STIFFNESS OF COVER PLATE CONNECTIONS WITH SLOTTED HOLES

Transcription

1 STIFFNESS OF COVER PLATE CONNECTIONS WITH SLOTTED HOLES František Wald 1, Zdeněk Sokol 1, Matthieu Moal 2, Vratislav Mazura 1, Jean-Pierre Muzeau 2 ABSTRACT The work describes the prediction of stiffness of bolted connections with slotted holes perpendicular to the acting force. Three sets of tests with slotted holes are available: experiments on assemblages prepared at CRIF laboratory in Liege, experiments with components completed at Czech Technical University in Prague, and experiments with long slots made at the laboratory of Technical University Nottingham. The work shows the application of the component method to the cover plate connections. A special attention is devoted to the modelling of the bolt force distribution for different bolt tolerances. Key Words: Steel structures, Bolted connections, Slotted holes, Cover plate connections, Experimental observations, Analytical modelling, Component method, Connection stiffness. 1. Introduction The slotted holes are used in bolted connections of steel structures to compensate the tolerances during the erection, to allow one type of endplate for more connected members and to enable a slip in joint. Preloading of the bolts may prevent deformation of the connection in direction of the slot. Even smooth tightening of the non-preloaded bolts reach up to 2% of the tensile resistance of the bolt and together with the corrosion pretends structural use of the slip in the joint. The Fig. 1 shows the main difference of behaviour of bolts in slotted holes perpendicular to acting force compare to the bolts in circular holes lower resistance and stiffness as well as higher deformation capacity of the connection. Drilling, punching, or gas and plasma cutting form the holes. Punching of the holes in steelwork is faster than drilling but cracks may appear in the material. The holes are not punched to full size but 2 mm less in diameter and then reamed. New punching machines, 1 Czech Technical University in Prague, CZ Praha 6, Czech Republic 2 Université Blaise Pascal, CUST, BP26, F Aubière Cedex, France 1

2 which operate at high speeds, induce less distortion in the material, and it is expected that punching will be used extensively in the future. The punching is approved for material up to 25 mm in thickness provided that the hole diameter is not less than thickness of the material, if there is no other specification. The burrs should be removed from the holes before the assembly. It can be omitted when the holes are drilled in one operation through parts clamped together which would not be separated after drilling. The gas and plasma cutting may also form the holes. In this case, similarly to fast drilling/punching, influence on material properties has to be studied experimentally M M circular holes, (test 1c-16-1-d+2) slotted holes, (test 5c-16-1-d+2,5) Displacement δ, mm Fig. 1 - Comparison of force - displacement diagrams of test with slotted holes (test 5C ,5 d) to circular holes (test 1C d+2), [1] The design requirements limit the bolt end and pitch distances, see Fig. 2 [2]. For regular slotted holes for M16 and M24 bolts, short slotted holes may not be greater than (d + 2) mm by (d + 6) mm, where d is the nominal bolt diameter in mm. Long slotted holes may not be greater than (d + 2) mm by 2,5 d. Extra large slots according to British rules may not be greater than (d + 2) mm by 3,5 d. min 1,5 d d short slot d + 6 long slot 2,5 d extra long slot 3,5 d e 3,5 d e4 1,5 d a) b) c) Fig. 2 - a) Slotted hole recommended geometry[2]; b) shear bearing failure (test 1C d+2 [1]); c) bending bearing failure (test 5C ,5 d [1]) At CRIF Liege assemblages with more bolts has been tested, see [4]. The plates were connected with bolts in each hole of the plate made by different technology. Very long slotted holes were experimentally investigated at University of Nottingham, see [5]. The behaviour of each particular component was observed in test at the Czech Technical University of Prague, see [1]. The double cover plates were used with only one bolt in an internal/external position. The tests results of bolted connections of the curtain wall connections with slots at different inclination compare to the acting force [6] are concluding the presented findings. The experiments with aluminium connections are available in the study by Gitter [7]. The study exhibits similar results, because the main structural 2

3 disadvantage of low ductility of aluminium alloys is reduced by slotted holes with higher deformation capacity, see Fig. 1. The design prediction model of stiffness, resistance, and deformation capacity by component method prepared at Czech Technical University with cooperation of Université B. Pascal Clermont Ferrand is presented. 2. DESIGN RESISTANCE Resistance of bolted connections loaded by shear force in plane of the plates is limited by failure of bolts in shear and in bearing. When the high strength friction bolts are used and no slip is allowed, bearing resistance is checked at ultimate limit state to eliminate the end shear failure. The bearing resistance represents the resistance of internal and external bolts in most design procedures. Based on experimental evidence, shear and bending type of failure may be recognised on the bearing failure. The bearing resistance is reduced in case of the slotted holes. The reduction factor for resistance applied in draft of European standard EN (22) is based on latest experiments, see [3]. The tests were carried out not only for resistance, but also for the deformation stiffness and the deformation capacity. Three basic concepts may evaluate the resistance of bolted connections: The traditional background of most codes indicates the resistance F exp;1,5 by deformation of 1,5 mm. The conventional (elastic) limit of resistance F exp;conv define the resistance as the intersection of a straight line with the initial stiffness and of a straight line having the slope equal to stiffness divided by ten, which drawn as a tangent to the nonlinear part of the curve, see Fig. 3. The conventional resistance depends more on the stiffness of the joint than on the type of failure. The ultimate design resistance F exp;ult depends strongly to the failure mode. It needs to be equipped by separate check at the serviceability limit state. 2 Initial stiffness F exp, ult Initial stiffness / 1 Experimental curve 3 mm (two connected plates) F exp, conv F exp; 1,5 Displacement, δ, mm Fig. 3 - Limits of the resistance of joint; deflection limit F exp;1,5 ; ultimate limit F exp;ult ; conventional limit F exp;conv ; test I 1-3 ( ,5d) [4] The prediction of bearing resistance is simplified [2] in expression where α is the smallest of e1 3 d o ; F 2,5 α f d t u b.rd = β R, (1) γ Mb p1 3 d o 1 f ub ; or 1,. (2) 4 f u 3

4 γ Mb the partial safety factor, β R a reduction coefficient for resistance of connection with slotted holes. The Annex Z, see [8], [9] and [1], brings a standard procedure for determining partial safety factors from the results of tests. The number of test with slotted holes available is limited to 7. It is a limited number compare to the number of tests in background documents [9]. The Annex Z model allows comparing values of different tests. The variation in the prediction of the design model is determined from the tests (in term d). This variation is combined with variations of the other variables in the resistance function, with the variation in material strength and stiffness and variation in geometrical properties. Not all the variations in geometrical properties and in strength were accessible for slotted hole tests and assumptions have to be made for the error term. The calculation of the error term is using the data available ([1] and [11]) and is extended to all tests. The tests with repeated loading were also not taken into statistical calculation. The theoretical resistance r t.i = F b.rd was compared to the experimental value r ei from the tests. The points representing pairs of corresponding values (r ti, r ei ) are plotted on Fig. 4. 1,4 1,2 1,8,6,4,2 r e r t Bolt size / bolt diametr,5 1 1,5 2 2,5 3 3,5 4 Fig. 4 - Influence of the slot length in the plate failure, [11] The β coefficient for the full set is below the β coefficient for very long slot due to small variation. The factor introduces higher errors, which are responsible for this low variation of the reduction factor β. The variation underlines the importance of division of the set into three sub-sets in order to predict more accurate results. Table 1 Application of Annex Z [1] on different sub-sets [11] Set All test specimens Normal and short slotted holes Long slotted holes Very long slotted holes From d + 2 mm d + 2 mm 2 d 3,125 d To 3,5 d d + 6 mm 2,5 d 3,5 d Number of test γ R * 2,14 1,34 1,76 2,5 β,58,93,71,61 3. DESIGN STIFFNESS The application of component method requires tree basic steps: listing of the components of the joint, evaluation of force-deflection diagram of each individual component, in terms of initial stiffness, strength and deformation capacity, and assembly of the components in view of the evaluation of the whole joint. The stiffness, the resistance and the deformation capacity are assembled separately for simplicity. The cover plate connections 4

5 may be dismantled into the components: plate in tension, bolts in shear, and bolts in bearing. Behaviour of each component may be predicted by bilinear model. Zoetemeijer [12] described the stiffness of components of the end plate joints based on non-linear prediction known from its resistance. The model was simplified by Wald and Steenhuis [13] applying the prediction of the stiffness at the elastic stage. A concentrated research of bolted angle cleats with un-threaded non-preloaded bolts in circular holes was finalised by Jaspart [14] with full description of the components behaviour. The model is explored in European design practice; see ENV (1998) [1]. The initial stiffness of the component bolt/plate in bearing is calculated as k b 24 n b k b k t d f u = β S (3) E with k= b k b1 but k b k b2 ; k b1=, 25 eb / d +, 5 but k b1 1,25; kb2 =, 25 pb / d +, 375 but kb2 1,25; and kt = 1,5 t j / d M 16 but kt 2,5. Prediction of stiffness of the bolts with thread in shear plane in circular bolt holes was evaluated on test by Mazura [1] based on the measured values of geometry and materials, see Fig. 3. The reduction of the initial stiffness due to the thread may be assumed as β S =,75, see [11]. The reduction due to the slot may be approximated as β S =,5, see [11]. Two levels of modelling, like in the member design, are significant: at the design stage (with yield stress of steel f y ) and at the ultimate (using ultimate tensile strength f u ). For component in bearing the second stiffness may be applied to predict mode accurate the ultimate resistance with inclination 1/1 of the initial stiffness, see Fig. 9 and Fig ASSEMBLAGE Based on the behaviour of each component the assembling may be provided based on the joint geometry, see [15]. The assemblage is shown at Fig. 5 for tree bolt rows. The compatibility conditions are e.g. b,p,1 F = F + F (4) c2 p1 c1 p2 b2 F = F + F (5) s,1 b,c,1 b2 δ + δ + δ + δ = δ (6) b,p,2 s,2 b,c,2 T,c,1 T,c,2 T,p,2 δ + δ + δ + δ = δ (7) T,p,3 The total acting force is calculated as F = F b1 + F b2 + F b3. (8) The connection elongation is δ = δ + δ + δ + δ + δ + δ + δ. (9) T,p,e b,p,1 s,1 b,c,1 T,c,1 T,c,2 T,c,e With set of equations (4) till (9), the unknowns may be calculated at each load step, provided that the force-deflection diagram of each component is described. For more than tree bolt rows the FE code was used to assembly the diagrams represented as non-linear springs of 5

6 components into the connection, which allows to include the gaps related to the production tolerances. Cover plate connection cover plates bolts plate e 1,e p 1,b1 p 1,b2 e 1,p Geometry cover plates Fc,1 Fc,2 F bolts Fb,1 Fb,2 Fb,3 F F F p,1 p,2 plate first bolt row second bolt row third bolt row Internal forces cover plates bolts k b,p,1 k s,1 kt,p,e k T,p,1 plate k b,c,1 k k k T,c,1 T,c,2 T,c,e k b,p,2 k s,2 k b,c,2 k b,p,3 k s,3 k b,c,3 k T,p,2 Mechanical (spring) model Fig. 5 Assemblage of components, an example of case with tree bolts rows in cover plate 18 M F exp,conv test 1A 16-1-d+2, [1] test 1B 16-1-d+2, [1] test 1C 16-1-d+2, [1] prediction Displacement δ, mm Fig. 6 Evaluation of model to tests with circular bolt holes, test 16-1-d+2, [1] The predicted stiffness of components was evaluated on tests with one bolt only, see Fig. 6, 7, and 8. The components are in this case in series. The total deformation stiffness k tot of the connection may be calculated as 1 k tot = (1) k k k k k t,p b,p s b,c t,c The good prediction of stiffness in case of slotted holes is illustrated at Fig. 7 and 8 based on measured values of geometry and of material properties. 6

7 M test 5A ,5 d, [1] test 5B ,5 d, [1] test 5C ,5 d, [1] prediction F exp,conv Displacement δ, mm Fig 7 - Evaluation of model to the test with bolts in slotted holes, tests ,5 d, [1] M test 3A F exp,conv test 3B test 3C prediction , d, [1] , d, [1] , d, [1] Displacement δ, mm Fig. 8 - Evaluation of the prediction model to test with bolts in long slotted holes, tests , d, [1] 14 F exp,conv,44,45 Prediction model 12 F exp,conv,31, 32, 33 Model with second stiffnes 1 Biliear model Test 32 [4] 8 Test 31 [4] 6 Test 33 [4] 4 Test 44 [4] 2 δ el 3 δ el δ Cd Test 45 [4] Displacement δ (mm) Fig. 9 - Comparison between model and experiments, see [4], tests with bolts M16 For the test of assemblages, see [4], the stiffness was calculated based on the characteristic values of the test set up geometry and the measured characteristics of the plate material. On 7

8 Fig. 9 and Fig. 1 are compared the predicted force-deformation diagrams to the experimental values. The prediction was prepared based on the design model, using f y as well as for ultimate model based on f u. The non-linear part of the curve is simulated by linear approximation at 2/3 of the design resistance till 3 δ el. The prediction of stiffness and of resistance shows good accuracy of the presented model. The accuracy of the deformation capacity using simple assumptions described in [16] is limited. The model gives a conservative prediction of the available experiments, but the safety level is not included into the model yet F exp,conv Prediction model Model with second stiffness Bilinear model Test 34 [4] Test 35 [4] Test 46 [4] Test 47 [4] Test 48 [4] δ el 3 δ el δ Cd Displacement, δ,mm Fig. 1 - Comparison between model and experiments, see [4], tests with bolts M27 5. TOLERANCES The influence of erection tolerances was observed on model of connections with eight bolts M in plate P16-8 S275 with the standard pitches 5 mm. The first and the last bolts are in contact. The gap of 2 mm; 1,5 mm;,5 mm; and mm was simulated by the internal bolts. The influence of the tolerances during the loading is shown on the Fig. 11. Distribution of the bolt forces during loading is presented at Fig. 12. The bolt forces are reported in column diagrams for different assumption of the gap of internal bolts. In one diagram are collected force distributions for different gaps under one loading step represented by the connection total deformation. The deformation capacity of the joint allows eliminating the unfavourable influence of tolerances in cover plate connection [17]. The resistance may decrease in case of change from ductile bearing failure mode into brittle bolt shear failure mode by using the thick cover plates of very long bolt pitches. 1 g = mm,5 mm 1, mm 2, mm!"#$%&'( Fig 11 - Influence of gap of internal bolts of cover plate bolted connection with slotted holes; bolts M16-8.8; plate P16-8 S275; pitch 5 mm g Total deformation, δ, mm 8

9 Bolt 8 Bolt 1,5 mm δ = δ =,75 mm δ = 1, mm gap,,5 1, 2, gap,,5 1, 2, gap,,5 1, 2, δ = 1,25 mm δ = 1,5 mm δ = 1,75 mm gap,,5 1, 2, gap,,5 1, 2, gap,,5 1, 2, δ = 2, mm δ = 2,25 mm δ = 2,5 mm gap,,5 1, 2, gap,,5 1, 2, gap,,5 1, 2, Fig Distribution of bolt forces during loading (represented as connection deformation δ) under changing the gap; external bolts in contact; bolts M16-8.8; plate P16-8 S275; pitches 5 mm; for 8 bolts 6. CONCLUSIONS Bolted connections with slotted holes perpendicular to the acting force exhibit lower stiffness and higher deformation capacity compare to connections with circular holes. Due to the lower stiffness a lower design resistance is incorporated into the proposal of EN based on common work [3] at Liege [4], Nottingham [5], and Prague [1]. A conservative assumption incorporates a reduction factor β r =,6 of the design bearing resistance. Component model of the cover plate connection, which is included in ENV /A2 (1998) [1], enables to simulate the influence of the tolerances and the length in the connections with a good accuracy. Prediction of the stiffness of bolts presented by Jaspart [14] for untreated bolts may be extended to the fully threaded bolts as well as to the bolts with slotted holes. 9

10 ACKNOWLEDGEMENTS The authors dedicate this work to Mr. Martin Steenhuis, who brought great ideas into the structural connection design. This research has been supported by grant J1-98:214 of the Czech Ministry of Education, Youth and Sports and by grant Barrande No REFERENCES [1] Mazura V., Slotted Holes in Structural Bolted Connections, PhD. thesis, in Czech, CVUT, Praha 22, p [2] ENV , Design of Steel Structures - General rules and roles for buildings, European Prenorm, CEN, Brussels [3] Wald F., Mazura V., Moal V., Sokol Z., Experiments of bolted cover plate connections with slotted holes, CTU reports, Vol. 2, 2/22, CVUT, Praha 22, pp , ISBN [4] Piraprez E., Behavior of plates with slotted holes CRIF Belgium, Proceeding of International Conference on Steel Structures of the 2 s, IABCE, Istanbul 2. [5] Tizani W., The bearing capacity of plates made with long-slotted bolt holes, Internal copy, University of Nottingham, Nottingham [6] Kersten O., Zum Last-Verschiebungs-Verhalten geschraubter Scher-Lochleibungs- Verbindungen im Stahlbau unter statischer Belastung, Dissertation, TU Hamburg-Namburg, Hamburg 1997, p [7] Gitter R., Piraprez E., Sedlacek G., Schneider R., Lochleibungsfestigkeit von Schraubenverbindungen mit Langlöchern, DASt Forchungsbericht, Aachen 21, p.15. [8] Bijlaard F.S.K., Sedlacek G., Stark J.W.B., Procedure for the determination of design resistance from tests, Background report to Eurocode 3, BI , Delft [9] Snijder H. H., Ungerman D., Stark J.W.B., Sedlacek G., Bijlaard F.S.K., Hemmert- Halswick A., Evaluation of test results on bolted connections in order to obtain strength functions and suitable model factors, Part B: Evaluation, Background documentation, 6.2, BI-88-87, Delft [1] ENV /A2, Design of Steel Structures - General rules and roles for buildings, Annex J, Annex Z, CEN, Brussels [11] Moal M., Assemblages avec trous oblongs et boulons non-precontraints, Diploma theses, CUST, Départment Génie Civil, Université Blaise Pascal, Clermont-Ferrand 21, p. 11. [12] Zoetemeijer P., Summary of the Research on Bolted Beam-to-Column Connections (period ), Rep. No M, Steven Laboratory, Delft [13] Wald F., Steenhuis M., The Beam-to-Column Bolted Joint Stiffness according Eurocode 3, in Workshop COST C1, Proceedings of the State of the Art Strasbourg 1993, pp [14] Jaspart J.P., Recent advances in the field of steel joints Column bases and further configurations for Beam-to Column Joints and Beam Splices, Thesis, Université de Liège, Liège 1997, p [15] Gresnigt A.M., Steenhuis C.M., Stiffness of lap joints with preloaded bolts, in The Paramount Role of Joints into the Reliable Response of Structures, NATO Science Series, ed. Banitopoulos C.C., Wald, F., Series II, Vol. 4, Kluver Academic Publishers, Dortrecht 2, ISBN , pp [16] Wald F., Mazura V., Moal V., Sokol Z., Component method for bolted cover plate connections with slotted holes, in International Colloquium on Stability and Ductility of Steel Structures, Budapest 22, in printing. [17] Zygomalas, M., Kontoleon M.J., Banitopoulos C.C., A hemivariation inequality approach to the resistance of the aluminium riveted connection, in 6 th national congress of mechanics, ed. Kounadis A.N., Thessaloniki 21, p