Path dependence in OSB sheathing-to-framing nailed connection revealed by biaxial testing

: Oriented strand board (OSB) sheathing-to-wood framing connections, as typically used in light-frame shear walls, were experimentally examined in a novel biaxial test setup with respect to possible path dependence of the load-displacement relation. The connection with an annular-ringed shank nail was loaded under displacement control following nine different displacement paths within the sheathing plane, which coincided at a number of points. At intersection points, the resultant connection force, its orientation, and work performed on the connection system to reach the specific point were calculated and compared. Evaluation of experiments revealed significant path dependence with respect to the orientation of force resultants at path intersection points. However, the magnitude of the forces and the work carried out showed relatively small dependence of the displacement path undertaken. Comparison of uniaxial connection tests with the European yield model demonstrated a strong contribution of withdrawal resistance of the ringed shank nail to its lateral strength. Results of this type are a valuable basis on which to build better models when simulating such connections in wood structures. DOI: 10.1061/(ASCE)ST.1943-541X.0002112. This work is made available under the terms of the Creative Commons Attribution 4.0 International license, http:// creativecommons.org/licenses/by/4.0/.


Introduction
In light-frame wood structures, shear walls are typically composed of a wood frame, which is cladded by a sheathing material in order to be able to serve as structural element in the lateral bracing system of buildings.The in-plane load-deformation behavior of such shear walls is mainly determined by the properties of the laterally loaded connections between the sheathing and the wood framing (Gupta and Kuo 1987).Experimental investigations of this type of connection are almost exclusively performed under uniaxial conditions (e.g., Dolan and Madsen 1992); based on this, several models with different degrees of complexity have been suggested for simulations of shear walls (e.g., Foschi 1974Foschi , 1977;;Erki 1991;Judd and Fonseca 2005;Xu and Dolan 2009).In structural elements, however, the loading path may not be uniaxial due to complex loading situations as a consequence of combination of load cases and their history.The ability of ductile nailed connections to redistribute loads within the structural system of a shear wall (Källsner and Girhammar 2009), as well as within whole buildings (Paevere et al. 2003), can lead to nonuniaxial loading paths of connections (Vessby 2011) as well.Hence, possible changes in the in-plane loaddeformation behavior caused by changes in the direction of the loading path must be well understood in order to account for them in structural models and to make conclusions about their effect on the global behavior of shear walls.This motivates an experimental study of path dependence of nailed sheathing-to-framing connections, which is presented in this contribution.Judd and Fonseca (2005) addressed the issue of overestimation of capacity when assuming uncoupled springs in simulation models; alternative suggestions for coupling two springs in the orthogonal directions in order to prevent overestimation of strength and stiffness have been suggested (Vessby et al. 2010).Using different ways of coupling in connection models, either a conservative or a nonconservative system can be assumed, i.e., the behavior of the connection can be either path-independent or path-dependent with respect to consumed energy to reach a specific displacement point.The latter is mostly related to the work on the connection system, whereas the resultant force and its orientation are, in almost all modeling approaches, assumed to be path-independent.
In shear walls, dowel-type steel fasteners, such as nails, screws, or staples, with small diameters are often used in practical applications.These are predominantly laterally loaded in shear.Due to stress concentrations in the embedment behavior together with the bending deformation of the fasteners, there is compliance between the connected elements.Hence, a relative displacement between the sheathing and the framing is observed, which governs the load-displacement behavior of the shear wall.Nonlinear behavior, i.e., relative displacement and force of connections, is a function of fastener diameter, number of shear planes, wood member thickness, and embedment lengths, as well as the wood embedment stressdisplacement relationship and steel fastener bending momentrotation relationship (Bader et al. 2016).Furthermore, the connection behavior depends on the withdrawal resistance of the fastener in wood materials, which is a function of the withdrawal behavior of the shank and head pull-through resistance.Development of the so-called rope effect in the axial direction may contribute to increased lateral strength of the connection.This phenomenon describes the development of tensile forces along the axis of the fastener, as a consequence of its bending deformation and axial constrains along threaded parts or at the heads of fasteners.Hilson (1995) emphasized the pronounced contribution of frictional forces in the shear planes that contribute to increased strength of laterally loaded connections.The axial force component parallel to the shear plane will only become important for large relative displacements.The rope effect is also observed in the case of annular-ringed shank nails (Humbert et al. 2014;Izzi et al. 2016), which were investigated in the current experimental study.Inherent anisotropy in wood and engineered wood-based products, such as oriented strand board (OSB), may affect connection behavior.This effect was found to be significant in the embedment behavior of wood and OSB, although it was less pronounced in the connection behavior (Vessby et al. 2014).Comprehensive testing of the uniaxial behavior of nailed sheathing-to-framing connections was presented in Girhammar et al. (2004), to name one example.Engineering design of laterally loaded connections [e.g., per Eurocode 5 (CEN 2004)] with mechanical fasteners in wood, including sheathing-to-framing connections, is based on the fundamental work of Johansen (Johansen 1949), using the so-called European yield model and additionally accounting for a possible rope effect.The design of nailed connections according to Eurocode 5 neither accounts for possible orientation dependence nor for path dependence.It assumes a linear elastic-ideal plastic slip behavior and recognizes a difference in stiffness between serviceability and ultimate limit state design only.
In this contribution, we aim to experimentally examine a specific nailed sheathing-to-framing connection with respect to its possible dependence on the displacement path undertaken.Special focus is laid on the monotonic ultimate limit state behavior of nailed connections.To the best of our knowledge, this is the first time that the path dependence of this type of single mechanical connection has been quantified using a novel biaxial test setup.The latter allows testing arbitrary displacement paths within the sheathing plane.Monotonic testing was performed in this test series.Additionally, component behavior under embedment loading and tension behavior of the steel nail wire were characterized in a previous experimental campaign (Vessby et al. 2014).Thus, a consistent experimental database has been established.Results will be compared to design equations in the European design standard for timber structures [Eurocode 5 (CEN 2004)], i.e., using the European yield model.It should be noted that path dependence can be relevant to connections with all types of fasteners, not only sheathing-to-framing connections.Experimental testing of all imaginable combinations of loading paths is impossible.This is why numerical models are important for assessing the effect of path dependence on the global behavior of shear walls, and thus on the load-deformation behavior of wood structures.Findings presented herein may lead to better understanding of the behavior of mechanical fasteners, so that more accurate models may be suggested and used for modeling connections in shear walls and wood structures in the future.

Sheathing-to-Framing Connection and Its Components
The sheathing-to-framing connection investigated in this study consisted of an 11-mm-thick oriented strand board (OSB/2, Kronoply, Lucerne, Switzerland), which was connected to a C24-graded Norway spruce wood frame with dimensions of 60 × 60 mm by an annular-ringed shank nail with a diameter of 2.5 mm (Gunnebo Fastening Systems AB, Gunnebo, Sweden); see Fig. 1.Hence, a single shear connection between the OSB and wood was established.The growth ring structure of the wood was placed in a way that the nail penetrated several growth rings, i.e., pointing as much as possible in the radial direction.Edge distances to the vertically loaded edge in the wood framing as well as in the OSB were 22.5 mm, i.e., 9 times the nail diameter.Thus, for wood, the distance was equal to the minimum edge distance a 4;t , according to Eurocode 5 [see Table 8.2 in CEN ( 2004)], considering no predrilling and characteristic density larger than 420 kg=m 3 .The edge distance in the OSB was larger than the minimum distance to the loaded edges, which was equal to 7 times the fastener diameter [ÖNORM B1995-1-1 (Austrian Standards Institute 2015)].Connection geometry yielded an overlap length for OSB and wood of 45 mm.The horizontal distance to the loaded edge in the OSB amounted to 50 mm, i.e., 20 times the nail diameter, or half of the OSB width, which was 100 mm.The edge distance was considerably larger than the minimum edge distance, which should be at least 7 times the dowel diameter (Austrian Standards Institute 2015).The OSB consisted of three layers of strands sprayed by a resin binder and glued together in directions perpendicular to each other, the length direction, and the cross directions, respectively.Mean density values of ρ OSB ¼ 634 kg=m 3 and ρ C24 ¼ 420 kg=m 3 (with a standard deviation of AE23 kg=m 3 , n ¼ 10) were measured for the two materials, respectively.The nail was made of stainless steel (material AISI 316/A4) and had a diameter, d, of 2.5 mm and a length of 60 mm.This yielded a penetration depth, t pen , of 49 mm, which was larger than the required minimum length of 6 times the nail diameter, according to Eurocode 5 [see 8.3.1.2(2)in CEN (2004)].The nail was driven through the sheathing and the wood without predrilling, by using a hand-held hammer.
The material properties of the components were evaluated in a previous experimental campaign (Vessby et al. 2014), which included embedment testing of OSB and wood in the principal material orientations according to the European testing standards EN 383 (CEN 2007).Tension testing of the nail material itself was done as well.Load orientation dependence of the embedment behavior was revealed for both OSB and wood.Stiffer initial behavior was measured when both materials were loaded in the longitudinal direction (coinciding with the grain direction in the wood and the strong direction in OSB) than for loading in the transverse direction.Pronounced displacement hardening led, however, to higher strength values for loading in the transverse direction than for loading in the longitudinal direction at large displacements.The corresponding embedment strength values, measured, according to EN 383 (CEN 2007), as the maximum nominal stress up to a displacement of 5 mm, amounted to f h0;5 mm;C24 ¼ 44.4 N=mm 2 and f h90;5 mm;C24 ¼ 53.1 N=mm 2 for wood and f h0;5 mm;OSB ¼ 64.2 N=mm 2 and f h90;5 mm;OSB ¼ 59.8 N=mm 2 for OSB.Interestingly, design equations for embedment strength of the materials [Eqs. (8.15) and (8.22) in Eurocode 5 (CEN 2004)] fit well to experimentally determined stresses at 1-mm relative displacement.The corresponding values amounted to f h0;1 mm;C24 ¼ 32.6 N=mm 2 and f h90;1 mm;C24 ¼ 20.6 N=mm 2 for wood and f h0;1 mm;OSB ¼ 51.5 N=mm 2 and f h90;1 mm;OSB ¼ 38.3 N=mm 2 for OSB [see also Figs. 10 and 11 in Vessby et al. (2014)].Initial embedment behavior was stiffer parallel to the grain than perpendicular to the grain.Up to 1-mm displacement, this yielded higher f h0 than f h90 .For loading perpendicular to the grain in timber and in the weak direction of OSB, substantial displacement hardening was observed in embedment stresses.This is why f h90;5 mm;C24 was higher than f h0;5 mm;C24 for timber.Similar displacement hardening was observed in OSB tests, in which f h90;OSB exceeded f h0;OSB for displacements larger than 7 mm.
Before testing, wood materials were stored in a climate chamber at a temperature of 20°C and relative humidity of 65%.The moisture content of the wood materials was measured by oven-drying small-scale samples (with dimensions of about 60 × 60 × 60 mm 3 for wood and 100 × 200 × 11 mm 3 for OSB) after testing.The mean values of moisture content amounted to 13.9% (standard deviation AE0.4%, n ¼ 10) for wood and 9.4% for OSB.
Tension testing of the steel wire, of which the nail was manufactured, revealed yield stress, f y , of about 866 N=mm 2 .Because no hardening of the steel material was observed, the ultimate stress, f u , can be considered to be equal to the yield stress.

Biaxial Testing of Sheathing-to-Framing Connection
The displacement path dependence of this sheathing-to-framing connection was investigated by means of a biaxial test setup under displacement control, by prescribing various displacement paths (Fig. 2).Test Frame 322 by manufacturer MTS (MTS Systems, Gothenburg, Sweden) was equipped with two servohydraulic actuators, MTS Model 244.21 (piston stroke AE75 mm) and MTS Model 244.22 (piston stroke AE140 mm), with a capacity of 50 and 100 kN (both load cells of type MTS Model 661.20F) for the horizontal, x, and the vertical, y, orientation, respectively (see coordinate system in Fig. 1).The resolution of the force indicator in the transducer was 0.002 kN, i.e., 2N.Calibration revealed a relative error of about 0.04% at a compression force of 5 kN.This corresponds to an absolute error of 2.5 N. It can, however, be expected that measurement errors increase at smaller forces and this is why the repeatability of the force transducer, specified by the manufacturer as equal to 0.03% of the rated capacity, is considered as uncertainty.This yields an absolute uncertainty of about 30 N in force measurements.
The biaxial test frame was designed with comparably stiff steel sledges, running on roller bearings, that are connected to the actuators and the load cells, in order to avoid eccentricity in the load cells (Fig. 1).The OSB sheathing was connected to the vertical actuator of the hydraulic testing machine by means of bolts and a steel plate.The steel plate could freely rotate around one horizontal axis in the connection to the crosshead of the machine, allowing the OSB sheathing to undertake unconstrained displacements out of its own plane (Fig. 1).The wood framing was fixed to the horizontally movable sledge by a steel hold-down device.Thus, the grain direction of wood was parallel to the horizontal direction, whereas the strong axis of the OSB sheathing was parallel to the vertical direction.
Test series were performed along nine different displacement paths with various combinations of prescribed horizontal, u x;MTS , and vertical, u y;MTS , displacements.This included three paths with initial vertical, u y;MTS;1st , and subsequent horizontal, u x;MTS;2nd , displacement (Paths A, B, and C in Fig. 2); three paths with initial horizontal, u x;MTS;1st , and subsequent vertical, u y;MTS;2nd , displacement (Paths D, E, and F in Fig. 2); and three diagonal displacement paths (Paths G, H, and J in Fig. 2).For each test series, a minimum number, n, of 3 and up to six specimens were investigated (Fig. 2).Each connection was loaded under displacement control with a constant loading rate, uMTS , of 2 mm=min, i.e., the two orthogonal displacement rates, ux;MTS and uy;MTS , were adjusted in Paths G, H, and J, in order to end up with the same loading rate in the diagonal directions.Obviously, the stiffness of the nailed connection was very low compared to the inherent machine stiffness and the stiffness of the connected members, i.e., the OSB sheathing and the wooden member.
The prescribed actuator displacements, u x;MTS and u y;MTS , as well as the corresponding horizontal and vertical reaction forces, F x and F y , were measured with a frequency of 4 Hz.Relative out-of-plane displacement, u z;LVDT , was monitored by means of a linear variable differential transformer (LVDT) attached to the wood framing, and measuring the out-of-plane translation of the OSB sheathing relative to the wood frame (Fig. 1).
In order to evaluate the inherent stiffness of the test setup and, thus, the difference between the relative displacement of the OSB sheathing in relation to the wood frame and the prescribed displacement of the testing machine, full-field surface deformation measurements on the OSB sheathing and the wood framing were performed on selected specimens (E04, G04, H04, and J06).For this purpose, an optical displacement measurement system based on digital image correlation with two 12-mpx cameras (ARAMIS, GOM, Braunschweig, Germany) was used.Images were taken with a frequency of 0.2 Hz.The procedure for speckle pattern application and settings for the evaluation are described in Schweigler et al. (2017) and Serrano and Enquist (2005), to name two examples.Basically, points on the sheathing and the wood framing were chosen and their relative change of distance in the horizontal, u x;ARAMIS , and vertical, u y;ARAMIS , directions were evaluated and compared to corresponding displacements in the actuators of the testing machine.

Displacement Paths and Data Evaluation
The displacement path dependence of the connection properties was evaluated at the intersection points of the displacement paths.This related to the resultant force, F tot , i.e., the vector sum of the horizontal, F x , and the vertical, F y , force components, as measured by the load cells of the biaxial test setup, and its orientation, γ, with respect to the grain orientation of the wood framing.The term γ was calculated as the arctangent of the vertical, F y , and the horizontal, F x , force components and was equal to 0°for orientation along the x-axis and 90°for orientation along the y-axis [Fig.1(a)].
The relative displacement of the connection, u tot , was calculated as the true displacement of the same.Thus, it was calculated as the sum of the incremental displacement, u i , calculated as the vector sum of the incremental orthogonal displacements, u x;i and u y;i .
Potential energy, or, in other words, work on the connection system, W, along the displacement path, C, up to the intersection points of the displacement paths, was calculated as In addition to the external work derived from measuring reaction forces, the deformation energy of the nail was estimated.It was based on an idealized deformation state as well as on the assumption of rigid-ideal plastic bending moment.The shape of the bending deformation of the nail was approximated by limit-state analysis of the connection (Johansen 1949).Theoretically, two plastic hinges, one in the sheathing and one in the wood member, could occur in this type of single shear plane connection.The position of plastic hinges is then given, by parameters b 1 and b 2 (Lidelöw 2015), as the distance from the shear plane to the plastic hinge.In experiments, only one plastic hinge in the sheathing was observed and distance b 2 from the surface of the timber frame is then given as with the nail diameter, d, the mean value of the embedment strength of wood, f h;2;m , and the mean value of the ultimate strength of the connection, F v;Rm , as described in the following.The yield moment of the nail, M y;nail , was derived from the plastic cross-sectional moment, W pl , times the yield strength of the steel wire, f u .Assuming a bending about the plastic hinge position and a linear nail axis, the bending angle, θ, was derived via trigonometric functions, using b 2 (along the nail) and the relative displacement, u tot;MTS .The deformation energy, due to bending of the nail, was then calculated as which simplifies to the product of the yield moment times the bending angle, as a consequence of the ideal-plastic material behavior assumption.This rough estimation was considered for uniaxial bending of nails only.Finally, experimental data were compared to results of design equations for nailed connections specified in the European timber engineering design standard, Eurocode 5 (CEN 2004).These design equations are based on the fundamental work of Johansen (1949).There are six possible failure modes of the nail that have to be assessed for the strength, F vR;m , of this single shear woodto-panel connection [Eq. (8.6) in Section 8.2.2 in Eurocode 5 (CEN 2004)].Component properties were considered in terms of mean values, which gave a mean value of connection strength.Experimentally measured embedment strengths, f h , were applied together with yield moment, M y , using Eq.(8.14), reading as with f u = ultimate strength of the steel wire and d = diameter of the nail.The embedment strength was considered as the mean value of the strength in the two orthogonal loading directions, which yielded f h;1 mm;C24 ¼ 26.6 N=mm 2 , f h;5 mm;C24 ¼ 48.7 N=mm 2 , f h;1 mm;OSB ¼ 44.9 N=mm 2 , and f h;5 mm;OSB ¼ 62.0 N=mm 2 .The contribution of the rope effect to the lateral strength in Eq. (8.6) was calculated with withdrawal strength according to Eq. (8.23), reading as where d h , as the diameter of the nail head, was considered to be equal to 5 mm; and t pen , as the penetration depth of the nail, was equal to 49 mm.Because design equations for withdrawal, f ax , and head pull-through strength, f head , are not provided in Eurocode 5 (CEN 2004) The stiffness of the connection in the serviceability limit state, K ser , and in the ultimate limit state, K u , was calculated based on equations in Table 7.1 in Eurocode 5 (CEN 2004).

Results and Discussion
Relative Displacement of the Sheathing-to-Framing Connection Full-field deformation measurements were used to check the relative displacement between the OSB sheathing and the wood frame, u tot;ARAMIS , which might have been different from the prescribed machine displacements, u tot;MTS , due to the inherent stiffness of the test setup.Differences of up to 0.5 mm between the aforementioned displacement quantities were measured.No clear trend in the difference in displacement, either with time or with absolute displacement, was observed.In some cases, the absolute difference between the two displacement measures hardly changed after an initial increase.Hence, the relative difference between u tot;MTS and u tot;ARAMIS decreased with increased displacement-controlled loading.It amounted to less than 10% for u tot;MTS of larger than about 5 mm and less than 5% for u tot;MTS larger than about 10 mm.The initial stiffness of the connection, quantified using u tot;MTS , was considerably underestimated.Uncertainties in force measurements strongly affected the quasi-elastic loading path.Relative displacements at the intersection points of the displacement paths will, however, be less affected.Thus, the analysis based on displacements of the horizontal and vertical actuators of the biaxial testing machine, which will be used in the following discussion, can be considered reliable.It should be noted that the initial stiffness of connections is sensitive to displacement measurement and shows high variability due to many influence parameters, whereas the ductile connection behavior at larger displacements is less variable and is hardly affected by initial stiffness, which confirms the findings for dowel embedment behavior in Schweigler et al. (2016).
The full-field deformation measurements were well in line with the LVDT measurements of relative out-of-plane displacement of the OSB sheathing with respect to the wood frame.In the initial behavior, u tot;MTS of up to about 15 mm and u z;LVDT values of up to −0.2 mm were measured.This represents compression of the OSB sheathing toward the wood framing, as an effect of the rope effect in the nail, which is also expressed by compression of wood under the head of the nail on the OSB sheathing.A pronounced increase in u z;LVDT with separation of the OSB from the framing was observed for u tot;MTS of more than 15-20 mm.It was associated with the softening behavior of the connection due to head pull-through failure of the nail head.The following discussion will be limited to in-plane relative displacements u MTS for describing the slip behavior and path dependence of the connection.Considerable softening in the in-plane slip curves can be associated with considerable out-of-plane displacements.

Uniaxial Slip Behavior of Sheathing-to-Framing Connection
The uniaxial behavior of the connection will be discussed in the following, before taking a closer look at its displacement path dependence.Mean values of the uniaxial slip curves of Paths C and F (up to 15 mm), as well as those of Paths G, H, and J, are illustrated in Fig. 3.They showed rather stiff behavior up to u tot;MTS of about 1 mm, where transition to lower stiffness was observed.This was related to the bending deformation of the nail.Consequently, the rope effect of the nail was induced.It allowed increasing overall load on the connection and increased with increased bending deformation of the nail.Thus, stiffness even partly increased in this second section of the slip curve (see Path J in Fig. 3).The rope effect was, however, limited by the pull-through strength of the nail head.Hence, softening behavior was observed after peak load, representing the strength of the connection.
Only minor differences were observed between the investigated displacement paths, although orientation dependence in connection behavior could have been expected because of the orientation dependence of the embedment behavior (Vessby et al. 2014).The connection was, however, assembled with the stronger directions of OSB and wood perpendicular to each other.This led to a combination of stiffer and weaker embedment behavior in both principal loading directions of the connection.A slightly higher stiffness became obvious for diagonal displacement paths.However, differences in Fig. 3 were clearly within the variability of the test series, which will be discussed later.Hence, it seems to be reasonable that design standards consider the behavior of this type of connection to be independent of loading direction [e.g., Eurocode 5 (CEN 2004)].
In addition to the rope effect, the strength of the connection is limited by the bending resistance of the nail.In this case, a single plastic hinge within the wood member was observed for all connections, corresponding to Failure Mode (d) according to Fig. 8.2 in Eurocode 5 (CEN 2004).This failure mode was also predicted by Fig. 3. Uniaxial load-displacement behavior of nailed connection with comparison to stiffness and strength predicted by design equations.
the European design equations for wood connections.The term F vR;m;EC5 amounted to 1,050 N, using f h5 mm as the average of parallel and perpendicular embedment strength for both materials, OSB and wood, together with the rope effect calculated as F ax =4.The axial strength of the connection was predicted to be limited by head pull-through strength.This corresponded to experimental observation as well as to findings in previous works (Humbert et al. 2014).The axial withdrawal would be limited according to Eurocode 5 (CEN 2004), Section 8.2.2(2), by 50% of the Johansen part, F vJohansen5 mm;m , which amounted to 799 N. Therefore, the rope effect considered in the design equation was about 30% of the Johansen part only, due to limitation in head pull-through strength.
The initial behavior of the connection up to the transition in the slip curves was dominated by embedment behavior.Neglecting the rope effect, i.e., the axial withdrawal of the nail, and using the embedment strength at 1 mm, f h1 mm , gave a lateral strength prediction, F vJohansen1 mm;m , of 592 N. The latter value corresponds well to the transition of the slip curve and highlights the strong contribution of the axial withdrawal of the nail in combination with increased embedment strength, which leads to strength of the connection of more than twice the initial Johansen part; see Fig. 3. Thus, the rope effect was about the same size as the Johansen part.The rope effect is, however, only partly exploited for threaded nails in the design equations.This was, however, not due to limitation of the rope effect in design equations, which only amounted to 30% compared to the maximum allowed 50% of the Johansen part.It was due to an underestimation of withdrawal strength.Thus, the design equation underestimated the experimental data, which gave a mean value of F vR;m;EXP ¼ 1,280 N (n ¼ 5).The stiffness of the connection was slightly overestimated by K ser , whereas displacements in the ultimate limit state design were obviously underestimated by K u .It should, however, be noted that the experimentally determined stiffness was underestimated due to the use of machine displacements in this evaluation (see the discussion in the "Relative Displacement of the Sheathing-to-Framing Connection" subsection).

Path Dependence in Slip Behavior of Sheathingto-Framing Connection
In addition to the diagonal displacement paths (Series G, H, and J) discussed previously, there were two groups of connection tests, which can be described by similar overall behavior, that is, connection tests with vertically and, subsequently, horizontally prescribed displacement (Series A, B, and C), and connections subjected to horizontal and, subsequently, vertical displacement (Series D, E, and F).The slip behavior of these tests will be discussed first before the experimental data are compared at intersection points of the paths.
Slip curves are presented in Fig. 4 with the resultant force, F tot , as well as with force components, F x and F y , over true displacement, u tot;MTS .Variability in the test series was more pronounced than variability between mean values of the test series.Mean values of the slip curves initially followed the previously discussed uniaxial slip behavior of the connection.It changed, however, at the points of sudden change in the displacement direction.At these points, a drop in force was found for all investigated displacement paths (Series A-F in Fig. 4).This drop is a consequence of a strong decrease in the force component parallel to the first displacement direction in combination with a slow increase in the force parallel to the second displacement direction.Obviously, change in the displacement direction weakens the overall behavior of the connection, because irreversibly compressed and densified wooden areas with high density and resistance are left behind and undeformed wooden cells must be compressed first, before additional loads can build up.The force drop is more closely assessed in Fig. 5, where the force decrease after the point of displacement orientation change is plotted over the residual displacement, u tot;MTS;2nd .There was a clear difference in the absolute values of the force drop between the first (A and D) and subsequent (B and C, and E and F) transition points; see Fig. 5(a).Moreover, differences related to the orientation of displacement change (Groups A, B and C, and D, E, and F) became obvious in the mean values of the slip curves.
The load increase in the second displacement direction seems to be very similar to the initial (uniaxial) behavior of the connection, yielding strength values similar to those for the uniaxial loaded connection.This is graphically illustrated in Fig. 5(b), where variability of the initial slip curves of Paths A-F is represented by the grayish area.For Paths A-C, a slightly reduced load increase was found, whereas for Paths D-F the load increase was hardly affected by the first relative displacement.This might again demonstrate the orientation dependence of the connection.Similar observations have been made regarding the strength of the connection.All investigated connections finally failed by pull-through of the nail head.
Path dependence is now revealed by comparing the resultant force, F tot , its orientation, γ, and the work, W, done by the connection up to the intersection points of the displacement paths.A comprehensive illustration of mean values of the experimental data is shown in Fig. 6(a), where the force and its orientation are plotted at the intersection points.Obviously, the orientation of the force vector depends on the displacement path undertaken.The orientation closely followed the displacement direction for diagonal loading paths (Series G, H, and J), whereas it deviated from the displacement direction for nonuniaxial paths.In the latter case, orientation is a consequence of the change in the force components (Fig. 4), which changed continuously.Thus, as the force component parallel to the second displacement direction increased, the force orientation changed toward this displacement direction.At the intersection points, the orientation of the resultant force was stronger leaning toward the second displacement orientation, as compared to the diagonal displacement paths.The difference seems to depend on the ratio of the first and the second displacement up to an intersection point.In other words, force orientation changes seemed to be similar along the diagonal paths, e.g., well visible in the intersection points of Series A/D/H, B/E/H, and C/F/H.This is more closely examined and illustrated in Fig. 6(b), where the change in resultant force orientation is plotted over the residual displacement, u tot;MTS;2nd .The definition of force orientation follows angle γ, which is equal to 0°for horizontal orientation and 90°for vertical orientation [Fig. 1(a)].The graph shows clearly the transition from the initial force orientation toward the second displacement direction orthogonal to the initial one, with an abrupt change at the point of displacement orientation change.Significant differences in the rate of mean values of force orientation change, between the first (A and D) and subsequent (B and C, and E and F) transition points, became obvious.Hence, changes in force orientation were more pronounced the less initial displacement was prescribed.This was a consequence of the stronger increase of forces in the second loading direction for the same situations [Fig. 5(b)].
The absolute value of the resultant force did, however, not differ in as pronounced a way as its orientation.Differences at intersection points between test series were mainly within their variability; see Fig. 7(a).It seems, however, that the mean value of F tot was slightly higher in uniaxial paths (Series G, H, and J).This was particularly observed at lower true displacements.Thus, reduced connection force compared to uniaxial paths might be explained by additional slip in the biaxial displacement paths (Fig. 4).
Variability in orientation of the resultant force, γ, at the intersection points was comparably small and, as discussed before, significant differences became obvious; see Figs.Comparably small variability was also found for force components parallel to the two principal orientations of the connection (not shown).The pronounced variability of the connection force is expected to be a consequence of the inhomogeneous OSB layup, i.e., a consequence of local fluctuations of strand position, orientation, and composition.As for the connection force and its orientation, the external work performed on the connection system according to Eq. ( 1) is illustrated and compared at intersection points.Absolute values of the work are represented by the size of circles in Fig. 8(a) and plotted over true relative displacement in Fig. 8(b).Path dependence in the work was found to be moderate.Still, there is a tendency showing that if there is a change in the displacement path, the work becomes somewhat larger as compared to a uniaxial displacement path.The difference was rather small and slightly increased with increased true displacement.It was, however, within the variability of the test series [Fig. 9(a)].Mean values of the increase of external work at abrupt changes in the displacement orientation are plotted over the residual displacement, u tot;MTS;2nd , in Fig. 9(b).As mentioned before, a slightly reduced gradient in the work increase at larger initial displacements was given.Small differences in the work of the connection system are well in line with slightly reduced resultant force at the intersection points, i.e., even if Path C is longer in biaxial displacement paths, slightly reduced force components led to small increases in the work up to the intersection points.As for other connection properties, negligible orientation dependence was present in the external work of the connection system.
The work on the connection was evaluated by externally measured connection forces.It could be assumed to be equal to the change in potential energy of the connection.The latter is mainly composed of strain energy of the connection components, namely, steel nail and wood products.Both are difficult to evaluate based on the test setup, because strains as a consequence of the deformation state of the components would have to be known.We can, however, assume one plastic hinge in the nail at distance of 21 mm from the head.The distance was calculated as the sum of the OSB thickness and the parameter b 2 , according to Eq. (2) derived based on Johansen's theory (Johansen 1949).Additionally, we calculate the yield moment of the nail based on the plastic cross-sectional moment times the yield stress.The yield moment amounted to 2,158 Nmm.This yielded strain energy of the nail according to Eq. (3) of about 1 and 3 J, at u tot;MTS of 10 and 20 mm (uniaxial), respectively, compared to about 8 and 21 J external work [see Paths G, H, and J in Fig. 8 calculation, this clearly indicates that most of the internal energy is built up by phenomena in the wood products.A closer investigation of the distribution of strain energies between the components using, e.g., numerical methods, would be very interesting for a deeper understanding of the energy balance and dissipation behavior of the nailed connection, but it is beyond the scope of this paper.

Conclusions
The use of a biaxial test setup allowed establishing novel experimental data for the investigation of path dependence in OSB sheathing-to-wood framing connections with annular-ringed shank nails.Slip curves in the uniaxial loading of the connection clearly showed the pronounced contribution of the rope effect in the ringed shank nail to the strength of the laterally loaded connection.Differences in the slip curves for various loading directions with respect to the principal directions of the connection were found to be within their variability.Thus, it seems reasonable that the behavior of this kind of connection is considered to be load orientation independent in engineering practice.Path dependence of the nailed connection was clearly observed in the orientation of the resultant connection force at the intersection points of different displacement paths.This is, however, expected to have less relevance for the strength design, because the strength of nailed connections is assumed to be orientationindependent.Sudden changes in the displacement direction resulted in a load drop in the resultant force of the connection, before a load increase was observed at larger displacements.A continuous force-displacement relationship without a load drop was found for uniaxial displacement directions.Less path dependence was found for the size of the resultant connection force, defined as the vector sum of the components, and the work of the connection system.In the latter, differences between test series were overlaid by a high variability in the slip curves, as a consequence of local fluctuations in material properties of the OSB sheathing.Nevertheless, changes in deformation behavior of the investigated connection under different displacement paths may be important for the prediction of shear wall deformations and can affect their dissipation behavior.
Phenomena underlying path dependence are the embedment behavior of the nail in OSB and solid wood, as well as the bending properties of the nail itself together with the rope effect in the nail.The corresponding material properties have been characterized in a previous study.It would, however, be of interest to also investigate path dependence in the embedment behavior, which could be expected to give results similar to those presented herein.Extending this study to reversed cyclic loading would be of great interest.It could be speculated that path dependence is more distinct in connections with larger-diameter fasteners, in which orientation dependence is well-known to be more pronounced.A consistent experimental database for the development and verification of numerical models for predicting connection behavior was established and will be used in a future paper.

Fig. 1 .
Fig. 1.(a) Biaxial test setup for in-plane displacements u x and u y ; (b) cross section through setup of connection test, with out-of-plane displacements u z .

Fig. 2 .
Fig. 2. Prescribed in-plane displacement paths (Series A-J), with number of test specimens n.

Fig. 4 .
Fig. 4. Force components, F x and F y , and resultant force, F tot , over true displacement, u tot;MTS , for (a) Paths A-C; and (b) Paths D-F.

Fig. 6 .Fig. 5 .
Fig. 6.(a) Path dependence of resultant force and its orientation plotted at intersection points of investigated displacement paths (Series A-J); and (b) changes in force orientation after displacement path transition points plotted over the residual relative displacement u tot;MTS;2nd .

Fig. 8 .Fig. 7 .
Fig. 8. (a) Path dependence of connection work plotted at the intersection points of the investigated displacement paths (Series A-J); and (b) connection work plotted over true relative displacement.