Predicting the Row Shear Failure Mode in Parallel-to-Grain Bolted Connections

Transcription

1 Predicting the Row Shear Failure Mode in Parallel-to-Grain Bolted Connections Morgan Bickerdike, MASc. Graduate Student Pierre Quenneville Professor and Head of Civil Engineering Department Royal Military College of Canada Kingston ON, Canada Summary In this paper, a numerical model developed to study the behaviour of bolted connections loaded parallel-to-grain is presented. The model is based on the experimental load-slip curves of single bolted connections tested to failure and exhibiting the possible ductile and row shear failure modes. Other variables such as bolthole gaps and wood stiffness were also considered. From this model, numerical predictions of the ultimate loads were made for various end distances and bolt spacings. From these predictions, it is confirmed that the minimum of the end distance or the bolt spacing is a critical variable in determining the failure mode and resistance. From this finding, a simple design equation was developed for row shear and compared to existing laboratory results available. Very good agreement is obtained. 1. Introduction The strength and behaviour of bolted connections loaded parallel-to-grain is governed by brittle and ductile modes of failure. Johansen s set of equations (Johansen, 1949), also known as the European Yield Model (EYM) predicts well ductile failure in the form of bolt yielding and/or wood crushing. Currently, there is no mechanics-based model available for predicting the strength of connections failing in a brittle manner; i.e. the row shear-out and the group tear-out modes. Fig 1 Single Bolt Spring Representation A finite element model based on assumed load-slip behaviour of a single bolt was initially developed by Tan & Smith (1999) and constitutes a potential predicting tool. It is based on a combination of numerical and experimental observations. In their model, each bolt transfers its load to the wood through a spring having an assumed non-linear behaviour. A bolt is thus participating in the connection resistance if its load or slip is within the assumed bolt load-slip response. It was shown that a prediction of the strength at failure along with its failure mode is possible for a brittle connection.

2 2. Numerical Model The model presented in this paper was developed to predict the ultimate load of a multiple-bolted connection. This is based on 2-D finite elements where the wood, steel plates and bolts are represented as elements made of linear-elastic material, as shown in Figure 1. The non-linear springs represent experimentally tested load-slip curves for single bolted connections at 4d, 7d and 1d end distances, at slenderness ratios of 4.2 or 6.8, and for different wood species. The failure modes of these connections varied from row shear to various EYM ductile failure modes. These experimental load-slip curves of the individual bolts are engaged when the bolts come in contact with the wood. Once a load-slip curve reaches its slip limit, the load decreases to zero while the slip continues to increase, otherwise signalling failure in the wood at that individual bolt. In order to adequately simulate the load-slip response for the non-linear springs, no failure in the wood elements is possible. The model is developed on the ANSYS software where the connection geometry and material properties are created, and the non-linear analysis is instructed by a pre-written batch file code. The gaps between the bolts and the holes were randomized and contact elements between the steel and wood were used. The stiffness of the wood was also made random. The refinement of the model utilized in this study in comparison with the one developed by Tan and Smith, is the load-slip behaviour of each individual bolt is randomized based on standard deviations and averages from experimentally developed load-slip relations. 2.1 Bolt Load-Slip Curves A series of single bolted connections of various configurations was tested to record the load-slip parameters. For each one of the tests, the load-slip curve, from zero to ultimate, was idealized by the relationship given in equation [1]. Further, the load-slip relationship shown in Fig 2 was recorded for each tested specimen configuration at the 4d, 7d and 1d end distances. P ( bδ ) = a( 1 e ) c From this assemblage of information, average and COV values for equation [1] parameters were determined to simulate the variation in bolt loads and slips of an individual fastener within a connection (refer to Table 1). Further, a relationship between the end distance and the corresponding single fastener slip, δ x, was established from the results of the three tested end distances. This relationship, given in equation [2], allows the computer model to generate the load-slip response for a single fastener at any end distance, a 3t, or bolt spacing, a 1. In this equation, x refers to the a 3t /d or a 1 /d factor for the individual fastener. ( x x = e. 41 ) δ [2] [1]

3 The slip at which failure occurred in tests for a single fastener described by equation [2] varies with respect to the end distance. For a large end distance, the slip at failure had a large variation (refer to Table 1). The standard deviation of the slip at failure is utilized in the computer model by implementing the idealized relationship in equation [3]. This instructs the computer model to adjust the slip in Fig 2 about its average value, resulting in further variation of the individual bolt loads within the modelled connection. δ st. dev = e x (.85x ) [3] Average Bolt Load, P (kn) Connection Slip, δ (mm) a = b =.61 c = 1.84 Table 1 Load-Slip Parameters for 8 mm S-P Glulam Used in Idealized Equation. Unit Average St. Dev. a kn b mm c δ 4d mm δ 7d mm δ 1d mm Fig 2 Single bolt load-slip curve for 19 mm bolt in 8 mm S-P glulam with 1d end distance. 2.2 Connection Modelling The numerical model was developed with the capacity to set the number of rows, number of bolts per row, member thickness and bolt diameter along with the connection spacings; i.e. end distance, spacings in the row and of the rows, if applicable. The reminder of the parameters such as gaps, individual load-slip curves, and wood stiffness were left as random variables within known ranges. Non-linear analysis was conducted for each given possible combination of the parameters and the ultimate load and load-slip behaviour recorded for. A graphical representation of the individual bolt loads and ultimate resistance of a 2-row, 3-bolt model is presented in figure 3. The number of analysis required was monitored through the constant evaluation of the population average ultimate load. It was thus deemed satisfactory to limit the number of runs when the average ultimate load prediction did not vary significantly. This was attained, on average, after 4 runs for a typical connection configuration with two-rows of three-bolt.

4 3 25 Resistance Connection Slip (mm) B11 B12 B13 B21 B22 B23 Ult. Load Fig 3 2-D numerical model load-slip curve for 8 x 19 mm S-P glulam connection, n r =2,n fi = Numerical Predictions Numerical predictions for specific connection configuration were first made so as to judge the model s ability to predict the average ultimate load of known experimental connections. These comparisons for steel-wood-steel S-P glulam connections that failed in row shear are listed in Table 2. Table 2 Comparison of numerical and experimental average ultimate loads Species t d a 1 a 2 a 3t n r n fi Average Ult. Loads (kn) (mm) (mm) Experimental Numerical S-P d -- 7d S-P d -- 1d S-P d -- 7d S-P d 5d 7d Note: t = glulam member thickness, a 1 = in-row bolt spacing, a 2 = row spacing, a 3t = loaded end distance, n r = number of rows, n fi = number of bolts per row. From these trial runs, confidence in the model was obtained. Further numerical predictions of the average ultimate load were made for different connection configurations. The results of these are given in Table 3. It became evident from these predictions that the minimum of the end distance and the bolt spacing constituted a determining factor in triggering the failure. The average ultimate load for all of the configurations that had either their minimum of end distance or bolt spacing at 4d was similar. The same was observed when the minimum of the end distance or bolt spacing was 7d. This observation was made for connections at 2, 3 and 4 bolts per row. Thus, any equation developed for predicting the resistance of bolted connections should consider this triggering length. This has also been observed in other studies (Quenneville, 1998).

5 Table 3 Results from 2-D Finite Element Analysis 8 x 19 mm S-P Glulam 19 mm bolts SWS connection Model Configuration a 1 a 2 a 3t Average Ult. Load (kn) 4d 5d 4d 151 4d 5d 7d 156 4d 5d 1d bolts per row 2 rows 3 bolts per row 2 rows 3. Design Equation 3.1 Row shear prediction equation 7d 5d 4d 158 7d 5d 7d 187 7d 5d 1d 189 1d 5d 4d 158 1d 5d 7d 189 1d 5d 1d 198 4d 5d 4d 223 4d 5d 7d 228 4d 5d 1d 228 7d 5d 4d 24 7d 5d 7d 279 7d 5d 1d 281 1d 5d 4d 24 1d 5d 7d 284 1d 5d 1d 297 From experimental studies available in the literature of Quenneville and Mohammad (21), connection configurations of the specimens that failed in row shear were selected. All experimental data was found for connections loaded in ten-minute durations. The following equation format was then used to arrive at the best solution to predict the average ultimate load. RS n r = Σ 2 RS i [4] i= 1 Where: RS i f v avg G t n fi a cr n r = shear resistance along one shear plane of row i, in N = f v avg t n fi a cr = (16.6 G.85 ) t n fi a cr = member average shear strength, MPa, equal to 16.6 G.85, from Forestry Products Society (1999) = mean oven-dry relative density of material = member thickness, mm = number of fasteners in row i = minimum of a 3t and a 1, mm = number of rows in connection For connection configurations of steel-wood-steel bolted connections that failed in row shear, the best fit was obtained when dividing the average shear strength by 3. A graph showing row shear predictions and experimental averages is shown in Figure 4.

6 6 R 2 =.95 Prediction Averages (kn) Experimental Averages (kn) Fig 4 Comparison of experimental and predicted average ultimate loads for steel-woodsteel (SWS) configurations In light of the fact that the row shear failure modes is a function of the triggering length and of the number of loaded shear planes in the member (Mohammad and Quenneville, 21), the design equation was further refined to: RS n r = Σ 2 RS i [5] i= 1 Where: RS i K ls = shear resistance along one shear plane of row i, in N = (f v avg ) K ls t n fi a cr = (16.6 G.85 ) K ls t n fi a cr = 5.53 G.85 K ls t n fi a cr 3 3 = factor for member loaded surfaces =.65 for side member (one contact surface) = 1 for internal member (two contact surfaces) Fig 5 shows the comparison of average load predictions using equation [5] vs. experimental averages for seven wood-steel-wood connection configurations that failed in row shear. For these cases as well, the fit is very good. Finally, predictions were made for seven single shear, steel-wood configurations. A graph showing the comparison of average load predictions vs. experimental averages, using equation [5], is presented in Fig 6.

7 3 8 Average Prediction (kn) 2 1 R 2 =.93 Prediction Averages (kn) R 2 = Experimental Average (kn) Fig 5 Comparison of experimental and predicted average ultimate loads for wood-steel-wood (WSW) connections Experimental Average (kn) Fig 6 Comparison of experimental and predicted average ultimate loads for wood-steel (WS) connections 4. Discussion The predictions based on the proposed design equation are acceptable for addition within a design standard. The simple format of equation [5] is also very attractive to practitioners. To predict the characteristic resistance values for the row shear failure mode, equation [5] would need to be multiplied by a factor, F, assuming a normal distribution and using a COV of 25%. F = COV [6] The fact that the original concept was developed for SWS bolted configurations, and that it can be further used for WSW and WS cases attest to its robustness. It should be made clear at this point that this equation does not apply to all practical cases. It is well known that for configurations with rows of bolts very closely spaced, the governing mode of failure is controlled by group-tear out. More research is required to investigate this other mode of failure and to develop a corresponding design equation. 5. Conclusions A numerical model based on finite elements was developed to predict the average ultimate resistances of bolted wood connections that fail in row shear. The model provides good approximations when compared to available experimental data of bolted connections in sawn lumber and glulam loaded parallel-to-grain. The model confirms the fact that the minimum of the end distance or bolt spacing is the triggering length, affecting the resistance of the connection. A design equation based on this concept, combined with observations obtained in other research studies was then developed and is presented. It provides very good approximation of the experimental average resistance of bolted connections failing in row shear.

8 6. References [1] Bickerdike, M. 26. Predicting the row shear failure mode and strength of bolted connections loaded parallel-to-grain. MASc Thesis, Royal Military College of Canada. Kingston, Ontario. [2] Canadian Wood Council. 21. Wood Design Manual. Canadian Wood Council. Ottawa, Ontario. [3] Forest Products Society Wood handbook: Wood as an engineering material. Forest Products Laboratory General Technical Report FPL-GTR-113. United States of America. [4] Johansen, K.W Theory of timber connections. International Association of Bridge and Structural Engineering. Vol. 9, pp [5] Mohammad, M. and Quenneville, J.H.P Bolted wood-steel and woodsteel-wood connections: verification of a new design approach. Canadian Journal of Civil Engineering, Vol. 28, pp [6] Quenneville, Predicting the failure modes and strength of brittle bolted connections. Proceedings from the 5 th World Conference on Timber Engineering. Montreux, Switzerland. Vol. 2, pp [7] Quenneville, J.H.P., and Mohammad, M.. 2. On the failure modes and strength of steel-wood-steel bolted timber connections loaded parallel-to-grain. Canadian Journal of Civil Engineering, Vol. 27, pp [8] Smith, I., and Tan, D Failure in-the-row model for bolted timber connections. ASCE Journal of Structural Engineering, Vol. 125, No. 7, pp