Development of Plastic Theory for Malaysian Timber Nailed Joints

Transcription

1 Development of Plastic Theory for Malaysian Timber Nailed Joints Dr. Mohd. Zamin Jumaat Associate Professor Dept. of Civil Engineering University of Malaya Kuala Lumpur Malaysia. Tel Bona Murty Research Assistant Dept. of Civil Engineering University of Malaya Kuala Lumpur Malaysia. Dr. Tan Yu Eng Senior Research Officer Products Development Division, Forest Research Institute of Malaysia (FRIM) He is currently an Associate Professor at the Department of Civil Engineering., University of Malaya. His research interests are in the analysis and design of timber and concrete structures. He obtained his B.Sc(Civil Eng.)., M.Sc. and PhD degrees from the University of Southampton, United Kingdom. He obtained his B. Eng.(Civil Eng.) in 1998 from the University of Bandar Lampung and M.Eng Sc.(Structural Engineering) in 2003 from the University of Malaya. He has been working as a Research Assistant since 2001 at the Department of Civil Engineering, University of Malaya. He is a Senior Research Officer in Forest Research Institute Malaysia (FRIM). He obtained his Ph.D degree in Wood Eng from the University of Brighton, UK. His major interests are in structural and non-structural glue-lamination, and stress grading of Malaysian timbers. Summary This paper describes the study on the development of plastic theory for Malaysian timber nailed joints. In the study, 270 timber nailed joint specimens were fabricated, tested and analyzed. The specimens were from Kempas, Mengkulang and Pulai which represented the heavy, medium and light hardwoods. From the results, several empirical equations were used to determine the yield load of Malaysian timber nailed joints. The study also came out with a mathematical model which can be used to predict the yield load of Malaysian timbers using their specific gravities and the diameter of the nails used. The mathematical model presented here was derived from Brock[1]. Comparisons of the predicted yield loads with experimental results and other empirical methods such as EYM [3] [5] [8] and Foschi [2] are also presented. Keywords: Yield Load, Model, Maximum Load, Nail Diameter, Timber Density. 1. Introduction 1.1 General The use of plastic theory for timber engineering is now quite established in Europe, Canada, Australia, New Zealand and North America. This is not surprising because plastic theory is logical and resulted in structures that are more economical. For timber joints, the basis of the approach is the determination of the yield load. There are many methods that can be used to determine the yield load for timber joint such as Johansen [3], Foschi [2], Smith et. al. [5] [8] and the US 5% nail diameter offset [6]. Some of these models have already been adopted to establish the new standards based on the limit state design approaches. This study is a preliminary study for gathering data and also for reviewing the most suitable approach to establish the Malaysian Code of Practice for the design of timber structures based on the limit stated design concept. 1

2 1.2 Objective The objectives of this study are: i) To review several methods of determining yield load of nailed joints ii) To obtain the relationship between yield loads and maximum loads iii) To propose a new mathematical model to determine yield load of nailed joints 2. Theoretical Approaches There are four theoretical models, which were used to access the purpose of this research. Brock s model [1] was used to predict the maximum load of Malaysian timber nailed joints using specific gravity and nail diameter of the joint [4][6] [7]. European Yield Model s (EYM) [3] [5] [8] and Foschi model s [2] [8] were used to predict the yield load for Malaysian timber nailed joints. 3. Experimental Programme and Result The 270 specimens used were fabricated from Kempas (Koompassia Malaccensis), Mengkulang (Terrietia Spp), Pulai ( Alstonia Spp) which was representing heavy, medium and light hardwood categories respectively. Plate 1.The specimen was tested using the Instron Testing machine The nails used were of 2.6 mm, 3.3 mm and 4.1 mm in diameter and 50 mm, 63mm and 76 mm in length respectively. There were 4 nails on each of the single shear joint. The specimens were tested in single shear under a uniform rate of loading of 1.25 mm per minute until failure using an Instron Universal Testing Machine. These test were done in accordance with the AS 1720 and AS The subsidiary tests were also carried out to establish the moisture contents and specific gravities of the specimens. The slippages were measured using Linear Variable Displacement Transducers and a TML Data Logger. The load-slip curves and maximum loads of each specimen were tabulated as in [7]. The best curve fitting lines of maximum loads versus specific gravities were then plotted using a spreadsheet computer package Microsoft Excel. The coefficients of correlation were calculated to check the goodness of fit. Plate 1 shows the specimen being tested using the Instron Testing Machine and Plate 2 shows the typical mode of failure of the joints which were noticed to be crushing of timbers and bending of nails. Plate 2. Typical mode of failure 4. Discussions 4.1 Maximum Loads The relationship between the maximum loads and specific gravities is shown in Fig. 1. Fig. 2 shows the maximum load versus nail diameter for the average specific gravities i.e. 0.34, 0.56 and 0.72, from the three species. From this, the maximum loads versus nail diameters for the three chosen specific gravities were plotted. Three curve fitting equations were obtained. Substituting the three values of the average specific gravities to Brock model s [1] resulted in the following equations; P max 1 = 2245 Gd 1.61, P max 2 = 2244 Gd 1.61, P max 3 = 2311 Gd 1.61 (4.1) (4.2) (4.3) 2

3 Max. Load (kn) mm nail 3.3 mm nail 4.1 mm nail R 2 = Pmax = d 1.61 Pmax = d R 2 = kn 10 Pmax = d R 2 = Specific Gravity Fig.1. Relationship between maximum load and specific gravities of 3 species of timber of different size of nails (After Fig. 2 of [4] ) mm S.G of 0.34 S.G of 0.56 S.G of 0.72 Fig.2. The relationship between max. loads and nail diameter of the 3 species of timber (After Fig. 3 of [4] ) Using these equations, the maximum loads for Malaysian timber nail joints can be predicted by averaging the three equations into single equation. Finally, the maximum loads for Malaysian timber nail joints can be predicted with the following equation. P max. = 2270Gd 1.61 (4.4) 4.2 Correlation factor between maximum loads and yield loads To obtain the correlation factors between the maximum loads and yield loads, the 270 Malaysian timber nail joints data were used to calculate the yield load from the four methods. These were then compared to the maximum loads, which were obtained using Eq The percentages of yield load to the maximum load for each specimen were calculated. The average percentages for each species and nail diameter were used as correlation factors to determine the yield load for Malaysian timber nail joints. Typical comparison between yield load and maximum load is shown in Fig.3. The average percentages of the yield loads to the maximum loads from the four methods on the three different species and three different nail diameters can also be shown in Fig. 4. Load (kn) Max. Load Johansen YL Foschi YL Smith YL No. of Test Specimens Fig. 3. Typical comparisons between maximum loads and yield loads in four methods Percentage of Yield Load to Max Load (%) Kempas Mengkulang Pulai 2.6 mm 3.3 mm 4.1 mm Avgs. Timber Species Fig. 4. The average percentages of yield load to maximum load To obtain the yield load for each species, the maximum load from Eq. 4.4 is multiplied by the average percentage load from Fig. 4 and divided by 4. The number of nails per specimen used in this study was four. The yield load that resulted from these approaches are as follows, P yield. = 248 Gd 1.61, P yield. = 322 Gd 1.61 and P yield. = 354 Gd 1.61 (4.5) (4.6) (4.7) From Eqs. 4.5, 4.6 and 4.7 which corresponded to the whole range of Malaysian timber, a general single equation can be obtained to be used to predict the yield carrying capacity for Malaysian timber nail joints. The equation is, P Yield. = 308 Gd 1.61 (4.8) 3

4 Where; P Yield = Predicted yield load of the joint, (N), d = Diameter of nail (mm), G= Specific gravity of the timber A typical comparison of yield loads obtained from Eq. 4.8 and other methods is shown in Table Conclusions From the study conducted, the following conclusions can be drawn: i) There seems to be a direct relationship between yield loads and maximum loads of the specimens tested. ii) From the study carried out, the yield load for Malaysian timber nailed joints can be satisfactorily predicted if the specific gravities of the timber and nail diameters were known and it could be shown that this will be given by the equation P Yield. = 308 Gd 1.61 iii) The mathematical model suggested in this study, is expected to be able to predict the yield load of joints from other timber such as softwoods. The only different would be the constant in the formula would have a different value. iv) The mode of failure for Malaysian timber nailed joints seemed to be that of crushing of timbers and bending of the nails. 6. Acknowledgments The authors would like to thank all staff of the Department of Civil Engineering, Universiti Malaya and co-researchers who had contributed either directly or indirectly in this project. In particular the authors would like to acknowledge the contribution from Sa at E.S. and Zainuddin A.N. for the help in the experimental works. The authors would also like to acknowledge the funding given to this project by the Majlis Penyelidikan Kebangsaan Sains Negara under IRPA project References [1] Brock GR, The Strength of Nailed Timber Joints. Forest Product Research, London, HMSO, London, Bulletin N [2] Foschi RO, Load-Slip Characteristic of Nails, Journal of Wood Science, Vol. 7 No. 1 July1974. [3] Johansen, K.W., Theory of Timber Connections, International Association of Bridge and Structural Engineering Vol. 9 pp [4] Jumaat MZ, Murty B, The Relationship Between Yield Load Point Using Foschi Plastic Theory and Maximum Load on Malaysian Timber Nail Joints, Proceedings of 7 th World Conference on Timber Engineering, WCTE 2002, August 2002 Shah Alam, Malaysia., pp [5] Hilson BO, Whale LRJ, Smith I, Characteristic Properties of Nailed and Bolted Joints Under Short-Term Lateral Load Part 5 Research Philosophy and Test Program. Journal of the Institute of Wood Science, Vol. 11 No. 2, pp , 1989/90. [6] Murty, B., The Use of PlasticTtheory on Selected Malaysian Timber Nailed Joints, M.Eng.Sc. Thesis, Dept. of Civil Eng. University of Malaya, August [7] Sa at ES, Strength of Mechanical Timber Joints, Graduation Exercise, Dept. of Civil Eng., Universiti Malaya [8] Smith I, Whale LRJ, Characteristic Properties of Nailed and Bolted Joints Under Short-Term Lateral Load Part 1 Research Philosophy and Test Program, Journal of the Institute of Wood Science, Vol. 11 No. 2, pp 53-59,

5 The appendix of Development of Plastic Theory for Malaysian Timber Nailed Joints paper Table 1. Typical comparison of the new yield load approach and other common yield load methods (Mengkulang and 3.3 mm nail diameter) No. of Spec. Johansen Foschi YL Smith YL YL (kn) (kn) (kn) New YL Method (kn) Total Avg Note. The values in New YL Method column were obtained using Eq 4.8 5

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