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Three-dimensional (3D) constitutive models for wood were developed and evaluated for use in a 3D numerical model of a bolted wood connection. The connection model applies to parallel-to-grain loading of wood. Nonlinear parallel-to-grain compression of wood and degradation of shear stiffness are described using a trilinear stress-strain relationship. Elastic parameters were determined that best fit numerically predicted load-displacement curves to those obtained from experiments on bolted connections. The connection model also accounted for an elastic-perfectly plastic steel pin, oversized hole, and a changing contact surface at the pin-hole interface. The numerically obtained load-displacement curves were generally stiffer than the experimental curves but displayed important characteristics found in the experimentally obtained curves. Effects of material property assumptions and different forms of trilinear curves were also evaluated.

A three‐dimensional finite element model was developed to predict the strength and failure location of nine wood transmission poles made from three commonly used North American species. All poles were 1,524–1,829 cm (50–60 ft) long, and were tested to failure as cantilever beams. The analysis methodology involved considering several 45.7‐cm‐ (18‐in.‐) long segments, located along the pole length, that contained the most severe inherent characteristics. Each segment was analyzed recognizing actual material properties and appropriate boundary conditions. Important material properties for each segment were determined by measuring clear‐wood elastic and strength parameters in undamaged sections taken from tested poles. The flow‐grain model was used to describe the grain deviation around knots. For the nine poles studied, predicted and experimental strength values differed on average by 7%. The correct location was predicted in six of the nine poles studied. Where failure location was not predicted correctly, ...

Two hundred ninety-two nailed joints in seven species of Amazonian hardwoods were tested to evaluate their load-slip (P-Δ) behavior when subjected to lateral loading. The seven species commonly used in Brazilian light-frame construction had a range of specific gravities from 0.36 to 0.85 (based on an oven-dry volume) Four sizes of common wire nails were used to construct joints with main and side members of the same species. From these tests, embedding strength values associated with a 5% offset load were obtained from the experimental (P-Δ) curves and equations derived from the European Yield Theory. The results suggest that the behavior of nailed joints made with tropical hardwoods is similar to that found in temperate zone species. Wood moisture content, in the range studied, did not meaningfully affect joint P-Δ behavior. In addition, embedding strength was influenced by the specific gravity of the connected material. However, no species effect was observable between species of similar specific gravity. Finally, an effect of nail diameter on embedding strength was seen; however, the lack of homogeneity of test materials precluded the accurate prediction of this effect. Since the embedding strength data demonstrated some degree of positive skewness, three commonly used statistical distributions (log-normal, three-parameter Weibull, and Johnson's SB) were evaluated to quantify the variability of this parameter. All three distributions were excellent descriptors of behavior. Therefore any of these mathematical models would be a rational choice for representing embedding strength.

It has been the author's experience that researchers will routinely use linear models to describe the relationships between correlated variables when that approach to modeling may not be the most rational. This article illustrates some of the circumstances when linear modeling is and is not the most viable alternative in characterizing the relationship between correlated variables. In this study, several data sets are examined to illustrate how amenable they are to linear modeling. One data set selected shows a nearly ideal example of when linear least-squares regression is a realistic descriptor of the relationship between correlated variables. A second data set shows how material idiosyncrasies, such as species, size, or grade effects, can result in misleading models for parameter prediction. A third data set illustrates a more subtle inhomogeneity that is frequently found in experimental data involving tests of clear wood. When the relationship between correlated variables changes due to a shifting failure mechanism, a presumed linear relationship may misrepresent the relationship between variables in a large portion of the domain. It is the intent of this paper to remind or make researchers aware of the subtle characteristics of data sets that can influence modeling results. One possible mechanism for modeling nonlinearly related variables (the univariate S B and the bivariate S BB distribution) is offered for consideration. This model has the unique feature of quantifying, in an analytic, closed-form fashion, the probability of a predicted variable for any value of the domain. In addition, when certain input values used to calculate S BB bivariate distribution parameters are defined correctly, convergence to the clear wood strength of a material or product is achieved.

A three-dimensional (3-D) finite-element model was developed and verified which is capable of predicting the failure mode and load-deformation (P - Δ) behavior of a single bolted connection in wood. The 3-D geometry of the model is complemented by a trilinear orthotropic constitutive model for wood and an elastic-perfectly plastic constitutive characterization of the pin (bolt). The model accounted for the nonlinear behavior found in bolted wood connections associated with wood crushing and geometric nonlinearities at the wood/metal interface. A special contact element was used at the wood/pin interface to enforce a criterion of no pin penetration (i.e., strain compatibility) through the wood member. Experimentally obtained P-Δ curves were compared against those obtained numerically. For all geometries studied, the model proved to capture the characteristics of the experimental analyses.

Two hundred forty-three experiments were conducted on bolted wood connections having a variety of aspect ratios (length of bolt in member/bolt diameter) and end distances with loading applied in tension and compression. Load-displacement (P-Δ) curves were generated for each test from which pertinent characteristic values were derived. Important connection characteristics observed included ultimate load and displacement, 5% offset load, proportional limit, and failure mode. Results show the effects of connection geometry and load application on the strength and stiffness of single bolt connections. Among the most important of these are that tension and compression loadings produce different P-Δ behavior and failure modes. These differences are amplified or muted depending upon connection aspect ratio. Furthermore, connection aspect ratio and end distance interact to influence P-Δ behavior and failure mode.

This paper presents information regarding the distribution of critical stresses and regions where failure is likely to initiate in single bolt wood connections loaded in tension. Predicted stresses are the results of a three-dimensional numerical analysis of a connection consisting of a single steel pin and a wood member with a hole. Stresses of particular interest are: parallel-to-grain compression and shear and perpendicular-to-grain tension. Failure location is determined by considering the regions of the member where the material capacity is exceeded in at least one of the three aforementioned stresses. No stress interaction is assumed in this analysis. A recently developed and verified three-dimensional (3-D) finite element model was used in this study. Important features of this model include a trilinear constitutive model of the nonlinear behavior of wood and a mechanism to describe the contact between the pin and the hole with changing connection load. The connection geometries studied included a single ratio of end distance to pin diameter ( e ∕ d = 4 ) and three bolt aspect ratios (length of bolt in wood member/bolt diameter) ( l ∕ d = 2 , 5 , and 7 ) . Stress contours are illustrated on the 3-D wood member surface, on the contact surface, and on planes of symmetry. Pin and wood deformations are also illustrated. The results show that for connections with an ( l ∕ d ) = 2 , stresses are nearly uniform through the wood member thickness with negligible pin yielding. For connections with the larger bolt aspect ratios, considerably more pin bending and yielding is predicted with nonuniform stress distributions through the member thickness. The maximum stress failure criterion is found to be useful for comparing numerically predicted stress distributions to failure modes observed experimentally. By making these comparisons, it is possible to make qualitative interpretations of the critical stress states to indicate the regions where failure is likely to occur.

In a companion paper, a characterization is presented of stress fields in a single-shear bolted connection subjected to tension loading. Numerous stress contours are presented that illustrate the magnitude of the parallel-to-grain compression and shear stresses, as well as the perpendicular-to-grain tension stresses. In addition, regions of potential failure in the selected specimens are identified based on a maximum stress failure criterion. The work presented in this paper represents additional efforts to identify the effect of stress interactions on the strength of the previously mentioned connections. The Tsai-Wu criterion, quantified by its failure index, is used as the tool to identify stress interactions between the aforementioned stress components. Connection geometries similar to those discussed in the companion paper [end distance/bolt diameter ( e ∕ d ) = 4 ; and length of bolt in main member/bolt diameter (aspect ratio) ( l ∕ d ) = 2 , 5 , and 7 ] are studied. In addition, several other geometries are discussed that illustrate the effects of changing aspect ratio and end distance. A number of significant findings are reached in this study. As is the case in the companion study, all connections with ( l ∕ d ) = 2 have nearly uniform distributions of the Tsai-Wu failure index (FI) through the specimen thickness. No significant pin bending is associated with this geometry. Connections with l ∕ d > 4 have a failure mode (interpreted from the numerical model) that includes substantial pin bending due to steel yielding, wood crushing, and localized cracking.

A total of 19 440 virtual structural floors of a geometry and material configuration consistent with those used in commercial construction (commercial floors) throughout North America was numerically analyzed to determine deflection characteristics under a constant uniformly distributed load of 95 lbf/ft2 (4.55 kPa). The intent of these analyses was to determine the effect of joist variability on the deflection behavior of floors with and without elastomeric construction adhesive (ECA) between sheathing and joists. The joist property (modulus of elasticity, MOE) was allowed to vary in a systematic fashion between 1250 (8.62) and 3250 (22.4) ksi (MPa) in increments of 250 ksi (1.72 MPa). In addition, the variability of the joists (at each value of MOE) varied between coefficient of variation (COV) values of 0.025 to 0.150 in increments of 0.025. One hundred eighty floors were evaluated with and without ECAs at each mean MOE value and at each COV value for the joists. All other sheathing and connector properties remained constant. The results indicated that the contribution of the ECA to reducing floor deflection under uniformly distributed loads was dependent in large part on the mean stiffness of the floor joists and to a much lesser extent on the COV of the joists. For joists of lower stiffness, the contribution of ECA had a more pronounced effect on mitigating the floor deflection level. Reductions of nearly 10% were realized when the mean joist MOE was 1250 ksi. For floors made with stiffer joists (mean MOE 4 3250 ksi), floor deflections were reduced by only about 5.5% when adhesive was used. The presence of ECA between joist and sheathing did not have much effect on reducing the variability of floor deflection behavior.

Research related to structural stressed-skin panels (SSP) and their component parts has been ongoing at Chalmers University of Technology. In recent years, attention has been focused on SSP with lumber webs and sheet metal and chipboard panels as tension and compression flanges, respectively. In this study, certain mechanical and rheological properties of structural lumber were evaluated as part of a larger project designed to predict the long-term behavior of SSP under load. In this study, several test series were conducted to evaluate short- and long-term properties of European redwood (called Scotch pine in North America) (Pinus sylvestris). From 22 pieces of lumber measuring 25 by 125 by 4000 mm, specimens were cut for use in several test series to determine solid wood properties. Wood modulus of elasticity (MOE), accounting for the shear effects, was evaluated from initial deflections of long-term tests. Mean MOE values of about 14 500 MPa were obtained. Four series of long-term tests were conducted under different combinations of stress level and distribution, as well as loading history. The results suggested that the magnitude of relative creep was greatest under lower stress levels. Different stress distribution (resulting from center- and third-point loading) proved to have little effect on creep behavior. Two mathematical models, i.e., power functions (Clouser function without exponential terms and power function with exponential terms) [1] were evaluated as predictors of the deformation-time relationship for lumber under constant loading. Differences in accuracy of predicting creep behavior between the two models studied were very modest.

In recent years, attention has been focused on structural stressed-skin panels (SSP) with lumber webs and sheet metal and chipboard panels as tension and compression flanges, respectively, at Chalmers University of Technology. In this study, certain mechanical and rheological properties of structural chipboard were evaluated as part of a larger project designed to predict the long-term behavior of SSP under load. Several series of tests were conducted to evaluate short- and longterm properties of urea-formaldehyde bonded chipboard. From eight full-sized panels, specimens were fabricated for use in the determination of chipboard properties. Compressive strength and modulus of elasticity (MOE) were evaluated from short-term tests. Average strength and MOE values of 20 and 4100 MPa, respectively, were obtained. The MOE value was virtually identical to that obtained from initial deformations found in subsequent creep tests, indicating that test method had no effect on MOE. Three series of long-term (11 000-h) tests were conducted under constant and similar environmental conditions and different combinations of stress-level and loading history. The results suggested that the magnitude of relative creep was greatest under lower stress levels. Two empirical models, a Clouser function without exponential terms and a power function with exponential terms (Clouser, W. S. “Creep of small wood beams under constant bending load,” FPL Report 2150, U.S. Forest Products Laboratory. Madison, WI., 1959), were evaluated as predictors of the deformation-time relationship for chipboard under constant loading. The power function with the exponential terms proved to be superior at extrapolating short-term results to long-term predictions. However, both functions were relatively similar with respect to describing the long-term behavior of chipboard as the compression flange in a SSP. Measuring methods and definition of the initial deformation were found to be important, especially for predicting the relative creep factor for chipboards under different load histories.

An advanced finite element program was developed to predict the elastic stresses and strains in a specimen of finger-jointed lumber subjected to uniaxial tension. In this study, two techniques were examined to experimentally determine the deformations in the finger joint. The first method involved photographing at incrementally increasing load levels, predefined targets mounted on the finger joint and measuring the changing distances between targets using stereoscopic instruments. The second method consisted of placing microstrain gages at key locations in the finger-jointed region of the lumber. The results showed that even when the most sensitive film was used with a camera and planar lens, the photographic technique lacked the sensitivity to accurately measure the small deformations in the finger joint. The actual errors in deformation measurement were approximately twice the magnitude expected from an analysis of the properties of the film being used. Much of the error was due to the thermal expansion of the film in the stereoscopic instrument used to measure deformation. The microstrain gage technique was shown to be sufficiently sensitive to measure the deformations in the finger joint. However, the time, effort, and cost required to mount the tiny sensors with appropriate attention to their alignment made this technique impractical for any experiment other than those that involved placing only a modest number of sensors on a small number of specimens.

A plane-stress, Finite element model has been developed to predict the stress distribution in wood members subject to perpendicular-to-grain compression. This model exploits linearstrain, isoparametric triangular elements used in sufficient number to achieve a convergent solution. Model verification was achieved through comparison of numerically obtained deformation predictions with corresponding experimental data obtained from actual test specimens. Twenty-seven specimens were instrumented to determine their deformations at numerous locations. Test materials were sampled from three logs (two eagelemann spruce, one western hemlock). Specimens were fabricated with three widely different orthotropic ratios, three geometries (length/depth ratios), and three loading geometries (uniformly distributed load across the estire length, one-half length, and one-quarter length). In total, 377 experimental measurements on 27 specimens were compared to finite element predictions. The results showed that on average the model predicted local deformation to within 5%.

A model based on concepts involving nonlinear superposition of nail and glue joint characteristics was examined to predict the load-slip (P-Δ) behavior of nail joints with elastomeric construction adhesives (nail/glue) in wood subjected to lateral loading. Four combinations of two wood species (lodgepole pine and hard maple) and two nail sizes (6d and 8d) were explored. One brand of commercially-available elastomeric construction adhesive was used. One-hundred-sixty-nine nail, glue, and nail/glue joints were tested to evaluate the P-Δ curve from the origin to 0.08125 in. (2.1 mm) slip. Theoretical predictions based on nail and glue joint stiffness were compared with experimental data from nail/glue joint tests. The results showed that the presence of glue used in conjunction with nails proved to substantially increase joint stiffness. Increases in joint stiffness from 25 to 100% per square inch (645 mm2) of bonded surface over the stiffness of joints without glue were realized. The superposition model proved to be a reasonable predictor of nail/glue joint stiffness at levels of slip not exceeding 0.03 in. (0.762 mm). For slip levels greater than 0.03 in., superposition consistently underpredicted (conservatively) joint stiffness for all four combinations of nail size and wood species studied. Therefore, superposition has been shown to be an accurate predictor of joint stiffness in the range of slip values from which allowable loads are determined in the allowable stress and draft reliability-based design codes.

A study was conducted which utilized data obtained from 1056 tests of nailed joints in 18 commonly used species of southern hardwoods. The data was developed in 1950 by Scholten. This data included information regarding joint geometry, material specific gravity, discrete load-slip curves, and the ultimate load for each joint. The test specimens were laterally loaded and contained one 8d common wire nail in each joint. Joints were tested in compression at a rate of 0.07 in./min (1.78 mm/min) to ultimate load. With a British model to predict wood embedding strength from specific gravity and nail diameter, and an estimate of nail yield strength,the European Yield Model was employed to predict the failure mode and yield load of the joints. Failure modes which create one or two theoretical plastic hinges in the nail were predicted for all joints. The data suggested that behavior modes of the joints were consistent with model predictions. Further, theoretical nail yield load showed a high correlation (r2 = 0.90) with the experimentally obtained load at 0.015 in. (0.381 mm) slip, 5% offset load, and ultimate load (joint capacity).

Research was conducted to define and compare the mechanical behavior of nailed joints connecting solid wood to eleven commonly used side member products frequently used in construction. Two hundred twenty eight (228) joints were laterally loaded to the allowable load defined by the National Design Specifications, unloaded to zero, then loaded to failure. Solid-sawn Douglas-fir and Engelmann spruce 2 × 4 nominal dimension lumber was used as the main members, while side member materials consisted of southern pine and Douglas-fir plywood of two thicknesses, oriented strand board (OSB), hardboard, particleboard, waferboard, insulation board, gypsum board, and western red cedar solid wood siding. Nail sizes were 6d and 8d common wire nails. Experimental load-slip curves were developed for all joints tested. Information reported includes first and second cycle secant slip modulus, loads at 0.003 in. (0.0765 mm) and 0.015 in. (0.381 mm) slip, ultimate load, and ultimate slip. Parameters are also given for empirical equations describing the load-slip behavior of the joints. Comparative statistical analysis was performed using nonparametric multi-response permutation procedures. The results suggest that for both main member species, the strength and stiffness behaviors of OSB, waferboard, particleboard, and ¾ in. (19.05 mm) nominal southern pine and Douglas-fir plywood were statistically indistinguishable. The stiffness of joints made with the higher specific gravity main member was generally statistically superior to joints made with lower density material. Strength was much less sensitive to this parameter. Joints made with western red cedar, insulation board, and gypsum board were substantially less stiff and strong than those made with the other side member products. Hardboard joints with a 6d nail performed similarly to particleboard, OSB, waferboard, and plywood joints connected with 8d nails. This suggests that hardboard could be used in applications where nail joint resistance is important.

Eight generically similar (i.e., rubber base) commercial elastomeric construction adhesives were evaluated to determine the differences in strength and load-slip behavior when wood joints were subjected to lateral (shear) loading. Eighteen joints were made with each of the eight adhesive brands. Ten of these specimens were exposed for various lengths of time (1 to 80 days) to temperatures of 150°F (65°C), before equilibrating to room temperature, then testing. The remaining eight specimens made with each adhesive were used as a control. Analysis of the control group indicated that not all adhesives of a common chemical base could be considered to behave similarly under lateral loading. At 0.003 inch (0.0762 mm) slip, five of the adhesives carried statistically indistinguishable mean loads which were greater than the other three adhesives, which also showed insignificant differences. At 0.015 inch (0.381 mm) slip, six of the adhesives could not be demonstrated to have different mean load-carrying levels. The remaining two adhesives were similar and significantly inferior. The results indicated that at low slip levels (0.003 inch), no statistically significant differences in load level was identifiable between treated and control specimens for any of the adhesives. At a significantly higher slip level (0.015 inch), two of the adhesives showed marginally significant differences at the 0.05 level of probability. When load level was plotted versus duration of exposure to elevated temperature, no relationship between the parameter could be found at either 0.003 or 0.015 inch slip. Therefore, for the elastomeric construction adhesives studied, the issue of whether or not the joints will be exposed to elevated temperatures, not the length of time of exposure, will be more critical.

Six different test configurations were studied to evaluate the effect of test methods on the load-slip behavior of nailed joints. The apparati considered are those used by five researchers in addition to that described in ASTM Method for Testing Mechanical Fasteners in Wood (D 1761). The load-slip parameters evaluated were: first and second cycle secant slip moduli at design load, loads at 0.38- (0.015-) and 2.54-mm (0.100-in.) slip, ultimate load, and slip at ultimate load. These parameters were evaluated for joints nailed with 6d and 8d nails in single shear and interlayer (connector) gaps of zero and 0.51 mm (0.02 in.). Douglas fir lumber and plywood were used as main and side members, respectively. The results indicate that first and second cycle slip moduli are highly sensitive to the test apparatus used. Sensitivity decreases as parameters are taken further along the load-slip record. Beyond 2.54-mm (0.100-in.) slip, no statistically significant differences were found as a result of the methods used. The profound effect of interlayer gap on slip modulus is apparent, while the influence of number of nails used in a specimen is insignificant. Finally, the need for accurate slip measurement and three-point support foundation for test specimens loaded in compression is emphasized.