Determination of Engineering Properties and Modeling of Wood I-Joists

Transcription

1 Determination of Engineering Properties and Modeling of Wood I-Joists Summary Jean-Frédéric Grandmont, ing.jr. Ph.D Candidate Université Laval Québec, Canada Constance Thivierge, ing. B.Sc.A Industry Advisor Forintek Canada Corp. Québec, Canada Alain Cloutier, ing., ing.f., Ph.D. Professor Université Laval Québec, Canada Guy Gendron, ing. Ph.D. Professor Université Laval Quebec, Canada Wood I joist is a well known product. However, further improvement could be made in its design. This paper presents results of experimental work carried out to support the development of a model that simulates I-joist s behaviour under load. The shear strain in the web and the I-joist deflection from full scale experimental results were compared with model output. Results showed a good correlation between simulated deflection values and those from laboratory full scale joist bending tests. However, the model overestimated the shear strain. These differences are believed to be due to the local variability of OSB properties and the assumptions made in th model regarding the web to flange and web to web joints. Further work to address these descreapancies is on-going. 1. Introduction Since the late 1970s, many companies have been manufacturing wood I-joists. The "I" configuration provides high bending strength and stiffness. The product is now well recognized and is used extensively for both floor and roof framing. It is one of the engineered wood products showing the fastest growth on the market.. The I-Joist market is becoming more competitive and the need for optimization is increasing. Most of the research done on wood I-joists has focused on joists configuration parameters (e.g., web opening, stiffners and creep) using empirical approaches. The shear performance of the web material and the contribution of the web to the overall performance of the joist have also been investigated but to a limited extent.

2 As early as 1979 efforts were made to develop simulation models of wood I-joists. Fergus [1] developed a model based on the finite element method. At that time he mentioned that it would be possible to save time and money in experimental work if a good model able to simulate an I-joist with enough precision was available. Bearing that idea in mind, the general objective of the study was to develop a model that would simulate the behavior of a wood I-joist to get a better understanding of the impact of the web s parameters on it. The specific objectives were to 1) characterize the mechanical properties of the web and 2) to use this information in a finite element model of the I-joist under load.. 2. Wood I-Joist models This study is not the first one aimed at developing a model that would represent a wood I-joist with enough precision to use it as an optimization tool. The following part presents some of the previous and current work that have been done in this area. 2.1 Literature review One problem in developing a simulation model of wood I-joists is the difficulty to get good data on the material properties of the joist components. A lot of data is available on the flanges since they are made of solid wood for which engineering properties are readily available in textbooks such as Bodig and Jane [2] or Guitar [3]. By engineering properties we mean modulus of elasticity (MOE), shear modulus (G) and Poisson s ratio (υ). It is more difficult to get properties for OSB. Panels manufacturers tend to carry out quality control tests only. It is also generally recognized that OSB has heterogeneous properties at small scale and homogeneous properties at a larger scale. If the OSB is considered as a continuous material in a model, the tests used to get the properties should be done on a large scale. As our work focus, not only but specifically, on the web part of the I-joist, studies about OSB alone have been reviewed. One of the most important studies that have been conducted in Canada on OSB panels was carried out by Karacabeyli et al. (1996) [4]. The study presents results of tests that were performed to develop the Canadian standards for OSB. The objective of the study was to set design values for OSB made following CSA O452 and to include those values in CSA O86.1. To get OSB properties, series of tests were performed on medium to large scale specimens of different thicknesses and from different mills. That study gives a good idea of the engineering properties distribution and how it varies for different nominal thicknesses. Poisson s ratio seems to be the less documented property of OSB. Thomas [5] is one of the few authors who worked on it. He calculated Poisson s ratio of OSB in the plane of the panel by measuring the deformation in the two principal directions while applying a load in one of these directions. The deformations were measured over a 20.3 cm span. He found Poisson s ratio (υ 12 and υ 21 ) to be 0.23 and 0.16 for major and minor axis, respectively the major axis being parallel to the strand orientation of the faces of the panel while the minor axis is perpendicular. A large amount of work has been done by the University of Brighton. Zhu et al. [6] developed a finite element model of wood I-Joist. The model was used up to failure. Once the model was validated they have studied the influence of web openings and buckling. The material properties of OSB was also performed. They used a 6 specimen technique (similar to what is used for wood and suggested by Guitar [3]) to get a complete elastic matrix of properties. The OSB, like wood, was indeed considered as an orthotropic material. They have also determined properties in tension and compression. They have considered that the OSB properties were the same in both tension and compression for the elastic zone but they have considered them different beyond the elastic zone.

3 Another team recently worked on a finite element model of wood I-joist. Chui et al [7] worked on such a model to improve the web design in order to reduce knife through failure and study the impact of multiple web openings on stress distribution in the web. They made recommendations on the design of the web to flange joint and on the minimum distance between some types of web openings. 2.2 Model development and determination of OSB material properties For the purpose of this study, it was decided to develop and validate a simple model of a wood I- Joist. It was clearly demonstrated that a finite element model of wood I-joist based on an elastic behaviour law performed well to predict deflection under load [6, 7]. However, the impact of the web in the joist under load was not studied before. In the current study, the finite element model was developed with a commercial software (Abaqus 6.4.1). The model was considering OSB and wood as orthotropic materials with an elastic behaviour. The same properties were used for tension and compression. The domain was meshed with triangular prisms. Figure 1 on the left shows a typical meshing for an I-joist. The base simulates the height of the reaction point over the pivot. Web Figure 1 :I-joist meshing Flanges Base Two types of I-joist were tested Short span (shear critical) Long span (moment critical) The short joists were 3.048m long with a 2.438m long span. The long ones were 6.096m long with a span of 5.486m. We have tested and simulated 8 long and 8 short I-joists with 4 of each having the main axis of the web parallel to the length of the joist and 4 with the main axis perpendicular to the joist. The long joists were simulated as if they were in a 10 points loading setup to simulate a uniform loading. The short ones were simulated as if they were in a 3 points loading setup. The real joists were tested following the same conditions then those for the simulation. The long joists were tested with a 10 points loading setup and the short ones were tested with a 3 points loading setup. A set of two LVDTs was used to measure the deflection of the joist. The shear strain was not measured directly. Two pairs of potentiometer (PT101 from Intertechnology) were used to measure the deformation on the web at 45º on each side. The strain was calculated from those deformations. Measurement were made in the middle of each shear section for the long span ones while for the short ones two measurement were made in the main shear section. The joists were loaded more then one time to cover every shear section since we had only 4 potentiometers. They were always loaded in the elastic zone. The OSB properties were partially tested to have a good simulation. The available properties for OSB did not cover our needs because certain properties were missing and, more importantly, no

4 reliable data were available for web stock OSB. This type of OSB is a slightly different product from construction grade OSB. I-joist manufacturer have their own specifications for the panels they buy. The OSB was considered as an orthotropic material with no difference between tension and compression properties. We were then looking for MOE, G (shear modulus) and υ (Poisson s ratio). Other studies such as Zhu [6] provide such properties but they do not have the same kind of panel (i.e. different wood species, etc.). The properties have been determined for the two axes in the plane of the panel. The major axis is considered to be the direction parallel to the orientation of the face strands. Tests through the thickness have not been conducted since they were considered to be critical in order to model correctly the I-joist. Series of tension tests were performed following ASTM D1037 in order to determine MOE and Poisson s ratio in the plane of the board (ASTM 2003). The tests were performed with two types of measuring devices. A first serie of tests was performed with an optical measurement device (Figure 2) to determine MOE and Poisson s ratio. The system is able to follow the movement of pre-specified marks on the specimen on two axis. The other series of tests were carried out following the same standard but a DCDT was used instead of the optical measuring device to determine the strains. Figure 2 : Tension test with optical measuring device Test specimens for both method of measurement were cut from the same panel. Other properties tested were the two shear modulus in the plane of the board. Tests were done following two ASTM standards: ASTM D1037 (small scale test) and ASTM D2719-c (large scale test). The use of ASTM D1037 was intended to provide an idea of differences between panel s properties. The test specimens were small and therefore not appropriate to measure near pure shear deformation. We were then not able to get real shear modulus by those tests. The large scale tests were done by APA (Tacoma) as they already have the setup to do such tests. That test gave us real shear modulus that we were necessary in the model. The flange of each reference I-joist was tested with an E-computer to get the MOE in bending. The E-computer is a device that gives MOE based on density and resonant vibration frequency. Results of other tests conducted at Forintek that were comparing E-computer results and static tension tests were then used to adjust E-computer results. As the MOE in tension or compression is the most important properties of I-joists flanges, the other mechanical properties of the flanges were taken from literature [2][3]. 3 Results and discussion 3.1 Material properties of OSB Table 1 presents the results obtained from the tension tests using the optical measurement device. Those tests were done to see if the Poisson s ratio was comparable to what was found in the literature. With results of 0,23 and 0,15 for the major and minor axis in the plane of the panel the results are comparable with what was found by (Thomas [5] and Zhu [6]). Occasional problems of points tracking by the measurement device explain some missing values in the table.

5 Table 1 : Poisson s ratio of OSB panels Sample Parallel* Perpendicular* Average SD CV 30% 50% *Orientation of the major axis of the web compared to the axis of the test Table 2 : OSB MOE in the plane of the panel MOE (MPa) Parallel Perpendicular Average Optical Min measuring Max device SD COV % Average Min DCDT Max SD COV % *Orientation of the major axis of the web compared to the axis of the test The MOE was also calculated from those tests in order to compare the MOE obtained by the optical method and those obtained with the DCDT. Table 2 shows results of the two different tests used for MOE determination. It was found that there was no significant difference at the 95% confidence level between the two types of tests. That particular conclusion confirmed that optical measurement could be useful to determine mechanical properties of non-homogeneous material such as OSB. The other property investigated was shear modulus in the plane of the board. The results of the tests conducted at Tacoma by APA following ASTM D2719-c are presented in Table 3. Table 3 : OSB Shear modulus properties Orientation* and nominal thickness (mm) G (MPa) SD COV (%) Par Per Par Per Par Per *Web's major axis orientation to the axis of the test (par=parralel, per=perpendicular) Three different nominal thicknesses have been tested in two directions. Obviously the results are similar in both directions as the test is large enough to create near pure shear stress. The other part of the tests conducted following ASTM D1037 was used for comparison only (always with data from the same nominal thickness). A first series of tests was done on the same panels that were used for the ASTM D2719-c (same nominal thicknesses). That series of test results was used for comparison because the panels used for the validation I-joist were too small to be tested otherwise then with the ASTM-D1037 setup. The difference found between the series that was also tested with 2719-c and the series from the panels that were used in the I-joist fabrication was recorded. That difference was then applied to the results found with the large scale tests Model validation tests The next tables present the results obtained for the deflection and shear strain on the web for both laboratory and simulation tests. The shear strain is presented for each shear section. There is 4 shear sections for half a joist because of the 10 points loading setup. Table 4 presents results for the critical moment joist and Table 5 presents the critical shear results.

6 Simulation Real I-Joist* Table 4 :Long span I-joist tests results Section 1 (near reaction point) Shear Strain m x10-4 Section 2 Section 3 Section 4 (near center) Deflection Par Par Per Per par par per per par par Difference % per per *Web orientation of the major axis to the length of the joist (par=parallel, per=perpendicular) mm The deflection is close to the laboratory results and the difference is constant. The laboratory results for the shear strain are the average of measurements made on both sides of the web and on each side of the centre. The shear strain difference near the reaction point and the second shear section from the pivot is constant which indicates that we have a systematic error involved. The difference is also not so big in those particular shear sections. Sections 3 and 4 (following section 1 and 2 from reaction point to the center) show a lot of variability although some results seem to be close to the laboratory results. The variability is believed to come from difficulty to measure the very small shear deformation as we were close to the center and because the moment is more important near the center. Other possible issues will be discussed below. Table 5 presents results for the short span I- joist. It shows that this time again the predicted deflection is Table 5 : Short span I-joist tests results I-joist* Simulation Real Difference % Shear strain Deflection Shear strain Deflection m x10-4 mm m x10-4 mm Shear strain Deflection Par Par Par Par Per Per Per Per *orientation of the web's major axis to the length of the joist (par=parallel, per=perpendicular) constant although the results are not as close as they are for the long span ones. That bigger difference could be attributed to a web simulation problem because the shear stress is much more involved in the deflection for that test then for the longer span one. The other point is the large differences and the high variability that were found for the shear strain results. The more surprising variability is the one into the real shear strain. That particular variability might come from the assumption that the web is a continuous material does not apply for OSB. Par 04 Figure 3 : Short span test setup and joint localisation Figure 3 shows the short span test configuration and where there was a joint on the sample Par04. The X represent the places were the shear have been measured. The shear strain was the double (1,34 x10-3 compared to 6,57 x10-4 ) on the left side of the joint (vertical bar on the web) when compared to the right side.

7 That particular case was not unique and it is then believed that the web to web joint introduce an important discontinuity into the web. As we did not always have so much difference from one side of a joint to the other it seems to introduce what could be called a potential of discontinuity for the shear stress distribution. Obviously that type of joint is not always at the same place and thus do not have always the same impact on the behaviour of the joist. 6 Conclusions The main objective of the study was to develop a model that would simulate the behavior of a wood I-joist to get a better understanding of the impact of the web s parameters on it. The study shows that a simple model assuming continuous material and no joints gives a reasonable prediction of the general behavior of a wood I-joist, especially for the case of a critical moment. On the other hand, when looking at the specific behavior of the web within the I-joist under load some assumption seems to create accuracy problems with the model. Our findings show that the web-to-web joint can affect greatly the shear stress distribution into the web. It is then believed that a wood I-joist model where the shear stress is important or where the accuracy is critical should include that element. Further work has been initiated to include the web-to-web joint as well as the web to flanges joints. Other work have been undertaken to see if the OSB properties variability should be included in a future model. 7 Acknowledgements The authors would like to thank Forintek Canada Corp. and the Natural Sciences and Engineering Research Council of Canada (NSERC) for their financial support. 8 References [1] Fergus David Andrew, 1979, Effect of web voids and stiffeners on the structural performance of composite beams, PH.D. thesis, Purdue University, États-unis, 220p. [2] Bodig J. and Jayne B Mechanics of wood and wood composites. Krieger puplishing compagny, Florida, 712pp. [3] Guitard D Mécanique du matériau bois et composites. Imprimerie du Sud, Toulouse, France. 238pp. [4] Karacabeyli Erol, Lau P., C.R. Henderson, F.V. Meakes, W. Deacon, Design rated oriented strandboard in CSA standards, Canadian journal of civil engineering, 1996, pp [5] Thomas W.H., Poisson s ratio of an oriented strand board, Wood and Science Technology, #37, 2003, pp [6] Zhu Enchun, Modelling the structural behaviour of OSB webbed timber I-beams, Thesis, University of Brighton, 2003,147p.

8 [7] Chui Y. H., Ghulam Pirzada, Shouyong Lai, 2005, Enhancing Shear and Bearing Strength of wood I-Joists, Value to Wood Program, Université du Nouveau Brunswick, 78p.