CIB-W18/39-7-2 INTERNATIONAL COUNCIL FOR RESEARCH AND INNOVATION IN BUILDING AND CONSTRUCTION WORKING COMMISSION W18 - TIMBER STRUCTURES SELF-TAPPING SCREWS AS REINFORCEMENTS IN BEAM SUPPORTS I Bejtka H J Blaß Lerstul für Ingenieurolzbau und Baukonstruktionen Universität Karlsrue GERMANY MEETING THIRTY-NINE FLORENCE ITALY AUGUST 2006
Self-tapping screws as reinforcements in beam supports I. Bejtka, H.J. Blaß Lerstul für Ingenieurolzbau und Baukonstruktionen Universität Karlsrue, Germany 1 Introduction Te compressive strengt of timber perpendicular to te grain is muc lower tan te respective strengt value parallel to te grain. Te ratio of te caracteristic compressive strengt perpendicular to te grain to te compressive strengt parallel to te grain for solid timber is about 1/8. Particularly beam supports sould ence be detailed in order to minimise compressive stresses perpendicular to te grain. Increasing te load-carrying capacity of beam supports may be obtained by enlarging te area loaded perpendicular to te grain or by reinforcing te beam support area. Selftapping screws wit continuous treads represent a simple and economic reinforcement metod. Te screws are placed at te beam support perpendicular to te grain direction. To evenly apply te support load on te screws and on te timber, a steel plate is placed between te beam surface and te support. Fig. 1: Bottom view of a reinforced beam support Comparing te test results, te load-carrying capacity of reinforced beam supports was at maximum 300% iger tan te load-carrying capacity of non-reinforced beam supports. 1
Te maximum ratio between te stiffness perpendicular to te grain of reinforced beam supports and te corresponding stiffness of non-reinforced beam supports was about 5. To calculate te load-carrying capacity and to estimate te stiffness of reinforced beam supports two calculation models were derived. In tis paper bot calculation models will be presented. 2 Calculation model for te load-carrying capacity 2.1 Assumptions Te load-carrying capacity reinforced beam supports is calculated taking into account tree different failure modes. Te governing failure mode depends primarily on te geometry of te beam support and on te geometry of te reinforcing screws i.e. teir slenderness ratio. Furter parameters influencing te load-carrying capacity are te number and te yield strengt of te screws and te strengt class of te timber. Te first failure mode occurs in reinforced beam supports wit a low number of sort screws. In tis case, te load-carrying capacity of te reinforced beam support is caracterised by pusing te screws into te timber. Simultaneously, te compressive strengt perpendicular to te grain at te contact surface is reaced. For screws te pusing-in capacity is considered equal to te witdrawal capacity. Te second failure mode occurs in beam supports wit slender screws. Here, te reinforcing screws are prone to buckle. Simultaneously, as in te first failure mode, te compressive strengt perpendicular to te grain at te contact surface is reaced. A typical buckling sape of slender reinforcing screws is sown left in Fig. 2. Te tird and last failure mode is observed in beam supports wit multiple sort screws. Here, te load-carrying capacity of te reinforced beam support is caracterised by reacing te compressive strengt of timber perpendicular to te grain in a plane formed by te screw tips (rigt in Fig. 2). Taking into account te tree possible failure modes, te pusing-in capacity and te buckling load of te reinforcing screws and te compressive strengt perpendicular to te grain at te contact surface as well as in a plane formed by te screw tips affect te loadcarrying capacity of reinforced beam supports. Te compressive strengt perpendicular to te grain at te contact surface may be calculated according to [4] (see also in [1]). Te pusing-in capacity and te buckling load of te reinforcing screw as well as te compressive strengt perpendicular to te grain in a plane formed by te screw tips are presented subsequently. For te first two failure modes it is assumed, tat te compressive strengt perpendicular to te grain at te contact surface of te beam and te load-carrying capacity of te axially loaded screws are reaced at te same time. For te compressive strengt perpendicular to te grain a linear-elastic - ideal-plastic and for te axially loaded screw a linear-elastic load-displacement beaviour is adopted. In spite of different load-displacement beaviour, numerical and analytical calculations confirm tat te load-carrying capacity of te axially loaded screws is reaced wen te compressive strengt of te timber is already reaced. For tis reason, bot load-carrying capacities can be added to calculate te load-carrying capacity of reinforced beam supports. 2
Failure (bow) due to acieve te compressive strengt perpendicular to te grain Fig. 2: Buckling of te screws and timber failure in a plane formed by te screw tips 2.2 Pusing-in capacity of self-tapping screws Preliminary tests ave confirmed, tat te pusing-in capacity of self-tapping screws is equal to te witdrawal capacity R ax. To determine te pusing-in capacity, 413 witdrawal tests wit self-tapping screws were performed. Here, te screw diameter d between 6 and 12 mm and te penetration lengt of te screw l S in te timber between 3,33 d and 16 d were varied. Te angle between te screw axis and te grain direction was 90. Te best correlation between te test results and te calculated values can be acieved, wen te witdrawal capacity is calculated by te following equation. 0,9 0,8 S R = 0,6 d ρ (1) ax Te best correlation between caracteristic values and test results can be acieved by replacing te factor 0,6 by 0,56 in eq. (1) (see Fig. 3). In Fig. 3 te calculated caracteristic witdrawal capacities in comparison to te test results are displayed. 3
20000 15000 Test results [N] 10000 5000 6 mm 7,5 mm 8 mm 10 mm 12 mm 0 0 5000 10000 15000 20000 Calculated caracteristic values R ax,k [N] Fig. 3: Calculated caracteristic witdrawal capacities in comparison to te test results 2.3 Buckling load of self-tapping screws as reinforcements Te second failure mode is caracterised by screw buckling. Here, te reinforcing screws are axially loaded in compression. Te ultimate load-carrying capacity for buckling of screws wit a circular cross section can be calculated taking into account amongst oters te buckling load. Te buckling load for axially loaded screws, wic are embedded in te timber, was determined by a numerical model (Fig. 4). Detail Nki Axial force Nki Detail: Fixed support K= N ki,e c l S Detail: Hinged support c v K=0 N ki,g Fig. 4: Numerical model to determine te buckling load N ki 4
Te axially loaded screw wit te elastic foundation c and wit te elastic support c v is displayed left in Fig. 4. Te elastic foundation c was determined from tests to determine te embedding strengt of te timber loaded by screws (400 tests). Te elastic support c v was determined from tests to determine te witdrawal or pusing-in capacity of te screws (300 tests). Te best correlation between te test results and te calculated values can be acieved, wen te elastic foundation c is calculated by te following equation. c ( 0,22 0,014 d ) + ρ = 2 2 1,17 sin α + cos α Te angle α is te angle between te grain and te force direction. For α = 90 te elastic foundation is smaller tan te representative value for an angle of 0. Hence, reinforcing screws bedded into te timber are prone to buckle perpendicular to te grain. For te elastic support c v, te best correlation between te test results and te calculated values can be acieved, wen te elastic support c v is calculated by te following equation. c v = 234 ( ρ d ) 0,2 0,6 S Te distribution of te axial force (Fig. 4) depends on te ratio between te elastic support c v and te longitudinal stiffness of te screw. An approximately triangle-saped distribution of te normal force leads to buckling of te screw close to te screw ead. Taking into account te elastic foundation c and te elastic support c v, te buckling loads for screws as reinforcements were calculated by a finite element calculation. Tereby, a clamped screw ead support and a inged screw ead support were modelled. A inged screw ead support must be assumed, wen te surface of te screw eads is flus wit te beam surface. In tis case, using a steel plate, loads from te beam support can be transferred simultaneously into te timber and into te screws. A clamped screw ead support may only be assumed by clamping te screw eads i.e. in te steel plate. For tis, it is necessary to countersink te steel plate in te form of te screw eads in suc a way as te surface of te screw eads is flus wit te lower steel plate surface. Te buckling loads were derived depending on te screw lengt and on te density of te timber, for inged and clamped screw ead supports, wit E S = 210000 N/mm 2 and wit a ratio between te core and te tread diameter of d k /d = 0,7 (see Tab. 1 and 2). Tab. 1: Caracteristic buckling loads for inged screw ead supports N ki,g,k [kn] Screw lengt l S [mm] Screw diameter [mm] Screw diameter [mm] Screw diameter [mm] Screw diameter [mm] 4 6 8 10 12 4 6 8 10 12 4 6 8 10 12 4 6 8 10 12 20 3,99 4,51 4,95 5,37 5,79 4,85 5,52 6,06 6,58 7,10 5,22 5,95 6,54 7,10 7,66 5,70 6,53 7,18 7,79 8,40 40 7,50 12,5 14,5 15,9 17,3 8,38 14,9 17,6 19,5 21,1 8,73 16,0 19,0 21,0 22,8 9,16 17,3 20,7 23,0 25,0 60 7,44 16,4 24,2 28,3 31,2 8,30 18,4 28,7 34,3 38,1 8,64 19,2 30,5 36,8 41,0 9,08 20,2 32,7 40,1 44,8 80 7,41 16,5 28,5 39,0 45,4 8,24 18,5 32,2 45,9 54,7 8,58 19,2 33,6 48,7 58,6 9,00 20,2 35,4 52,1 63,7 100 16,6 29,0 43,9 56,9 18,6 32,5 49,7 66,7 19,3 34,0 52,1 70,6 20,3 35,8 55,0 75,4 120 29,4 44,9 62,4 33,0 50,6 71,1 34,4 52,9 74,5 36,2 55,8 78,8 140 29,7 45,7 64,2 33,2 51,4 72,5 34,6 53,7 75,9 36,4 56,7 80,2 160 46,4 65,4 52,1 73,9 54,3 77,3 57,2 81,6 7,25 16,7 180 46,8 66,5 8,06 18,6 52,4 75,0 8,38 19,3 54,7 78,4 8,80 20,3 57,6 82,7 200 29,8 67,4 33,3 75,8 34,7 79,2 36,5 83,5 220 47,1 68,1 52,7 76,4 55,0 79,7 57,8 84,0 >240 68,6 76,9 80,2 84,4 6,81 16,1 29,9 48,6 72,6 7,54 17,8 33,1 53,8 80,4 7,83 18,5 34,3 55,9 83,5 8,20 19,4 36,0 58,5 87,5 N ki,k 1) ρ k = 310 kg/m 3 ρ k = 380 kg/m 3 ρ k = 410 kg/m 3 ρ k = 450 kg/m 3 (2) (3) 5
Tab. 2: Caracteristic buckling loads for clamped screw ead supports Screw lengt l S [mm] N ki,e,k [kn] Screw diameter [mm] Screw diameter [mm] Screw diameter [mm] Screw diameter [mm] 4 6 8 10 12 4 6 8 10 12 4 6 8 10 12 4 6 8 10 12 20 13,3 16,9 18,5 20,0 21,6 14,5 20,7 22,6 24,6 26,5 15,0 22,4 24,4 26,5 28,6 15,7 24,6 26,8 29,1 31,3 40 16,2 24,5 36,1 39,1 42,2 19,1 28,2 44,2 47,9 51,7 20,3 29,8 47,7 51,7 55,8 21,7 32,0 50,8 56,8 61,2 60 17,2 31,9 41,1 56,4 62,7 19,3 38,0 48,4 64,4 76,9 20,1 40,5 51,5 67,8 82,9 21,2 43,7 55,6 72,3 91,0 80 17,2 36,6 51,2 61,7 76,5 19,1 41,2 61,4 73,3 89,1 19,8 43,0 65,6 78,2 94,5 20,8 45,3 71,2 84,8 102 100 36,9 60,7 73,9 85,7 41,7 69,5 88,9 102 43,6 72,8 95,2 110 46,0 77,0 103 119 120 62,1 86,8 99,8 70,5 102 120 74,0 108 129 78,4 115 140 140 63,7 92,2 115 72,3 105 137 75,7 111 146 80,0 117 157 160 94,5 126 108 145 114 153 121 163 180 15,6 36,1 97,2 130 17,3 40,0 111 149 17,9 41,6 116 157 18,8 43,7 123 167 200 64,8 134 73,0 154 76,2 162 80,3 172 220 99,1 137 112 157 117 165 124 175 >240 140 159 167 177 13,6 32,1 59,7 97,2 145 15,1 35,6 66,1 108 161 15,7 37,0 68,7 112 167 16,4 38,7 72,0 117 175 N ki,k 2) ρ k = 310 kg/m 3 ρ k = 380 kg/m 3 ρ k = 410 kg/m 3 ρ k = 450 kg/m 3 Useful for comparison, te buckling loads N 1) ki,k and N 2) ki,k are displayed in te bottom line 1) in Tab. 1 and Tab. 2. Here, Nki, k = c ES IS corresponds to te buckling load for elasticly bedded beams witout supports (Zimmermann, 1905). Te buckling load for 2) elasticly bedded beams on two supports can be calculated by Nki, k = 2 c ES IS (Engesser, 1884). For slender and long beams, N 1) ki,k and N 2) ki,k is independent of te beam lengt. Subject to tese limitations, te buckling load for long screws can be easily calculated using N 1) ki,k or N 2) ki,k, E S = 210000 N/mm 2 π and I ( 0,7 ) 4 S = d. 64 2.4 Load distribution in beam supports Te load-carrying capacity for te tird failure mode is caracterised by reacing te compressive strengt perpendicular to te grain in a plane formed by te screw tips. In tis case, te load-carrying capacity for tis failure mode depends on te compressive strengt perpendicular to te grain and on te compressed area in a plane formed by te screw tips. Te load distribution and consequently te lengt of te plane formed by te screw tip were compressive stresses occur were determined from a numerical calculation (see [2]). Two different beam supports were studied: Directly loaded sleepers and indirectly loaded beam supports. l ef,2 l ef,2 l S l S ~ 45 ~ 45 l l Fig. 5: Load distribution in directly loaded beam supports 6
l ef,2 l ef,2 l S z l S z l l Fig. 6: Load distribution in indirectly loaded beam supports In directly loaded sleepers a linear load distribution may approximately be assumed (see in Fig. 5). Te lengt of te plane formed by te screw tips were compressive stresses occur can be calculated taking into account te lengt of te screws and te lengt of te beam support. In contrast, te load distribution in indirectly loaded beam supports is nonlinear and te increase becomes less wit increasing beam eigt (see in Fig. 6). As a result of te nonlinear load distribution in indirectly loaded beam supports (see in Fig. 6), te lengt of te plane formed by te screw tips were compressive stresses occur can be calculated as follows. For single-sided load distribution see eq. (4), for double-sided load distribution see eq. (5). S 3,3 ef = + S e,2 0, 25 (4) S 3,6 ef = + S e,2 0,58 (5) 2.5 Design equations for te load-carrying capacity of reinforced beam supports Taking into account te tree different failure modes, te load-carrying capacity R 90,d of a reinforced beam support may be calculated as follows: n Rd + kc,90 ef b fc,90, d R90, d = min b ef,2 fc,90, d were {,, } R = min R ; R (7) R d axd cd = κ N (8) cd, c pld, (6) κ = 1 for λ 0, 2 c 1 κc = 2 2 k+ k λ for λ > 0, 2 wit ( ) 2 k = 0,5 1 + 0, 49 λ 0, 2 + λ (9) (10) 7
N pl, d λ = (11) Nki, d and R ax,d Design value of te witdrawal capacity (see eq. (1)) calculated wit k mod and γ M = 1,3. n Number of screws b Widt of te beam l ef l ef = l + max {l ; 30 mm} for single-sided load distribution, see in [1] l ef = l +2 max {l ; 30 mm} for double-sided load distribution, see in [1] l ef,2 see in Fig. 5 and 6 k c,90 Coefficient k c,90 [1 ; 1,75] for te load distribution, see in [1] f c,90,d Design value of te compressive strengt perpendicular to te grain N pl,d Design value of te plastic load-carrying capacity calculated wit te cross section of te core diameter of te screw. N ki,d Design value of te buckling load for a screw taking into account te elastic foundation perpendicular to te screw axis, a triangular normal load distribution along te screw axis as well as te support condition of te screw ead. For inged ead supports te design values of te buckling load are summarised in Tab. 1. For clamped ead supports see Tab. 2. Te design value is calculated from te caracteristic value wit k mod and γ M = 1,3. 3 Calculation model for te stiffness Te effective stiffness perpendicular to te grain in te range of te reinforced beam support is derived using te Volkersen Teory (1953). Te complete derivation for te effective stiffness of a reinforced beam support is specified in [2]. Te effective stiffness of a reinforced beam support can be estimated by te following equation: E tot ψ E90 fld n S + 1 ω sin( ω S ) n = ψ φ ψ + n + 1 cos ω + 0,7 φ ω sin ω n ( ) f ( ) S LD S S wit te load distribution factor f LD for a linear load distribution f 1 S LD = + L tanα (13) and wit te ratio between te extensional stiffness of te timber and te screw φ as well as te coefficient ψ and ω: ( ω S ) ( ω ) E cos 90 A n + φ 1 n φ = ψ = fld ω = + c ES AS cos S 1 ES AS E90 A Furter notation: 8 v (12) (14)
n E 90 A Number of screws E S A S c v see eq. (3) extensional stiffness of te beam at te beam support perpendicular to te grain direction extensional stiffness of te reinforcing screw l S, l, α = 45 see in Fig. 5 L L = 1 for single-sided, L = 2 for double-sided load distribution It must be pointed out, tat te effective stiffness estimated by eq. 12 to 14 is only valid for reinforced beam supports using self-tapping screws. Furtemore, te equations only apply for a linear load distribution, suc as in directly loaded beam supports. Te effective stiffness for reinforced beam supports in te range of te reinforcing screws is only valid, wen te surface of te screw eads is exactly flus wit te surface of te beam support. To receive an impression about te size of E tot depending on te reinforcement, two diagrams were generated. Left in Fig. 7 te effective stiffness depending on te screw number n and te screw lengt l S is displayed for a screw wit 6 and 12 mm diameter. Remarkable is te increasing of E tot wit increasing screw lengt. Rigt in Fig. 7 te effective stiffness depending on te beam support area and te screw diameter for one screw (n = 1) is displayed. Remarkable is te increase of E tot wit decreasing spacing between te screws. For large screw spacing, E tot is ardly iger tan te MOE for solid timber perpendicular to te grain. Fig. 7: E tot depending on l S and n (left) and E tot depending on A and d (rigt) 4 Tests To verify te calculation models, different reinforced beam supports were tested (15 test series). To demonstrate te effectiveness of reinforced beam supports, furter nonreinforced beam supports were tested (4 test series). All tested specimens are specified in Tab. 3. Te averaged load-carrying capacity for eac test series is displayed in column four. In te following column te averaged effective stiffness of te reinforced beam supports is displayed. Information about te geometry of te beam support and te screws as well as te plastic load-carrying capacity N pl for te screws are displayed in column 6 to 12. 9
A remarkable effect of tis reinforcing metod is te ig increase in load-carrying capacity compared to te non-reinforced geometrically identical beam supports. For example, te averaged load-carrying capacity for te test series A_6_6 is 132 kn and consequently 130% iger tan te corresponding value for te test series A_2. Te greatest increase in load-carrying capacity was reaced wit te test series D_8b_6. Here, compared to te test series D_2, te increase in load-carrying capacity was 330%. Furtermore, for reinforced beam supports a ig increase in stiffness perpendicular to te grain direction is observed. Compared to solid timber wit a MOE perpendicular to te grain of about 300 500 N/mm 2, te effective stiffness E tot perpendicular to te grain in te range of te reinforcing screws reaced a maximum value of about 1870 N/mm 2. Tab. 3: Properties of tested beam supports and test results number mean mean mean beam support reinforcing screws specimen of density load- MOE direct/ widt lengt number screw lengt of ductile spec. carrying indirect of diameter te treaded axial capacity screws part force n ρ R 90 E tot t l ef n d l S N pl [-] [-] [kg/m 3 ] [kn] [N/mm 2 ] [-] [mm] [mm] [-] [mm] [mm] [kn] A_1 5 463 43,2 - indirekt 100 80 - - - - A_7_2 5 444 77,5 790 indirect 100 80 2 7,5 180 32,7 A_8_2 5 459 92,0 1293 indirect 100 80 2 8 340 32,7 A_10_2 5 448 104 845 indirect 100 80 2 10 200 51,8 A_7_4 4 446 126 635 indirect 100 120 4 7,5 180 32,7 A_10_4 5 449 133 764 indirect 100 120 4 10 200 51,8 A_2 10 464 57,1 - indirekt 120 90 - - - - A_6_6 10 466 132 861 indirect 120 90 6 6,5 115/160 22,5 D_1 5 451 46,0 - direkt 100 80 - - - - D_7_2 5 460 96,1 1050 direct 100 80 2 7,5 180 34,2 D_8_2 5 425 98,0 1350 direct 100 80 2 8 340 32,7 D_10_2 5 439 104 1119 direct 100 80 2 10 200 51,8 D_7_4 14 443 127 985 direct 100 120 4 7,5 180 34,2 D_8_4 6 445 169 1247 direct 100 120 4 8 340 32,7 D_10_4 5 456 173 836 direct 100 120 4 10 200 51,8 D_2 3 450 56,4 - direkt 120 90 - - - - D_7_6 3 459 195 1196 direct 120 90 6 7,5 180 34,2 D_8a_6 3 453 228 1435 direct 120 90 6 8 260 39,1 D_8b_6 3 455 242 1870 direct 120 90 6 8 400 37,5 In te following Fig. 8 and Fig. 9 te test results (R 90 and E tot ) for eac test series are compared wit te calculated values. All values were calculated wit te averaged density and te averaged plastic load-carrying capacity for te screws. Furtermore, te compressive strengt perpendicular to te grain was assumed as 5 N/mm 2. Te effective stiffness perpendicular to te grain E tot was calculated using a MOE of 300 N/mm 2. 10
Te calculated values sow a good agreement wit te test results. Furtermore, te calculated failure modes mainly correspond to te failure modes observed in te tests (see in Fig. 8). 250 200 f c,90 = 5,0 N/mm 2 R ax and N pl from tests Test results R 90 [kn] 150 100 50 Failure mode I (pusing-in capacity of te screws) Failure mode II (buckling of te screws) 0 0 50 100 150 200 250 Calculated values R 90 [kn] Failure mode III (compressive strengt of te timber) Fig. 8: Calculated load-carrying capacities in comparison wit te test results 2200 2000 E 90 = 300 N/mm 2 E S = 210000 N/mm 2 1800 Test results E tot [N/mm 2 ] 1600 1400 1200 1000 800 600 600 800 1000 1200 1400 1600 1800 2000 2200 Calculated values E tot [N/mm 2 ] Fig. 9: Calculated effective stiffness in comparison wit te test results 11
5 Summary Self-tapping screws wit continuous treads provide a good opportunity to reinforce beam supports and consequently to increase te load-carrying capacity and te stiffness perpendicular to te grain or to minimize te elastic displacement perpendicular to te grain. In tis paper a calculation model for te load-carrying capacity and for te effective stiffness reinforced beam supports using self-tapping screws is presented. Wit te first calculation model it is possible to calculate te load-carrying capacity and to predict te failure mode of a reinforced beam support. Te second calculation model may be used to estimate te stiffness or te elastic displacement perpendicular to te grain in te support area. Bot calculation models were verified by test. 6 References [1] DIN 1052:2004-08, Entwurf, Berecnung und Bemessung von Holzbauwerken Allgemeine Bemessungsregeln und Bemessungsregeln für den Hocbau [2] Bejtka, I. (2005). Verstärkung von Bauteilen aus Holz mit Vollgewindescrauben. Band 2 der Reie Karlsruer Bericte zum Ingenieurolzbau. Herausgeber: Universität Karlsrue (TH), Lerstul für Ingenieurolzbau und Baukonstruktionen, Univ.-Prof. Dr.-Ing. H.J. Blaß. ISSN 1860-093X,ISBN 3-937300-54-6 [3] Volkersen, O. (1953). Die Scubkraftverteilung in Kleb-, Niet- und Bolzenverbindungen. Aus Energie und Tecnik, Marc.1953 [4] Blaß, H.J.; Görlacer, R. (2004). Compression perpendicular to te grain. In proceedings of te 8t World Conference on Timber Engineering Volume II, page 435 440; WCTE 2004, June 14-17, 2004 in Lati, Finland 12