WITHDRAWAL CAPACITY OF LONG SELF-TAPPING SCREWS PARALELL TO GRAIN DIRECTION

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1 WITHDRAWAL CAPACITY OF LONG SELF-TAPPING SCREWS PARALELL TO GRAIN DIRECTION Pål Ellingsbø 1, Kjell Arne Malo 2 ABSTRACT The behavior o mid- sized sel-tapping screws are considered when the inclination between grain direction and screw axis is zero and the application no longer is covered by Eurocode 5. Both experimental tests and a numerical analysis are carried out, and the results compared with state o the art analytical expressions based on the Volkerson model combined with an average stress ailure criterion. The criteria accounts or initial shear stresses introduced by the damage done to the wood as the screw are driven in. The initial shear stress is used as the itting parameter, but considerations o the racture energy are also given. Good agreement is ound or all the test data. The Volkerson model assumes shear stress along the length o the sel-tapping screw and numerical analysis have been perormed or veriication. KEYWORDS: Sel-tapping screws, withdrawal capacity, average stress analysis, numerical simulations INTRODUCTION Over the last decades the use o long sel-tapping screws and threaded bars has increased with the development o more pre assembled constructions and construction parts[1]. The behavior o sel-tapping screws have been studied in a number o numerical and experimental test e.g.[2-4]. The most common approach is probabilistic, however the number o itting parameter are large and other methods and new approaches exists. Numerical analysis suggests[5] that the strain ield along the screw axis is exponentially distributed with zero magnitude at the screw tip and increasing towards the head. The studies indicates that the outmost part o the timber will ail due to large strains in the steel member o the connection, prior to the global ailure o the connection, introducing a zipper eect o the strain distribution in the timber member. The guidelines or axially loaded screws in Eurocode 5[6] require a minimum inclination between grain and screw axis o 30 degrees. These requirements are probably introduced because to avoid parallel to grain cracks, moisture induced cracks and shear stresses introduced by the insertion o the screw itsel. The introduction o larger and longer sel-tapping screws with base diameter up to 30 mm makes these inclination limitations questionable. The longer anchor length o the screws makes moisture induced cracks less critical because o their limited extension. On the other hand the initial shear stress introduced need special consideration. 1 Pål Ellingsbø. Department o structural Engineering, NTNU, Richard Birkelandsvei 1a, 7491, Norway. pal.ellingsbo@ntnu.no 2 Kjell Arne Malo. Department o structural Engineering, NTNU, Richard Birkelandsvei 1a, 7491, Norway. kjell.malo@ntnu.no Figure 1: Stress distribution rom numerical analysis in the timber along a threaded bar.

2 The sel-tapping screw considered in this report are all considered mid-sized, with a diameter o 8 mm and length o 300 mm. These screws are covered by the Eurocode when the screw inclination towards the grain direction is larger than 30 degrees. Test results reported herein consist o withdrawal tests o sel-tapping screws with 0 degree grain screw axis inclination. The results are compared with the existing rules o Eurocode 5 and a mean average stress method based on the Volkerson method[7]. This method is valid in cases where a shear orce along the screw axis is the driving orce during ailure. A numerical analysis o the test series has been carried out or comparison o strain ields and better understanding o the stress and strain distributions. 2 ANALYTICAL EXPRESSIONS 2.1 EUROCODE 5 The ultimate withdrawal capacity or a sel-tapping screw is described in Eurocode 5. The expressions are only valid i the ollowing criteria are ulilled: The ratio d 1 /d between the screw base diameter d 1 and the outer diameter d is between 0,6 and 0,75. The outer diameter d o the screw is smaller than 12 mm. The eective anchor length l e o the screw is larger than 6d The inclination between screw and grain axis is larger than 30 degrees. The latter requirement is not ulilled or the test analyzed here, but a comparison with the test results is carried to see the validity o the equations at this coniguration. From Eurocode 5 the ollowing equation gives the withdrawal capacity o the screw: n d l k F 1, 2 cos( ) sin( ) e axk. e d ax.. Rk 2 2 (1.1) The equation depends on the eective length o the screw, l, the density o the wood and the base e diameter o the screw d. The characteristic withdrawal is given by: and k by: d d l (1.2) ax. k e k d k min(,1.00) (1.3) d 8 The criteria or the minimum edge and end distances are given in Figure 2. Figure 2: Requirements or spacing, edge and end distances or axially loaded screws in EC5[6] 2.2 AVERAGE STRESS ANALYSIS The ailure load calculation o screws based on the Volkerson model is presented in[7]. Figure 3: Assumed shear stress distribution along the screw axis[7] The average stress needed to initiate ailure is calculated over a length l 0 dependent on the material parameters. In the Volkerson model the shear stress distribution shown in Figure 3 is assumed. The load calculations are presented or two kinds or load conigurations. The pull-pull coniguration where the head o the screw is pulled out, and the bottom end o the timber member is restricted, and the pull-push method where the timber member is constrained at the top. In all the tests analyzed here in the pull-pull coniguration is used.

3 The racture energy G or the material is used in order to estimate the length l 0 in which the shear stress is averaged to see i the ailure criterion is ulilled. The racture energy is deined as the energy needed to separate a given area o the material completely[9]. Since the Volkerson model assumes a shear stress distribution along the screw axis, the racture energy is a unction o the shear strength: G ( ) d (1.7) 0 In [10] a calculation o the racture energy based on a idealized linear behavior was presented. The racture energy then becomes: Figure 4: Load conigurations[7]. The pull-pull coniguration to the let hand side is the one considered in the tests herein The theoretical solutions or lag screws are compared with test results o withdrawal o sel-tapping screws. In [7] the damage o driving a screw into timber is introduced as a initial shear stress. The magnitude o the initial shear stress is itted against experimental results. In addition the material shear strength and mode II racture energy, G, is the only material parameters needed. The ailure load is calculated as where P l 2t 1 1 l d 0 u initial dim T T initial v mean, initial (1.4) dl( ) (1.5) G 1 2 v v (1.8) where is the idealized shear stiness o the shear layer in the material that ractures. In the calculations v is used. A racture energy o G 0,7 was obtained In [10] and are applied in the calculations here in. 3 EXPERIMENTS 3.1 MATERIALS AND TEST CONFIGURATIONS The test series looks dierent eective insertion lengths o the screw, and the impact o pre-drilling. Two test series were carried out with dierent widths, 19 and 48 mm. Only the 48 mm specimen is considered in detail. For all specimens the edge and end distances is smaller than the requirement the Eurocode 5. The small edge distances were used to get strain measurements rom a digital image correlation[11] (DIC) system as close to the screw axis as possible. For a width o 48 mm the edge distance is 25 mm, while the Eurocode requirement is 32 mm. and dim 1 l l 0 0 sinh( ) sinh( w(1 )) l 1 l sinh sinh min 1 1 l l sinh l l sinh 0 0 sinh( (1 )) sinh( ) (1.6)

4 Figure 5: Test specimen or withdrawal o screw parallel with grain direction. Width o 48 mm, and eective load carrying length o the screw o 200 mm The outer surace o the specimen was treated with spray paint prior to test to allow the DIC system to monitor surace strains during the analysis. The strain ield is super imposed on the specimen as shown in Figure 19, and simpliies the comparison between the experimental results and the numerical simulations. The material used or testing was graded according to strength class C24 in EN338[12]. In Table 1 the material properties used or the analytical calculations are shown. 3.3 FAILURE MODES Four ailure modes were observed during testing. In specimens with width 48 mm, plug shear ailure around the screw and head tearing o the screw was observed. For the specimen with 19 mm width splitting o the wood perpendicular to grain, and block ailure around the screw dominated. The ailure modes are given in Figure 7 and Figure 8. Table 1: Strength and stiness properties or C24[12] Mean elastic modulus parallel E 0,mean MPa Mean elastic modulus perp. E 90, mean 370 MPa Mean shear modulus G mean 960 MPa Mean density ρ mean 410 kg/m 3 The sel-tapping screw used has a base diameter o 5 mm and outer thread diameter o 8 mm. The length o the screws is 300 mm, but only 150 and 200 mm eective length were used in the test series. The steel has a yield strength o 640 MPa and ultimate strength o 800 MPa. No testing o the steel strength beyond the declaration rom the manuacturer was carried out. Figure 7: Failure modes or specimens with 48 mm width. Plug shear ailure on the let hand side, screw head ailure on the right hand side. Figure 6: Sel-tapping screw, base diameter o 6 mm and length o 300 mm Although the screws are o the sel-tapping type one test series with pre-drilling was perormed to check or any eect. These tests are marked with an additional ø6 in the tables and igures where applicable. 3.2 TEST SETUP The test setup was a pull-pull coniguration, where displacement and load was measured at the screw head. 30 specimens were tested in each series and three dierent conigurations are presented here. The specimens were tested in a displacement controlled hydraulic rig. During testing the specimens where irst loaded to a level corresponding to 40 % o the calculated ailure load. The level was kept or 60 seconds beore unloading to a level o 10 % o the ailure load. The total time or the test should be between 600 and 1200 seconds, so a displacement speed o 0,75 mm/min was used. All testing was done according to EN380[13] Figure 8: Failure modes or specimens with 19 mm width. Perpendicular to grain splitting on the let hand side, block shear ailure on the right hand side. The three dierent classical ailure modes rom racture mechanics are shown in Figure 9. In Mode I splitting is due to tension orces, mode II is splitting due to shear and mode III o torsional orces. The plug shear ailure in the 48 mm width specimens is a result o a mode II ailure and hence the average stress analysis is applicable.

5 Table 2: Comparison o characteristic ailure load, measured average ailure load and calculated ailure load Figure 9: Classical ailure modes rom racture mechanics 4 RESULTS 4.1 EXPERIMENAL RESULTS In Figure 10 the results rom three dierent test series are plotted with ailure load against eective load carrying length o screw. For the 150 mm eective length test series K the spread covers ailure loads rom 15 up to 22 kn. The large spread reduces in the characteristic values compared with the average values as shown in Table 2. For the predrilled tests in series K ø6 the spread is more conined, but with a lower average. However the calculated characteristic value was in the same region as without pre-drilling. The dierence between the characteristic values and average values also decrease rom the no pre-drilled test series. When the eective length was increased to 200 mm in the K test series, the observed spread is even lower. For 150 mm eective length, the observed ailure mode was pullout o screw or screw head tear o. When the eective length was increased only screw head tear o ailure was observed. The screw head tear o ailure is more conined since the capacity is deined by the steel properties rather than the timber, and less spread in the results were expected here. F k / F average (%) F k / F EC5 (%) K ,00 106,51 K ,12 123,62 K Ø6 86,24 104,29 As mentioned briely above the dierence between average and characteristic value or pre-drilled and no pre-drilled dier. The dierence are 20 % or the test no pre-drilling, while pre-drilling decrease the value to 14 %. With pre-drilling no observations o screw head tear o was observed, only shear plug ailure. The riction between screw base and timber in some o no pre-drilled tests will increase the capacity until screw head tear o occur. While this gives higher average ailure values, the uncertainty o the riction parameter gives nothing extra when the characteristic values are calculated. The characteristic values compared with Eurocode 5 shows a dierence around 5 % or both pre-drilled and no pre-drilled tests at 150 mm eective length. When the eective length is 200 mm the dierence is only 3 %. Compared with the Eurocode 5 values the measured values are 23 % higher. The need or predrilling on the 200 mm eective length test were considered unnecessary since the ailure mode observed on no pre-drilled tests were all steel ailure. In Figure 11 the characteristic values rom the test series with screw is plotted against the analytical expression or withdrawal capacity in EC5. For all tests the characteristic values is larger than the analytical value. It s worth taking notice that the dierence is larger or the test series with 200 mm eective length. This is mainly due to the act that the ailure is governed by the steel properties rather than the timber at this eective length. Figure 10: The eect o the load carrying length o the screw on the spread and average ailure load In Table 2 the results or the characteristic capacity o the three tests series are measured against the average ailure load o the test results, and the calculated ailure load according to Eurocode 5. A comparison with the average stress analysis is not shown since the validity o the model is based on a chosen initial shear stress. Figure 11: Characteristic values or ailure load against eective load carrying length o screws A urther extension o the eective load carrying length o the threaded screw would presumably not yield higher ailure loads than already obtained with 200 mm length. The Eurocode however does not limit the value o the load carrying length and thus overestimates the design strength or the longer threaded screws. The problem has

6 not been important earlier due to the lack o screws with the correct thickness length ratios. The commercial available threaded screw used or this test series however, with a diameter o 8 and length o 300 mm, could be overestimated i the EC5 equations are applied. Figure 13: Sensitivity o change in racture energy the ailure load G on Figure 12: Failure load versus eective load carrying length compared with average stress analysis and varying initial shear stress The ailure loads based on average stress analysis with a racture energy o G 0,7, and the corresponding The racture energy also impacts on the estimation o the initial shear stress. In Figure 13 the ailure load is calculated or racture energies between 0,4 and 1,0. All results are normalized against the a initial shear stress o 1,2 and a the racture energy G 0,7. length l over which the stresses are averaged is l 0 0 = 24 mm is shown in Figure 12. The initial shear stress is ranging rom 0,5 to 1,5 MPa. A value o the initial shear stress o 1,2 MPa gives the best it or the experimental data. This also coincide with results obtained in[7]. In Figure 13 the eect o changing the racture energy is shown. G was varied rom 0,3 to 1,4 and the change was normalized against G 0,7. A reduction o the racture energy G gives larger negative responses on the ailure load than the increase provided by a increase. When G are doubled the increase is 13,62 %, while a halving o the value reduces the strength to 79,44 % o the original. It seems to be more critical or the strength analysis i the G is overestimated. A more accurate estimation o the racture energy value should be given special care. Figure 14: Impact o change o the racture energy on initial shear stress For racture energies above 0,7 G the change in ailure strength is small or all initial shear stresses. For the lower values o the initial shear stress the dierence increases. It s evident rom these simple calculations that the racture energy is o great importance in the calculations o the ailure loads. The introduction o the initial shear stress gives good agreement with the test results. In addition the average stress analysis seems to not overestimate the ailure load as the Eurocode 5 expressions does when the eective load length o the screw is increased. The results also show that the pre-drilling is not aecting the initial shear stress as the same value o 1,2 corresponds well with all test series regardless o pre-drilling. For sel-tapping screws the initial shear stress seem to be introduced by the threads rather than the base o the screw. The average stress analysis yields good overall results compared with the experimental results when the initial

7 shear stress is itted. More tests with dierent eective lengths should also be carried out to check the validity o the equations in the uture. In addition the diameter o the screw should also be considered, the initial shear stress could dependent on screw geometry or the ratio between base diameter and thread size. 4.2 NUMERICAL SIMULATIONS A small numerical analysis was run or comparison with the results rom the DIC analysis. In the numerical simulations a transversal isotropic model was used or the timber. No non-linear or plastic eects were implemented or the wood properties, only linear elastic. The timber material properties used were all according to grade C24 in EN 338[12]. The sel-tapping screw was modelled isotropic with yielding strength according to the material properties provided by the manuacturer and E 210 GPa and 0,33. The geometrical representation o the seltapping screw was described by the dak ile provided by the manuacturer (available online at the SPAX homepage). The mesh was with a adaptive process due to the complicated geometry o the sel-tapping screw. The remeshing resulted in a average element size o 0,25 mm. This gave only one element over the height o the thread on the sel-tapping screw, but this was considered adequate because the bending is neglect able in this part. The element chosen was the 1. order, eight-node element C3D8R. As discussed in[14] a 1. order element is preerred in cases with contact due to convergence problems when introducing higher order elements. The contour plot o the stresses in the timber in the grain direction is shown in Figure 15. The stresses show a decreasing intensity rom the entrance side downwards in the timber or both the parallel to grain and perpendicular to grain direction. This is in concurrence with the results o the analyses made in [5]. The magnitude o the stresses parallel to grain ranges rom 20 MPa in the head. This is close to the maximum strength o the material, but probably not destructive. Perpendicular to the grain the stresses have a maximum magnitude o 14 MPa which exceeds the material strength. Some internal splitting and crushing o ibres would be observed in this area and reduced withdrawal capacity close to the entrance is the result. However the intensity alls rapidly so the area exposed to this large stresses are limited in this linear model. Figure 15: Stresses around sel-tapping screw, stresses parallel to grain in the upper igure, perpendicular to grain in the lower The interaction between sel-tapping screw and glulam was modelled with contact elements. For the normal behaviour an augmented Lagrangian ormulation was used, while the tangential behaviour was modelled with a rictionless deinition. The rictionless behaviour was chosen because o the lack o data concerning the riction properties. The impact on the results is probably small. Figure 16: Stresses on the outer surace o the wooden, stresses parallel to the grain in the upper igure, stresses perpendicular to grain in the lower In Figure 16 the stresses are shown on the ree outer surace o the timber specimen. For the stresses parallel to grain shown in the upper igure the stresses show the

8 same tendency with a decrease in intensity when the distance rom the top increases. For the stresses perpendicular to grain there are neglect able stresses close to the head. There are two peaks in the intensity, the irst approximately a length one third o the screw length into the wood. The second peak is in the area o the screw tip. In maximum intensity the two peaks are the same, but the area aected by the peak close to the screw is larger. length o the sel-tapping screw. The stress and strains is at the maximum close to the head o the screw with a decrease towards the tip. In the strains an increase was also ound towards the tip o the screw perpendicular to grain. This behaviour coincides with the assumptions done or the Volkerson model that the average stress analysis is based on. Figure 18: Displacements perpendicular to grain direction Strains perpendicular to the grain close to the entrance was close to zero. This occurs because the total displacement in this area is large and that a splitting o the material in the grain direction rom the entrance side is observed. This reinorce the theory o a zipper eect in the timber during withdrawal, making the part o the material closest to the entrance reaching ailure irst, activating the material urther towards the tip o the screw. Figure 17: Linear strain on the outer surace o the wooden specimen part, strains parallel to the grain in the upper igure, strains perpendicular to grain in the lower The magnitudes o the stresses are all well within the material strength expect or the maxima in the perpendicular to the grain stress. Some splitting o the material could be observed in these areas, but the size aected are limited and the magnitude decreases rapidly. The strains are also considered to get the ull picture and a comparison with the DIC data obtained rom the tests. In Figure 17 the strains parallel and perpendicular to grain are shown. Parallel to grain the strains are largest close to the head o the screw, while perpendicular to the grain the stresses are o the same size rom approximately one third down the length o the seltapping screw and down towards the tip. The displacement in the x-direction, perpendicular to grain, is shown in Figure 18. The largest displacement occurs close to the entrance o the screw and decrease rapidly downward and is zero at the tip o the screw. The stress and strain plots backs up the claim that the average stress method is applicable or sel-tapping screw by showing a distribution o shear orces along the Figure 19: Surace strains in the y-direction shown directly on specimen during testing made possible with digital image correlation Compared with the results rom the DIC analysis shown in Figure 19 the strains rom the numerical simulation in Figure 17 shows good agreement. The maximum strains occur at the entrance side, and a reduction is observed towards the tip o the screw.

9 In Figure 20 reaction orce is plotted against displacement o the screw head or two tests samples rom the B series and the numerical simulation. Good agreement is shown between the maximum loads in both experimental and numerical simulations. Since the ailure is governed by the steel strength when the eective length is 200 mm, good agreement was expected between the simulations and the tests. The stiness o the connection is also compared. The tests procedure includes a preloading cycle that is clearly shown in the test graphs, and the stiness is calculated ater the sideway shit in the curve. The displacement caused by the preloading does not aect the end result, but makes the total displacements diicult to compare directly. The stiness in the numerical simulation is calculated to be MPa while the stiness in the test lies between and MPa. Since only linear elastic material parameters are used this gives a stier behaviour than the experiments where crushing o the timber is likely. Previous studies have shown that some plasticity is expected to occur[15] in the timber, and urther numerical simulations should include plastic properties or use a reduced stiness. Since not all the displacements occur in the specimen, comparison between the ailure displacements lengths beyond the point that numerical simulations seems to produce more ductile results than the experiments are not made. expression show good general agreement with the characteristic values obtained in the experimental test. For longer eective lengths than tested here, an overestimation o the ailure could occur. By adjusting the initial shear stress, which account or the damage introduced when driving the screw in to the wood, in the average stress analysis is itted to the test result with high accuracy. Variations on the racture energy in the theoretical expressions gave large impacts on the calculated ailure load. As a result o this more accurate racture energies are needed to achieve a more valid analytical expression. More tests with dierent eective lengths should also be carried out to check the validity o the equations in the uture. In addition the diameter o the screw should also be considered, the initial shear stress could dependent on screw geometry or the ratio between base diameter and thread size. The numerical simulations were compared with a strain ield obtained by the DIC system, and the results show good agreement. The numerical simulations also veriy that the Volkerson model is a valid approach or the calculation o the withdrawal capacity. Only linear elastic material parameters are used in the simulations and this have provided a stier behaviour than the experiments. Plastic properties should be implemented in urther analysis or a reduced stiness in the elastic properties could be used. ACKNOWLEDGMENTS The authors acknowledge the support o the work rom Norges Forskningsråd (NFR) under KMB project /I10. Experimental results were obtained with the support o Kjeldstad Trelast. Figure 20: Comparison o test data with numerical simulation or withdrawal capacity o sel-tapping screws 5 CONCLUSION The behavior o mid- sized sel-tapping screws are considered when the inclination between grain direction and screw axis is zero and the application no longer is covered by the EC5. The results have been compared with theoretical expressions ound in the Eurocode 5 and a newly developed average stress analysis based on the Volkerson model. A small numerical analysis has also been carried out or comparison with results obtained rom a digital image correlation (DIC) system used during testing. The comparison between test and theoretical expressions gives good agreement in general. The Eurocode 5 REFERENCES [1] Blass, H.J.B., I. Reinorcements perpendicular to grain using sel-tapping screws. in 8th World Conerence on Timber Engineering, Proceedings Lathi, Finland. [2] Jönsson, J., Load carrying capacity o curved glulam beams reinorced with sel-tapping screws. Holz als Roh- und Werksto, (5): p [3] Danielsson, H. and P. Gustasson, A probabilistic racture mechanics method and strength analysis o glulam beams with holes. European Journal o Wood and Wood Products, (3): p [4] Danielsson, H., The strength o glulam beams with holes - A survey o tests and calculation methods, in TVSM 2007: Lund. p. 91. [5] Ellingsbø, P. and K.A. Malo. Cantilever glulam beam astened with long threaded steel rods. in 11th World Conerence on Timber Engineering, Proceedings Riva del Garda, Italy. [6] Standard, N., Eurokode 5: Prosjektering av trekonstruksjoner, Del 1-1, Allmenne regler og

10 regler or bygninger 2010, Lysaker: Standard Norge. 117, 4 s. [7] Jensen, J., et al., A simple uniied model or withdrawal o lag screws and glued-in rods. European Journal o Wood and Wood Products, (4): p [8] Eurokode 5: prosjektering av trekonstruksjoner, [9] Walsh, P.F., Linear racture mechanics in orthotropic materials. Engineering Fracture Mechanics, (3): p [10] Serrano, E. and P. Gustasson, Fracture mechanics in timber engineering Strength analyses o components and joints. Materials and Structures, (1): p [11] Aramis, 2010, GOM mbh - Gesellschat ür Optische Messtechnik: Braunschweig. p. 3D nummerical meassurement tool. [12] Konstruksjonstrevirke: Fasthetsklasser 2009, Oslo: Standard Norge. 10 s. [13] Norges, s., Trekonstruksjoner : prøvingsmetoder : generelle regler or prøving med statisk belastning 1993, Oslo: Norges standardiseringsorbund (NSF). 8 s. [14] Fish, J. and T. Belytschko, A irst course in inite elements 2007, Chichester: Wiley. XIV, 319 s., pl. [15] Dahl, K.B. and K.A. Malo, Nonlinear shear properties o spruce sotwood: experimental results. Wood Science and Technology, (7-8): p