Study on Load Carrying Capacity and Stiffness of Curved Glulam Beam

Transcription

1 October -4, 2, Geneva, Switzerland Study on Load Carrying Capacity and Stiffness of Curved Glulam Beam Bambang Suryoatmono Department of Civil Engineering Parahyangan Catholic University Bandung, Indonesia Adhi Bukhari Department of Civil Engineering Parahyangan Catholic University Bandung, Indonesia Abstract One of the advantages of using glue laminated timber (glulam) is that it can be made a curved beam in order to increase its load carrying capacity and its stiffness. Under the same load, the more rise a curved beam has, the less bending moment it undergoes, but the more axial force exists. The interaction between the axial force and the bending moment will control the optimum ratio between rise and span of a curve beam. In this paper, a number of curved beams made of meranti (shorea) laminas with different rises were statically loaded at midspan. The adhesive used for gluing the laminas was polyvinyl acetate. Each beam was assumed to follow parabolic equation and supported by a hinge at each end. For each specimen tested destructively, the load carrying capacity was recorded. By analyzing the experimental results, the relationship between the ratio (between rise and span) and load carrying capacity of a curved glulam beam was obtained. Numerical analysis using linear finite element method considering the orthotropic nature of wood was also carried out in the study of stiffness of curved glulam beams. Both experimental and numerical results show that there are optimum span/rise ratios that results in largest load carrying capacity and smallest stiffness. Keywords load carrying capacity, stiffness, glulam, orthotropic, finite element analysis Paper WS-8 of 9

2 October -4, 2, Geneva, Switzerland Introduction Indonesia is a country that has one of the largest area of tropical rain forests in the world. More than 25, species of plant can be found in the country (Hadi 29). The demand of wood in many parts of the world, both for structural and non structural applications, has caused the rate of deforestation in Indonesia very high. In the long run, this may cause environmental impact on the country and its surroundings. Therefore, it is necessary to utilize wood more efficiently. Some possible ways are by establishing mechanical properties of wood and creating engineered wood products. Glulam, one of engineered wood products, is a good representation of an efficient use of available resources. One of the advantages of using glulam is that it can be made a curved beam in order to increase its load carrying capacity and its stiffness. Another case that might need a curved beam is the necessity of higher space in a building. It is, of course, almost impossible to have a curved beam made of solid lumber, especially a curved beam with large ratio between rise and span. In this paper, some of the mechanical properties, namely load carrying capacity and stiffness of curved glulam beams are studied both experimentally and numerically. Experimental studies were carried out by loading a few curved glulam beams at midspan. Numerical studies were performed utilizing finite element method. Materials Experimental Procedures Forty four meranti (shorea) laminas of the size 2 mm by 6 mm by 5 mm were air dried until the moisture content approximately reached 5%. Meranti was chosen because it is a species that is widely used around the world. In the USA it is used extensively in plywood with genus of kapur (dryobalanops) (Miller 999). Polyvinyl acetate (PVA), commercially known as carpenter s glue, was prepared as adhesive of the laminas. PVA is suitable as adhesives for porous materials such as wood (AITC 27). A temporary support were used to make the desired rise. Few steel clamps (see Figure ) were needed to give pressure of at least.7 MPa between each lamina (Thelandersson and Larsen 23). Methods Productions of Glulam Beams To study experimentally the effect of the rise on the mechanical properties of glulam beams, two straight glulam beams and nine curved glulam bemas were made. As mentioned above, each glulam beam consists of four meranti laminas. See Table for complete list of the beam dimensions. Producing straight beams (beam A and beam B, see Table ) were straightforward. Four laminas were glued thoroughly to produce a glulam with a cross section of 8 mm by 6 mm. To produce a curved glulam, the bottom lamina was placed on top of a temporary Paper WS-8 2 of 9

3 October -4, 2, Geneva, Switzerland support right in its middle and bent using steel clamps as seen in Figure. Glue was applied completely on top of the bottom lamina and another lamina was placed on top of it and bent using steel clamps. These steps were repeated until all four laminas were glued together making a curved glulam beam. Each specimen ends were cut so that it had plane cross sections. Table. Rise and span of each specimen Beam Designation f = rise (mm) L = span (mm) f/l Beam A, B Beam 3A, 3B, 3C Beam 5A, 5B, 5C Beam 7A, 7B, 7C Figure. Producing curved glulam beam Static Bending Tests To investigate the load carying capacity and stiffness of each curved glulam beam, destructive static bending tests were performed. The test arrangement is shown in Figure 2. As seen in the figure, load was applied at midspan and a transducer was used to measure midspan deflection. The load given by the Universal Testing Machine (UTM) was displacement controlled with a displacement rate of 2 mm/minute. This was so slow that dynamic effects could be neglected. Both vertical and horizontal displacements at beam ends were restrained as seen in Figure 3 so the supports were hinges. These supports were needed in curved beams in order to reduce the bending moment in the beams. However, the use of these supports also causes the precence of compressive force in the beam. Paper WS-8 3 of 9

4 October -4, 2, Geneva, Switzerland Figure 2. Test arrangement for static bending test of curved glulam beam Figure 3. Typical support condition of a curved glulam beam By using the computer attached to the UTM and the transducer, the load versus midspan deflection for each test was recorded. Examples of load versus midspan deflection curves for straight beam and curved beam are shown in Fig. 4 and 5, respectively. As seen in the figures, all beams ceases behave elastically at much lower load level than the maximum load. Another feature in the load versus midspan deflection curves is that the beam stiffness degradation increases as displacement increases. This indicates the increase in failure material in the beam. It is interesting to note that unlike in a solid beam, failure can occur in middle lamina of a curved glulam beam, as seen in Figure 6. The load carrying capacity of the beam is the maximum load in the load versus midspan deflection curve. Table 2 shows the load carrying capacity (P max ) of each beam tested and the average P max for each rise and span ratio. Paper WS-8 4 of 9

5 October -4, 2, Geneva, Switzerland Figure 4. Load (N) versus midspan deflection (mm) of Beam A (straight glulam beam) Figure 5. Load (N) versus midspan deflection (mm) of Beam 7A Paper WS-8 5 of 9

6 October -4, 2, Geneva, Switzerland Figure 6. Failure mode of Beam 3B. Table 2. Load carrying capacity (P max ) of each specimen tested Beam Designation P max (N) Average P max (N) Ratio of Average P max to that of straight beam Beam A 277 Beam B Beam 3A 756 Beam 3B Beam 3C 9454 Beam 5A 229 Beam 5B Beam 5C 2259 Beam 7A 3325 Beam 7B Beam 7C 9572 Finite Element Model Finite Element Analysis If wood is assumed as an orthotropic and elastic material with three mutually perpendicular material principal axes (longitudinal, radial, and tangential), then the relationship between strain components and stress components can be expressed as (Bodig and Jayne 993) Paper WS-8 6 of 9

7 October -4, 2, Geneva, Switzerland EL µ LR ε L EL ε R µ LT εt = EL γ LR γ LT γ RT µ RL ER ER µ RT E R µ TL ET µ TR ET E T G LR G LT G RT σ L σ R σ T τ LR τ LT τ RT () where E i are moduli of elasticity, µ ij are Poisson s ratios, and G ij are shear moduli, where i = L, R, and T. The elastic properties of meranti were taken from Suryoatmono and Tjondro (28), namely: E L = 5529 MPa, E R = 85 MPa, E T = 453 MPa, µ LR =.35, µ LT =.45, µ RT =.56, G LT = 275 MPa, G LR = 33 MPa, and G RT = 7 MPa. In the three dimensional finite element analysis the type of element used is 8-node solid element with three translational degrees of freedom at each node. Example of finite element mesh in undeformed and configurations is shown in Figure 7. The fiber direction of wood (the longitudinal axis of the material) is assumed to coincide with the tangential direction of the beam. The lamina plane is regarded as the longitudinal-tangential plane of the material. Compatibility between each lamina is assumed to be perfect, i.e. no slip occurs between laminas. Figure 7. Deformed and undeformed configurations of three dimensional finite element model of a curved glulam beam The analysis was performed for straight and curved glulam beams. Elastic midspan deflection due to concentrated load of 5 N for each beam is shown in Table 3. This very low load was chosen to ensure that the material was still in the elastic range. Longitudinal, tangential, and radial stress distribution throughout the curved glulam beam can be plotted using the finite element software. In Figure 8, longitudinal stress distribution is plotted. As seen in the figure, the area with compressive longitudinal stress is much larger than the area with tensile longitudinal stress. This is a characteristic of vertically loaded curved beam if both ends are restrained against horizontal displacement. Paper WS-8 7 of 9

8 October -4, 2, Geneva, Switzerland Table 3. Elastic midspan deflection due to concentrated load P = 5 N obtained from finite element analysis Beam Designation f/l Midspan deflection (mm) Ratio of Midspan deflection to that of straight beam Straight..34. Curved, f = 3 mm Curved, f = 5 mm ,264 Curved, f = 7 mm Figure 8. Elastic longitudinal stress distribution of a cirved gluman beam under a midspan load Discussion Load Carrying Capacity As seen in Table 2, experimental results show that there is an optimum rise/span ratio that results in the largest load carrying capacity of a curved glulam beam. The regression equation for load carrying capacityof a curved glulam beam obtained from experimental results is f f k = L L 2 (2) where k = ratio between load carrying capacity of a curved beam and that of straight beam. The coefficient of determination R 2 of Equation (2) is.953. This indicates that the regression equation fits almost perfectly the experimental results. Using Equation (2) the largest load carrying capacity of curved glulam beam of 3.89 times the load carrying capacity of a straight glulam beam can be obtained if the rise/span ratio is approximately.38. This fact is not surprising because increasing rise/span ratio means decreasing bending moment and increasing compressive force in the beam and the interaction between bending moment and compressive force limits the strength. Stiffness The regression equation for elastic midspan deflection as obtained from finite element analysis is f f k2 = L L Paper WS-8 8 of 9 2 (3)

9 October -4, 2, Geneva, Switzerland where k 2 = ratio between elastic midspan deflection of a curved beam and that of straight beam. The coefficient of determination R 2 of Equation (3) is.934. Using Equation (3) the largest elastic midspan deflection of curved glulam beam of.54 times the elastic midspan deflection of a straight glulam beam can be obtained if the rise/span ratio is approximately.29. It should be noted that the largest deflection means the smallest stiffness of the beam. Conclusions The effect of rise/span ratio of curved glulam beams made of meranti on load carrying capacity and stiffness has been studied. It can be concluded that load carrying capacity can be increased as high as approximately four times if the ratio is increased from zero to approximately four percent. On the other hand, the stiffness of curved glulam beam decreases approximately thirty three percent if the rise/span ration increases from zero to approximately three percent. Regression equations to predict load carrying capacity and stiffness of a curved glulam beam has been found in this study. Caution has to be made before using these equation because mechanical properties of wood, adhesive of glulam, cross grain, moisture content, and many other factors may affect the load carrying capacity and stiffness of a curved glulam beam. Acknowledgements The authors gratefully acknowledge financial support of Parahyangan Catholic University, Indonesia. The authors also gratefully acknowledge the assistance of staffs at the Structural Laboratory at the university. References American Institute of Timber Construction. 27. Adhesives For Glulam Explained. Engineered Wood Week. Bodig, J and Jayne, B.A Mechanics of Wood and Wood Composites. Krieger Publishing Company, Malabar, Florida. Hadi, Y.S. 29. Forest Products Research Achievement and Trend in Indonesia. Proceedings of The First International Symposium of Indonesian Wood Research Society. Bogor. Indonesian Wood Research Society. Miller, R.B. 999, Characteristics and Availability of Commercially Important Woods. Wood Handbook. Forest Product Laboratory. Suryoatmono, B and Tjondro, A. 28. Lateral-torsional buckling of orthotropic rectangular section beams. Miyazaki, Japan. Proceedings of th World Conference on Timber Engineering. Thelandersspm. S and Larsen, H.J. 23. Timber Engineering. West Sussex, England. John Willey & Sons Ltd. Paper WS-8 9 of 9