures under earthquakes A summary of current applications in passive energy dissipation systems for seismic resistance of buildings is presented by Symans (2008). Various passive energy dissipation systems are considered to reduce seismic damage to the framing system, which includes viscous fluid damper, viscoelastic solid damper, friction damper and metallic damper. The mechanical behavior of each type of passive energy dissipation system is discussed along with the advantages and disadvantages of each device, design philosophy, and design considerations. The damping system employed in this research is similar to the Page 6

16 viscoelastic solid damper, which generally consists of solid elastomeric pads bonded to steel plates. The viscoelastic solid damper described in the paper is frequency and temperature dependent. A general design procedure is recommended for the passive energy dissipation system based on the 2004 NEHRP Recommended Provisions and ASCE Lin (2002) presents a displacement-based design procedure for added passive energy dissipation systems by a rational linear iteration method. By specifying a target displacement, the nonlinear behavior structure is replaced by a static equivalent linear system which is composed of an equivalent effective stiffness, and an equivalent hysteretic damping ratio similar to the ASCE 7-05 procedure. In addition, Lin gives various effective viscous damping ratio and effective stiffness for different energy dissipation system: viscous device, friction device, metallic yielding device, and viscoelastic device. Burtscher (1998) presents an overview of natural rubber which is frequently used in seismic isolation of structures because of its high elasticity and high damping. A plot (Fig. 2.1) is shown in the paper to illustrate the effect of shear strain on shear modulus and damping ratio. The damper philosophy of energy dissipation is explained in the paper. By targeting a shear strain for the damper, shear modulus and damping ratio could be read from the plot. These two parameters will be used in the elastomeric damper design. Although the temperature, strain and cyclic loading would affect the rubber behavior, it will not be considered in the damper design. Page 7

17 Karavasilis (2011) investigated the hysteretic behavior of compressed elastomer damper and its application on seismic response improvement of steel moment-resisting frames (MRF). The elastomer damper is represented by a model with a Bouc-Wen model and a dashpot connected in parallel, and calibrated using experimental data obtained under sinusoidal loadings at different amplitudes and frequencies. The high-damping elastomer material is pre-compressed together into a steel tube, and energy is dissipated due to the slip of the elastomer relative to the tube. After nonlinear seismic response analyses under both the design basis earthquake and the maximum considered earthquake, Karavasilis drew conclusions that elastomer dampers equipped on the steel MRF are effective on the control of drift and floor acceleration. Also, the compressed elastomer damper is more effective for lighter weight steel MRFs. Page 8

18 Figure 2.1 Shear Modulus and Damping Ratio Strain Dependence (Adapted from Burtscher (1998)) Page 9

19 Section 3 Investigation of Merchandise Flexibility on Storage Rack Seismic Response 3.1 General In previous analysis of the seismic behavior of industrial racks, focus is often placed on the behavior of the rack itself, and the merchandise behavior grossly approximated in analysis as described in Section 2. The merchandise behavior is very complex exhibiting nonlinear force-deformation response with large deformation effects. The force-deformation behavior is affected by sliding of the pallet relative to the rack shelf, sliding of the material (item to item), and potentially engagement of shrink wrap (if present). Explicitly modeling merchandise behavior is included in the analyses of this section which will allow assessment of merchandise flexibility on rack response and also allow quantification of merchandise response to predict failure (merchandise shedding). Two models are considered in this section to describe the merchandise flexibility: (1) Linear-Viscous model with varying merchandise frequency and (2) Linear-Viscous with sliding model which includes varying merchandise frequency and sliding (assumed between the pallet and shelf). 3.2 Linear viscous modeling The behavior of the merchandise is first considered linear viscous and modeled by a spring and a dashpot connected in parallel. The damping ratio is assumed to be 10 % to account for the energy dissipated by the merchandise consistent with past studies. The frequency of the merchandise is varied from 0.5 Hz to 4 Hz to investigate the trends and bounds in response due to the variability in actual merchandise behavior. The weight of Page 10

20 the merchandise is assumed to be 5 kip. Only cross-aisle direction response is considered since merchandise can only shed off the rack in this direction. Based on varied merchandise frequency and constant weight, the stiffness input into the spring could be calculated by Eq. 3.1: (3.1) The damping coefficient c is calculated with the damping ratio ξ (10%) by: (3.2) The tributary mass for each upright column is ¼ of the total mass for each shelf (5 kip). The merchandise properties used in the linear viscous model are provided in Table Rack/Merchandise transient analysis model The rack considered in the analysis is typical of a 4-shelf, heavy-duty retail rack with dimensions shown in Fig Rack configuration and sections were obtained from a large rack manufacturer. The material of the rack is steel. The rack is fabricated with two cold-formed steel sections in the cross-aisle direction (Section A and Section B). Section A is used for uprights, and section B is used for cross-aisle beam and bracing. Section properties are shown in Table 3.2. All rack members are modeled using elastic beam elements. By modal analysis, the rack described above with fixed merchandise has a first mode of 3.66 Hz, a second mode of about Hz, a third mode of about Hz and a fourth mode of about Hz. Page 11

21 The merchandise is modeled using a spring and damper element as seen in Figure 3.2 connecting the tributary merchandise mass to the upright at the down-aisle beam connection point. Ten ground motions are applied as uniform nodal horizontal acceleration histories at the base of the uprights. Fig. 3.3 shows the spectral acceleration of the motions applied. The average one-second spectral acceleration (S D1 ) equals 0.69 g, and short period acceleration (S DS ) equals 1 g. These spectral values and ground motions are consistent with a Los Angeles, CA design basis earthquake on a firm rock site. The ground motions used in this study were developed as part of the SAC steel Project (FEMA 355C) and used as design basis earthquake (DBE). There are another ten ground motions used as maximum considered earthquake (MCE) from SAC Steel Project (FEMA 355C), which have an average S 1 of 1.25 g and an average S S of 1.75 g. The spectral acceleration of the MCE set of ground motion is shown in Fig Results and discussion The median response value of linear viscous merchandise for ten ground motions are shown in Fig The peak acceleration for merchandise and shelf is compared in Fig. 3.5 (a) and (b). The peak relative displacement for merchandise and shelf is compared in Fig. 3.5 (c) and (d). With a larger frequency, the peak absolute acceleration is bigger. 3.3 Linear viscous with sliding Page 12

22 3.3.1 Linear viscous with sliding modeling A more sophisticated approach of modeling merchandise behavior, compared to the linear-viscous merchandise model, would include sliding between the pallets and rack shelves. The merchandise is not commonly attached to the rack for operational flexibility, and thus it can slide relative to the rack. The linear viscous model includes 10 % inherent damping which in part is intended to account for the energy dissipated through frictional sliding. Thus, with the sliding explicitly modeled, the inherent merchandise damping will also need to be decreased. The static and dynamic friction coefficient μ between the pallet and the rack is assumed to be The same 4-shelf rack described in section 3.2 is also used here. The weight of the merchandise is 5 kip, and the frequency of the merchandise is ranged from 0.5 Hz to 4 Hz. The merchandise behavior is modeled using a bilinear hysteretic model and viscous damper in parallel connected between the mass (representing the merchandise) and the rack as shown in Fig 3.6. The merchandise is considered to have a combined frictional and viscous behavior as shown in Fig The merchandise flexibility relative to the pallet is assumed linear up to the initiation of sliding, which is captured with the bilinear hysteretic model. A small amount of additional damping exists due to the deformations of the merchandise relative to the pallet and is modeled using a viscous damping with 2% damping. The model is represented with the nonlinear beam element (BEAM188) in ANSYS. A bilinear, kinematic plasticity model is assigned to these elements. The elements are oriented to behave in the axial degree of freedom. The material model is Page 13

23 defined by the elastic modulus, post-yield modulus ratio and yield stress to simulate the linear viscous with sliding merchandise behavior. The elastic stiffness is obtained using Eq. 3.1with varying frequencies of the merchandise and setting it equal to the axial stiffness of the beam element (EA/L). The post-yield modulus is assumed to be very small (sliding), and the post-yield modulus ratio, is set to be The yield force could be calculated with the friction coefficient by: (3.3) Results and discussion The analysis results are presented in Fig Compared to merchandise behavior for linear viscous model, the sliding merchandise has a smaller peak absolute acceleration and a bigger peak relative displacement with same frequency. The sliding behavior dissipated a certain amount of energy of merchandise, which results in a reduction on merchandise acceleration compared to the linear viscous merchandise. The relative displacement for linear viscous with sliding model defined as the merchandise displacement relative to the rack is larger than the linear viscous merchandise due to the sliding displacement added to. 3.4 Failure Conditions Discussion The advanced merchandise model allows for direct calculation of merchandise response to evaluate key merchandise limit states. To further investigate the behavior of merchandise, the merchandise displacement relative to the rack is obtained from the nodal displacement in ANSYS separated to sliding displacement D s and product Page 14

24 deformation D m as shown in Fig A few merchandise failure conditions are evaluated using the sliding displacement and product deformation. Three failure conditions are considered here for the flexible merchandise and are shown in Fig. 3.10: Failure Condition 1 (D s > 3in): the merchandise pallet is supported directly on the two down-aisle beams as shown in Fig (a). Failure occurs when the pallet outside edge passes the inside edge of the down-aisle beam. The width of the pallet is assumed to be 48 in, and the width of the down-aisle beams is 42 in, thus the failure condition will happen when the sliding displacement exceeds 3 in. In this failure condition, merchandise might not fall off the rack immediately, but would likely be significantly damaged and produce a significant falling hazard. Failure Condition 2 (D s +D m > 21in): the failure happens when the displacement of the centroid of the mass exceeds the half width of the rack (21in) as shown in Fig. 3.10(b). The displacement includes the merchandise deformation relative to the pallet and sliding of the pallet. This failure condition considers overturning instability about the edge of the down-aisle beam. Failure Condition 3 (D m > 18in): the failure occurs when the center of mass of the merchandise exceeds its edge resulting in overturning instability of the merchandise on top of the pallet, which is shown in Fig (c). This failure may only happen for very flexible of slender merchandise such that sliding is not the dominant mode of response. Page 15

25 The median value of merchandise displacement for ten ground motions are plotted in Fig with varying merchandise frequencies. As the frequency increases, the total displacement and merchandise deformation gets smaller. The sliding displacement decreases as the frequency increases to 2 Hz but increases with increasing frequency to 4 Hz. The reason for that is the merchandise frequency is reaching the natural frequency of the rack, and a resonance happens. When sliding displacement D s is bigger than 3 in, failure condition 1 has occurred and is observed for nearly all frequencies and all shelves. The use of a stiffened wire rod rigid is attached on top of the down aisle beams which would prevent this failure condition. The other two failure conditions do not occur under the LA DBE motions. The merchandise displacements under the MCE motions are similarly plotted in Fig The failure condition 1 occurs for all merchandise as expected since it occurs during the DBE motions. Failure condition 3 does not occur for all merchandise frequencies. Failure condition 2 only occurs with 0.5 Hz frequency merchandise, since the total displacement exceeds 21 in. The results show that Failure condition 1 occurs under both DBE and MCE motions and a horizontal diaphragm is needed on top of the two down-aisle beams. Failure condition 2 only occurred for very flexible merchandise. Failure condition 3 is not observed for the frequencies considered. Note that while this merchandise model is more sophisticated and believed to more accurately capture merchandise and pallet sliding behavior, the linear behavior of the merchandise should be revisited in future research to determine appropriate nonlinear hysteretic behavior for merchandise and account for the Page 16

26 cumulative permanent deformations that occur as a result of merchandise package to package sliding, shrink wrap stretching, and package damage. Page 17

27 Figure Shelf Heavy-Duty Retail Rack Page 18

28 Figure 3.2 Analytical Model for Linear-viscous Merchandise Behavior Figure 3.3 Spectral Acceleration for DBE motions Page 19

29 Figure 3.4 Spectral Acceleration for MCE motions Page 20

30 Merchandise Shelf (a) (b) (c) (d) Figure 3.5 Response for linear viscous merchandise: (a) Peak acceleration for merchandise; (b) Peak acceleration for shelf; (c) Peak displacement for merchandise; (d) Peak relative displacement for shelf Page 21

31 Figure 3.6 Analytical Model for Behavior of Linear-viscous With Sliding Figure 3.7 Fundamentals of Linear-viscous with Sliding Merchandise Page 22

32 Merchandise Shelf (a) (b) (c) (d) Figure 3.8 Response for sliding merchandise: (a) Peak acceleration for merchandise; (b) Peak acceleration for shelf; (c) Peak relative displacement for merchandise; (d) Peak relative displacement for shelf Page 23

33 Figure 3.9 Merchandise Deformation for Linear-viscous with Sliding Page 24

34 (a) (b) (c) Figure 3.10 Failure Conditions: (a) Failure condition 1; (b) Failure condition 2; (c) Failure condition 3. Page 25

35 0.5 Hz 1.0 Hz 1.5 Hz 2 Hz 3 Hz 4 Hz Figure 3.11 Merchandise Deformations for Linear-viscous with Sliding under DBE Motions (Failure Condition 1 noted by the solid vertical line) Page 26

36 0.5 Hz 1.0 Hz 1.5 Hz 2 Hz 3 Hz 4 Hz Figure 3.12 Merchandise Deformations for Linear-viscous with Sliding under MCE Motions Page 27

37 Table 3.1 Merchandise Properties Considered for Linear-viscous Model f (Hz) k (kip/in) c (kip*sec/in) m (kip*sec 2 /in) Table 3.2 Section Properties for Rack Members Section A Section B I x (in 4 ) I y (in 4 ) A (in 2 ) Page 28

38 Section 4 Damper Design 4.1 General An elastomer damper is designed in this project to improve the seismic performance of racks during earthquakes. The dampers are intended to be implemented in the rack cross-aisle direction in place of the steel bracing member. It is anticipated that the damper will increase the rack drift however the rack will still remain within elastic limits and will reduce peak acceleration and total impulse to the merchandise, thus reducing likelihood of merchandise shedding. The proposed damper dissipates energy through shear deformations of two layers of a highly damped rubber material which is adhered to steel plates as shown in Fig A unique characteristic of this damper design is incorporation of high-strength bolts which are capable of providing a prescribed precompression to the elastomer which is expected to enhance the elastomer to steel bond and also increase the effective damping of the rubber. Under small shear strain, elastomer material is commonly considered to behave in a viscoelastic manner however under earthquakes the elastomer is commonly expected to undergo shear deformations of % strain. Under these levels of strain, the elastomer behaves similar to a bi-linear hysteretic device with less rate dependence. 4.2 Elastomeric damper behavior The force-deformation behavior of the damper can be determined for design purposes based on mechanics principles and empirical relationships (Naeim and Kelly, 1999). Establishing this behavior is critical for design of the dampers. General forcedeformation behavior is shown in Fig Due to the complex constitutive behavior of Page 29

39 the material, a number of the mechanical properties are dependent on cyclic shear strain and are read from experimentally derived curves. As shown in Fig. 4.3, the effective shear modulus and damping ratio are shear stain dependent for different elastomer material properties. The effective stiffness, K d, is the stiffness at the design displacement and determined by the effective shear modulus, G eff, the area of the rubber pads, A, and the total thickness of the rubber pads, T, and is equal: (4.1) Thus, G eff can be obtained from curves similar to that shown in Figure 4.3 with shear strain corresponding to the design damper displacement. The second-slope stiffness, K p is defined as: (4.2) Where the characteristic strength, Q d, is the force-intercept at zero displacement and calculated to provide the same empirical effective damping, β d, such that: (4.3) Where β d is the damping ratio of the damper pads and is shear strain dependent. Highdamping rubber bearing is considered here, which has a damping ratio of 15% at 100% shear strain from Fig 4.3. The design damper deformation, δ, will be calculated based on the design rack drift. The yield displacement Y is commonly taken as approximately 10% of the elastomer thickness, or (4.4) Page 30

40 Note that the damping ratio and the effective stiffness here are strictly for the damper. 4.3 Damper implementation to rack The objective of the damper design is to limit rack drift to 1.5 % which is within elastic limits of the rack. For the 4-shelf rack used in previous sections, the maximum displacement at the top shelf is thus limited to 2.90 inches in terms of the total height of in. As noted previously, the purpose of the damper design is to reduce the absolute acceleration and total impulse to the merchandise without exceeding the elastic limits of the rack itself. Dampers are implemented at every panel and replace the diagonal steel member and are proportioned to achieve a uniform drift assuming an inverted triangular force distribution along the rack height. The shear force distribution factor at each floor is thus 1.0, 0.9, 0.7 and 0.4 from bottom to top. The target displacement of the damper is calculated from compatibility with the rack target drift and is defined as the local damper displacement δ as: (4.5) Where h is the height of the cross-aisle panel and θ is the angle between the diagonal bracing member and the horizontal. Fig. 4.4 shows one shelf panel deformations with damper implemented to illustrate the relationship between the target displacement and local target displacement. Total rack stiffness with the dampers is obtained by considering the bare frame rack stiffness and damper stiffness together similar to a dual braced and moment frame. 4.4 Damper Design Procedure Page 31

41 There are two approaches considered here to design the elastomeric dampers: (1) A simplified iterative design procedure described in ASCE 7-05 and (2) Iterative time history analysis. The first procedure is amenable for hand calculations but requires a series of iterations due to the shear strain deformation dependence of a number of input parameters. The time history procedure is more accurate but time consuming to iterate damper dimensions until a target rack drift is achieved. These two approaches are described in section and respectively. A sample calculation of the simplified iterative design procedure is provided in Appendix A Simplified Iterative Design Procedure The ASCE 7-05 specifies that the response of the structures with damping systems is reduced by spectral damping coefficient, B D, which is based on the effective damping coefficient, β T, of the mode of interest. Effective damping of the fundamental mode of the damped structure is based on the nonlinear force-displacement behavior of the rack with implemented dampers. This behavior is calculated by hand accounting for the elastic moment frame behavior of the bare rack without dampers and the nonlinear force deformation of the dampers. Similar to multi-story frames, lateral loads must be consistent with the distribution of inertia forces. For the uniform vertical distribution of merchandise and short period of the rack, the distribution can be assumed to be inverted triangular. For response in the fundamental mode, the effective damping at the target displacement is calculated based on an equivalent linear-viscous representation of the nonlinear system. The displacement of the equivalent system is calculated using a spectrum reduced for the equivalent damping. If the calculated displacement is the same or is within an acceptable tolerance with the initially assumed target drift, the solution has Page 32

42 converged. If not, damper properties should be modified and the calculation repeated until the calculated displacement converges to the assumed target drift. The effective damping for this system consists of two components: (1) inherent damping of structure at or just below yield, β I, and assumed equal to 2% for this bare steel frame structure; (2) hysteretic damping of the elastomeric dampers, β H. For the damping system design, the effective damper stiffness in the first crossaisle panel is used as the iterated parameter and all other dampers sized accordingly. The nonlinear pushover capacity of the generalized dynamic SDOF system is calculated. The effective stiffness and period of the damped system at the target displacement, u, can be calculated. The effective damping β T is calculated by adding the inherent damping β I and the damper hysteretic damping β H together, where the hysteretic damping is calculated from the energy dissipated per cycle from the elastomeric dampers as: (4.6) Where µ is the effective ductility demand of the rack, and q H is hysteresis loop adjustment factor, which is set equal to 1 here. From the effective damping, the spectral damping coefficient can be taken from ASCE 7-05 with the values shown in Table 4.1 The displacement of the structure is calculated with effective period, and the damping coefficient using Eq. 4.7 or 4.8: ( ) (4.7) Page 33

43 ( ) (4.8) Where S DS =the design spectral response acceleration parameter in the short period range S D1 =the design spectral response acceleration parameter at a period of 1 s Γ=mode participation factor T eff =effective period of the structure of the design displacement with added damping system as defined by Eq. 4.9: (4.9) If the calculated D D converges with the initially assumed target drift u, the design is complete. Otherwise damper effective stiffness is changed and the calculation repeated until the displacement converges. The spectral values used for the calculation here are the average value of the ten Los Angeles DBE ground motions used in Section 3, which S D1 is 0.69 g and S DS is 1 g. The thickness per pad of the rubber is determined by the target local displacement of the damper divided by the target maximum strain set by the designer, or: (4.10) The target maximum strain is set to be 100%, so the thickness per pad for the damping system could be determined. The resulting damper properties using the simplified iterative design process are shown in Table Time History Analysis Page 34

44 A more rigorous approach of damper design is performing a series of time history analyses of the damped rack. By changing the damper properties until the target rack drift is achieved. The analysis program used here is ANSYS. The rack is modeled using elastic beam elements as described in section 3.2. The only difference to the model is the elastomeric damper with force-deformation response shown in figure and is simulated using a nonlinear beam element (BEAM188). The merchandise flexibility is not considered here to keep consistent with the simplified iterative design procedure and focus on damper design. The Los Angeles DBE ground motions described in Section 3 are input into the program, which has the same spectral values used in simplified iterative design process. The median value of the maximum displacement for the ten ground motions is compared to the target displacement to determine if the damper design objective is satisfied. Using time history analysis for design results in a set of dampers with properties shown in Table 4.3 to achieve the target drift of 1.5 % at the top shelf. 4.5 Results and discussion As seen in Table 4.2 and 4.3, the simplified iterative design procedure results in damper sizes significantly smaller compared with the results of time history analysis. The iterative design process is a simplified analysis and design approach that replaces the nonlinear system by an equivalent linear-viscous system. The procedure represents an approximation that does not appear to be valid for the damped system considered here. The baseline rack with the steel diagonal member was first analyzed for comparison and has calculated response using time history analysis shown in Fig Page 35

45 The median value for the maximum displacement of ten ground motions is 1.2 inches at the top shelf. The median value for the maximum acceleration of ten ground motions is 1.6 g and the median value plus the standard deviation is 2.5 g. After replacing the diagonal member with the dampers, the response of rack has been improved in terms of maximum absolute acceleration however drift is increased. Fig. 4.6 shows the improved response of the rack. Without exceeding the 1.5% drift limit (2.90 inches) at the top shelf, the median value for maximum acceleration reduced to 1.1g and the median value plus the standard deviation reduces significantly to 1.6g. Total shelf impulse could be used as a measure of merchandise damage and is calculated by the integration of absolute acceleration times the mass for each shelf over duration, or: (4.11) Furthermore, a normalized impulse ratio is used here to compare the baseline and damped rack for protection of merchandise. The normalized impulse is defined as the impulse for damped rack divided by the impulse for rigid rack. Fig. 4.7 shows the median normalized impulse. The minimum normalized impulse is 0.65 and occurs on the third shelf. A much smaller reduction in impulse is observed in general over the lower shelves however note that the peak acceleration is also less on the lower shelves and merchandise shedding less likely and risky from the lower shelves. Finally, the elastomeric damper is considered effective at reducing merchandise damage for the analyses and assumptions considered however the simplified iteration design procedure is not effective for design. Page 36

46 Figure 4.1 Sketch of Proposed Elastomeric Damper Page 37

47 Figure 4.2 Force-deformation curve for elastomeric damper Page 38

48 Figure 4.3 Shear Modulus and Damping Ratio Strain Dependence Figure 4.4 Sketch of Rack with Damper Page 39

49 (a) (b) Figure 4.5 Response of Baseline Rack. (a) Maximum displacement for baseline rack; (b) Maximum acceleration for baseline rack Page 40

50 (a) (b) Figure 4.6 Response of Damped Rack: (a) Maximum displacement for damped rack; (b) Maximum acceleration for damped rack Page 41

51 Figure 4.7 Normalized Impulse Page 42

52 Table 4.1 Values of Spectral Damping Coefficient (Adapted From ASCE 7-05) Effective Damping β T Damping coefficient B D Table 4.2 Resulting Damper Properties from Simplified Iterative Design Procedure Shelf No. K d (kip/in) n lay t r (in) A r (in 2 ) Q (kip) Page 43

53 Table 4.3 Resulting Damper Properties from Time History Analysis Shelf No. K d (kip/in) n lay t r (in) A r (in 2 ) Q (kip) Page 44

54 Section 5 Impact of Merchandise Mass Configuration On Seismic Response of Damped Racks 5.1 General The ability to quickly and easily reconfigure pallet merchandise by forklifts makes industrial racks popular in large warehouses. However this significant variation in mass results in challenges for damping system design. Unlike conventional buildings, the seismic weight of the rack is highly variable due to the large portion of the weight from the merchandise (likely 90% or more). Warehouse employees can load the merchandise on different rack shelves preferably without load configuration constraints. Rated load limits for the shelves must still be respected. In seismic design, the total mass and mass configuration significantly affects design through variation in inertia mass and dynamic characteristics. Therefore, this section seeks to consider the impact of mass variation on the design of damped racks. In this section, analysis is performed on the 4-shelf Heavyduty industrial rack described in Section 3 with varying merchandise weights (1kip, 3kip, 5kip) and merchandise configurations (i.e. fully loaded, top shelf only, etc.) and using the final damper design properties from Section Parameters and analysis input The weight of merchandise is varied from 1 kip to 5 kip, which is consistent with the rack considered and warehouse operation. It is assumed that only one weight condition (1kip, 3 kip, or 5 kip) would load the rack at one time. Five mass configurations are considered: fully loaded, top shelf loaded, top two shelves loaded, bottom shelf loaded, and bottom two shelves loaded as shown in Fig While other

55 mass configurations are possible, it is expected that these configurations would bound the racks critical response. The total number of the analysis cases considered is 15 cases. For each analysis case, the ten LA DBE ground motions described in section 3 are input into the analysis here. Due to the large amount of calculations and post-processing with the analysis results, the parametric analyses are performed using the ANSYS parametric design language (APDL) to perform the analyses. The ANSYS input files are divided into five different files: Run Control, Model Input, Generate Run, Post-process, and Modal. The function of each input file is described in the list below. Run Control: Calls all the other files in a certain sequence Model Input: Defines all of the model input data to perform dynamic analysis. Includes the merchandise weight and configuration parameters. Generate Run: Defines the element types and material properties. Builds the model using the input data from the Model Input file. Initiates both the modal and transient analysis. Modal analysis is performed for each mass configuration. Time history analysis is performed by applying the ground motion acceleration to the base of the rack. Post-process: Extract the solution of time history analyses. Modal: Defines the input to perform modal analysis. A flowchart is shown in Fig. 5.2 to illustrate the programing command structure. The solution data is extracted for every mass configurations and ground motions. MATLAB

56 is then used to perform further post-processing on the analyses output and calculate response quantities of interest. 5.3 Results Results of the parametric analysis are compared between the baseline rack and damped rack. Note that the merchandise flexibility discussed in section 3 has not been added in parametric analysis Results with 5 kip merchandise The peak shelf acceleration is compared between the baseline rack and the damped rack in Fig. 5.3 for 5 kip merchandise. From the comparison, we can see that the damping system is effective to reduce the acceleration of the rack in mass configuration 1, 4 and 5, which are fully loaded, top shelf loaded, and top two shelves loaded. Especially for case of the top two shelves loaded, the maximum acceleration of the rack, which happened at the top shelf, is reduce about 41 %. For the fully loaded case, the maximum acceleration is reduced about 31%, and for the case of loaded only on top shelf, it is reduced about 35 %. The damping system has the opposite effect for mass configuration 2, which is the case of loading only on the bottom shelf. The maximum acceleration increases from 0.7 g to 1 g. The reason for acceleration increasing is that the damper increases the flexibility of the rack, however does not generate inertia forces to activate the dampers. The first mode frequency of the baseline rack with these mass configurations is quite large and likely out of the strong energy content of the ground motions. The dampers increase the flexibility of the frame and for these mass configurations likely move the response into a frequency range with larger ground motion

57 energy content. Similar response is observed in mass configuration 2 with a reduced frequency and dampers in the 3 rd and 4 th shelf are not activated. Modal properties for bare rack and damped rack are shown in Table 5.1 and Table 5.2. The median value for the Fourier transform of ten LA DBE motions is shown in Fig The median value for maximum peak acceleration doesn t have a significant change, but the standard deviation is reduced for the damped rack Results with 3 kip merchandise The weight of the merchandise also influences the performance of the rack and dampers. Using damper properties developed for 5 kip merchandise, the rack performance from the parametric analysis with 3 kip merchandise is shown in Fig Due to the reduced total weight, damper activation does not occur but simply increases the rack flexibility compared to the baseline rack. Mass condition 1 and 5 are the two worst conditions considering the peak acceleration and damping system works good to reduce the peak acceleration. For mass condition 2 and 3, peak acceleration is increased, due to the increased flexibility due to the inactivated damping system. For mass configuration 4, peak acceleration is not changed much. After implemented by dampers, mass condition 3 has the biggest peak acceleration, which reaches 1.5 g from 1.25 g for baseline rack. For 3 kip merchandise, damping system does not work as good as in 5 kip merchandise cases Results with 1 kip Merchandise Fig. 5.6 shows the peak acceleration comparison between baseline rack and damped rack. From the comparison, the peak accelerations for all mass configurations are

58 all increased for the damped case. The reason for this phenomenon is that most dampers are not activated due to the huge reduction of the total weight. Before implementing the damping system to the rack, the maximum peak acceleration is 1.25 g occurring at mass configuration 1. The elastic behavior of the damping system increases the rack flexibility for all mass configurations, and maximum peak acceleration reaches 1.55 g at mass configuration 1 and 5. The displacement for all mass configurations at three weight conditions never exceeds 1.5 % drift, which was the target and design drift. The displacements from both baseline rack and damped are compared in Fig. 5.7, 5.8 and 5.9. As defined in section 4, the normalized impulse is used as a measure of damper performance on merchandise shedding. When the normalized impulse is less than one, the damping system decreases the cumulative impulse imparted to the merchandise compared to the baseline rack. The results shown in Fig. 5.10, 5.11 and 5.12 are consistent with the peak acceleration comparison discussed above.

59 Mass Configuration No. Figure Figure 5.1 Mass Configuration Conditions

60 Figure 5.2 Flowchart for ANSYS Program Input File

61 Mass Configt. Bare Rack Damped Rack 1 2

62 3 4

63 5 Figure 5.3 Peak Acceleration Comparison for 5 kip Merchandise Figure 5.4 Median Value for Fourier Transform of DBE Motions

64 Mass Configt. Bare Rack Damped Rack 1 2

65 3 4

66 5 Figure 5.5 Peak Acceleration Comparison for 3 kip Merchandise Mass Configt Bare Rack Damped Rack 1

67 2 3

68 4 5 Figure 5.6 Peak Acceleration Comparison for 1 kip Merchandise

69 Mass Configt Rigid Rack Damped Rack 1 2

70 3 4

71 5 Figure 5.7 Peak Displacement Comparison for 5 kip Merchandise Mass Configt Bare Rack Damped Rack 1

72 2 3

73 4 5 Figure 5.8 Peak Displacement Comparison for 3 kip Merchandise

74 Mass Configt Bare Rack Damped Rack 1 2

75 3 4

76 5 Figure 5.9 Peak Displacement Comparison for 1 kip Merchandise Mass Configuration Normalized Impulse 1

77 2 3

78 4 5 Figure 5.10 Normalized Impulse for 5 kip Merchandise

79 Mass Configuration Normalized Impulse 1 2

80 3 4

81 5 Figure 5.11 Normalized Impulse for 3 kip Merchandise Mass Configuration Normalized Impulse 1

82 2 3

83 4 5 Figure 5.12 Normalized Impulse for 1 kip Merchandise

84 Table 5.1 Modal Properties of Baseline Rack Weight per shelf Mass configuration Frequency 1 (Hz) Frequency 2 (Hz) Frequency 3 (Hz) Frequency 4 (Hz) kip kip kip

85 Table 5.2 Modal Properties of Damped Rack Weight per shelf Mass configuration Frequency 1 (Hz) Frequency 2 (Hz) Frequency 3 (Hz) Frequency 4 (Hz) kip kip kip

86 Section 6 Conclusions and Future Research This research investigated the seismic behavior of steel storage racks and its supported merchandise. The effect of merchandise flexibility is investigated using finite element models. Linear viscous model and linear viscous with sliding model are used to predict the merchandise behavior with varying merchandise frequencies. The linear viscous with sliding model is believed to more accurately reflect merchandise behavior compared to existing practice which often only considers rigid merchandise with 10% equivalent damping of the merchandise. However, a more sophisticated model should be considered to capture the actual nonlinear hysteretic merchandise behavior arising from the merchandise package-to-package sliding, possible rocking of slender merchandise and effect of the shrink wrap. Shaking table testing is likely required in future research to evaluate behavior to incorporate in analysis. The research also proposed an elastomeric damper to improve the cross-aisle rack performance during earthquakes. Without exceeding rack elastic limits, the dampers are capable of dissipating earthquake energy, decrease peak acceleration and cumulative impulse to reduce likelihood of merchandise shedding. A parametric analysis of a damper equipped steel storage rack was performed to assess the impact of mass variation. The damper effectiveness is reduced for mass configuration for which it was not designed, however in terms of cumulative impulse the damper was effective for fully loaded or upper shelf loaded mass configurations. The merchandise flexibility was not considered in the damper design nor in the parametric analysis, but should be considered in future work. Furthermore, a prototype damper should be designed and tested to evaluate its performance and damper design should consider both seismic and operational performance objectives.

87 Appendix

88 DATE 07 December 2012 PROJECT Seismic Evaluation and Performance Enhancement of Industrial Storage Racks BY Yuan Gao SUBJECT Appendix A: Damper Design for Steel Storage Rack Number of Shelfs n 4 i 12 n Cross-Aisle Width b 42in Shelf Weight W 2.5kip w si W Shelf Heights and Damper Orientation Angles h i 40in 44in 44in 48in θ atan i h i b θ deg Target Drift Drift 1.5% Rack Height H 193.5in Target Top Shelf Rack Displacement Maximum Local Displacement Rack "Bare Frame" Effective Stiffness (Moment Frame without dampers) Shear Force Resisted by Bare Frame at Target Displacement u max DriftH δ Drifth i i K M V M cosθ i kip in K M u max 2.902in δ 0.458kip in Total Rack Weight W T Wn 10kip Page A-1

89 Damper Dimensions Effective Damper Stiffness -Iterated Parameter Shelf Shear Distribution Factor K damp1 C vi kip in Effective stiffness of elastomer K di K damp1 C vi Effective damping of elastomer β d 0.15 Target Strain γ max 100% K d kip in Page A-2

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