Ultra-light gauge steel storage rack frames. Part 1: Experimental investigations

Journal of Constructional Steel Research 124 (2016) 57–76

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Journal of Constructional Steel Research

Ultra-light gauge steel storage rack frames. Part 1: Experimental investigations A.N. Trouncer ⁎, K.J.R. Rasmussen School of Civil Engineering, University of Sydney, NSW 2006, Australia

a r t i c l e

i n f o

Article history: Received 13 January 2016 Received in revised form 16 May 2016 Accepted 17 May 2016 Available online xxxx Keywords: Steel storage rack frames Interactive buckling Geometric imperfections

a b s t r a c t This paper presents an experimental investigation into locally unstable ultra-light-gauge steel storage rack frames that are prone to flexural-torsional buckling. The aim of the research was to understand how local instabilities and interactive buckling affect the strength of ultra-light gauge frames and to create reliable data through a controlled experimental investigation. A total of twelve full scale tests were conducted in the Civil Engineering Structures Laboratory at the University of Sydney. Prior to testing, the geometric imperfections of each member were measured, as were the material properties of the cold-rolled sections and the virgin steel from which the sections were formed. The cross-sectional deformations, ultimate loads and observations regarding failure modes were accurately captured and documented. The tests were also successful in capturing the post-ultimate response of the frames as well as the rotational stiffness of the beam-to-upright connections. Results from nominally identical tests were in good agreement. The tests provide comprehensive data for assessing the effects of interactive buckling and the extent to which cross-sectional deformations amplify the second-order deformations in locally unstable storage rack frames. Crown Copyright © 2016 Published by Elsevier Ltd. All rights reserved.

1. Introduction Thin-walled cold-formed steel sections are increasingly being used as structural members in light-gauge steel structures due to their high strength-to-weight ratio and efficient use of material. However, due to their reduced wall thickness, thin-walled cold-formed steel sections are prone to local and distortional buckling as well as overall buckling. It is well understood that these cross-sectional deformations reduce the rigidity of the section, and hence amplify sway deflections and cause a redistribution of the internal forces in the structural frame. Unless accounted for, the internal bending moments are underestimated and the structural design may become inadequate. This paper forms the first part of a research program undertaken at the University of Sydney investigating the effects of additional second order moments in unbraced steel frames caused by cross-sectional buckling and the extent to which these need to be accounted for in design. The aim of this paper is to present the results from the full scale tests on ultra-light gauge steel storage racks conducted. Based on the results provided, further investigations into the effects of these additional second order moments are described in a companion paper [1]. Although promising research has been completed in extending the scope of geometric and material nonlinear (GMNIA or “advanced”) ⁎ Corresponding author.

http://dx.doi.org/10.1016/j.jcsr.2016.05.014 0143-974X/Crown Copyright © 2016 Published by Elsevier Ltd. All rights reserved.

analysis to the direct design of steel frames consisting of non-compact sections, there is an information gap in relation to large-scale physical testing of steel frames consisting of non-compact members. While a significant amount of research has been conducted for steel frames comprised of cold-formed compact sections [2–5], and the idealization of joints using advanced analysis [5–8], only a few researchers [9–11] have completed large scale tests of steel frames consisting of non-compact members. If methodologies for the design by advanced analysis are to extend to include non-compact members, it is imperative that additional accurate full scale testing is completed on steel frames consisting of noncompact members, in order to provide data for model verification purposes. A secondary aim of the paper is to make such experimental data on the behaviour and failure modes of locally unstable steel frames available. A total of 12 full scale tests were completed in the Civil Engineering Structures Laboratory at the University of Sydney. While the overall system failure was recorded, emphasis was also placed on capturing the local instabilities in the uprights during loading. Hence, deformations in the uprights during testing were captured, and observations regarding local failure modes were documented. The relative joint rotation between the pallet beam and upright was also measured. In addition, the geometric imperfections of each member were measured before testing, as were the material properties of sections and the virgin steel from which the sections were formed. The experimental set-up, the observed failure

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Fig. 1. Test Setup - Frame orientation, bracing dimensions and transducer locations.

modes, the recorded ultimate strengths and the load-deflection responses of the frames. 2. Test frames In order to accurately obtain imperfection data for the storage rack sections, it was first necessary to assemble the uprights in the upright frames prior to the imperfection measurement. To construct the upright frames, two nominally 5100 mm long storage rack sections were connected with eight 40 × 26 × 8 mm lipped channel bracing members using M8.8 zinc coated bolts. The first bracing member connected the members horizontally, 150 mm from the base, as shown in Fig. 1. A

spacer ensured that the brace member was pressed flush against the flange of the upright at the first bolt hole. Eight other bracing members then ran diagonally up the frame, 600 mm vertically apart, crisscrossing until the final horizontal member was connected 150 mm from the top. The uprights used in the frame tests were nominally 5100 mm long and 1.0 mm thick. Two types of cross-section were investigated, viz. the 90 mm wide rear-flange section (90RF1.0) and 90 mm standard upright section (90SD1.0). Both types of section were cold-rolled from G550 galvanised strip to Australian Standard AS1397 [12] with a guaranteed minimum proof stress of 550 MPa. Details of the nominal cross-section dimensions, measured thickness and measured material properties are provided in the references [13,14].

Fig. 2. Locations of laser lines for RF and SD sections.

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full results for the imperfection measurements may be found in the reference [13].

Table 1 Geometric properties of beam, diagonal and upright sections. Property

t (mm) A (mm2) Anet-min (mm2) Ix (mm4) Iy (mm4) Iw (mm6) J (mm4) Xo (mm) Yo (mm)

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Section 90SD1.0

90RF1.0

110 × 52 mm 155 × 52 mm 40 × 26 × 8 mm closed box closed box lipped channel beam beam brace

1.0 230.3 202.6

1.0 254.8 226.7

1.6 550.8 550.8

1.6 711.1 711.1

1.6 111.8 111.8

2.67 × 105 1.27 × 105 3.28 × 108 84.17 −53.7 0

3.02 × 105 1.85 × 105 3.77 × 108 93.23 −62.75 0

8.96 × 105 4.34 × 104 – – 0 0

2.15 × 106 4.34 × 104 – – 0 0

2.864 × 104 5.472 × 103 1.636 × 106 89.07 −14.35 0

In total, 14 and 10 upright frames (each consisting of two uprights connected by diagonal bracing) were constructed from the 90SD1.0 and 90RF1.0 sections, respectively. Each upright was named using a standard classification, e.g. SD-7-1 describes the first upright in 90SD1.0 upright frame number seven, while SD-7-2 describes the second upright in 90SD1.0 upright frame number seven. While each member was nominally 5100 mm in length, 1–3 mm variations in length were observed and recorded prior to testing [13]. 2.1. Imperfection measurement In order to characterise the imperfections present in the test specimens and to gain an appreciation of their shape and magnitude longitudinally, measurements were taken on the edges and centre-lines of component plates at closely spaced points along the member. To achieve this, a laser rig was constructed which measured imperfections along eight lines parallel to the longitudinal axis for each of the RF and SD uprights. For both types of section, readings were taken on the flat parts of sections at least 3 mm from corners and perforations. Diagrams detailing the location and number of each of the laser lines may be seen in Fig. 2 for both the RF and SD sections. Further details about the laser imperfection measurement set-up can be found in [13,14]. Before each measurement started, the upright frame was placed horizontally, supported at the ends and its verticality checked using a level. For each of the eight laser lines, measurements then began 5 mm from the end of the upper upright and the results were taken 1 mm apart until reaching the other end. Two runs of the laser rig along the full length of the upright were conducted to enable spurious readings to be identified and eliminated. The measurements from the two runs were then averaged. Photographs of the laser rig set-up and

2.2. Frame preparation In the construction of the test frames, great care was taken to ensure that no additional imperfections were introduced during erection. Each frame consisted of two storage rack upright frames connected by four pairs of evenly spaced 2700 mm long pallet beams with a wall thickness of 1.6 mm. The centre of beam heights for each level were evenly spaced 1200 mm apart, starting from the base, as shown in Fig. 1. Two different beam depths of 110 mm and 155 mm were used during testing; however the same spacing between beam levels was used for each of the frames. Table 1 summaries the geometric properties for the bracing, beam and upright sections used during testing. As each of the uprights had already been measured and marked for imperfections, frames consisted of uprights in sequential order. For example, the first SD test frame consisted of the upright frames SD-1 and SD-2, which included upright members SD-1-1, SD-1-2, SD-2-1 and SD-2-2. In the following, the members will be referred to sequentially for each test, e.g. member 1 refers to SD-1-1 while member 4 refers to SD-2-2, as shown in Fig. 3. In total, five SD (SD1, SD-2…SD-5) and seven RF test frames (RF-1, RF-2…RF-7) were constructed, which consisted of totals of 20 SD (SD-1-1, SD-1-2, SD-2-1, SD-2-2…SD-10-1, SD-10-2) and 28 RF (RF-1-1, RF-1-2, RF2-1, RF-2-2…RF-14-1, RF-14-2) upright members respectively. Fig. 4(a) and (b) display the sign conventions used for the top and bottom rotations, lateral overall displacements (u,v) and local displacements of the web, flange and rear flange. All diagrams refer to either the second or fourth upright members as these were the upright members where the majority of transducers were housed. Similar to the imperfection measurements, positive local displacements were always taken as being in the direction away from the centroid of the cross-section. Fig. 4(a) displays the definitions used for different parts of the cross-section as well as the positive x-axis and y-axis sign conventions used when describing displacements of the cross-section. 3. Design of test rig The test rig was designed to ensure that well-defined idealised boundary and loading conditions were achieved at all times. All upright frames were constructed as per the recommended manufacturing guidelines. Thickness of the uprights, beam depths, beam heights and boundary conditions were selected so that significant cross-sectional deformations in the uprights would occur well before the ultimate load of the frame was reached.

Fig. 3. Frame, upright frame and upright member nomenclature.

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Fig. 4. Sign conventions used for testing. (a) Local displacements and definitions. (b) End rotations and lateral displacement.

Fig. 5. Pin connections at top and base of uprights.

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uprights were transferred to the strong floor beams through the two universal beams. A pin bearing for each upright was then bolted through the flange of the UB sections, whereby the uprights were pinned about their major x-axis (axis of symmetry) and fixed against rotation about the minor y-axis. A similar pinned arrangement was used at the top of the frames where vertical loads were applied. Fig. 5 displays the pinned bearings used at the base and top of each upright. In order to ensure that no torsion at the top and base of the uprights could occur, and to replicate ideal boundary conditions, a 6 mm base plate was welded to the ends of each of the storage rack uprights, as shown in Fig. 5. A thin 6 mm base plate was used and great care was taken during welding to minimise the extent of localised yielding and the development of residual stresses. 14 mm diameter holes were then drilled in the base plates which allowed them to be bolted to the pin bearings, as also shown in Fig. 5. Fig. 6 shows a photograph of the fully constructed test set-up. 3.2. Loading frame

Fig. 6. Photograph of full frame test setup.

For all of the tests, load was applied vertically and concentrically through the centroid of each upright's cross-section. The loading rig was fabricated to ensure that the concentric axial force was equally distributed between the four uprights. As no down-aisle bracing in the frames was present, the test set-up ensured that frames would always fail in the down-aisle direction. 3.1. Boundary conditions As shown in Fig. 1, the storage racks were orientated such that the down-aisle direction was parallel to the strong floor beams in the laboratory. At a spacing of 2680 mm, two universal beam 250UB37.3 sections were connected on top of the strong-floor beams in the cross-aisle direction. In this way, the loads from the

The vertical loads were applied to the top of the uprights by a rectangular loading frame. The loading frame was constructed by connecting two 3200 mm long 250UB37.3 members to a 150 × 150 × 10 mm SHS, as seen in Fig. 7. To ensure that the loads were distributed evenly between the storage rack uprights, a cross-aisle pin connection was required for the two points connecting the SHS to the two 250UB loading beams. To reduce torsion of the loading beams, the SHS was connected underneath the beams using a 40 mm round bar pin between two 20 mm flat thick plates welded to the beam. A single row cylindrical bearing (NJ2208 ECL) was then press-fitted into an 80 mm diameter hole in each of the plates and the round bar was inserted through the bearings. As also shown in Fig. 7, at the centre of the loading frame, a vertical 50 × 50 × 6 mm SHS shaft was connected to the 150 × 150 × 10 mm cross-beam used to apply loading. At the bottom, the SHS shaft was connected to a 250 kN hydraulic actuator and Gravity Load Simulator (GLS). To create a pinned connection, the shaft was connected to a makeshift open box section (Fig. 7) constructed using two 50 mm flat plates and two 300 × 90 × 12C-sections. A 50 mm round bar was welded onto the base of the top plate and a 20 mm grooved flat plate was welded on top of the 150 × 150 × 10 mm SHS cross-beam of the loading frame. This connection allowed the actuator to apply a downward force on the loading frame, while not preventing rotation of the loading shaft at the connection point. To connect the base of the loading shaft to the actuator, the 50 × 50 × 6 mm SHS shaft was welded to a 20 mm top plate and bolted to the load cell and actuator. The actuator was orientated so that it could pull down, creating tension in the shaft and consequently producing a compressive force from the loading frame onto

Fig. 7. Photographs of the loading frame.

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Table 2 Summary of ultimate loads – RF and SD frame tests. Frame Beam depth (kN)

“180 degree flip” (mm)

Horizontal force (HF) (kN)

Average net out-of-plumb (mm)

Average critical distortional imp. buckling mode magnitude (mm)

Average critical member imp. buckling mode magnitude (mm)

Initial sway due to HF (mm)

Ultimate load (kN)

RF-1 RF-2 RF-3 RF-4 RF-5 RF-6 RF-7 SD-1 SD-2 SD-3 SD-4 SD-5

N N Y Y N N N N N N N N

0 0 0 0 0 0.49 0.29 0 0 0 0.15 0.49

1 2 −2 −1 1 3 2 2 1 12 1 1

0.13 0.19 0.20 0.16 0.16 0.13 0.11 1.10 1.14 1.38 1.19 1.05

0.46 0.16 0.56 0.50 0.07 0.46 0.29 0.81 0.51 0.56 0.38 0.34

0 0 0 0 0 18 13 0 0 0 1 11

199.3 185.3 194.5 218.3 200.2 114.5 129.5 136.1 148.9 108.4 138.7 115.6

155 155 110 110 110 110 110 155 155 110 110 110

the uprights. A gravity load simulator (GLS) supported the actuator. The GLS could move with the frame, allowing the applied load to stay perfectly vertical at all times. Full details of the GLS arrangement may be found in the reference [13]. After the test frame had been assembled and the loading frame had been connected to the top of the uprights, 500 kg pallet loads were placed on each of the beam levels. These pallet loads ensured that the semi-rigid beam-to-column connections were adequately locked in to provide representative down-aisle rigidity to the frame. As the loading shaft hung down through the centre of the test frame, it was necessary to apply the 500 kg weights by using two 250 kg concrete blocks on either side, as shown in Fig. 6. Round bars were placed through the concrete blocks on either side, allowing the blocks to be safely attached to the beams and thus reduce the risk of the blocks falling during loading. A small horizontal load in addition to the vertical loads was also applied to test frames SD-4, SD-5, RF-6 and RF-7. The horizontal load was applied using a weight and pulley system that was connected to the frame at the height of the loading frame. The small horizontal force increased the initial displacements of the frame and the net sway of the system, and was kept constant during the tests. Table 2 details the horizontal force applied during each of the tests and the initial sway displacement at 4800 mm (beam level 4) caused by the force. The purpose of these horizontal forces was to increase the initial downaisle displacements of the frame to help investigate whether or not the local instabilities of the upright members led to an amplification of the sway deflections of the frame.

3.3. Transducer locations A total of 24 transducers was used to measure the response of the frame during loading and to capture the local distortions in the uprights. Transducers T1-T4 were positioned on the base plates of uprights 2 and 4, 150 mm apart, as shown in Fig. 8. Two transducer boxes were also fabricated to house the transducers. The transducer frames were attached 600 mm from the base of each of the uprights, corresponding to the mid-height of the lowest beam level. This location was selected because it was half-way between bracing connection points suggesting that the cross-sectional deformations would be most prominent. The transducer boxes were fastened to the uprights using a novel spring connection, similar to ones used during upright testing [13]. By attaching the transducer box to the frame, the transducers could move as the upright swayed, allowing the transducers on the transducer frame to measure the local distortions of the uprights at the same points in the cross-section during sway. Three transducers labelled (T8, T9, T10) and (T14, T15, T16) were housed by the transducer frames on uprights 4 and 2 respectively. Two of these transducers measured the local

distortion on the flange while the third measured the local distortions on the web. Fig. 9 displays the locations of the transducers on the transducer frames around the cross-section for the RF and SD uprights. Three additional transducers were also positioned on the outside of the transducer frames to measure the global movements of each upright. Transducers (T5, T6, T7) and (T11, T12, T13) were positioned on the transducer frames for uprights 4 and 2 respectively. Two of these transducers on each upright (T5, T6 and T11, T12) measured the translation of the upright in the down-aisle direction (flexure about the major x-axis), while the third transducer (T7 and T13) measured translation in the cross-aisle directions (flexure about the minor y-axis). In order to simplify calculations of the translations and twist rotations of the uprights about their shear centres, transducers T6 and T12 were positioned in line with the shear centre and transducers T5 and T11 were positioned 150 mm from the shear centre. The same transducer locations were used for each of the tests, with the exception of tests RF-3 and RF-4. For these tests, the frames were rotated 180 degrees and the transducer boxes were attached to opposite upright members 1 and 3 accordingly. Eight additional 200 mm transducers (T17-T24) were used to measure the down-aisle displacements of the frame at each beam level, as shown in Fig. 1.

3.4. Relative joint rotation measurements In order to verify the accuracy of the beam-to-upright stiffness values captured by portal sway and cantilever tests, inclinometers were used to measure the relative joint rotations of the beams and

Fig. 8. Transducer box locations.

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Fig. 9. Transducer frame and transducer locations.

uprights during testing. In each of the tests, sixteen Accustar Single Axis Inclinometers were attached to the frame. For each of the joints, one inclinometer was attached to the upright, while a separate adjacent one was attached to the beam at the same height. During testing, each inclinometer recorded the rotation of the member with respect to vertical. By subtracting the rotations between each, the relative rotation between the beam and upright could be measured accurately. Two of these inclinometers can be seen in Fig. 7. 4. Test procedure Before applying any vertical load to the uprights, safety chains (preventing complete down-aisle collapse) were added and then the concrete pallet loads were carefully secured on each beam level. The loading frame was lowered from the overhead crane and the pin

bearings were connected to the uprights. Transducers were then attached in all the relevant positions and the vertical loading shaft was connected to the vertical actuator. Once instrumentation and loading arrangements had been assembled, a theodolite was used to measure the out-of-plumb for each upright and readings were recorded. In the tests of frames RF-6, RF-7, SD-4 and SD-5, the out-of-plumb was measured before the horizontal load was applied. Care was also taken to ensure that the loading shaft connecting the vertical actuator was in fact vertical at the start and the transducer controlling the horizontal gravity-load-simulator actuator had a zero reading. In order to capture the post-ultimate behaviour of the frame, a special software modification was made to the controllers. The modification meant that the 250 kN vertical actuator would load the structure at 0.25 mm/min until the frame swayed a set distance (say 2 mm), as recorded by an auxiliary horizontal transducer at the top registering on

Fig. 10. Applied axial load vs. horizontal down-aisle displacements (v) at beam height four (4860 mm above pins at base) - (a) RF tests and (b) SD tests.

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Table 3 Average initial joint stiffness measurements, SD and RF frames. Frame

Beam level

Beam type

Average rotational rigidity (kN·m/radians)

SD-3 SD-5 Average RF-6 RF-7 Average

1 1

110 × 1.6 CC × 2590 110 × 1.6 CC × 2590

1 1

110 × 1.6 CC × 2590 110 × 1.6 CC × 2590

193.2 230.2 211.7 260.2 260.5 260.4

All the transducer, inclinometer and load data were captured using three Vishay data-loggers and all tests were filmed using two high speed Cannon EOS 1100D digital video cameras. The tests were also paused for 2 min approximately 5 kN before reaching the ultimate load of each frame to determine if there was any difference between the dynamic and static ultimate loading values. No difference between static and dynamic ultimate loads was seen, meaning that the failure load was essentially elastic. All the ultimate load results recorded in Table 2 are static values. 5. Test results

the loading frame. Once this set distance had been reached, the actuator would either increase or decrease the load necessary to hold the structure at this point. The set point would then be increased incrementally until well after the ultimate load was reached. In practice however, once a spatial plastic hinge had occurred and the ultimate load was passed, the vertical actuator was no longer able to hold the frame in stable equilibrium and an uncontrolled collapse occurred relatively shortly after passing the ultimate load.

5.1. RF and SD frames Table 2 displays the out-of-plumb measurements and ultimate loads for each of the seven RF frames and five SD frames tested. Out-of-plumb and initial sway due to horizontal force refer to the horizontal deviation between the top and bottom pins, and were measured after the weights of the concrete blocks and loading frame had been applied. The average net out-of-plumb was calculated as the average of the out-of-plumb

Fig. 11. RF-1 test results.

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imperfection buckling mode magnitude is the average imperfection magnitude in the shape of the critical distortional buckling mode for each of the four upright members of a particular frame. Similarly, the average critical member imperfection magnitude is the recorded member imperfection averaged for four upright members of the frame. As previously mentioned and noted in Table 2, frames RF-3 and RF-4 were rotated 180 degrees to confirm that the test set-up did not influence the failure direction, (note that the bracing arrangement of the upright frames was asymmetric, as shown in Fig. 1b). Figs. 10a and 10b show the load vs. horizontal displacement curves for each test at the height of the centre of the top pallet beam for frames composed of RF and SD uprights respectively. All ultimate and axial loads shown in tables and graphs respectively refer to the applied vertical loads. The applied vertical load neither includes the dead loads from the two 250 kg blocks added at each beam height nor the weight of the loading frame (372.8 kg) placed on top of the uprights. Test results from a selection of tests are presented in this paper while the full set of results for all twelve tests conducted may be found in the reference [13]. The full set of test results include graphs for the load vs. horizontal displacement of the frame at each beam level, rotations of two bottom pins, local displacements of the web and flanges, as well as the global displacements and twist rotations with respect to the shear centre of the instrumented uprights, 600 mm from the base. Global translations of the shear centre have been recorded using the sign conventions displayed in Fig. 4, where u and v correspond to translations in the minor and major axis directions respectively. Similarly, all local displacements use the sign conventions shown in Fig. 4. Video footage of all of the tests may also be found in the reference [13].

5.2. Joint moment vs. relative rotation results Fig. 12. Distortional buckling deformations RF-2 at 145 kN.

measurements for the four upright members of each frame. Positive out-of-plumb and sway displacements indicate the frame was displacing to the South. Table 2 also displays the measured imperfection data for the RF and SD frames. The average critical distortional

Table 3 shows the average initial joint stiffness calculated for SD and RF frames. An example of the joint stiffness calculation and full joint moment-rotation curves for each of the tests may also be found in [13]. Note that due to the negligible beam-to-upright rotations experienced for the RF and SD frames using 155 mm deep beams, useful data was only captured for frames constructed with 110 mm beams.

Fig. 13. Plastic spatial hinges RF-2.

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Fig. 14. Frame RF-1 and RF-2 failed.

6. Discussion 6.1. RF frames 6.1.1. Ultimate loads The ultimate loads recorded by the nominally identical frames RF-1 and RF-2 show that the tests results were repeatable with only a slight deviation of 7% between the recorded ultimate loads. The lower outof-plumb measurement and higher distortional cross-sectional imperfection of frame RF-1 in comparison to RF-2 explain the reason for the lower ultimate load of frame RF-2. Tests RF-3, RF-4 and RF-5 had very little initial out-of-plumb and no side load. Although each of these tests used the shallower 110 mm deep pallet beams, the ultimate loads achieved were 6% higher than those of the RF-1 and RF-2 tests, which used 155 mm deep pallet beams. The reasons for the higher ultimate loads for these tests were due to the failure mode and failure direction, as discussed below. The ultimate load results for the RF-6 and RF-7 frames were substantially affected by the 0.29 kN and 0.49 kN horizontal forces applied to the frames using 30 kg and 50 kg weights. The 30 kg and 50 kg weights corresponded to 1.5% and 2.5% of the total applied concrete pallet loads respectively. Applying a 0.29 kN horizontal force to RF-7 reduced the ultimate load by 37% when compared to the average of tests RF-2, RF-3 and RF-4. Similarly, increasing the horizontal force to 0.49 kN further reduced the ultimate load of the system, with RF-6 reaching an ultimate load of 45% less than the average ultimate load of the tests where no side load was included. 6.1.2. Frame behaviour The first two frames tested (RF-1 and RF-2) behaved and failed in very similar ways. As shown in Fig. 11, only relatively small crosssectional deformations were recorded for test frame RF-1 as load was applied. Up to an applied load of about 100 kN, the horizontal displacement of the frame was negligible. As the load gradually surpassed 100 kN, transducers T8 and T9, along with transducers T14 and T15 started to record an increasingly positive displacement reading, meaning that distortional buckling was beginning to occur and the flanges of the uprights 600 mm from the base were moving outwards. The

distortional buckles formed in one or two half-waves along the upright between the bracing and beam connections. Similarly, at this point, transducers T16 and T10 also started to record an inward displacement of the web. Unlike the large distortions experienced by the SD uprights, these displacements were only small for the RF uprights and could not easily be observed during testing. Fig. 12 shows the total extent of the cross-sectional deformations at a vertical load of approximately 145 kN. As load continued to be applied, the rate of cross-sectional deformations began to increase, decreasing the rigidity of the uprights and causing the gradual horizontal displacement of the frame. As the load increased past 150 kN, flexural-torsional buckling, involving major axis flexure and twisting of the bottom lift of the uprights, gradually began to occur, as seen in Fig. 11. The horizontal down-aisle displacement began to occur at a faster rate as load was gradually increased. Unlike the SD sections, no local buckling deformations were observed in the flanges for the RF-1 and RF-2 frames. After the frame had displaced 5 mm at the top, the ultimate load was reached and localised deformations occurred in the flange of all four uprights, just below the first beam level. Spatial plastic hinges formed in the uprights causing the system to become unstable subsequently and rapidly displace horizontally in the down-aisle direction. A photograph of the spatial plastic hinge may be found in Fig. 13. Interestingly, for one of the uprights in frame RF-2, the spatial plastic hinge developed closer to the base of the upright than in other tests. This difference may have been due to the higher distortional imperfection present, which may have contributed the lower ultimate load of frame RF-2. Frames RF-1 and RF-2 both failed in the sway mode and photographs for each may be seen in Fig. 14. Frames RF-3, RF-4 and RF-5 all had similar test set-ups and behaved in a very similar manner. Fig. 15 shows representative results for frame RF-5. While each of these frames used shallower 110 mm beams compared to the previous RF-1 and RF-2 tests, in some instances the ultimate loads were significantly higher. Only a small out-of-plumb measurement was recorded for each frame. As load was gradually applied, the transducers housed in the transducer boxes began to record distortional deformations at the bottom level of each of the uprights. Similar to the SD sections, the flanges of the sections began to displace outwards with the web gradually

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Fig. 15. RF-5 test results.

moving in towards the centroid of the section, as shown in Fig. 16. As more vertical load was applied, horizontal down-aisle displacements of the frame began to occur at a load of about 50 kN. Interestingly, prior to reaching the ultimate load there was virtually no horizontal displacement of the frame at beam level one. In addition, the greatest displacements were in some tests (but not RF-5) experienced at levels two and three, rather than at the top beam level. As the applied load continued to increase, horizontal displacements at the higher beam levels continued to increase. When the load increased above 150 kN, significant distortional deformations began to occur between beam levels, with localised deformations forming close to the beam-to-upright connections. As the frame moved closer to its ultimate capacity, the uprights below the first beam level began to bend and gradually moved horizontally in the opposite direction to the sway of the frame. Consequently, the recorded pin rotations at the base of the uprights also very gradually began to reverse directions, as seen in Fig. 15. Just before the failure of the frame, the inside flange of the upright moved inwards and created a localised spatial plastic mechanism underneath the beam connection at the first level. Failure occurred instantly after this, with the frame

dramatically reversing direction and failing in the opposite direction to its initial horizontal displacement. Fig. 17 illustrates the localised failure mechanism while the photographs in Fig. 18 show the failed frame. The deformations seen in the upright in Fig. 18 clearly indicate the interaction between distortional and flexural-torsional buckling. The unexpected result that the ultimate loads for frames RF-3, RF-4 and RF-5 were generally higher than those for RF-1 and RF-2 (which featured deeper beams) was due to fact that each of the RF-3, RF-4 and RF-5 frames failed in the opposite direction to their initial sway movement. To confirm that the loading rig and bracing configuration did not influence the test results, the loading frame and frame orientation were reversed for frames RF-3 and RF4 compared to frame RF-5. However, neither the loading frame nor the direction of bracing was found to influence the direction of frame failure. Subsequent detailed finite element modelling [13] revealed that the snap-through experienced in the RF-3, RF-4 and RF-5 tests resulted from the global (member) imperfection profiles of the upright frame members. Frames RF-6 and RF-7 had a horizontal side load applied which caused the frames to behave and fail in a typical sway failure mode.

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Fig. 16. Local and distortional deformations in RF-5.

Fig. 17. Initial failure mechanism RF-5.

The additional side load for each of the frames amplified the out-ofplumb and dramatically increased the horizontal displacements of the frame. The 0.49 kN side load by itself caused frame RF-6 to displace an additional 18 mm at the top loading frame, 13 mm at the fourth beam level and approximately 4.5 mm at the first beam level. Similarly, the smaller 0.29 kN load caused frame RF-7 to sway an additional 13 mm at the top, 8 mm at the fourth beam level and 3 mm at the first beam level before any load was applied by the vertical actuator. Both frames gradually continued to sway horizontally as the vertical load was applied. Unlike frames RF-3, RF-4 and RF-5, the lowest levels of frames RF-6 and RF-7 also substantially displaced as load increased, as shown in Fig. 19 for RF-7. In both tests, the frame stayed relatively linear with the greatest sway displacements occurring at the top of the frame. As also shown in Fig. 19, local and distortional deformations began to occur as the applied load surpassed 50 kN, while the two pin rotations at the base continued to rotate at the same rate as further load was applied. Interestingly, for both frames, the local and distortional deformations caused one of the flanges of the upright in the bottom level to move inwards. This differed from the earlier tests where typically both flanges displaced outwards. In some instances, local deformations of the rear-flange were also observed. As the applied load was increased past about 100 kN, twisting and major axis flexure near the base of the uprights began to occur, signalling that flexuraltorsional buckling was also occurring. Although less pronounced, similar to the SD frames, interaction between the distortional and flexural-torsional buckling deformations also occurred. As horizontal displacements at the top beam level surpassed 40 mm, the ultimate load was reached and the failure of the frames occurred. The failure was more gradual than in the earlier RF-3, RF-4 and RF-5 tests, and the frames failed in the same direction as that imposed by the applied horizontal side load and initial sway displacements.

Fig. 18. Failed RF-5 frame.

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Fig. 19. RF-7 test results.

Fig. 20. Failure mechanisms RF-7 frame.

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Fig. 21. SD-1 test results.

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plumb of frame SD-3. For this reason, frames SD-3 and SD-5 had very similar ultimate loads and failure modes. As expected, the reduced beam depth also led to a decrease in ultimate load as a result of the less rigid beam-to-upright connections. SD-4 provides a good comparison to investigate the effect of the reduced depth of the beams as it had negligible side load and a comparable out-of-plumb to tests SD-1 and SD-2. The reduced rigidity of beam-to-upright connections due to the shallower 110 mm beams meant that SD-4 had a 4% lower ultimate load than the average ultimate load of tests SD-1 and SD-2. Finally, comparing the average RF results with the SD results for the frames with 155 mm deep beams, we see that on average the ultimate load of the RF frames was 26% greater than that of the SD frames. The RF section uses an additional 9.4% material in comparison to the SD section which means that the additional rear stiffeners of the RF section adds significantly to the efficiency of the section.

Fig. 22. Distortional buckling deformations, SD-1.

6.2.2. Frame behaviour and failure The SD-1 and SD-2 frames behaved in a very similar manner. As the load gradually increased and reached 40 kN, cross-sectional deformations started to occur, as shown for SD-1 in Fig. 21. The flanges of the SD uprights started to move outwards, as recorded by transducers T8, T9, T14 and T15 and simultaneously the web of the section began to move inwards, as recorded by transducers T10 and T16. These distortional buckling deformations continued to increase and formed single or double half-waves between the bracing and beam levels, as shown in Fig. 22. As a result of the onset of the cross-sectional deformations, the frame began to very gradually displace in the down-aisle direction as load continued to increase. At a load of about 100 kN, the top beam level had displaced approximately 5 mm and flexural-torsional buckling was beginning to occur in the lowest levels of the uprights. As shown in Fig. 21, transducers attached to the bottom uprights were now recording twisting and a significant horizontal displacement (v) of about

Once again, a local spatial plastic failure mechanism occurred in the flange of the uprights just below the first beam height. Fig. 20 displays a photograph of the failure mechanism and failed RF-7 frame. 6.2. SD frames 6.2.1. Ultimate loads Similar to the nominally identical frame tests RF-1 and RF-2, as shown in Table 2, the ultimate loads recorded by the nominally identical frames SD-1 and SD-2 demonstrate the repeatability of the test results. Again, only a 7% difference between the ultimate loads of the tests was recorded. In this instance, the lower ultimate load achieved by SD-1 may have been due to a small slip that occurred in the test rig during testing. A bolt had not been adequately tightened which meant that the frame slipped and displaced approximately 2 mm horizontally when the load was close to 90 kN. In addition, the slightly higher out-of-plumb value may have also contributed to the small deviation in the recorded results. Comparing tests SD-3, SD-4 and SD-5 to tests SD-1 and SD-2 allows the effects of the out-of-plumb and shallower beam depths on the ultimate load of the frame to be determined. Large out-of-plumb values were seen to dramatically decrease the ultimate load of frame SD-3. The initial out-of-plumb led to greater horizontal displacement of the frame at lower loads, implying increased moments at the bottom levels and a lower ultimate load. Accordingly, frame SD-3 recorded a 22% lower ultimate load than SD-4. While frame SD-4 had a small horizontal side load, the initial out-of-plumb was only 1 mm and the side load had negligible effect on this value after it was added. Similarly, SD-5 recorded an ultimate load that was 17% less than that of SD-4. Increasing the horizontal side load from 0.147 kN to 0.49 kN in test SD-5 caused the frame to move an additional 10 mm off centre, whereby the total initial side sway before applying vertical load became similar to the out-of-

Fig. 23. Plastic hinge failure, SD-1.

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Fig. 24. Frame SD-1 and SD-2 failure.

3 mm. The uprights SD-1-2 and SD-2-2 were buckling flexural-torsionally in the same direction as the frame sway displacement. In addition, transducers T1-T4 were recording small rotations of the base plates, as displayed in Fig. 21. As the GLS arrangement continued to apply perfectly vertical load, deformations continued to increase. At approximately 120 kN, highly localised deformations were seen to occur in different regions of the uprights. These deformations were especially prominent in the flanges of the uprights under the first level beam-to-upright connections and at the very top below the top loading pins. The frame continued to sway at a faster rate as the load approached its ultimate value. At the ultimate load, a spatial plastic hinge and local failure occurred just below the first beam level in the flange of all four uprights and caused a very rapid failure. The plastic hinge meant that the frame could no longer withstand any additional load and subsequently failed. As shown in Fig. 21, at all times, the uprights were relatively vertical, with little deviations in displacements between beam levels and the majority of displacements occurring in the bottom level. Fig. 23 shows photographs of the spatial plastic hinge for frame SD-1. Photographs of frames SD-1 and SD-2 after failure are shown in Fig. 24. In the case of frame SD-1 where the post-ultimate displacement was not heavily restrained, there was also significant tearing of the uprights as seen in Fig. 25. The tearing primarily occurred through the upright's perforations by the tangs of the beam connector brackets at the first two beam levels. While frame SD-3 had no horizontal load, it did however have a large initial out-of-plumb and shallower 110 mm deep beams. The large initial out-of-plumb and reduced rigidity of the beam-to-upright connections (due to the shallow beams) meant that there was considerably more horizontal displacement of the frame at lower loads compared to frames SD-1 and SD-2. As shown in Fig. 10b, horizontal displacements of the frame occurred much earlier compared to the other SD frames. Nonetheless, considerable cross-sectional deformations due to local and distortional buckling were still seen well before the ultimate load was reached. Similarly, flexural-torsional buckling was also evident in the lowest lift, as shown by the horizontal displacement and twist measurements in the full set of test results [13]. Once again, failure occurred in the uprights just below the first beam level. As the horizontal displacement of the frame increased, the moments

increased in the uprights and eventually a spatial plastic hinge was created and the ultimate capacity was reached. The small horizontal side load on SD-4 seemed to have a negligible effect on the initial sway of the frame. With only a very small initial side sway of 1 mm caused by the applied horizontal load, frame SD-4 recorded a substantially smaller horizontal displacement than frame SD-3. As a result, a 27% higher ultimate load was achieved, as seen in Fig. 10b and Table 2. As a consequence of the higher loads and smaller horizontal displacements, in order to resist the applied forces and absorb the energy of the system, considerably larger cross-sectional deformations were recorded. The full set of test results [13] also show that the outward distortion of the flanges in the lowest level reached between 6 mm and 7 mm. Distortional buckling was once again seen to form one half-wave between bracing connection points with local distortions occurring around the beam connections. Similarly, flexural-torsional buckling was also more prominent, as seen from the twist and horizontal displacements recorded by the transducers on the lowest lift. The lower

Fig. 25. SD-1 tearing of uprights.

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values of bottom pin rotations also confirm the smaller horizontal sway displacements compared with the SD-3 frame. Similar to the other frames tested, the frame eventually failed by sway failure in the down aisle direction with spatial plastic hinges occurring just below the first beam level. Fig. 26 displays the failed SD-4 frame. Placing the larger 0.49 kN horizontal side load on frame SD-5 greatly increased the initial horizontal displacement. While the initial out-ofplumb measurement for frame SD-5 was 1.2 mm, the horizontal side load added an extra 11 mm of sway, meaning that the total side sway before applying vertical load was 12.2 mm. Thus, the initial horizontal displacement of frame SD-5 was very similar to the out-of-plumb measurement of frame SD-3. Similar to previous tests, considerable local and distortional deformations were observed as was flexural-torsional buckling in the lowest level. Full transducer results may be found in the reference [13]. 6.3. Other observations

Fig. 26. Failed frame SD-4.

As noted, both local and distortional buckling occurred well before reaching the ultimate load in each of the frame tests. Distortional buckling typically occurred in one or two half-waves below the first beam level or between beam levels, with local deformations often occurring in the flanges of the uprights close the beam-to-upright connections. Considerable interaction between distortional and flexural-torsional buckling was also evident below the first beam level, as captured by the transducer measurements. As to be expected, local and distortional deformations were more prominent in the SD tests than the RF tests. It was also observed that the down-aisle frames (see Fig. 3) could act seemingly independently of one another. In other words, one upright (e.g. SD-1-2) would typically sway more than the other (SD-1-1). Fig. 27 shows an example of this situation. As a result, for the majority of tests, one down-aisle frame (uprights SD-1-1 and SD-2-1) would often be swaying an additional 1-4 mm further than the other (uprights SD-1-2 and SD-2-2) and ‘pulling’ it across. The difference in sway was

Fig. 27. Examples of differing sway displacements of down-aisle frames.

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Fig. 28. Applied axial load vs. measured rotations, RF-6, RF-7, SD-3 and SD-5,

usually due to differences in the initial out-of-plumb of the down-aisle frames. In many cases, the recorded out-of-plumb for one down-aisle frame was considerably greater than (or in the opposite direction of) that of the other.

6.4. Measured beam-to-upright joint stiffness The initial stiffness of the beam-to-upright connections could be calculated using the measured rotation data captured from the

Fig. 29. Average moment vs. relative beam-to-upright rotation, RF-6, RF-7, SD-3 and SD-5.

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inclinometers and the measured displacements at each beam level. Accurate data was captured for four of the test frames (SD-3, SD-5, RF-6 and RF-7). Fig. 28 displays the relative beam-to-upright rotation vs. the applied vertical load for the first beam level of each frame, while Fig. 29 displays the relative beam-to-upright rotations vs. bending moment. Note that for frames SD-5, RF-6 and RF-7 the initial beam to upright rotation does not start at zero due to the horizontal forces applied to each of these frames before vertical loading began. Also, in the figures, the relative rotation and the bending moment are averages of the values for the two beam-to-upright connections for the first beam level. The gradients of the moment-rotation curves were used to derive the initial beam-to-upright rotational stiffness, as shown in Table 3. Interestingly, comparing these values to those derived from the portal sway tests described in [13], it follows that the initial rotational stiffness derived during full scale testing is approximately 1.5–2.5 times greater than the stiffness obtained from the portal sway tests. Previous research [15] at the University of Sydney had also found this value to fall within a 1.2–3.5 multiple during full scale storage rack tests. The increased rigidity as measured by the full scale test is most likely a result of the additional down-aisle rigidity provided by the other beam levels, which is not factored into the standard portal sway test set-up. 6.5. Rotational rigidity of bracing configuration During full scale testing, it was observed that the diagonal and horizontal bracing connections to the upright frames were, in fact, semirigid for rotation about the vertical axis. The semi-rigid connection meant that uprights of the same upright frame (e.g. SD-1-1 and SD-12) would not always sway horizontally in unison. A separate component test was therefore conducted to determine the rotational bracing-to-upright rigidity. The test set-up comprised of laying a full upright frame on

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Table 4 Rotational stiffness of bracing-to-upright - SD Sections. Frame type

Bracing

Test #

Rotational stiffness of bracing connection (kN·m/radians)

SD SD Average SD SD Average SD SD Average

Diagonal Diagonal

1 2

End - Spacer Up End - Spacer Up

1 2

End - Spacer Down End - Spacer Down

1 2

0.214 0.218 0.216 0.281 0.282 0.282 0.235 0.234 0.235

its side and cutting the bracing members at a set distance so that they could move freely where cut. A small force perpendicular to the plane of the upright frame was then applied at the centre of the diagonal braces or to the horizontal brace to induce a moment in the brace-toupright connection. Transducers were used to measure the displacement of the bracing element so that the relative rotation of the bracing member to the upright could be determined. Tests were repeated on two different frames for each of the SD and RF sections for both the horizontal and diagonal bracing members. Fig. 30 shows a photograph of the test set-up. Based on the displacements and applied moment to the beam-toupright connections, plots were generated and may be found in the reference [13]. Tables 4 and 5 show a summary of the calculated stiffness for each of the SD and RF tests respectively. For each type of upright, both bracing members and horizontal members were tested. In addition, the horizontal bracing member was tested in both directions in order to determine if there was a difference in rotational stiffness for the different orientations of the bottom bracing spacer. Consistent results are observed for nominally identical tests. Based on the tabulated results, it is evident that the rear flange on the RF section slightly increases the rotational rigidity of the bracing connections compared with the SD sections. Furthermore, slight differences between the rigidity of the diagonal and horizontal end bracing connections can also be seen, as well as a small variation in the stiffness due to the direction of the SD spacer.

7. Conclusions An experimental investigation into the behaviour of ultra-light gauge steel storage rack frames was conducted. Ultra-light gauge uprights were selected so that significant local, distortional and flexuraltorsional buckling would develop well before the ultimate load was reached. A total of twelve full scale steel storage rack frames were tested. The applied horizontal load, beam depths and orientation of the upright frames were varied between tests. A gravity load simulator was fabricated to ensure that the applied vertical load stayed vertical at all times.

Table 5 Rotational stiffness of bracing-to-upright - RF Sections.

Fig. 30. Bracing-to-upright rotational rigidity test setup.

Frame type

Bracing

Test #

Rotational stiffness of bracing connection (kN·m/radians)

RF RF Average RF RF Average RF RF Average

Diagonal Diagonal

1 2

End - Spacer Up End - Spacer Up

1 2

End - Spacer Down End - Spacer Down

1 2

0.359 0.329 0.344 0.274 0.282 0.278 0.268 0.275 0.272

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Geometric imperfections in each of the members were measured prior to testing. The tests were successful in capturing the cross-sectional deformation of the uprights, the ultimate loads and the post-ultimate response of the frames as well as the relative beam-to-upright rotations. Results from nominally identical tests were in good agreement. The reported full-scale tests provide valuable data for the effects of interactive buckling and the extent to which cross-sectional deformations amplify the second-order deformations in storage rack frames. Further analysis and design considerations relating to the amplification of these secondorder affects are presented in a companion paper [1]. Acknowledgments This research was supported by the Australian Research Council under Discovery Grant DP0989030. This support is gratefully acknowledged. Dematic Pty Ltd. rolled the uprights used for the experiments detailed in this paper. The authors are grateful for this substantial in-kind support. References [1] A.N. Trouncer, K.J.R. Rasmussen, Ultra-light gauge steel storage rack frames – part 2: analysis and design considerations of second order effects, J. Constr. Steel Res. (Dec 2015) Submission.

[2] C. Matsui, I. Minami, M. Wakabayashi, Elastic-plastic behaviours of full size steel frames, Technical Report 197: 7–19, Transactions of the Architectural Institute of Japan, 1972. [3] W.S. Toma, S. Chen, European calibration frames for second-order inelastic analysis, J. Struct. Eng. 14 (1) (1992) 7–14. [4] C.H. Yu, J.Y.R. Liew, N.E. Shanmugam, Large-scale testing of steel sway frames, Proceedings of the International Conference on Structural Stability and Design, Sydney, Australia, 1995. [5] J.B.P. Lim, D.A. Nethercot, Finite element idealization of a cold-formed steel portal frame, J. Struct. Eng. ASCE 130 (1) (2004) 78–94. [6] Y.B. Kwon, H.S. Chung, G.D. Kim, Experiments of cold-formed steel connections and portal frames, J. Struct. Eng. ASCE 132 (4) (2006) 600–607. [7] K.F. Chung, H.C. Ho, A.J. Wang, W.K. Yu, Advances in analysis and design of coldformed steel structures, Adv. Struct. Eng. 11 (6) (2008) 615–632. [8] D. Dubina, Structural analysis and design assisted by testing of cold-formed steel structures, Thin-Walled Struct. 46 (7–9) (2008) 741–764. [9] S.E. Kim, K.W. Kang, Large-scale testing of 3-D steel frame accounting for local buckling, Int. J. Solids Struct. 41 (18–19) (2004) 5003–5022. [10] P. Avery, M. Mahendran, Large-scale testing of steel frame structures comprising non-compact sections, Eng. Struct. 22 (8) (2000) 920–936. [11] X. Zhang, Steel Portal Frames with Locally Unstable Members(PhD thesis) School of Civil Engineering, University of Sydney, 2014. [12] Continuous hot-dip metallic coated steel sheet and strip - coatings of zinc and zinc alloyed with aluminium and magnesium, AS 1397, Standards Australia, 2011. [13] T. AN, Steel Storage Racks with Locally Unstable Members(PhD thesis) School of Civil Engineering, University of Sydney, 2014. [14] A.N. Trouncer, K.J.R. Rasmussen, Flexural-torsional buckling of ultra light-gauge steel storage rack uprights, Thin-Walled Struct. 81 (2014) 159–174. [15] E. Harris, Sway Behaviour of High-Rise Steel Storage Racks(PhD thesis) School of Civil Engineering, University of Sydney, 2004.