This paper describes the development of over strength factor and ductility for high level storage system called rack clad building (RCB) system. Unlike the steel storage structures which are common in superstores, these structures are built outside and the outer most frame is used for supporting cladding. As these structures have frequent interaction with people, they pose a great threat towards public safety during any windstorm or earthquake event. Several research works have been done on steel storage rack structures but not on RCB systems and currently no seismic design guideline exists for designing RCB structures. The over strength factor is an important parameter required for calculating design seismic force for a type of structure. The RCB structures generally use teardrop connectors at the beam column joint. These connection systems have semi rigid behavior and shows very different hysteresis behavior compared to a conventional joint. For simulating this behavior in finite element model, nonlinear behavior has been introduced using moment rotation data from a previously done laboratory experiment. Using this experimental data a set of three dimensional models have been generated and several nonlinear static analysis have been performed to determine the over strength factor and ductility with varying heights and bay lengths.
Steel storage racks in supermarket, hardware stores and handy man stores have become very common in Canada. These places are visited by people every day. Due to high proximity of these structures to people, these structures pose a great threat towards public safety. During earthquake these structures if not properly designed to withstand the inertia force can collapse and injure people. Until now very little effort has been put into the Seismic design of these structures.
As these structures are an integral part of everydays public activity the importance of a proper design guideline for these structures is very high. As rack structures are generally located inside of a larger structures wind forces were generally ignored and there was reluctance in considering seismic loading also. The National Building Code of Canada (NBCC, 2005) recognizes the seismic risk of rack storage systems and recommends that seismic provisions be provided while designing these types of structures. FEMA 460, 2005 provides seismic guidelines for designing these storage structures. However RCB is a new type of steel storage structure which is generally installed outside of a building and the sides and roof of the structure is used as the wall and roof of the structure. These types of structures are called rack clad building systems. This idea of using the Rack structures peripheral frame as a wall reduces the need for a larger storage structure for the protection of the racks which significantly reduces cost. This type of structure is getting popular because of low cost and rapid rate of construction. Rack clad building has to withstand the full force of earthquake or wind. For these structures wind forces cannot be ignored and they have to be properly designed against lateral forces as they pose higher risk towards public safety compared to conventional steel storage racks. There are some guidelines in practice for designing steel storage rack system but there are no similar standard in place for designing RCB system against seismic and wind loading. This research is very important as it is going to be a great help for structural designers and construction industry of Canada.
As the number of superstore and warehouses getting increased and public access to them also becoming frequent, safety is becoming a major concern. Safety and security of the citizens of a country is very important and this is also the primary objective of this analysis. The objective of the proposed RCB system analysis is to develop a standard design guideline for the structural design practitioners, contractors and the construction industry. To develop mathematical model several finite element models have been developed. From the finite element model the over strength, force reduction factor, natural time period and ductility have been calculated which are some very important parameters of seismic design. These parameters will be used for calculating seismic base shear for future RCB frame designs and also help in member size proportioning. The expected design performance level of this structure will be used as collapse prevention against maximum considered earthquake.
As the RCB frame comes with elements containing holes at regular interval, the frame elements lose stiffness. So the stiffness of the frame elements have been reduced in the model to take account of the preinstalled holes in the frames. A simple model of a frame element has been generated in FEM software using shell elements to calculate the stiffness with holes and without holes and thus the relative stiffness have been calculated. Using the relative stiffness, several RCB frame models have been produced using line elements and analyzed using computer simulation. The analysis has been carried out using nonlinear static procedure. The results produced from the FEM model was checked against existing test results from the published literature. The beam column joint behavior strength was simulated using the FEM model and checked against the previous experimental values from literature. A hysteresis load deflection relationship curve was produced for result verification and further studies.
This research was carried out to produce a design guideline which is going to enable the design practitioners design the RCB frames based on a solid ground. The standard design methodology for RCB system will enable the designers to achieve life safety performance level against design basis earthquake with minimum time and cost implication. With desired level of performance level these structures will be safer in public interaction during any severe wind load or seismic event. Also by achieving the desired level of performance we will be able to reduce the risk of overdesign and as well as cost.
The first step of the guideline is to calculate over strength and ductility of RCB systems. The second step is the calculation of the natural time period and force reduction factor. The following figure shows these factors and how their relationships.
: Over strength, force reduction factor and ductility
Generally racking systems consists cold-rolled steel sections. The frame system consists of upright posts with holes at regular interval for connecting beams on one side and braces on the other side. They rely on portal frame action in the down-aisle direction and frame action in the cross-aisle direction to resist lateral loads. The story height can vary depending on the stock required to be stored [7]. The RCB structure under consideration has a story height of 1600mm. A typical arrangement of a racking system is given in the following figure.
Beam
Diagonal
Pallet support bar
Guard Corner
Frame
Drum Chock
Plywood clipboard
Galvanized steel shelf panel
Base plate
: Basic components
The frame system used in the down-aisle direction of steel storage racks which uses teardrop beam to upright connection, although appear similar to steel moment-resisting frames defined in the 2003 NEHRP commended Provisions FEMA 2004, behave very differently than the connection system commonly used in buildings. Generally moment resisting connections in buildings are designed to cause inelastic deformations in the beams away from the beam column joint, but this inelastic behavior occurs directly in the beam-to-column connections in RCB structures. [6]
In rack industry, the columns are called uprights. Although the system exhibits highly nonlinear behavior up to very large relative rotations between the beams and column, it remains almost elastic in the sense that the behavior does not cause permanent deformation in the beams and uprights joint. The inelastic rotation capacity of beam-to-upright connections is significantly high and for the connection under consideration has exceeded 0.06 radians and some researcher [6] found out that it can be as high as 0.2 radians. In general building moment-resisting connections have inelastic rotation capacity in the range of 0.04 radians for special moment-frame systems. However, the rotational demands on rack moment resisting connections are much greater than that that of buildings because of the relatively short height of rack structures for comparable fundamental time periods. Therefore, the high rotational capacity of beam-to upright moment-resisting connections is necessary in order for the structure to withstand strong earthquake ground motions. [6]
The performance expectations and design intentions of the 2003 NEHRP Recommended Provisions: “The design earthquake ground motions specified herein could result in both structural and nonstructural damage. For most structures designed and constructed to these provisions and constructed according to these provisions, structural damage from design earthquake ground motion will be repairable although perhaps not economically so. The actual ability to accomplish these goals depends upon a number of factors including the structural framing type configuration, materials, and as-build details of construction for ground motions larger than the design levels; the intent of these Provisions is that there is a low likelihood of structural collapse.” [6]
The performance expectations can be stated for the structural design of steel storage racks as follows; the rack structures have a low probability of collapse when subjected to the Maximum Considered Earthquake or MCE ground motions. Storage racks are currently designed using equivalent lateral force procedures that use reduced Design Basis Earthquake DBE ground motions. Collapse prevention at the MCE ground motions is taken to be 1.5 times larger than the DBE ground motions, is not completely based on solid mathematical ground and only based on past experience. As the inelastic behaviors of rack structural members and connections are significantly different from building structural systems, it would be desirable that in addition to the equivalent DBE lateral force design, a check of collapse prevention at the MCE be explicitly made [6].
In the following figure a side view of a RCB structure is shown which shows the use of braces in the down isle direction
: Side view of a RCB with braces
In the subsequent figures some important components of RCB are shown
: Spacer beams connecting two racks
: Typical upright post detail
: Typical upright post to beam connection [4]
The posts are made of 1.8mm, 2mm, 2.6mm and 3mm thick steel. The shape of the section is shown the figure above. Beams are generally rectangular box section with thickness varying from 1.5mm and 1.8mm. The beam depth ranges from 72mm to 150mm. The width is generally 50 mm.
Braces are made of ‘C’ sections with typically two types of sections 45mmX30mmX2mm and 60mmX30mmX4mm. These braces are generally connected with the upright with a single nut and a bolt.
For computer modeling of the actual beam column joints moment rotation data were used from [1]. The moment rotation behavior of beam column connection is shown below.
: Double cantilever test setup
The experimental moment rotation plots for different combinations are shown below. From these moment rotation graphs the one suitable for the project under consideration was selected,
: Moment rotation plots for varying column thickness and beam depths for a 4 lipped connector
which is the curve corresponding to 2.5UT-4L-100BD. An idealized curve was plotted with secant stiffness and strain hardening slope. The idealized curve is shown below.
: Experimental and Idealized moment rotation curve
Several analytical models are generated in finite element modeling software to calculate section properties and to simulate the beam-to-upright joint nonlinear moment rotation behavior.
This calculation was carried out to eliminate the need for modeling the post section with holes for the full structural model. Modeling with holes requires shell element based modeling for the column section, which is time consuming and impractical from analysis point of view. The approximate section properties of the post section were calculated partially using computer model and hand calculation. And a relationship has been developed between the section with and without hole. . The calculated properties are moment of inertia, shear area, average cross sectional area and torsional constant. Below is a FE post model with holes
: A cross section and a finite element model of an upright with hole
Some calculated section property is shown in the table below
Moment of Inertia about 2 axis
90.35%
Moment of Inertia about 3 axis
86.11%
Average cross sectional area
95.60%
Torsional Constant
98.16%
Shear area in 2 direction
84.39%
Shear area in 3 direction
89.22%
: Relative stiffness with respect to section without holes
In order to take account of the non linear moment rotation behavior into account, a non linear hinge has been modeled in the FE software. The hinge model was tested using a beam column joint. The hinge was inserted at the end of the beam and a non linear static load was monotonically applied until the hinge reached its ultimate capacity. The output from the finite element model is shown below.
: Beam column joint model
: Simulated moment rotation behaviour in the model
The frames were created using FEM software fully capable of dealing with nonlinear material property and geometrical nonlinearity. The beam column joint rotation property is simulated using nonlinear plastic hinges and they were assigned at the beam column joint. The steel plastic hinge behavior is used in the critical length of columns to form plastic hinges after yield moment is reached. Axial nonlinearity (Axial P hinge) is used for braces so that they take considerably lower load in compression. This nonlinear object can automatically calculate the buckling load and can make the braces ineffective after the buckling load has reached. The pushover analysis that is used here is nonlinear static in nature. The load is applied in a specified direction using a accelaration in that direction and subsequent roof top displacement and base shear is monitored until the structure reaches its ultimate capacity. With the monitored data the following curves are generated. Some pushover curves were genereated with self weight only others are with self weight plus content weight. Content weight is 2000Kg per tray which equates to 4.35KN/m for the beams.
Fig 13: Two dimensional analysis model for down isle direction
Fig 14: Two dimensional analysis model for cross isle direction
Fig 15: Three dimensional analysis model of a single rack in down isle direction (without braces)
Fig 16: Three dimensional braced model with 2X4 bays
Single frame pushover analysis in downisle and cross isle direction. For these analysis the content weight was assumed zero.
Fig 17: Pushover curve for down isle direction (self weight only)
The calculated overstrength factor for the above mentioned frame is 2.5 and ductility is 2.9
Fig 18: Pushover curve for down isle direction (1/3rd content weight)
The calculated overstrength factor for the above mentioned frame is 2.0 and ductility is 2.6
Fig 19: Pushover curve for down isle direction (2/3rd content weight)
The calculated overstrength factor for the above mentioned frame is 4.4 and ductility is 2.8
Fig 20: Pushover curve for down isle direction (full content weight)
The overstrength factor could not be calculated as the beam to upright connections got completely plastisized due to content load alone but the ductility facctor was calculatead to be 2.5
Fig 21: Pushover curve for cross isle direction (Self weight only)
Overstrength factor and ductility for the above mentioned frame is 1.48 and 1 respectively.
Fig 22: Pushover curve of a single rack in down isle direction (Self weight only)
Overstrength factor and ductility for the above mentioned frame is 1.3 and 1.9 respectively.
Fig 24: Pushover curve of a 2X4 unbraced 3d model in down isle direction (Self weight )
Overstrength factor and ductility in cross isle direction for the above mentioned frame is 2.5 and 1.45 respectively.
Fig 25: Pushover curve of a 2X4 fully braced 3d model in down isle direction (Self weight )
Overstrength factor and ductility for the above mentioned frame is 1.9 and 1.0 respectively.
Fig 24: Pushover curve of a 2X4 fully braced 3d model in cross isle direction (Self weight )
Overstrength factor and ductility for the above mentioned frame is 1.3 and 1.33 respectively.
Down isle
2D unbraced
Self weight (SW)
2.5
2.9
Down isle
2D unbraced
SW+1/3rd content
2
2.6
Down isle
2D unbraced
SW+2/3rd content
4.4
2.8
Down isle
2D unbraced
SW+full content
Indeterminate
2.5
Down isle
2D unbraced
SW
1.3
1.9
Cross isle
2D unbraced
SW
1.48
1
Table 3: Overstrength and ductiliity for various types of configuration
From the above mentioned study done for RCB frames it is found out that the overstrength factor is a function of the content weight in the down isle direction and it varies from 1.3 to 4.4, on the other hand the ductility has a range from 1 to 2.9. For full content weight all the beam column joint became plastisized only due to gravity load and hence the overstrength factor could not be calculated. So it is highly recommended that the racks should not be loaded to their full capacity in any situation.
For cross isle direction the frame behaviour is totally governed by the performance of the braces. The buckling failure of the braces are the critical events during a pushover analysis. It was observed that the ductility is only on in this direction which implies that the frame is almost elastic in the cross isle direction upto failure. And the calculated overstrength is 1.48 in cross isle direction.
The most important parameter is the overstrength factor of the fully braced 3d model. It was found out that the overstrength factor in the cross isle direction is 1.3 and ductility is 1.33 and in down isle direction they are 1.9 and 1.0 respectively. The ductility 1.0 in the down isle direction very different from the single frame ductility which was 2.9. It is because the braces are present in the full 3D model. Which induces a fully linear base shear vs roof displacement response to the structure. Due to the braces the structure is unable to freely move laterally and the displacement we get is actually the axial elongation of the braces. On the other hand the same structure without braces shows 23 times more dformation in the down isle direction.
A full scale model will be generated for a RCB system and Incremental dynamic analysis will be carried out to calculate the force reduction factor. For these studies some ground motion data will be selected to best represent the seismicity of this region. For this further study the following nonlinear behavior is simulated in the model to take account of the pinched hysteresis with very low residual deformation observed during the experiment.
As the nonlinear hinge modeled in the FE software cannot take reverse cyclic loading, a Multi linear plastic link model was generated using elastic-plastic property and pivot hysteresis [3] behavior. The pivot hysteresis behavior best represents the moment rotation behavior of the RCB frames beam column joint which is semi rigid in nature. This model is able simulate hysteresis which has very low residual deformation which makes it unique among other hysteresis methods available. This plastic link will be used for incremental dynamic analysis in further studies.
Fig 20: Pivot hysteresis of RCB beam column joint
Fig 21: Simulated hysteresis comparison with experimental plot (Black line represents simulated reults)
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