The effect of inclination of scarf joints with four pins

International Journal of Architectural Heritage Conservation, Analysis, and Restoration ISSN: 1558-3058 (Print) 1558-3066 (Online) Journal homepage: http://www.tandfonline.com/loi/uarc20 The effect of inclination of scarf joints with four pins Petr Fajman & Jiří Máca To cite this article: Petr Fajman & Jiří Máca (2018): The effect of inclination of scarf joints with four pins, International Journal of Architectural Heritage, DOI: 10.1080/15583058.2018.1442520 To link to this article: https://doi.org/10.1080/15583058.2018.1442520 Published online: 30 Mar 2018. Submit your article to this journal View related articles View Crossmark data Full Terms & Conditions of access and use can be found at http://www.tandfonline.com/action/journalInformation?journalCode=uarc20 INTERNATIONAL JOURNAL OF ARCHITECTURAL HERITAGE https://doi.org/10.1080/15583058.2018.1442520 The effect of inclination of scarf joints with four pins Petr Fajman and Jiří Máca Faculty of Civil Engineering, Czech Technical University in Prague, Praha, Czech Republic ABSTRACT ARTICLE HISTORY During the renovation of roof trusses and roof structures, damaged wood must be replaced with new wood. To keep the original material adjustment slab joints can be used. Unfortunately, this type of joint has not been observed from the structural perspective. The shape of the joint, the inclination of its faces, the type and the number of connectors still represent an unknown area. A simplified analytical model is briefly derived in the article and the effect of the face inclination is solved. The results obtained from experiments are compared with the results from the model. Received 7 January 2018 Accepted 8 January 2018 1. Introduction Scarf joints are frequently used in the reconstructions of historical structures. In choosing the shape, the type of joint, and the number of connectors, the knowledge of their behavior is essential. In the literature, we primarily read about structural principles, but not much is known about their structural action. Different points of view interfere with each other in the design of the scarf joint. It is, for example, the joint labor intensity and accuracy, its length, historical aspect, and structural action. The above views are often controversial and a compromise must be sought. The analytical design of a joint with four pins is a follow-up to preceding designs of a joint with one, two, and three connecting pieces (Fajman 2014; Fajman and Máca 2014, 2015a, 2015b, 2017; Kunecky et al. 2014). The joint is characterized by the fact that both the connecting pieces and the abutment of the faces at the scarf joint’s end participate in the transfer of load. The distribution of forces in the scarf joint and the estimation of a change in the stiffness of a member with a scarf joint against a member without a scarf joint represented an interesting issue to investigate. The important finding obtained was that if a lower number of connecting pieces is used a change in the inclination of the faces plays a significant role in the joint behavior. To put it plainly, a lower inclination implies that the faces lean against each other more giving the joint a higher load-bearing capacity, but the long length of the joint is a disadvantage. In terms of practicality, on the contrary, a 90° inclination (perpendicular faces) KEYWORDS Experimental; numerical; oblique; pin; scarf joint; stiffness represents the easiest solution. A compromise is sought in using the inclination of 45°. The recent technology used for extending members is via a scarf with multiple pins; see Figure 1. The designers are convinced that the greater the number of pins the higher the joint stiffness. The experiments (Arciszewska-Kędzior et al. 2015a, 2015b; Kunecky et al. 2015) and calculations (Fajman 2014; Fajman and Máca 2014; 2015a, 2015b, 2017) performed, however, indicate that the increasing number of pins does not lead to an increased load-bearing capacity of the bar; for this reason, the article focuses on a scarf joint which minimises the number of connecting pieces to 4. The design and introduction of simplifying assumptions is based on the knowledge obtained from joints with 1, 2, and 3 connectors. Numerous experimental tests (ArciszewskaKędzioret et al. 2015a, 2015b; Kunecky et al. 2015) and FEM calculations (Kunecky et al. 2014) have been carried out within the Design and Assessment of Wooden Carpenter’s Joints of Historical Structures project in the last years, and several computational programmes based on theoretical models have been compiled by the authors. The results may serve for drawing conclusions which can help in the design of the respective joints. 2. Scarf joint If a timber structure shows lowered reliability, it must be repaired. In the case of repairing a historical structure, as much original material must be preserved as CONTACT Petr Fajman fajman@fsv.cvut.cz Faculty of Civil Engineering, Czech Technical University in Prague, Thákurova 7, Praha, Czech Republic. Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/uarc. © 2018 Taylor & Francis 2 P. FAJMAN AND J. MÁCA Figure 1. Repair of a ceiling at Kost Castle—performed by Hrdlicka. (a) Part 1 (b) pins Part 2 Figure 2. (a) Halved scarf joint with pins and (b) oblique scarf joint with pins. possible (Branco, Piazza, and Cruz 2010; Piazza and Riggio 2007). This can best be achieved by using a scarf joint; see Figure 1. A typical lapped scarf joint is drawn in Figure 2. Depending on its design, there are halved scarf joints or oblique scarf joints. There is also a scarf joint with an inside tenon where one part contains a central tenon and the other two scarfs. According to the connectors used, there are scarf joints secured by wooden pins, steel bolts, wooden dowels, or their combinations (Fajman 2014; Fajman and Máca 2014; 2015a, 2015b, 2017). One of the principal still open questions is the effect of the inclination of faces on the scarf’s load-bearing capacity. This issue was previously analysed for the case of a scarf with one pin in the middle (Fajman 2014; Fajman and Máca 2014). In that case, with only one pin, the results imply that a smaller inclination is structurally more favourable for the respective joint, but, on the other hand, it extends the scarf length. Considering manufacturing procedures, the face inclination of 45° appeared the most convenient, showing also sufficient load-bearing capacity in the structural perspective. In practice, however, a scarf joint with multiple connecting pieces is preferred. The most common design is a scarf with 4 pins or bolts in which the effect of the inclination of faces on the load-bearing capacity has not been investigated yet and whose design is presented below. 3. Structural action An important aspect for an easy design of a scarf joint is the possibility of simplifying its spatial action into a simpler problem. Under vertical loading, scarf joints produce eccentric forces, exerting a bending moment, which bends the structure perpendicular to the loading plane. At the same time, they exert a twisting moment in the scarf area. If the structure’s movement in the INTERNATIONAL JOURNAL OF ARCHITECTURAL HERITAGE 3 direction perpendicular to the loading plane is prevented, the structure can be simplified into a 2D problem. This condition is fulfilled, e.g., in roof truss beams, which are held by decking or by a soffit. In roof truss girders, in turn, the tensile normal force mostly helps to stabilize the structure. The design of a scarf joint can be based on structural principles (Piazza and Riggio 2007), a computation using the finite-element method (Kunecky et al. 2015), a simplified theoretical model (Fajman 2014; Fajman and Máca 2014; 2015a, 2015b, 2017), or experiments (Arciszewska-Kędzior et al. 2015b; Branco, Piazza, and Cruz 2010; Kunecky et al. 2015; Milch et al. 2014, 2017; Sangree and Schafer 2009). the scarf faces, which exerts a friction force Vai = Nai μi, where μi is the friction coefficient. The force distribution between the face and the pins depends on multiple factors; see Eqs. (1) and (2) (for more detail see Fajman and Maca 2015a, 2015b, 2017):
 N1 ¼ Na1 sin α1 þ μ1
cos α1 ; 3.1 Halved scarf joint where Ni, Vi are horizontal and vertical forces in the faces, αi is the angle of oblique faces (see Figure 4). Three equilibrium conditions—two force conditions in horizontal and vertical directions (3) and the moment condition (4)—can be defined: X Nf þ N1 þ N2 þ Nki ¼ 0 ; This scarf joint is easy to make, but the precise seating of its vertical surfaces cannot be guaranteed there. In structural terms, however, even in the case of a perfect fitting of the vertical surfaces, it seems less suitable than the oblique scarf joint. All load is initially only transferred by the connectors (see Figure 3), but, later, also by the abutment in the upper part of the face. The force acting in the pins can be substituted by two components, Nki, Vki. The respective structural system is statically indeterminate where the degree of indeterminateness depends on the number of connectors. N2 ¼ Na2 ðsin α2 μ
cos α2 Þ;
 V1 ¼ Na1 cos α1 þ μ1
sin α1 V2 ¼ Na2 ðcos α2 þ μ
sin α2 Þ ðcos α1 þ μ1 sin α1 Þ ¼ N1
k1 ; ð sin α1 þ μ1 cos α1 Þ ð cos α2 þ μ2 sin α2 Þ ¼ N 2
k2 V2 ¼ N2 ðsin α2 þ μ2 cos α2 Þ V1 ¼ N1 i¼1;4 N1 k1 þ N2 k2 þ In manufacturing, the seating of inclined surfaces onto each other must be secured so that they can participate in the structural action. All load is transferred by the scarf faces and connectors; see Figure 4. The forces in the connectors are assisted by the normal force Nai in N1 h N2 Nk1 V1 Vk1 Nk3 V2 Vk3 Nk2 Nk4 Vk2 Vk4 Figure 3. Forces participating in load transfer. Mf Nf Na1 N1 h _ Mf o: V1 Va1 Vf Figure 4. Forces participating in load transfer. 1 Vk2 Vki þ Vf ¼ 0 Vf
xf þ X Ni
z i i¼1;2 þ (3) X Nki :zi X Vki :xi ¼ 0: X i¼1;2 Ni ki
xi (4) i¼1;4 The unknown quantities in the above relations are the magnitude of the forces in pins Nki and Vki, and the magnitude of compressive forces Ni in the scarf faces. The origin of the forces in the faces can be obtained from experiments; however, a small change in the origin has no influence on the results. This implies that there are ten unknown quantities for three equilibrium conditions (3, 4). In this way, only three unknown quantities will remain, which can be identified by means of the condition for the scarf continuity. The force method with seven unknown quantities, e.g., the force Ni and the horizontal and vertical force in the pins Nki Vki, can be used. Nk1 Vk1 X (2) i¼1;4 i¼1;4 3.2 Oblique scarf joint (1) x Nk2 N2 Vk3 Nk3 Nk4 z Vk4 2 Va2 Na2 V2 4 P. FAJMAN AND J. MÁCA Part I 1 disconnected 1 X2 z1 11 1 1 Spring connection 1 X3 Part II 1 connected 1.k1 X1 1.k1 X1.k1 Part I X4 zk3 z2 X5 2 X7 X6 2 Part II Figure 6. Forces for δ11. Figure 5. Virtual set up with forces in Part 1. The part of a scarf between points 1 and 2 is shown in Figure 5. It is labeled I, with unknown forces X1, X1k1, X2 to X7 exerted in the disconnection with Part II. A similar scheme also applies to Part II. The choice of a real structure (RS structure without forces Xi and with loading) and a virtual structure (VS structure with forces Xi and without loading) is enabled in various ways, e.g., by disconnecting the parts shown in Figure 5. In order to calculate the yield coefficients, it is necessary to compile the moments from the loading Mf and the axial force Nf on RS and Mi, Ni from Xi on VS. In the connection part, there is a mutual zero shift perpendicular to the face plane, then a zero shift in the pin with a potential shift due to its stiffness. The conditional equation for shifts in the face describes the deformation at point 1 between Parts I and II due to the force effects; see Figure 5: X
 δi ¼ Xj δij þ δijr þ δif ¼ 0; (5) j¼1;7 By analogy, this holds for the deformation in positions X2 to X7. The symbols are  ð Mi Mj Ni Nj 1 dx ; δiir ¼ 1 þ δij ¼ ; kik2 EI EA Nk2;j Mk2;j δijr ¼ Nk2;i þ Mk2;i ; kuk2 kφk2  ð Nk2;f Mk2;f Mi MF Ni NF þ dx þ Nk2;i þ Mk2;i : δiF ¼ kuk2 kφk2 EI EA (6) The conditional equation for the shift in the face δ11 includes the deformation at point 1 between Parts I and II, due to the effects of the force X1, see Figure 6. A = bh/2, or I = bh3/24 is the area, or the moment of inertia, of the cross section of the scarf, and k is the effect of pin yielding. The pin stiffness can be calculated or obtained by experimental methods. In the case of the pin, the stiffness refers to the horizontal and vertical stiffness ku; see Figure 7. V U= ku v=1 u=1 V= kv Figure 7. Plotted stresses and deformations of the peg central line. 4. Comparison of experimental and numerical results The set-up defined for the experiment took into account the results of previous experimental campaigns and calculations. Based on the collected experience and knowledge, the basic recommendations that were adopted in the scarf joint design were: face inclination of 90° (normal) or 45° (inclined); scarf joint length ranging between 3h–7h; and ● distances of connectors must be at least 7Ø from the face. ● ● The geometry of the tested beam is displayed in Figure 8. Beams were tested in a three-point bending test in the laboratories of the Institute of Theoretical and Applied Mechanics in Prague, Czech Academy of Sciences. For more details, see Arciszewska-Kędzior et al. 2015b; Kunecky et al. 2015. Four groups of specimens were tested. Beams with a halved scarf joint (normal face), beams with an oblique joint (inclined face), beams with an inclined face under reverse loading, and beams without any joint. The modulus of elasticity and tensile stress in bending were obtained during the tests. INTERNATIONAL JOURNAL OF ARCHITECTURAL HERITAGE 5 1470 F 1000 b= 200 h= 240 45° 800 1370 830 3000mm L= 6000mm Figure 8. Tested beams and scarf joints—halved scarf with normal face (upper) and oblique scarf with inclined face (lower). 4.1 Load-bearing capacity—first limit state The load-bearing capacity of the joint depends on the failure modes which were obtained from several dozen experiments with a four-pin wooden joint. The most common failure mode was the face splitting—see Figure 9 on the left, then the pin failure; see Figure 9 on the right, or a failure around the pin, and, last but not least, the failure due to tension in the weakened cross section. In the joint with steel pins, the failure occurs by the tear of wood across the grain—experimentally verified during comparative tests; see Figure 10 (Fmax = 27.1 kN, Flin = 18 kN for a 200/240 section), Figure 9. Failure of a tested beam with four pins. Figure 10. Resulting failure of a joint with steel pins under three-point bending load. P. FAJMAN AND J. MÁCA 6 Kędzior et al. 2015b; Kunecky et al. 2015). The value is calculated using the formula σ = M/Wel where M = F.L/4 + g.L2/8 and Wel = bh2/6, F = 34,7 kN is taken from the last row of Table 1. and, simultaneously, rigid steel pins locally indent the material, which supports crack initiation. Assumptions for numerical analysis are as follows. The modulus of elasticity Eo,mean = 9.45 GPa was obtained from the experiments (ArciszewskaKędzior et al. 2015b; Kunecky et al. 2015) with a beam without a joint. The value is calculated using the formula E = F/(L3/(48.I]+L/(5/6. A.0,06)/4)/w, where values Flin = 11,25 kN, wlin = 24 mm are taken from the last row of Table 2, A is the area and I is the moment of inertia of the beam cross-section, the shear modulus G = 0.06.E; see (Eurocede 5, 2011). The obtained value of the modulus of elasticity corresponds the value of C20 class wood in Eurocode 5 (Eo,mean = 9.5 GPa). ● The limit force in the face (M1) is derived in the form V = A.fck90 = 0.5.l.b/2.fck90, where l is the distance of the connector from the face, besides, the effect of seasoning splits is considered at a value of 0.5, which is in agreement with experiments on beams stored under standard moisture conditions with dimensions used in construction practice, b is the width of the beam, and fck90 is the strength perpendicular to the grain. ● The maximum loading of the pin and longitudinal beam splitting (M2) is identified from the experiment (Milch et al. 2017) and depends on the pin’s diameter and material and the beam’s material— for a wooden pin with a diameter of 24 mm, Fx = 5.8 kN, Fz = 3.25 kN. ● The tensile stress in bending (M3) fmk = 27,5 MPa was obtained from experiments (Arciszewska● Table 1. Comparison of beam stiffness and failure modes. Experiment[7,8] k lin F lin (kN) (F max) (kN/m) 18 365 (27.1) 24.7 476 (32.7) 18 318 (26.3) 34,7 467 (44.2) Normal face Inclined face Inverse loading Without a joint Calculation for [C20] failure mode M2 F lin (kN) 14.0 k lin (kN/m) 381 failure mode M2 M1, M2 M2 22.5 420 M1 13.5 311 M2 29.5 (44.2) 474 F Normal face Inclined face Inverse loading Without a joint Calculation for C20 lin (kN) w lin (mm) F lin (kN) w lin (mm) 11.25 30 11.25 29.5 11.25 24 11.25 26.8 11.25 35 11.25 36.1 11.25 24 11.25 23.8 4.2 Deflection—second limit state The maximum short-term deflection for floor structures can be considered at a value of wmax = l/ 250 = 24 mm. The load corresponding to this deflection value in the case of a beam without a scarf was applied to beams with scarf joints. In this way, the deflection increment due to the joint can be identified. Table 2 presents the results measured during the experiments performed by (Arciszewska-Kędzior et al. 2015b; Kunecky et al. 2015) and the results calculated from the theoretical model developed, assuming a value of the load applied of F lin = 11.25 kN. For wooden pins, the agreement of the calculation with the experiment is sufficient for their application in practice. The table compares beams with a scarf joint against a reference beam without a scarf. This allows a simple design of the deflection of a beam with a scarf joint in practice. One just needs to calculate the deflection on the beam without a scarf joint and, successively, multiply the calculated deflections by the correction coefficient. The value of the correction coefficient for the tested structure is between 1.1 and 1.2. 5. Discussion over results Based on the experiments and theoretical analysis we can say the following. Table 2. Comparison of linear deformations. Experiment [7,8] Table 1 presents the forces and failure modes obtained from the experiment and the calculation. Due to the fact that a linear model is used, the force is labelled Flin. An important finding is that the calculation yields a lower load-bearing capacity than the linear value in the experiment, which is on the safe side. In normal faces, the precision rate and the pushing of faces onto each other are important. In a non-precise connection, the joint behaves as a contactless joint and all forces are only transferred by pins similarly to inverse loading. The results obtained by the calculation of different geometries assumed for the scarf joints studied are very close to the ones measured during experiments. ● Inclined faces have a favorable effect on the joint behavior. The angle of 45° is a good compromise ● Difference % 1.7 −11.7 −3.2 0.8 INTERNATIONAL JOURNAL OF ARCHITECTURAL HERITAGE between the static load-bearing capacity of the joint, its length, and labor intensity. ● The load-bearing capacity criteria of the computational model limit the load-bearing capacity by 80–90% of the linear values obtained by experiments. ● The scarf joint’s most frequent failure is by the splitting of its ends and at the point of a seasoning split. Here, the load-bearing capacity can be increased by means of vertical screws through the cracks (M2). ● If the limit state of serviceability is crucial, the deflection of a beam without a scarf can be easily recalculated for a beam with a scarf. 6. Conclusions The adjustment joint is a convenient means for use in repairs of historic beams. The joint retains the original shape of the structure and can be fabricated to be nearly invisible. In structural terms, the stiffness of a repaired structure is nearly the same as the original one. This is an excellent feature in structures where the second serviceability limit state is crucial. The load-bearing capacity can be increased by the inclination of faces and their mutual abutment. Using an inclination of faces of 45°, the loadbearing capacity can be increased by up to 50% against a joint with perpendicular faces. The presented analytical model describes the linear joint behavior very well. To determine the joint load-bearing capacity experimentally obtained partial load-bearing capacity values of connecting pieces, including their failure modes, are necessary. These values can subsequently be introduced in the theoretical model and the forces obtained compared against them. The safety level is then selected in compliance with standards. Funding The article was written with support from the Ministry of Culture’s project NAKI grant project – DF12P01OVVOO4 – Design and Assessment of Wooden Carpenter’s Joints of Historical Structures. References Arciszewska-Kędzior, A., J. Kunecký, and H. Hasníková. 2015a. Mechanical response of a lap scarf joint with inclined faces and wooden dowels under combined loading. Structural Health Assessment of Timber Structures. Proceedings of the International conference on Structural 7 health assessment of timber structures, SHATIS’15, Vol. 1, 201, 849–858. Wrocław: Dolnośląskie Wydawnictwo Edukacyjne. Arciszewska-Kędzior, A., J. Kunecký, H. Hasníková, and V. Sebera. 2015b. Lapped scarf joint with inclined faces and wooden dowels: Experimental and numerical analysis. Engineering Structures 94 (July):1–8. doi:10.1016/j. engstruct.2015.03.036. Branco, J. M., M. Piazza, and P. J. S. Cruz. 2010. Structural analysis of two king-post timber trusses. Non-destructive evaluation and load-carrying tests. Journal of Construction and Building Materials 24 (3):371–83. Eurocode 5. 2011. Design of timber structures – Part 1-1: General – Common rules and rule for buildings. Praha, UNMZ. Fajman, P. 2014. A scarf joint for reconstructions of historical structures. Advanced Materials Research – 969/2014, 7, 9– 15. Uetikon-Zurich: Trans Tech Publications. Fajman, P., and J. Máca. 2014. The effect of key stiffness on forces in a scarf joint. Proceedings of the Ninth International Conference on Engineering Computational Technology. Stirling: Civil-Comp Press Ltd, doi:10.4203/ ccp.105.40. Fajman, P., and J. Máca. 2015a. Scarf joints with pins or keys and dovetails. Proceedings of the International Conference on Structural Health Assessment of Timber Structures, SHATIS 15, 899–906. Wroclaw: Wroclaw University of Technology. Fajman, P., and J. Máca. 2015b. Change of beam stiffness with scarf joints. Proceedings of the Fifteenth International Conference on Civil, Structural and Environmental Engineering Computing. Stirling: Civil-Comp Press Ltd. doi:10.4203/ccp.108.262. Fajman, P., and J. Máca. 2017. Stiffness of scarf joints with dowels. Computer & Structures. in press. doi:10.1016/j. compstruc.2017.03.005. Kunecky, J., V. Sebera, J. Tippner, A. Arciszewska-Kędzior, H. Hasnikova, and M. Kloiber. 2015. Experimental assessment of historical full-scale timber joint accompanied by a finite element analysis and digital image correlation. Construction and Building Materials. doi:10.1016/j. conbuildmat.2014.11.034. Kunecky, J., V. Sebera, J. Tippner, and M. Kloiber. 2014. Numerical assessment of behaviour of a historical central European wooden joint with a dowel subjected to bending. Conference Proceedings of 9th International Conference on Structural Analysis of Historical Constructions, np. 8, Mexico City: Instituto de Ingenieria. Milch, J., J. Tippner, M. Brabec, and V. Sebera. 2014. Experimental verification of numerical model of single and double-shear dowel-type joints of wood. 57th International Convention of Society of Wood Science and Technology, 368–76. Monona, Society of Wood Science and Technology. Milch, J., J. Tippner, M. Brabec, V. Sebera, J. Kunecký, M. Kloiber, and H. Hasníková. 2017. Experimental testing and theoretical prediction of traditional dowel-type connections in tension parallel to grain. Engineering Structures 152 (December):180–87. doi:10.1016/j. engstruct.2017.08.067. 8 P. FAJMAN AND J. MÁCA Piazza, M., and M. Riggio. 2007. Typological and structural authenticity in reconstruction: The timber roofs of church of the pieve in Cavalese, Italy. International Journal of Architectural Heritage 1 (1, March):60–81. Sangree, R. H., and B. W. Schafer. 2009. Experimental and numeric analysis of a stop-splayed traditional timber scarf joint with key. Construction and Building Materials 23 (1):376–85. doi:10.1016/j.conbuildmat.2007.11.004.