BEARING CAPACITY OF BOLT WASHERS

Transcription

1 BERING CPCITY OF BOLT WSHERS d J.M. Leijten 1, ndré J.M. Jorissen 2 BSTRCT: The European Yied Mode (EYM) has been accepted to determine the oad-carrying capacity of structura timber connections. However, experiments of boted connections are sti not in agreement with the EYM uness the additiona bearing capacity offered by the washers is taken into account. This bearing capacity is depending on the compressive strength perpendicuar to grain of the structura timber. Tests resuts carried out with M16 and M24 washers on soid and gued aminated timber are used to verify the reiabiity of three strength capacity predicting modes, one of which is an anaytica mode whie the other two are empirica. It was concuded that the anaytica mode is the superior one. This mode shoud be incorporated in a new structura timber design code revisions.. KEYWORDS: Instructions bots, connections, chord effect, perpendicuar, strength, structura, timber, washer. 1 INTRODUCTION 123 Connections are considered to be the weakest ink in timber structures. Considering connections with ateray oaded fasteners such as nais, dowes and bots, the spacing requirements usuay dictate the timber dimensions. For this reason accurate prediction of the oad-bearing capacity and therefore the number of fasteners required, is important. It has been accepted that the pastic theory, originay proposed by Johansen [1], known as the European Yied Mode (YEM), is accurate in the prediction of the connection strength thus accounting for most of the important parameters. However, one phenomenon it does not consider for boted connections, is the additiona contribution by the washers. It is a we known fact that washers of boted connections contribute substantiay to the oad-bearing capacity when at imit state, pastic hinges appear in the bots shank. Large sip dispacements of the connection members and subsequent deformation of the bot activates a chord effect as in Figure 1. This phenomenon is described this way because the bot acts ike a suspension bridge cabe where the cabe is firmy anchored by the washer with a nut and screw at the outer surface of the side members. nother effect of the washer anchorage forces is the activation of friction between the connection members. This aso contributes 1 d J.M. Leijten, Structura Design Unit, Facuty of rchtecture, Buiding and Panning, TU-Eindhoven, P.O. Box 513, 5600 MB, Eindhoven, The Netherands. Emai: a.j.m.eijten@tue.n 2 ndré J.M. Jorissen, Structura Design Unit, Facuty of rchtecture, Buiding and Panning, TU-Eindhoven, P.O. Box 513, 5600 MB, Eindhoven, The Netherands. Emai: a.j.m.jorissen@tue.n Figure 1: Boted timber to connection the oad-bearing capacity. In Figure 1 the drawing suggests that the bot nut and screw do not rotate. This ony hods when the pastic deformation is ocated away from the washer. When the ratio between the thickness of the outer timber member that anchors the washers and the bot diameter is ow, the deformation of the bot wi extend to the washer. This makes the bot head and nut rotate and concentrate the anchorage forced on the edge of the washer. In structura design codes ike the Eurocode 5, [2], the atter (secondary) effect is not accounted for but the chord effect is. It assumes, as a crude approximation, that 25% of the maximum withdrawa or bearing capacity of the washer is attributed to the connection strength. The next question for the structura designer is how to determine the withdrawa capacity or, in fact, what is the bearing or strength capacity perpendicuar to grain. It is surprising to note that for the same wood species and grade, the standard test methods to determine the compressive strength perpendicuar to grain in the US/Canada, Europe and ustraia/new Zeaand resut in differences of 400% Ranta-Manus & Enjiy [3]. Furthermore, the design standards that shoud convert the standard compressive strength to design vaues are so crude that

2 their predicting abiity has to be questioned. For this reason the attention is now focused on the modes that predict the compressive strength capacity perpendicuar to grain. STM and CEN is shown in Figure. 4. In addition, the U/NZ standard takes the bearing strength at 2mm (4%) deformation, whereas STM takes 1mm (2%). The CEN method is defined by the intersection between the 2 DIFFERENCES IN COMPRESSIVE STRENGTH PERPENDICULR TO GRIN Not ony for the withdrawa capacity of washers, but aso for many structura detais in timber frame buidings, the compressive strength capacity perpendicuar to grain is important as shown by exampes in Figure 2. Figure 4: Compressive strength definition test oad deformation curve and a ine parae to the initia curve with 0.01h off-set, where h is the specimen height. The differences in test specimen dimension, oading configuration and strength definition cause major variants. Besides Ranta-Manus,. & Enjiy, V. [3], a comparative study by Pousse, M. et a. [8], showed a mean compression strength of 2,8 MPa for the uniform compression test according to CEN EN 408, compared to 7,0 MPa according to STM D143. Figure 2: Exampes of perpendicuar to grain situations The differences between the test methods to determine compressive strength of timber are first highighted. Then the modes are deat with that convert the strength vaues to washer bearing capacity vaues. Figure 3: Test pieces of EN408 and STM D143 The test standard to determine the compressive strength perpendicuar to grain in Europe is EN 408 [4]. This prescribes a method where a bock of timber is oaded in uniform compression over the fu surface as shown in Figure 3 (eft). In comparison, the merican STM- D143, [5] test standard, which dates from 1926, is based on a pragmatic, technoogica approach in which the test piece is a timber bock of 51x 51x152mm (2 x2 x6 ) and the oad is appied in the midde through a stee pate of 51 x 51mm as shown in Figure 3 (right). The ustraian and New Zeaand standard, S/NZS 4063, [6], is simiar to STM D143 except that the test piece is 35 x 50 x 200 mm. The STM and U/NZS tests are primariy intended to simuate the behaviour of a wood joist resting on a wa or foundation, Bodig & Jayne, [7], and do not intend to determine a physicay correct perpendicuar to grain strength. nother difference encountered in the interpretation of research resuts is the difference in definition of compressive strength. The definition according to both 3 COMPRESSIVE STRENGTH MODELS The aim is to find a suitabe mode to predict the bearing capacity of washers. In pursuit of suitabe modes, a we defined and physicay correct test method for the compressive strength of timber is considered a prerequisite. Therefore, the CEN EN 408 test method is chosen as starting point. This enabes the comparison of three modes that are then used to evauate test resuts. 3.1 FIRST MODEL The mode by Van der Put [9] is the ony non-empirica mode that caims to expain the test resuts reported by many researchers. In Leijten, et a.[10] the vaidity of this theory was confirmed, based on an even arger data base. The theory assumes stress dispersion, as shown in Figure 5, where the sope of the stress dispersion is 1:1 Figure 5: Stress dispersion according to van der Put [9] for sma (1%) and 1:1.5 for arge (10%) pastic deformations. ssociated with the dispersion of stresses, the theory recognises a oaded or contact ength of the oad introduction and an effective ength, ef, which is governed by the ange of stress dispersion. The theory

3 takes the standard or reference compressive strength, f, determined by the fu surface method of CEN EN 408 as starting point, and, with h as beam height, it is formuated as: F c (1) k b k f 3h ef (2) the tests evauated by Van der Put [9] and Leijten et a. [10] to prove the vaidity of the theory consisted of beams where the oaded area covered the fu width of the test pieces, x b, where b is the beam width. However, if the oaded surface does not cover the fu width, as in the case of washers, it coud be questioned as to whether the compressive stresses dispersion is the same in both materia directions. The argument that the stress dispersion in the theory is direction independent and therefore makes no distinction between grain orientations whatsoever was never verified. In case the sope of stress dispersion is steeper than parae to grain as shown in Figure 6, Equation (1) can be written as. F c b 1 k f with is the oaded area ef is the effective stress dispersion area. k ef (3) 3.2 SECOND MODEL This empirica mode, presented in the Eurocode 5/1, [2] takes the effective contact ength arger than the actua oaded ength as ef + 2*30mm. The cooperative action of adjacent wood fibres runs up to a maximum of 30mm on both sides of the oaded area in grain direction. The contribution of the fibres that run aongside the oaded area, seen in perpendicuar to grain direction, is ignored. ccording to this mode, the design oadcarrying capacity F c provided the distance between two oaded areas is smaer than twice the beam depth ( 1 2h), as shown in Figure 7, is: F b c Fc ef ef k f k f k f (4) c c, 90 c, 90 b ef k = 1,25 for soid softwood timber k = 1,5 for gued aminated softwood timber for a other cases; k = 1,0 The background for the k factors is obscure. ef b ef b b Figure 7: Timber member on continuous support 3.3 THIRD MODEL nother empirica mode presented in Eurocode 5, [11] is very simpe and the easiest to use: F k (4) c f c,90 k factor = 3 f standard compressive strength perpendicuar to the grain. e Figure 6: Stress dispersion parae and perpendicuar to grain of round and square washers. For the test series with two circuar or square washers where dispersion areas overap, the theory excudes the overap for the effective area, ef. 4 TESTS TO EVLUTE THE MODELS test programme is set up to investigate which of the modes predicts best the washer bearing capacity. The wood species chosen is Spruce. Prior to testing, the test pieces are conditioned to the standardized cimate of 20C and 65% RH. Soid wood is used for the tests with M16 washers, and gued aminated wood for the M24 washers. Before the production of the test pieces, sampes are cut from 2500mm ong boards to determine density as we as the standard compressive strength in accordance with CEN EN 408, [4]. From the remaining ength, the test pieces are cut. For the M16 washer test pieces, the 45mm thick and 216mm wide boards are used and, for the M24 washers test pieces, the 100mm thick and 240mm wide boards are used. The mean density of the conditioned specimens is 450 kg/m 3 at 12% moisture content, whie the standard deviation is 11 kg/m 3.

4 4.1 Test specimens n overview of the test pieces and the spacing of the circuar M16 washers, as we as the a other dimensions, are given in Figure 8. The same test Figure 8: Overview of M16 round washer test specimens specimens with the same dimensions and washer spacings are produced for M16 square washers. If two washers are used in a test piece the spacing is consistent with the Eurocode 5, [11] reguations for M16mm and M24mm bots, spaced 4d and 5d perpendicuar to grain and parae to grain respectivey. The outer M16 circuar and square washer dimensions are 60mm with a centre hoe of 18mm. The M24 circuar and square washers measure 80mm for the outer dimension and 26mm for the centre hoe. tests are carried out in accordance with CEN EN 408 [4] with respect to the oading procedure to determine the compressive strength capacity, using the 1% off-set procedure shown in Figure 4. To obtain some additiona information, the test went on unti at east a tota deformation of 10% was recorded. The oad introduction is achieved by the appying oad, to cut off threaded rods with nuts that oad the washers to refect the actua situation, Figure Test Series Top eft ER Top right DR Left D80R The short threaded rod is ony for stabiizing purposes and to fix the washer position during the test. Figure 9 shows the arge deformation of the M16 specimen hoding two circuar washers at the termination of the test. It was observed that the M24 square washers pasticay deformed more when compared to the circuar M24 washers. This is refected by the consistent ower compression stress at 1% off-set deformation (f 1% ). However, at deformation of 10%, the differences vanish. 4.2 TEST RESULTS In Poussa et a. [8] who performed 200 tests on Finnish Spruce, reported vaues that ranged from 1.9 to 4.1 N/mm 2 with an average of 2.8 N/mm 2. The mean standard compressive strength observed in the tests for this project is 2.64 N/mm 2, with a st. dev. of 0.15, which is cose to the mean vaues reported by Poussa et a.[8]. t 10% deformation, the average standard compressive strength recorded is 3.08 N/mm 2 with a st. dev of Tabes 1 present an overview of the average vaues per test series for both M16 and M24 washers. The number of tests (n) per series varied because the presence of even sma knots under the washer significanty affected the compressive strength in a positive way, and for that reason they are disregarded. Tabe 1:Test resuts;m16 (top), M24 (bottom) washers Test Test f f f max max. Series number 1% 10% disp. n [MPa] [MPa] [MPa] [mm] EV 9 5,93 8,66 13,51 16 ER 10 5,03 7,55 12,4 16 DR 9 5,28 6,41 13,71 33 DV 8 6 7,57 16,21 36 D80R 9 4,5 5,58 10,25 35 D80V 7 5,63 6,68 11,24 35 EV 7 6,77 10,09 15,56 32 ER 6 7,53 11,53 17,78 32 DR 6 7,05 10,93 15,45 31 DV 7 6,56 10,29 16,1 31 D120R 7 7,3 11,2 15,73 30 D120V 7 6,81 10,27 14,07 28 R= round; V= square; 80 and 120 =spacing The Tabe aso incude the additiona resuts of the maximum dispacement and compressive stress, at the termination of the test. Figure 9: Test with two round M16 washers 5 EVLUTION OF TEST RESULTS The test resuts are evauated using the three Modes presented earier and the resuts are presented in Tabe 2. Regarding the mode prediction by the First Mode by Van der Put, it is concuded that, in genera, the prediction overestimates the test data. The reason for this this anomay is the theory assumption of materia

5 Mode prediction [N/mm2] isotropy and therefore equa dispersion of the compressive stresses in both parae and perpendicuar Tabe 2: Overview of test resuts Test Test Mode Test Series data vd Put data Put EC5/ EC5 1% 1% 10% 10% 1 EV 5,93 6,44 8,66 8,71 9,37 7,9 ER 5,03 5,82 7,55 7,05 9,53 7,9 DR 5,28 5,86 6,41 6,64 9,53 7,9 DV 6,00 5,90 7,57 7,49 9,37 7,9 D800R 4,50 5,91 5,58 6,53 6,35 7,9 D80V 5,63 5,70 6,68 6,54 6,25 7,9 EV 6,77 7,70 10,09 10,3 7,2 7,9 ER 7,53 5,37 11,53 10,4 7,99 7,9 DR 7,05 6,69 10,93 7,87 7,99 7,9 DV 6,56 6,74 10,29 7,25 7,2 7,9 D120R 7,30 6,63 11,20 8,64 5,32 7,9 D120V 6,81 6,50 10,27 8,42 4,8 7,9 to grain direction. pparenty this assumption can be questioned. For that reason a steeper empirica stress dispersion perpendicuar to grain is take. n optimisation process showed that a much better fit is achieved aowing the stress dispersion perpendicuar to grain to be not 1:1 but much steeper to 1:0.4 for 1% deformation, and 1:0.7 for 10% shown in Figure 10. Whie, on average, the data is now coser to the diagona, deformation. graphica representation of these optimisation process resuts, is the scatter is smaer too. However, if the test resuts at the upper end of the scae, are considered, ie: those which originate from the Series with M24 washers, the prediction is now more conservative for unknown reasons. 12,00 10,00 8,00 6,00 4,00 M16 and M24 washer: Reduced stress dispersion type (sawn or gued aminate). Some of the test series with two washers, do not satisfy the minimum distance between the oaded areas ( 1 2h condition), and for that reason the k drops from 1.5 to 1,0 compared to the other tests. It appears that the sudden drop in k and therefore in strength prediction, adds consideraby to increasing mode uncertainty. In the simpe Third Mode, k = 3 irrespective of a parameters considered by the other modes. That makes the bearing stress capacity three times the reference or standard compressive strength, times the oaded area. In Figure 11 the predictions of both Second and Third Mode are presented for 1% deformation. The inabiity of the empirica modes to foow experimenta resuts is cear and becomes even more apparent at 10% deformation (graph not shown). Figure 11: Test data versus mode prediction 5.1 MODEL UNCERTINTY Comparison of the modes is achieved by evauation of the prediction of the mode uncertainties. This is a method to distinguish how we or bad the modes predict the test data. The ratio of test data and mode prediction is, for this reason, potted on a natura og scae as shown in Figure 12 and 13, for 1% and 10% deformation respectivey. The og norma distribution curves are fitted to the data of the modes. The coser the top of the curves to the nought vaue on the horizonta axes, the better the mean prediction. The sender or steeper the curves are, the more accurate in predicting abiity. Tabe 3 contains the average and standard deviation of the curves. Notice that for both 1% and 10% deformation the Third (EC5) Mode with k = 3 yieds 2,00 0,00 0,00 2,00 4,00 6,00 8,00 10,00 12,00 Test data [N/mm2] 1% deformation 10% deformation Figure 10: Test data versus vdput mode prediction In addition, the other two empirica modes are evauated to assess prediction abiity. It is unknown to which deformation both modes are caibrated (if they ever are), whie the modes do not account for differences in specimen depth either. What affects the resut of the Second Mode, is dependent on the spacing between oaded areas parae to grain and the materia Figure 12: Mode uncertainty at 1% off set

6 Figure 13: Mode uncertainty at 10% off set ess scatter than the more refined Second (EC5/1) Mode. The uncertainty pots ceary show the First Mode to possess the smaest scatter and the best fit. From the uncertainty anayses it is cear that the Second (EC5/1) Mode possesses the owest reiabiity in prediction abiity. Tabe 3: Uncertainty pot characteristics 1% off set van der EC5/1 EC5 deformation Put verage Stand. dev % deformation verage Stand. dev CONCLUSIONS From the anayses of the test data, it can be concuded that the best mode to predict the compressive strength perpendicuar to grain at 1% and 10% deformation is the Mode by Van der Put. This is provided the dispersion of the compressive stresses perpendicuar to grain is taken smaer than parae to grain. Instead of 1:1 and 1; 1.5, for parae to grain dispersion the best fit is achieved for a stress dispersion sope of 1:0.4 for 1% deformation and 1: 0.70 for 10% deformation. Further investigations are required to understand why ony tests with two M24 washers per test piece deviate from the prediction. Regarding the two remaining empirica modes it is shown that, for the Second (EC5/1) Mode, ignoring differences in specimen depth and deformation, contributes to the inabiity to foow the test resuts. In this respect the steps in the k vaue for cose spaced washers (oaded areas) contributes to the increase of the mode uncertainty. The Third (EC5) Mode with the fixed k =3 vaue takes a midde position in accurate prediction. REFERENCES [1] Johansen K. W.: Theory of Timber Connections. Internationa ssociation for Bridge and Structura Engineering, Vo. 9, [2] Eurocode 5/1: Design of timber structures - Part 1-1; Genera - Common rues and rues for buidings, mendment 1. European Committee for Standardization, Rue de Stassart 36, B-1050 Brusses, EN /1: 2004;E. [3] Ranta-Manus,. Enjiy, V.: Testing & Product standards - comparison of EN to STM, S/NZ and ISO standards. In: Proceedings of the CIB W18, paper , [4] EN 408: Structura timber and Gued aminated timber - Determination of some physica and mechanica properties. European Committee for Standardization, Rue de Stassart 36, B-1050 Brusses, [5] STM D143: Standard method of testing sma cear specimens of timber. STM Internationa, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, P, US, [6] S/NZS : Characterization of structura timber, part 1: Test methods, Standards New Zeaand, Radio New Zeaand House, Weington, New Zeaand, [7] Bodig J. & Jayne B.J.: Mechanics of wood and wood composites. Van Nostrand Reinhod Company, 1982 [8] Poussa, M., Tukiainen, P., Ranta-Manus,. Experimenta study of compression and shear strength of spruce timber. In: Proceedings of CIB W18, Paper , Bed, Sovenia, [9] Put, T..C.M. van der: Derivation of the bearing strength perpendicuar to the grain of ocay oaded timber bocks. Hoz- as Roh und Werkstoff, 66: , [10] Leijten,.J.M. Larsen, H.J. van der Put, T..C.M.: Structura design for compression strength perpendicuar to the grain of timber beams. Construction and Buiding Materias, 24: , [11] Eurocode 5: Design of timber structures - Part 1-1; Genera - Common rues and rues for buidings, European Committee for Standardization, Rue de Stassart 36, B-1050 Brusses, EN : 2004;E CKNOWLEDGEMENT The authors wish to thank ab assistant J. v.d. Oever for carrying out the tests and Mrs. M. Wood, who took care of the correct Engish wording.