EXPERIMENTAL AND THEORETICAL INVESTIGATIONS OF PALLET RACKS CONNECTIONS

Transcription

1 Advanced Steel Construction Vol., No., pp (007) 608 EXPERIMENTAL AND THEORETICAL INVESTIGATIONS O PALLET RACKS CONNECTIONS Lucjan Ślęcza and Alesander Kozłowsi Rzeszów University of Technology, Department of Building Structures, W. Pola, Rzeszów, Poland ax.: (Corresponding author: slecza@prz.rzeszow.pl) Received: 16 November 006; Revised: 4 January 007; Accepted: 5 ebruary 007 ABSTRACT: Steel storage pallet racs are three-dimensional framed structures, similar to multi-storey building structures. They are widely used for the storage of different types of materials. To provide the easy accessibility to stored products, pallet racs are not braced in down-aisle direction. The only source of the stiffness required for down-aisle stability is the stiffness of the nnections between lumns and beams, and the stiffness of the lumn bases. Connections between lumns and beams are realised by means of different types of mechanical devices (tabs, hoos etc) without the need of using bolts and welds. Such joints have non-linear M φ characteristic. Most of the recent design des and papers reend experimental tests of beam-to-lumn nnections to obtain semi-rigid joint characteristics that can be applied in the global analysis. The aim of this paper is to present application of the mponent method to assess main joint properties, i.e. the moment resistance and initial stiffness of storage rac joints. Results obtained using developed model are mpared with the test results. Keywords: Storage pallet racs, mponent method, semi-rigid nnection, experimental tests 1. INTRODUCTION Steel pallet racs are regular, D multi-storey, multi-bay structures, used in industry and warehouses for the storage of palletised goods (ig. 1). They are realised by using ld-formed steel profiles. Design analysis of such structures is carried out on D sub-assemblies, separately in the cross- and down-aisle directions. Stability in the cross-aisle direction is provided by bracings. To provide the easy accessibility to stored products, pallet racs are not braced in down-aisle direction. Because of lac of bracings in the down-aisle direction, structure analysis is carried out by adopting a semi-ntinuous sway frame model, i.e. unbraced frame with semi-rigid joints. Analysis of such structures were described in few papers (Abdel-Jaber et al [1], Bernuzzi and Castiglioni [6], reitas et al [11], Godley et al. [1], Peöz and Rao [17], The et al. [19]) Connections between lumns and beams are realised in such structures by means different types of mechanical devices such tabs, hoos etc, without the need of using bolts and welds. These joints have non-linear M φ characteristic (Baldassino and Zandonini [], Baldassino and Bernuzzi [], Marazi et al. [15], Marazi et al. [16]. Most of the recent design des and papers, reend an experimental-theoretical design approach and require experimental tests of beam-to-lumn nnections to obtain semi-rigid joint characteristics that can be applied in the global analysis. Such experimental tests were nducted for one of the ercially available steel racs system in Poland. Observation of joint behaviour during tests suggests possibility of using the mponent method to evaluate the main joint properties i.e. moment resistance and initial stiffness. The aims of the paper are to present model of the mponent method for investigated rac joints and mpare results from tests and mponent modelling.

2 Lucjan Ślęcza and Alesander Kozłowsi 609 igure 1. Typical Pallet Racs Configuration. EXPERIMENTAL PROCEDURE AND THE TEST RESULTS A setch of tested beam-to-lumn nnection with its dimensions is shown in igure. The joint nsists of a beam-end nnector with tabs, made of a 4- thic ld-formed angle, welded to each end of the beam. The leg of the angle with tabs is in ntact with lumn web after assembly, while there is a - gap between the send leg, perpendicular to the lumn web. A Beam-endnnector Beam RHS Column Slots 4 x Beam-end-nnector RHS Beam A gap A-A After the assembly 7 Before the assembly Cantilevered tabs 90 4 igure. Dimensions of Tested Joint

3 610 Experimental and Theoretical Investigations of Pallet Racs Connections Reendations (Instytut Logistyi i Magazynowania) suggest two possible ways of testing to evaluate the joint behaviour. One is bending test on isolated beam-lumn nnection, send is portal test, where frame is mposed of two lumns and one beam is loaded by vertical and horizontal forces. Bending tests on isolated nnections were nducted for analysed nnections. Research program is suarized in Table 1. The main aim of experimental tests was to obtain moment-rotation characteristics of tested joints and also observation of behaviour of joint mponents under loading and finally failure modes. igure shows general layout of the tests. Tests were carried out on five full-scale joint groups. Two groups ( D and ) nsisted of single-sided joints of external lumns. Other three groups (group B, C and E ) were double sided nnections of beams to internal lumns. Every tested group had the same nnector and lumn section, while the size of the beam was different in each group. To prevent lateral movements whilst loading, both lumn and beams elements were doubled and nnected to each other. Distance e 1 = e was established so, as the force equal to 5 % of shear capacity of nnection uld produce ultimate bending moment value with tolerance ± 0% (Instytut Logistyi i Magazynowania). In order to assess end rotations of the beams, two dial gauges were used at each beam. End rotations of beam were obtained as the relative gauges displacements divided by the separation between them. Because of large stiffness of beam, no rrection factor was used for calculation of the joint rotation (with regard to deflection of the cantilevered beam). In one sided-tests, rotations of the nnection was obtained by subtracting the rotation of the lumn from rotation of the beam. Testing procedures, instrumentation and detailed test results of analysed joints can be found in (Kozłowsi and Ślęcza [14]). Table 1. Research Program Symbol Number of Type of Type of tests specimens beam (RHS) Group B 6 Bending tests, internal lumn 100x x Group C 6 Bending tests, internal lumn 80x 40x Group D 5 Bending tests, external lumn 100x x Group E 6 Bending tests, internal lumn 10x 60x Group 6 Bending tests, external lumn 10x 60x Column Support Column e 1 e e 1 Beam-end nnector Beam-end nnector 00 Dial gauges Beam Beam igure. General Layout of Double-sided (Internal Column) and One-sided (External Column) tests The main test results are suarized in Table and Table. Every tested group has nsisted of six specimens. Values presented in Tables and are arithmetic mean values. The plastic flexural resistance M, was obtained as a point of intersection of a straight line representing initial pl ex p

4 Lucjan Ślęcza and Alesander Kozłowsi 611 stiffness S j, ini, with the line of slope,1s j, ini obtained in test (ig. 4). 0, which is tangent to the non-linear part of the curve Table. Material Properties Part of the joint Yield stress, [MPa] Ultimate stress, [MPa] Elongation, [%] Column Connector Beam Group B Group C Group D Group E Group Table. Main Test Results of Joints Initial rotational Plastic flexural stiffness resistance M S j, ini [Nm/rad] 19,40 116,70 71,5 1,06 96,15 [Nm],19,6,10,0,7 pl, exp Ultimate flexural resistance M [Nm],90,7,58,7,86 u, exp M [Nm] 4.0 S j,ini 0.1S j,ini.0 M pl,ex 1 M u,exp experimental curve φ [rad] igure 4. Experimental M φ Curve, Specimen B5. APPLICATION O COMPONENT METHOD TO MODELLING PALLET RACK CONNECTIONS The mponent method is now one of the most effective methods to analyse and predict the rotational behaviour of different types and different nfigurations of nnections. It is mainly used in case of steel joints made from hot rolled sections (EN [8]) and mposite joints (pren [18]), but recently has also found other applications (in et al. [10]). The application of the mponent method is usually performed in three stages. The first stage is the identification of mponents in the analysed joint, where the mplex joint is subdivided into parts. The send stage is the prediction, for each identified mponent, of its individual initial stiffness, strength and often deformation capacity. The behaviour of each mponent is described by a bilinear relationship between displacement and force. Components that do not affect the stiffness of the joint are modelled as rigid-plastic, while other mponents are modelled as elasto-plastic

5 61 Experimental and Theoretical Investigations of Pallet Racs Connections elements. The third stage is the evaluation of flexural strength and rotational stiffness of the whole joint. In this stage the lever arms should also be predicted for every group of mponents. Behaviour of nnection is then predicted by analysing group of springs with axial stiffness, joined in series or in parallel..1 Identification of Components In the case of analysed storage rac joint, the following mponents can be identified:.1.1 Column web in tearing A part of the lumn web situated between the slot and the flange of the lumn is subjected to a distributed load transmitted by the tabs in the nnector. ixed-ended beam of a span equal to the height of the slot, loaded by ntact stresses can be used to model the behaviour of this mponent (ig. 5). The resistance of the mponent depends mainly on shear stresses. This mponent is active only in a tensioned part of the joint. Tension zone A 19 5 A V 0.06 Compression zone A-A A V igure 5. Model to Determine the Resistance and Stiffness of Column Web in Tearing Acrding to igure 5, the resistance cw, tear can be obtained nsidering the relationship: cw, tear = Av fu. cw (1) where cw, tear - resistance of lumn web in tearing; AV - shear area of part of lumn web, as indicated in igure 5 and u, cw - ultimate tensile stress of lumn web. rom Equation 1 the resistance of lumn web in tearing can be calculated as cw, tear = 6,6 N. The initial stiffness of spring element modelling lumn web in tearing cw, tear is given by general rule: cw, tear = () δ where δ - deflection of the beam caused by bending and shear deformation under load. Using N deflection equations for beam shown in igure 5, it can be found that cw, tear = The effect of tearing of the lumn web observed during the tests is shown in igure 6.

6 Lucjan Ślęcza and Alesander Kozłowsi Column web in bearing igure 6. Tearing of the Column Web Observed during the Tests This mponent is active both in the tension and mpression zones of the joint (ig. 7). The resistance of the lumn web in bearing cw, b can be evaluated using analogy to bolted nnections, acrding to (EN [8]): cw, b =. 5α fu, cw d tcw () where tcw - thicness of lumn web; d - bolt diameter (here replaced by the thicness of the tab d = ttab = 4, 0 ); f u, cw - ultimate tensile stress of lumn web; and α - reduction factor. In the case of joint with tabs α f u f inally, the resistance of the lumn web in bearing can be predicted as =, / u, cw =, b = 8,07 N. cw Tension zone Tab 19 Compression zone 4 In mpression zone In tension zone igure 7. Local Stresses due to the Pressure Acting on the Hole Walls The stiffness of the mponent for snug tightened bolts: cw, b can be also estimated, as suggested by (EN [8]), cw, b 1 b t d fu, cw = (4)

7 614 Experimental and Theoretical Investigations of Pallet Racs Connections where d - bolt diameter (here replaced by the thicness of the tab d = ttab = 4, 0 ); f u, cw - as above; b, t - efficients ( b = 1, 5 ; t = 1,5 tcw / dm16, 5). In Eq. (4) efficient 1 was used instead of 4, acrding to one row of the bolts. Using the above equation it can be found N that cw, b = 48,5. The effect of local bearing stresses in mpression zone is shown in igure 8. igure 8. Effect of Bearing in Column Web Observed during the Tests.1. Column web in tension (mpression) A part of the lumn web is subjected to tension or mpression (ig. 9). The bucling resistance of the lumn web in mpression can be mputed acrding to (Chen and Newlin [7]) as: tcw, = f y, cw = 4. N (5) d cw c wc where t cw = thicness of lumn web, d wc = clear depth of lumn web, f y, cw = yield stress of lumn web. The resistance of the tensioned part of the lumn web cw, t can be determined acrding to (EN [8]) as: = b t f (6) cw, t ω eff cw y, cw where ω - factor acunting for the interaction with shear, b eff - effective width of the web, t cw, f y, cw - as above. Assuming the tangent of the spreading angle 1 :. 5 (ig. 9), b eff, t = 5 N. cw = 5 + 7,5 =,5 and The axial stiffness of the lumn web in tension and mpression cw can be evaluated by the relationship: ' cw = E beff tcw / dwc (7) where E - the elastic modulus, t cw, d wc - as above.

8 Lucjan Ślęcza and Alesander Kozłowsi 615 The effective width of the lumn web for stiffness calculation in the mpression zone is equal to the length of the zone where distributed load from bearing is acting ( 5,0 ). The b ' eff o 45 angle for the load spreading effective width in the tension zone is predicted by nsidering an N (ig. 9). So, the axial stiffness in the mpression zone is cw, c = 55 and in the tension N zone is cw, t = 488. The local bucling of lumn web, in mpression, observed during the tests is shown in igure 10. Tension zone 1:1 b eff stiffness t cw=.0 strength 5 1:.5 b eff Tension zone Compression zone Compression zone t cw=.0 d wc =17 b eff = b eff 5 d wc=40 igure 9. Model to Determine the Resistance and Stiffness of Column Web in Tension and Compression. igure 10. Local Bucling of Column Web in Compression Zone

9 616 Experimental and Theoretical Investigations of Pallet Racs Connections.1.4 Column web in shear Shear deformation of panel zone occurs only in case of external joints, when one-sided bending moment is acting from beam. Shear force in panel zone is not uniformly distributed. Its values change in the levels of nnector s tabs (or levels of perforations in lumns), see igure 11. The highest value of shear force is reached at the center of the panel zone, while a small reductions occurs at its ends. or the sae of simplicity it can be assumed that shear force is uniformly distributed in the entire panel zone. Transformation parameter β acunting distribution of shear force at lumn length can be in this case calculated as (aella et al. [9]): hp β = 1 (8) h c where h p is the height of panel zone and h c is lumn height. δ V Tension zone h 1 =19 h c h p Compression zone hp=00 h = Panel zone V V igure 11. Panel Zone in Shear The resistance of panel zone in shear including the effect of the distribution of shear force is given by: Vcw, s cw, s = (9) β where V, - resistance of lumn web in shear: cw s f y, cw Avc V cw, s = (10) A, is the shear area of lumn web, with acunting perforations of web. So the resistance of vc net panel zone can be calculated as:

10 Lucjan Ślęcza and Alesander Kozłowsi 617 f y, cw Avc cw, s = (11) β The height of panel zone is equal to equal to h c = 570 and h p = 00, the lumn height in tested nnections is A vc, net = 106, so β = and, s = 6, N. cw The stiffness of panel zone is affected by the presence of perforations at regular intervals at lumn height. The axial stiffness of spring modeling behavior of this mponent has to be predicted from general rule, (ig. 11): cw, s = (1) δ Deflection of panel zone under shear deformation δ can be predicted as sum of deformation of areas with net shear area A vc, net and with gross shear area A vc : h h δ = 1 + (1) G A G A vc, net vc where h and 1 h are total height of net shear area and gross shear area respectively. Taing into acunt that G = 0. 8 E and transformation parameter β acunting distribution of shear force at lumn length, equation (1) can be written as follow: 0.8 E cw, s = (14) h1 h β + Avc, net Avc which gives value of axial stiffness cw, s / = 89,8 10 N. Deformation of panel zone observed during the tests is shown in igure 1. igure 1. Deformation of Panel Zone

11 618 Experimental and Theoretical Investigations of Pallet Racs Connections.1.5 Tabs in shear Another mponent affecting the rotational behaviour of the rac joint is the tab of the nnector, subjected to bending and shear from local bearing stresses. To predict the resistance and stiffness of this mponent, the model of a cantilever beam subjected to a ncentrated load can be used (ig. 1). The distance between the load and fixed end of beam, measured by the developed length of tabs is equal l = 7, 0. The resistance of the tab t, s can be evaluated as shear resistance: t, s = Av ( fu, / ) (15) where AV - effective shear area of tab; f, - ultimate tensile stress of nnector. u Area of bearing Tension zone l Compr. zone 1 t tab igure 1. Tab in Shear and Bending Because of the existence of undercuts in tabs, made during punching in time of production, effective thicness of tabs is equal ttab, eff =, 0, instead the nominal value ttab, nom = 4, 0. The resistance is based on the ultimate tensile strength of the nnector f, rather than the yield stress, so resistance of the mponent can be calculated as The initial stiffness of this mponent t s t s u, = 9,1 N., can be calculated using equation (), where δ is the deflection of the beam (at the point where the ncentrated load is acting) from bending and shear: l l 1. δ = + E I G AV (16) Both moment of inertia I and shear area A V should be calculated taing into acunt the N effective thicness of the tabs. Using above equations it can be predicted that t, s = 714. This mponent is active both in the tension and mpression zones of the joint.

12 Lucjan Ślęcza and Alesander Kozłowsi 619 Deformations of tabs, due to shear and bending, observed during the tests are depicted in igure 14. igure 14. Deformation of Tabs due to Shear and Bending.1.6 Connector in bending and shear Behaviour of the nnector can be modelled taing into acunt a cantilevered part of the nnector, protruding over the flange surface of the beam, as shown in igure 15. δ Ext. A Int. A X 4 A-A x 7 igure 15. Connector in Bending and Shear

13 60 Experimental and Theoretical Investigations of Pallet Racs Connections Resistance of the mponent can be found as plastic resistance of an element subjected to bending and shear: V M, s = AV f y, / = 19, N (17) 4, b = Wpl f y, = 4, N. (18) where AV - effective shear area of nnector; section modulus of nnector. f y, - yield stress of nnector; Wpl - plastic The initial stiffness of this mponent is calculated as the ratio of the force to the deflection of the mponent under this force, equation (). Because of the openings (slots) in nnector, the deflection of the mponent was evaluated as for shear-wall structures ntaining openings under lateral loads acrding to (Benjamin [5]), including the effect of bending and shear. Every tested group of joints has different beam heights, so the initial stiffness of the mponent is different for each group. In every group two values of initial stiffness has been calculated: for external slot (force is acting in tab more distant to the beam), and for internal slot (force is acting in tab closer to the beam). Predicted values of the initial stiffness for each group are listed below. Group B : Group C : Group E : N N, ext = 540,, int = 5664 ; N N, ext = 68,, int = 689 ; N, ext = 66,, int =. or group D the values of initial stiffness of nnector in bending and shear are the same as in group B, and for group as in group E. This mponent is active both in the tension and mpression zones of the joint. Observed deformations of nnector during the test are shown in igure 16. igure 16. Deformation of Connector Observed during the Tests

14 Lucjan Ślęcza and Alesander Kozłowsi Connector web in tension (mpression) Regarding the tension and mpression zones of the nnector web, the resistance estimated acrding to (EN [8]) as: w can be w ω beff t f y, = (19) where ω - factor acunting for the interaction with shear; t f y, cw - yield stress of nnector. The effective width of the nnector web eff - thicness of the nnector s web, b acunts for the spreading of the stresses transmitted by the beam flange (igure 17). Assuming the tangent of the spreading angle 1 :. 5, b eff =7 can be adopted and the resistance in mpression and tension zones can be calculated as w t, = w, c = 7,4 N. d wc= beff t =4.0 igure 17. Connector Web in Tension or in Compression The axial stiffness of the nnector web in tension and mpression can be evaluated from the relationship: ' w = E beff t / dwc (0) Assuming an angle of N w, t = w, c = 5760 can be calculated..1.8 Beam flange in tension (mpression) o 45 for the load spreading, the value of the initial stiffness The last mponent, beam flange in tension and mpression, has to be nsidered only in the evaluation of the joint resistance. Its resistance can be mputed as: bf, c bf, t = beff tbf f y, bf = (1)

15 6 Experimental and Theoretical Investigations of Pallet Racs Connections where t bf - thicness of the beam flange, f y, bf - yield stress of beam flange. The spreading of stresses to calculate effective width of the beam b eff is depicted in igure 18. The value of resistance in tension and mpression zone can be predicted as bf, c = bf, t = 9,9 N. Weld toe b eff. Evaluation of the Rotational Stiffness igure 18. Stress Distribution in the Beam lange The mechanical model adopted to predict the initial rotational stiffness is shown in igure 19a. The springs representing the behaviour of the mponents are located at the level of the tabs of nnector and at the level of beams flange. Only lever arm of spring representing behaviour of panel zone is different. Acrding to (EN [8]) it can nservatively be taen as the distance from centre of mpression to a point midway between two rows of tabs in tension zone. In the calculation it is also assumed that the ntribution of the springs situated in the centre part of the joint is small and so their influence has been neglected. a) cw,s cw,tear cw,t t,s,ext,int b) w,t zp hb-tfb zp hb-tfb w,c cw,b cw,c c) d) e) zp h t h c hb-tfb S 1 S S S j,ini igure 19. Mechanical Model and Procedure for Evaluating the Rotational Stiffness

16 Lucjan Ślęcza and Alesander Kozłowsi 6 The procedure to evaluate the rotational stiffness is depicted in igures 19b 19e. The first step is the mputation of effective stiffness of each row (ig. 19b), followed by the prediction of the equivalent overall stiffness in the mpression and tension zones and of the lever arms (ig. 19c). Third step is change of two springs with axial stiffness into one spring with rotational stiffness (ig. 19d); and finally the prediction of the initial stiffness of the whole model, (ig. 19e). Adequate relationships to mae nversion of mechanical model from igure 19a to model depicted in igure 19e, can be found in mechanics handboos or in (aella et al. [9]). Presented model is general, spring representing panel behaviour is only active in external nnections. In internal nnections, panel zone is not affected by shear force and, =. cw s The most influencing mponent on the rotational stiffness in tested nnections is lumn web in bearing... Evaluation of the lexural Resistance Behaviour of such joints can be nsidered in two stages: before direct ntact of nnector with lumn flange (elastic stage) and after this ntact occurred (plastic stage). Mechanical model adopted to predict the elastic flexural resistance and lever arms for each group of mponents are presented in igure 0a. Because the weaest mponent governs the resistance of each row, model depicted in igure 0a can be easy simplified into model presented in igure 0b. a) cw,s cw,tear cw,t t,s b) cw,s 4 1 M,b w,t bf,t M,b zp hb-tfb hb-tfb zp w,c bf,c cw,b cw,c c) 1 M,b h 1 h i h z 1 Z igure 0. Mechanical Models for the Elastic and Plastic lexural Resistance Evaluation hb-tfb The resistance of mponents mared 1 in igure 0b is equal to =, = 6,6 cw tear when mponent is in tension (lumn web in tearing), or = cw, b = 8,07 N when mponent is in mpression (lumn web in bearing). The resistance of mponents mared (beam flange) is equal = bf, c = bf, t = 9,9 N and the resistance of the nnector in N

17 64 Experimental and Theoretical Investigations of Pallet Racs Connections bending (modelled as rotational spring ) is equal to M, b = 4, N. The resistance of 4 lumn web in shear ( 4 ) is equal to, s = 6, N, but this mponent should be nsidered only in case of external nnections. In internal nnections, panel zone is not affected by shear force and, =. Model presented in igure 0b, represents only the initial behaviour cw s cw of joint, when the gap between the lumn flange and nnector (ig. ) still exists. To describe ultimate behaviour of nnection, it can be assumed that the rotation of the nnector increases, the gap disappears and ntact stresses start acting between lumn flange and nnector directly, (ig. 0c), what change the lever arm. Also it is assumed that plastic distribution of internal forces can be obtained the tests (Kozłowsi and Ślęcza [14]) showed that all mponents have proper ductility. All forces acting in each row of mponents 1 in tension zone reach plastic capacity: minimum value between the resistance of their basic mponents - = cw, tear = 6,6 N (lumn web in tearing). rom ndition of equilibrium the reaction in mpression zone Z is equal to the sum of forces in each tension rows. When the gap has disappeared bearing stresses between nnector and lumn are non-uniformly distributed. Because the flexural resistance of nnector protruding over the flange surface of the beam can not be exceed, so centre of mpression can be determined from equation: M,b z1 = Z () where Z = reaction force in mpression zone, M, b = flexural resistance of nnector and 1 = distance of centre of mpression from bottom flange of beam, igure 0c. When the centre of mpression is found, plastic flexural resistance can be predicted using equation: z M pl = cw, tear hi + M, b i= 1 () where h i = the distance of i th mponent from the centre of mpression, cw, tear = minimum value of the resistance in each row (in this case lumn web in tearing) and M, = flexural resistance of nnector. In addition the flexural resistance of upper part of nnector should be checed. When the bending moment generated by two forces acting in upper rows is greater then the flexural resistance of nnector M,, than the value of force acting in upper row should be reduced to a value of cw, tear b b ψ to satisfy moment equilibrium. In case of external nnections plastic flexural resistance of nnection uld not be grater than resistance of lumn web in shear: z. igure 0c shows nfigurations of mponents only in internal nnections. M pl cw, s p Component method shows that plastic flexural resistance of almost joints (group B, D, E and ) is governed by the resistance of lumn web in tearing, in tension zone and nnector in bending and shear b cw tear M, in mpression zone (igure 1). Only in case of group C moment resistance is also influenced by flexural resistance of nnector reduction of the force acting in the first row to ψ (igure 1). cw, tear M, in tension zone, giving b

18 Lucjan Ślęcza and Alesander Kozłowsi 65 cw,tear Group E and cw,tear Group B and D ψ cw,tear Group C cw,tear M,b 65 M,b 75 M,b 5 85 Plastic hinge igure 1. Plastic Resistance Model of Each Tested Joint Group 4. COMPARISON O RESULTS Deformations of internal nnectors observed during the tests are depicted in igure, to mpare with these from the proposed models, as shown in igure 1. Collection of the resistances and stiffness of basic mponents, obtained using mponent method is presented in Table 4. It can be seen that the weaest mponent in tension zone is lumn web in tearing, which resistance is only, tear = 6,6 N. In mpression zone the weaest is cw lumn web in bearing:, b = 8,07 N. The biggest influence on the joint global stiffness shows mponent: bearing of the tab to lumn web. These findings were nfirmed during experimental tests and by failure modes of joints, see igure 6 and 8. cw igure. Typical Deformation of Internal Joints Observed in Each joint group

19 66 Experimental and Theoretical Investigations of Pallet Racs Connections Table 4. Stiffness and Resistance of Analysed Joint Components N Component Axial stiffness Resistance [ N ],[ N] Column web in tearing Column web in bearing Column web in tension Column web in mpression Column web in shear Tabs in shear Connector in bending and shear Group B and D Group C Group E and Connector web in tension (mpression) Beam flange in tension (mpression) cw, tear = 5599, = 48,5 cw b cw, t = 488 cw, c = 55, = 89,8 cw s t, s = 714, ext = 540, int = 5664, ext = 68, int = 689, ext = 66 =, int w, t = w, c = t V, = 6,6 cw tear, = 8,07 cw b cw t, = 5, = 4, cw c, = 6, cw s, s = 9,1, = 19, s M, b = 4, w, t = w, c = 7,4 bf, c = bf, t = 9,9 Comparison of predicted by mponent method values of initial rotational stiffness with values from tests is shown in Table 5. Analytical values of plastic flexural resistance M for all analysed groups and their mparison to values obtained during experimental tests are presented in Table 6. Table 5. Prediction of the Initial Stiffness and Comparison with Experimental Data Group B Group C Group D Group E Group Test results [Nm/rad] 19,40 116,70 71,5 1,06 96,15 Component method [Nm/rad] 98, 9,6 9, 100,4 95, 4 pl Difference: (mponent-test)/test [%] -9,6-19,8 0,7-18,4-0,8

20 Lucjan Ślęcza and Alesander Kozłowsi 67 Table 6. Prediction of the Plastic lexural Resistance and Comparison with Experimental Data Difference: Test results Component method (mponent-test)/test [Nm] [Nm] [%] Group B Group C Group D Group E Group,19,6,10,0,7,95,49,95,1,1 Comparisons of predicted by means of the mponent method results with those obtained from tests shows the high level of accuracy, both for the stiffness and for the flexural resistance, in case of analysed joints. -7,5 5,5-4,8 -, -7,1 5. CONCLUSIONS Behaviour of pallet rac joints is governed by few mponents. Some of them are very similar to the mponents in structural nnections of hot rolled I and H sections: lumn web in shear, lumn web in tension or in mpression, beam flange in tension or in mpression. Others are result of using ld-formed perforated lumns, special nnectors and tabs in beam-lumn nnection: tabs in shear, nnector in bending and shear and lumn web in tearing. Analysis of behaviour of particular basic parts of the joints, lie in mponent method, enable designers to understand joint performance and safety design. Next advantage of the mponent method is the possibility to predict mechanical characteristic of joints without expensive experimental wor. Traditionally, behaviour of such mplex joints as steel pallet rac joints is predicted by testing. The mponent approach presented in the paper can be used as mplementary method. Next important advantage of the mponent method is the possibility to provide clear and precise specification of the influence of each mponent on the resistance and stiffness of the joint. The weaest mponent can be easily identified and improved. It maes easier to nduct the optimisation of joints, especially in the systems, which are produced in long series, as steel storage pallet racs. Level of accuracy reached from mponent method shows possibility of using this method in practical application.

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