Behaviour and design resistance of long bolts in shear

Behaviour and design resistance of long bolts in shear Neda Jankovi´ c a,* , Filip Ljubinkovi´ c a , Jorge Conde b , Jelena Dobri´ c c , Luís Sim˜ oes da Silva a,1 a University of Coimbra, ISISE, ARISE, Department of Civil Engineering, Portugal b Universidad Polit´ ecnica de Madrid, Departamento de Física y Estructuras de Edificaci´ on, Av. Juan de Herrera, 4, 28040, Madrid, Spain c University of Belgrade, Faculty of Civil Engineering, Serbia ARTICLE INFO Keywords: Long bolts Bi-directional bolts Design shear resistance Initial stiffness Eurocode ABSTRACT The European standard EN 1993-1-8 lacks specific design provisions for bolted connections incorporating long bolts, despite their increasing use in innovative joint configurations. Long bolts are defined as structural bolts that are manufactured from circular steel, fully or partially, threaded rods instead of a steel coil and are not subjected to heat treatment. In contrast to standard structural bolts, they do not present a bolt head. They are assembled with standard washers and nuts at both ends and feature an extended length compared to standard bolts, offering unique advantages in addressing challenges that conventional bolts cannot resolve. Within the framework of the RFCS CONNECT4C project, which focuses on promoting circular economy principles in steel construction, adaptable and reusable steel joints are being developed, with long bolts playing a key structural role. As part of this initiative, the present study explores the mechanical performance of long bolts subject to shear through an extensive experimental campaign involving 60 tests. The aim is to characterise their behaviour and assess the applicability of the existing EN 1993-1-8 formulations for shear resistance and stiffness to this specific bolt type. Finally, a reliability assessment is conducted to establish a suitable partial factor (γ M2 ) for connections utilising long bolts, confirming that the values for standard bolts are appropriate for long bolts in shear. The outcomes provide direct guidance for incorporating long bolts into future CEN product standards and extend the current design provisions of EN 1993-1-8 to long bolts. Symbols and acronyms Acronyms B Black surface of the long bolt CoV Coefficient of variation G Galvanised surface of the long bolt GL Grip length LC Load cell LVDT Linear velocity displacement transducer PC Property class Latin letters AGross cross-section area A s Tensile area of a bolt A s,meas Measured tensile area of a bolt A s,nom Nominal tensile area of a bolt aPlate thickness bPlate width, Correction factor dExternal diameter of a fully threaded bolt d M16 External diameter of the M16 bolt EYoung’s modulus of bolt material FForce F m Maximum force F u Ultimate force F v,Rd Design shear resistance of bolt F v,Rk Characteristic shear resistance of bolt F 0.0048d Force at the beginning of bolt yielding f ub Bolt tensile strength f ub,meas Measured bolt tensile strength f ub,nom Nominal bolt tensile strength H r LVDT measuring relative horizontal displacement hHorizontal measurement of the long bolt hole K v Initial stiffness of a bolt K v,EN Initial stiffness of a bolt according to EN 1993-1-8 * Corresponding author. E-mail address: [email protected] (N. Jankovi´ c). 1 The author Luís Sim˜ oes da Silva is an editor of this journal. In accordance with policy, Luís Sim˜ oes da Silva was blinded to the entire peer review process. Contents lists available at ScienceDirect Journal of Constructional Steel Research journal homepage: www.elsevier.com/locate/jcsr https://doi.org/10.1016/j.jcsr.2025.110138 Received 2 September 2025; Received in revised form 30 October 2025; Accepted 13 November 2025 Journal of Constructional Steel Research 237 (2026) 110138 Available online 20 November 2025 0143-974X/© 2025 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ ). K v,exp Experimental initial stiffness of a bolt K v,prop. Proposed formula for initial stiffness of a long bolt k r Reduction factor to account for the length of a bolted lap connection k rd Reduction factor to account for the reduced ductility of grade 10.9 bolts k v Stiffness coefficient for bolts in shear according to EN 1993-18 LTotal bolt length L g Grip length L m Distance between LVDT_11 and LVDT_13 n n Number of shear planes with threads intercepting the shear plane n x Number of shear planes without threads intercepting the shear plane OV Holes ovalisation RCircular radius of bolt curvature uShear deformation of bolts u i,exp Isolated displacement component in the bolt middle u 0 Correction of the initial slip Δu i Relative displacement between plates for load application Δu i,c Corrected value of the relative displacement between plates for load application V a LVDT measuring absolute vertical displacement V r LVDT measuring relative vertical displacement V δ Estimator for the coefficient of variation vVertical measurement of the long bolt holes Greek letters α v Shear coefficient βReliability index γ M2 Partial factor Δ el Elastic deformation θAngle of bolt rotation ϕResistance factor, Capacity factor 1. Introduction Bolted connections are a fundamental component in steel structures, valued for their simplicity, ease of assembly, and potential for disassembly and reuse. Design standards such as the European standard EN 1993-1-8 [1] provide detailed guidance for the design of these connections, assembled with preloaded (EN 14399) [2] or non-preloaded (EN 15048) [3] bolts. However, recent trends in structural engineering, driven by sustainability and modular construction, are encouraging the development and use of non-standard connection solutions. Among these innovations, long bolts are gaining increased attention. Long bolts, also known as bi-directional [4] or stud bolts [3], characterised by their extended grip lengths, offer distinct advantages over conventional bolts in specific structural applications. They are particularly useful in connections involving thick intermediate plates, multiple joint components, or wider spacing between connected elements. They are also used in joints with concrete-filled tubes [5]–[6], as foundation anchors and for self-centring solutions aiming to improve the seismic response of the structure, as reported in [7–8]. Their ability to bridge larger gaps and facilitate adaptable joint configurations makes them especially suitable for reusable systems. Nevertheless, their mechanical behaviour remains insufficiently explored in existing design standards and available literature. The current provisions of EN 1993-1-8 were developed for conventional bolts with relatively short lengths. These formulas may not be directly applicable to long bolts, as their manufacturing processes and the increased length can lead to different failure modes, load distribution, and stiffness characteristics. The present research is conducted within the framework of the RFCS CONNECT4C project [9], which focuses on developing adaptable and reusable steel joints to support the circular economy in structural engineering. Long bolts are a critical component of these new joints, and their proper characterisation is critical for ensuring safe and efficient design. To address this need, the present study investigates the mechanical performance of long bolts under shear loading, complementing a previously published paper [10] that addressed long bolts in tension. A total of 60 experimental tests were conducted to evaluate their shear resistance and stiffness. The results are analysed and compared against the corresponding design provisions for standard bolts in shear as outlined in EN 1993-1-8. Special emphasis is placed on assessing the validity of the shear coefficient ( α v ) for long bolts. Finally, a reliability assessment is performed to validate the applicability of the partial factor (γ M2 ) for connections incorporating long bolts in shear. 2. Background review 2.1. Geometry of the long bolts The manufacturing process of long bolts differs significantly from that of standard bolts. Unlike standard bolts, which are typically made of steel coil and undergo heat treatment during production, long bolts are fabricated from steel rods without any subsequent heat treatment. A detailed description of their manufacturing process is provided in reference [10]. These bolts are usually available in lengths up to 1000 mm, though they can be cut to shorter sizes based on client specifications. In this study, fully threaded long bolts were used. Unlike conventional bolts, they do not feature a forged head. Instead, they are equipped with nuts and washers (HV in the present study) at both ends to create the necessary clamping force. The dimensions of a long bolt are illustrated in Fig. 1. The total length of the bolt is denoted as L, L g is the grip length, and d is the external diameter of the bolt. The calculation of the tensile stress area A s , referenced throughout this text, follows the provisions specified in ISO 898-1 [11]. 2.2. Behaviour of structural bolts in shear 2.2.1. Standard structural bolts Many studies have investigated the shear strength and behaviour of high-strength bolts under various load scenarios, including tension, shear and their combination, through experimental and numerical studies. Strangh¨ oner et al. [12] conducted a comprehensive literature review on high-strength bolts, compiling relevant findings from previous experimental studies on their behaviour in tension, shear, and the interaction of both, and reviewed design expressions for the resistance of carbon steel bolts as specified in EN 1993-1-8 [1], AISC 360–22 [13], and AS 4100 [14]. In addition to reviewing existing research, Strangh¨ oner et al. [12] carried out their own experimental investigations and performed statistical validation through a reliability analysis following EN 1990 Annex D [15]. Their study highlighted the significance of the shear coefficient α v in the shear resistance formula prescribed by EN 1993-1-8 [1], proposing a value of 0.65 for bolt classes 8.8 and 10.9, applicable to both threaded and unthreaded sections in the shear plane. Furthermore, they established a correlation between bolt tensile strength and shear coefficient, demonstrating an inverse Fig. 1. - Geometry of a structural long bolt (adapted from [10]). N. Jankovi´ c et al. Journal of Constructional Steel Research 237 (2026) 110138 2 relationship whereby an increase in tensile strength corresponds to a decrease in the shear coefficient. In Strangh¨ oner and Abraham [16], a similar approach was used for austenitic and duplex stainless-steel bolts. They evaluated the shear coefficients α v for these bolts, which are higher than the ones defined in EN 1993-1-4 [17]. Wallaert and Fisher [18] identified two methods for testing the shear strength of bolts: using plates in tension or compression. Their findings indicate that, because of lap plate prying action, bolts tested under tension exhibit shear strengths 6–13 % lower than those tested under compression and with lower scatter, which makes the test in tension the preferred testing layout. Additionally, Kulak et al. [19] reported that the shear strength to tensile strength ratio is independent of bolt class and is approximately 62 %. Li et al. [20] highlighted the influence of the shear plane position on the shear strength for 10.9-class bolts. Their study demonstrated that when the shear plane passes through the unthreaded shank, the shear capacity reaches approximately 80 % of the bolt’s tensile strength. However, when the shear plane passes through the threaded section, the shear capacity decreases to around 60 % of the bolt’s tensile strength. Considering that the gross area to tensile area ratio of the bolts in the study was approximately 1.28, the results are in good agreement with those by Strangh¨ oner et al. [12]. Xin et al. [21] conducted a numerical study on the behaviour of bolts under combined loading, incorporating the precise geometry of bolt threads in their models to enhance accuracy. Their study assessed the reliability of existing design standards by comparing the simulated shear resistance with the predictions provided by various codes. The results indicated that the simulated shear strength exceeded the values calculated using the EN 1993-1-8 expressions by 6 % for partially threaded bolts and by 22 % for fully threaded bolts. Authors [21] further concluded that the American AISC-360 [13], Chinese GB-50017 [22], and Australian AS 4100 [14] standards provide reliable estimates for the shear resistance of partially threaded bolts but tend to overestimate the resistance of fully threaded bolts. Numerous studies have been conducted to assess the behaviour of lap joint configurations, whereby the bolts work in shear, and it is required to establish appropriate geometrical criteria to prevent either the shear failure of the bolt or the splitting failure/shear failure of the connecting plates. In this context, significant research efforts have been dedicated to studying the bearing resistance of bolt holes. Moˇ ze and Beg [23–25] improved and extended the applicability of the bearing resistance equations to high-strength steel plates. As a result, Moˇ ze and Piculin [26] developed an analytical formula to predict the full range forcedeformation behaviour of steel plates at bolt holes. This formulation was included in the revised version of EN 1993-1-8 [27]. In particular, an alternative initial stiffness expression is provided for the loaddeformation behaviour of bolt embedment due to bearing action that gives a high level of accuracy. In contrast, studies focusing on the full range shear behaviour of bolts in shear, where the failure mode is the shear resistance of the bolt instead of plate bearing, are scarcer. Karmalin and Pavlov [28] carried out tests on bolts in shear with very high-strength steel plates (tensile strength fub ≥2000 MPa) to prevent bearing deformations. Based on this study, Jaspart [29] proposed Eq. (1) for the initial stiffness of one bolt in single shear, K v (kN/mm): Kv=0.93Asfub,(1) where the constant 0.93 has units of millimetres (mm), A s is the tensile stress area of the bolt in mm 2 , and f ub is the nominal tensile strength of the bolt in kN/mm 2 . Eq. (1) was adjusted in EN 1993-1-8 [1] to avoid dependence on units, as follows: Kv=kvE=8d2 dM16 fub,(2) where k v is the bolt shear stiffness normalised by Young’s modulus E, d is the nominal bolt diameter, and d M16 is the nominal diameter of an M16 bolt. Eq. (2) correlates well with Eq. (1), giving results approximately 13.5 % lower to match the 95th percentile of the results of the Karmalin and Pavlov tests. Ahmed and Teh [30] assessed the influence of shear on the threaded part of a bolt, showing a reduction of approximately 56 % of the initial stiffness compared to shear in the shank due to the threads cutting into the plates. However, in their tests, “the connection displacements were almost entirely due to the bolt hole deformation”. Lange [31] tested standard M20 bolts of grades 8.8 and 10.9 in single and double shear. His results confirm that there is a reduction in the initial stiffness of bolts with a shear plane on the threaded part when compared to the shear Table 1 Design specifications for bolts in shear in EN 1993-1-8 [27], AISC 360–22 [13] and AS 4100 [14]. Shear resistance EN 1993-1-8 [27] Shear plane in the threaded part Fv,Rd = α vfubAs γM2 , α v={0.6 for PC 4.6,5.6,8.8 0.5 for PC 4.8,5.8,6.8,10.9 (3a) Shear plane in the unthreaded part Fv,Rd = α vfubA γM2 , α v=0.6 for all PC (3b) AISC 360–22 [13] Shear plane in the threaded part Fv,Rd,AISC =ϕ0.45fubA(4a) Shear plane in the unthreaded part Fv,Rd,AISC =ϕ0.563fubA(4b) AS 4100 [14] Shear plane in the threaded part Fv,Rd,AS =ϕ0.62fubkrdkrnnAs,krd ={1.0 for PC 4.6,8.8 0.83 for PC 10.9 (5a) Shear plane in the unthreaded part Fv,Rd,AS =ϕ0.62fubkrdkrnxA,krd =1.0 for all PC (5b) Initial stiffness (for one bolt-row, with two bolts per bolt-row, normalised to the Young Modulus E) EN 1993-1-8 [27] Non-preloaded bolts (bearing type connection) kv=16d2fub EdM16 (6a) Preloaded bolts (slip-resistant connection) kv=∞(6b) α v : shear coefficient | f ub : nominal tensile strength of the bolt | A s : tensile stress area of the bolt | A: gross cross-section area of the bolt | γ M2 : partial factor (γ M2 =1.25) | d: nominal diameter of the bolt | ϕ: resistance factor according to AISC 360–22 (ϕ =0.75 (LRFD)), and capacity factor according to AS 4100 (ϕ =0.80 for bolts in shear) | k rd : reduction factor to account for the reduced ductility of grade 10.9 bolts | k r : reduction factor to account for the length of a bolted lap connection (k r =1.0 for other connections) | n n : number of shear planes with threads intercepting the shear plane | n x : number of shear planes without threads intercepting the shear plane | E: Young’s modulus of steel | d M16 : nominal diameter of an M16 bolt | PC: bolt’s property class. N. Jankovi´ c et al. Journal of Constructional Steel Research 237 (2026) 110138 3 plane on the shank. Henriques et al. [32] proposed a trilinear full-range law for the bolt in shear, establishing their strain hardening stiffness, ultimate resistance, and ultimate deformation, based on the Karmalin and Pavlov tests. The model incorporates parameters expressed as functions of the initial stiffness and nominal resistance. In summary, the reviewed literature on standard bolts does not provide much information that can be used to identify specific aspects that may be critical for long bolts. However, the reviewed papers allow for establishing reference results and procedures for the assessment of the shear resistance and initial stiffness of bolts in shear. Additionally, they also provide guidance on the testing methods for bolts in shear and how to minimise bearing deformations in the testing process. 2.2.2. Long bolts Long bolts have received limited attention in existing literature and design standards. Jankovi´ c et al. [10] conducted a literature review on the behaviour of long threaded rods under tensile loading, highlighting the need for further research in this area. Consequently, the present study focuses on the behaviour of long bolts subjected to shear forces, addressing a gap in the current understanding of their structural performance. The majority of the studies have investigated the behaviour of long bolts in end-plate beam-to-column joints with concrete-filled tubular steel columns [4]–[6]. The primary objective of using long bolts in such configurations is to solve the problem of having no access to the inside of the tubes, enhancing joint rigidity and resistance while minimising the number of additional components required for assembly, such as Uchannels, blind bolts [5], fin plates, angle, or tee cleats. Experimental testing on long bolts passing through concrete-filled tubular columns has demonstrated that bolt bending has no significant influence on joint performance. Based on these findings, Van-Long et al. [5] recommended the application of the shear resistance formula from EN 1993-1-8, originally developed for standard bolts, to long bolts as well. Fransplass et al. [33] investigated the behaviour of long bolts manufactured from threaded rods under tensile loading and combined tension and shear, considering both low and elevated strain rates. The experiments were conducted using a custom-designed fixture, allowing for the examination of different grip lengths ranging from 0.41 mm to 9.8 mm. Their findings revealed that the ultimate load in shear tests increases with the loading rate, indicating a strain rate sensitivity in the material response. Additionally, fracture surface analysis showed a smooth appearance with a slight inclination following the thread pitch, suggesting a failure mode influenced by the bolt’s threading geometry. However, since they tested small grip lengths and small diameter rods in mild steel, M5 class 4.6, the validity of their conclusions for the present study may be limited. 2.3. Design resistance and initial stiffness of bolts under shear loading Design standards differentiate the shear resistance depending on whether the shear plane passes through the unthreaded or threaded portion of the bolt. Table 1 summarises the expressions for shear resistance and initial stiffness of a bolt in shear according to the revised version of EN 1993-1-8 [27], AISC 360–22 [13] and AS 4100 [14]. The formula for initial stiffness defined in EN 1993-1-8 considers two bolts per bolt row and a single shear plane. Hence, for a single bolt and a single shear plane, Eq. (6a) must be divided by 2, effectively coinciding with Eq. (2). Furthermore, it is noted that EN 1993-1-8 [27] explicitly separates the initial stiffness of the bolt in shear (addressed in this paper) that only covers the deformability of the bolt (not the connecting plates) from the initial stiffness of the bolt in bearing (that only covers the deformability of the connecting plates). The total initial stiffness of the bolt-plate assembly consists of the addition of both initial stiffnesses. 3. Experimental programme 3.1. Programme definition The experimental campaign aims to characterise the behaviour of long bolts in shear. To achieve this objective, F-u curves for the long bolts are extracted, where F represents the total applied shear force (including the two shear planes, see Fig. 4) and u denotes the relative displacement of the shearing plates due to the deformability of the bolt. A total of 60 tensile tests were performed, covering the following parameters: •Bolt diameter (M20, M24, M27 and M30), Fig. 2. Studied grip lengths. Table 2 Summary of the performed tests. Bolt size Class Surface finish Grip length L g (mm) Plate thickness a (mm) No. of tests (−) M20 8.8 and 10.9 B and G 60, 220, 380 and 540 10 24 M24 8.8 and 10.9 B and G 60, 220, 380 and 540 10 20 M27 10.9 B and G 60, 220, 380 and 540 15 8 M30 10.9 B and G 60, 220, 380 and 540 15 8 Total Σ 60 N. Jankovi´ c et al. Journal of Constructional Steel Research 237 (2026) 110138 4 •Bolt property class (8.8 and 10.9), •Surface finish (B – black, uncoated and G – galvanised, zinc-coated), •Grip lengths excluding washers (60, 220, 380 and 540 mm), see Fig. 2. All tests were performed with one washer and nut per bolt side. Each test was labelled by combining the letter “S” (representing shear) with the specifications of its defining parameters. For example, “S31M24–10.9-B-380-P10” corresponds to the shear test (S), number of the test (31st), long bolt M24 in steel property class 10.9, with a black (B) surface finish, with a grip length of 380 mm and plate thickness of 10 mm (P10). A summary of all performed tests, with varying parameters, is given in Table 2. Two tests (S31-M24–10.9-B-380-P10 and S48-M30–10.9-G-540-P15) were excluded from the analysis due to instrumentation malfunctions, leaving, in total, 58 valid tests for post-processing. The thickness of the plates for load application is 10 mm for smaller bolt diameters (M20 and M24) and 15 mm for larger bolt diameters (M27 and M30). All tests with longer grip lengths (GL220, GL380, and GL540) involved two plates at each bolt ending. For the shortest grip length (GL60), the number of plates used was six (for M20 and M24 bolts) or four (for M27 and M30 bolts). The nominal hole diameters are in accordance with EN 1090–2 [34]: 22 mm, 26 mm, 30 mm, and 33 mm for M20, M24, M27, and M30 bolts, respectively. Table 3 contains the geometry of the bolts with corresponding nuts and washers’ thicknesses, and the unfactored shear resistance according to EN 1993-1-8 [27], AISC 360–22 [13] and AS 4100 [14]. Comparing AISC 360–22 and AS 4100 with EN 1993-1-8, the following differences are noted: the unfactored shear resistance values for 8.8 and 10.9 bolt classes, respectively, are 3.8 % lower and 15.4 % higher for AISC 360–22 and 3.3 % and 2.9 % higher for AS 4100. Comparing the factored results, the corresponding results are 9.9 % lower and 8.2 % higher for AISC 360–22 and 3.3 % and 2.9 % higher for AS 4100. 3.2. Experimental layout The experimental layout is presented in Fig. 3. It consists of permanent parts (labels 1–4 and 6–10) and replaceable parts (specimens and parts with labels 5, 11, and 12), presented in Fig. 3(a). The reaction frame (6) consists of two vertical columns and a strong beam that works as a support for the 6 MN hydraulic jack (10). With the hinge (9), the jack fixes the upper retaining beam (2) and pulls it up during the load application phase. The bottom retaining beam (1) is positioned in the lower part of the layout. Its movement is restricted by the supporting brackets (7) and two load cells (8) that measure the vertical reactions. Both upper and bottom retaining beams have a guiding system (4) that ensures they slide easily on the reaction frame columns. Plates for load application (5), which are fixed between angular plates (3) and spacers (11,12), have holes for positioning the specimens. When the load Table 3 Nominal geometry and resistance of the bolts. Bolt notation M20 M24 M27 M30 Bolt diameter dmm 20 24 27 30 Thread pitch Pmm 2.5 3.0 3.0 3.5 Tensile area A s mm 2 245 353 459 561 Nut thickness (nominal) t n mm 16 20 22 24 Washer thickness (nominal) t w mm 4 4 5 5 Class 8.8: Characteristic shear resistance, Eq. (3a) with γ M2 =1.0 and α v =0.60 F v,Rk kN 235.2 338.9 440.6 538.6 Class 10.9: Characteristic shear resistance, Eq. (3a) with γ M2 =1.0 and α v =0.50 F v,Rk kN 245.0 353.0 459.0 561.0 Class 8.8: Characteristic shear resistance, Eq. (4a) with ϕ =1.0 F v,Rk,AISC kN 226.2 325.7 412.2 508.9 Class 10.9: Characteristic shear resistance, Eq. (4a) with ϕ =1.0 F v,Rk,AISC kN 282.7 407.2 515.3 636.2 Class 8.8: Characteristic shear resistance, Eq. (5a) with ϕ =1.0 and k rd =1.0 F v,Rk,AS kN 243.0 350.2 455.3 556.5 Class 10.9: Characteristic shear resistance, Eq. (5a) with ϕ =1.0 and k rd =0.83 F v,Rk,AS kN 252.2 363.3 472.4 577.4 Fig. 3. Test layout: (a) 2D view with marked parts; (b) 3D view; (c) Photo from the test. N. Jankovi´ c et al. Journal of Constructional Steel Research 237 (2026) 110138 5 is applied with the hydraulic jack, the upper retaining beam (2) is pulled up together with the load application plates (5) connected to it. The load application plates (5) connected to the bottom retaining beam (1) are fixed, and hence, the specimen is subjected to shear forces. To accurately assess the shear capacity of long bolts, it is essential to minimise friction between the plates. This was achieved by applying lubricant to the contact surfaces of both the internal and external plates. Strong bars (13) are utilised to prevent the opening of load application plates (5) and to fix the constant grip length during the test performance. Since the primary objective of the experimental campaign is to evaluate the shear resistance of the bolts, the bearing deformation of the plates needs to be minimised. This is achieved by using thick plates made of high-strength steel S690. Ideally, the plates remain undamaged while the long bolts undergo shear deformation and subsequent failure. 3.3. Test procedure and instrumentation The test was performed by applying a displacement to the upper retaining beam, using a 6 MN hydraulic jack attached to the beam with a pin connection. The test speed was 0.025 mm/s. During the tests, the following data were acquired (see Fig. 4): •Applied force and reactions, using load cells (LCs); •Displacements, using LVDTs (Linear Velocity Displacement Transducers). Two 2 MN-capacity load cells, labelled LC-1 and LC-2, were used for load measurements. They were positioned between the lower retaining beams and the supporting brackets. In total, 13 LVDTs were used to measure vertical absolute (label V a ), vertical relative (label V r ), and horizontal relative (label H r ) displacements of parts of the test. LVDTs V r - 7 and 8 measured the relative vertical displacement between the external and internal plates for load and were positioned symmetrically on both sides of the layout. Four LVDTs (V a - 1, 2, 3, and 4) were positioned on the upper retaining beam to assess potential beam rotation during test execution. LVDTs V a - 5 and 6, positioned on the top flange along the axis of the bottom retaining beam, monitored the potential bending or rotation of the bottom Fig. 4. Instrumentation (all dimensions in millimetres). N. Jankovi´ c et al. Journal of Constructional Steel Research 237 (2026) 110138 6 Table 4 Geometrical (considering only bolts with black surface) and material characterisation [10]. Bolt Class Tensile stress area A s,meas A s,meas / A s,nom Tensile strength f ub,meas f ub,meas / f ub,nom Mean (mm 2 ) No. of meas. (−) Mean (−) CoV (%) Mean (MPa) No. of coupon tests (−) Mean (−) CoV (%) M20 8.8 229.52 9 0.94 0.77 950.61 6 1.19 1.14 10.9 240.47 9 0.98 0.28 1176.15 6 1.18 3.24 Both 235.00 18 0.96 2.46 –12 1.18 2.37 M24 8.8 344.84 9 0.98 0.91 995.87 6 1.24 4.30 10.9 342.34 9 0.97 0.34 1166.58 6 1.17 0.93 Both 343.59 18 0.97 0.76 –12 1.21 4.56 M27 8.8 – – – – 1013.73 4 1.27 0.53 10.9 441.27 9 0.96 0.60 1183.33 6 1.18 0.47 Both 441.27 9 0.96 0.60 –10 1.21 3.59 M30 8.8 – – – – 984.70 4 1.23 1.80 10.9 549.82 9 0.98 0.26 1187.03 5 1.19 1.26 Both 549.82 9 0.98 0.25 –9 1.21 2.39 All 8.8 –18 0.96 2.33 983.63 20 1.23 3.45 10.9 –36 0.97 0.98 1177.89 23 1.18 1.83 All –54 0.97 1.72 –43 1.20 3.47 Fig. 5. Force-displacement curves: (a) GL60; (b) GL220; (c) GL380; (d) GL540. N. Jankovi´ c et al. Journal of Constructional Steel Research 237 (2026) 110138 7 retaining beam. In addition, three LVDTs (V a - 11, 12, and 13) were used to capture the potential bending of the long bolts. These LVDTs were not used in the GL60 tests due to the lack of space for their installation. The opening of the external plates was tracked with two horizontal LVDTs (H r – 9 and 10). 3.4. Test results 3.4.1. General The results of the experimental campaign are presented in the following sections, showing the force-displacement curves and all relevant findings systematically. The failure modes observed during the tests are discussed, and the curvature of the bolts is analysed, including the calculation of the bending moments present in the bolts. Additionally, the influence of the bearing resistance of the load application plates on the performed tests is investigated. 3.4.2. Material and geometrical properties The material properties of the long bolts used in this experimental campaign were determined before testing by the bolt manufacturer FATOR. The manufacturer conducted coupon tests on machined cylindrical coupons extracted from the long bolts, following clause 9.7 of ISO 898-1 [11]. The geometric properties, including external and internal diameters and thread pitch, were measured using a calliper on a sample of bolts, categorised by diameter, class, and surface finish. The long bolts used in this study were produced concurrently with those reported in [10] as part of the same broader experimental campaign under the CONNECT4C project [9]. Both campaigns utilised bolts made from steel sourced from the same batch. For the present study, the bolts were only cut to specific lengths, while the material and geometric properties reported in [10] are also applicable to this study. These results are summarised in Table 4. For defining the tensile stress area (A s,meas ) of the galvanised bolts, the coating was included in the cross-sectional measurements, which may lead to unsafe estimations. Therefore, in the present study, only measurements of the black bolts are considered. For further calculations, a mean tensile stress area is adopted for each bolt diameter, treating both property classes (8.8 and 10.9) Table 5 Summary of the shear test results of the long bolts. Bolt Class Grip length L g (mm) No. of tests (−) Initial stiffness K v (kN/mm) Force at yielding point F 0.0048d (kN) Displ. at yielding point u 0.0048d (mm) Maximum force F m (kN) Displ. at maximum force u m (mm) Force at last step F u (kN) Displ. at last step u u (mm) Mean CoV Mean CoV Mean CoV Mean CoV Mean CoV Mean CoV Mean CoV M20 8.8 60 2 174.65 5.2 199.13 0.8 1.22 3.7 272.95 1.9 2.68 3.7 243.16 5.8 3.40 0.9 220 6 165.72 16.4 223.24 6.6 1.48 25.7 267.77 1.7 2.50 10.7 263.74 1.0 2.69 11.0 380 2 156.80 1.1 225.65 1.1 1.52 3.2 283.72 0.3 3.09 4.9 281.78 0.7 3.24 1.4 540 2 183.08 9.6 211.64 9.8 1.25 19.7 272.10 5.2 2.42 7.5 269.20 3.8 2.56 13.4 All 12 168.61 12.5 217.69 7.0 1.40 21.3 272.01 3.0 2.62 11.7 264.23 5.0 2.88 14.0 10.9 60 2 142.68 1.2 266.09 0.2 1.95 1.2 335.85 2.0 3.19 3.7 304.99 4.1 3.69 11.2 220 6 163.74 9.7 308.19 3.9 1.99 9.9 345.05 2.3 3.19 10.9 343.45 2.2 3.34 12.7 380 2 161.00 3.3 291.89 12.7 1.90 18.8 342.98 4.4 3.08 4.4 342.73 4.3 3.11 5.6 540 2 164.88 5.8 282.70 5.9 1.80 5.5 347.92 4.4 3.18 14.6 346.97 4.0 3.32 15.9 All 12 159.97 8.7 294.21 7.5 1.94 10.5 343.65 2.8 3.17 8.9 337.51 5.2 3.36 11.8 All All 24 164.29 11.0 – – – – – – – – – – – – M24 8.8 60 2 191.98 3.0 308.05 6.3 1.70 2.5 428.69 5.2 3.66 5.6 419.19 4.3 3.92 6.0 220 4 197.50 16.0 349.38 12.1 1.93 27.3 440.13 0.2 3.57 9.4 436.22 1.2 3.72 8.4 380 2 172.39 4.6 342.67 3.1 2.09 7.9 435.89 1.9 3.77 6.9 435.64 1.9 3.81 7.7 540 2 164.69 13.2 341.90 4.2 2.19 5.0 438.31 3.0 4.19 2.0 424.96 4.5 4.29 0.8 All 10 184.81 13.3 338.28 9.0 1.97 18.0 436.63 2.3 3.75 8.8 430.44 2.8 3.89 8.1 10.9 60 2 166.84 7.5 394.07 7.7 2.48 18.1 474.84 3.8 3.81 6.7 464.59 1.9 4.07 8.8 220 4 228.45 30.4 373.66 18.0 1.92 44.1 476.07 4.5 3.56 13.9 474.63 4.3 3.64 15.9 380 1 164.38 –411.52 –2.60 –514.59 –4.86 –514.24 –4.94 – 540 2 177.31 2.4 383.68 1.5 2.26 1.2 489.91 0.4 4.09 5.0 488.89 0.7 4.21 6.8 All 9 196.28 26.9 384.63 11.6 2.19 27.3 483.15 4.1 3.87 13.9 479.97 4.2 4.01 14.5 All All 19 190.24 20.9 – – – – – – – – – – – – M27 10.9 60 2 275.02 1.4 509.69 6.3 1.97 5.0 652.35 2.1 3.64 0.3 643.82 1.0 3.80 0.0 220 2 245.74 30.3 554.78 6.9 2.50 45.0 630.47 1.0 3.79 17.8 626.57 1.1 3.91 18.4 380 2 251.97 5.4 534.86 3.8 2.24 7.1 623.70 3.1 3.85 12.6 623.03 2.9 3.88 13.2 540 2 237.84 1.6 548.51 4.9 2.42 4.8 630.34 3.4 3.78 1.1 629.27 3.3 3.83 1.6 All 8 252.64 12.8 536.96 5.5 2.28 21.0 634.21 2.7 3.77 8.6 630.67 2.2 3.85 8.8 M30 10.9 60 2 274.89 7.9 610.22 7.1 2.35 1.6 755.66 4.1 4.04 3.8 753.92 4.2 4.15 4.8 220 2 202.36 33.6 716.71 –2.99 44.5 735.70 1.8 4.11 20.4 734.15 2.1 4.16 22.1 380 2 284.63 0.6 540.32 2.5 2.03 2.8 722.26 5.0 3.94 11.1 717.69 4.2 4.13 17.2 540 1 274.04 –629.57 –2.42 –751.29 –4.18 –743.80 –4.37 – All 7 256.83 18.5 607.89 11.3 2.36 44.4 739.79 3.4 4.05 9.9 736.48 3.3 4.18 11.7 Fig. 6. Points of interest on the experimental curves. N. Jankovi´ c et al. Journal of Constructional Steel Research 237 (2026) 110138 8 as a single value. The average ratio of measured to nominal tensile stress area is 0.97, with a CoV of 1.72 %. Tensile strength values (f ub,meas ) are taken as tested in [10], obtained by combining the tensile coupon tests on the exact bolt batches used in the experimental testing with additional coupon tests from different batches from the same manufacturer (not directly used in the experimental tests) to expand the database for statistical purposes, and considered separately for each bolt diameter and property class. In total, 43 coupon tests on long bolts were considered, including the 11 tests from the experimentally tested batches and 32 additional tests from other batches. Among these, 20 tests were performed on 8.8-class bolts (4 from the tested bolt batches and 16 from other batches) and 23 tests on 10.9-class bolts (7 from the tested bolt batches and 16 from other batches). The resulting statistical characterisation (CoV) for the tensile strength (f ub ) is 3.45 % for the 8.8-class bolts and 1.83 % for the 10.9class bolts. 3.4.3. Force-displacement curves The force-displacement (F-u) curves are presented in Fig. 5, categorised by the grip length. Bolt classes 8.8 and 10.9 are represented in red and blue, respectively, while full and dashed lines differentiate between black and galvanised bolt surfaces. Bolt diameters and property classes are labelled next to the corresponding curves. The y-axis represents the total force F calculated as the sum of vertical reactions recorded by the two load cells. The x-axis displays the shear deformation of the bolts, calculated as the average of the two LVDTs (V r – 7 and V r - 8), subtracting the elastic deformation of the connecting plates, determined according to Eq. (7): u=Δu7+Δu8 2−Δel,e−Δel,i−u0(7) where Δu 7 and Δu 8 are the displacements measured by LVDTs V r – 7 and V r - 8, respectively, Δ el,e and Δ el,i are the elastic deformations of the external and internal plates, respectively, calculated adopting an effective plate width of 0.5b =150 mm, and u 0 is the correction of the initial slip. This correction ensures that the line defining the initial stiffness (joining two points in the curve at 30 % and 60 % of the maximum achieved force F m , [35]) intersects the origin of coordinates. The bearing deformation of the plates is not considered in Eq. (7) because it is negligible, as shown later in Section 3.4.6. The elastic deformation component of the plates is very small, less than 5 % the shear deformability of the bolts. Table 5 presents a summary of the shear test results obtained for the long bolts, with the relevant parameters illustrated in Fig. 6. The initial stiffness (K v ), together with three characteristic points, is identified on the F-u curves. The onset of yielding, marking the end of the linear elastic region, is not distinctly visible from the curves themselves. Therefore, the method prescribed in ISO 898-1 [11] is applied, using the offset line through u =0.0048d, where d is the bolt diameter. The other two characteristic points correspond to the point of maximum force (Fₘ) with its associated displacement (uₘ), and the final point on the curve (Fᵤ, uᵤ). Fig. 7. Schematic representation of the corrected displacement Δu 7,c . Table 6 Average Δu 7,c /Δu 8,c ratios. Grip length L g (mm) Bolt M20 M24 M27 M30 All 60 1.30 1.09 1.26 1.36 1.24 220 1.38 1.42 2.06 1.72 1.48 380 0.92 1.16 1.63 0.89 1.11 540 1.43 1.25 0.97 1.06 1.25 All 1.29 1.27 1.48 1.28 1.31 Fig. 8. - Failure modes: (a) LS failure – test S27; (b) RS failure – test S47; (c) BS failure – test S17. N. Jankovi´ c et al. Journal of Constructional Steel Research 237 (2026) 110138 9