Yang Ping and Mai Takemoto ¹

Abstract: This study deals with enhancement of a wooden school chair manufactured from curved sugi (Cryptomeria japonica D. Don) laminated veneer lumber by utilizing the veneer residues of furniture industries. To verify the mechanical performance of the chair, a computer simulation by using a two-dimensional finite element analysis incorporated with Hoffman failure criterion was conducted under the subjected load provided in Japanese Industrial Standard JIS S1021. Although the strength of the chair has been assured from the analytical results, several approaches of modification for the further improvement in mechanical performance of the chair were put forth in this study. Consequently, the effectiveness of each modification plan on the chair' s strength improvement was evaluated quantitatively based on the maximum value of Hoffman failure index obtained from the numerical analysis.

Key words: Eco-School, environmental education, wooden school chair, finite element analysis, Hoffman failure criterion.

INTRODUCTION

Aware of the influence of the fragility of resources and the natural environment along with human activities exerts on the environment, Japanese goveronment launched an Eco-School Pilot Model Project in 1997 (Ministry of Education, Culture, Sports, Science and Technology, 2002), where the Eco-School is clearly defined as: School facilities that are designed and constructed with due consideration given to the environment, operated in an environmentally responsible manner, and which can be utilized in environmental education. In addition to promoting the construction of school facilities that take the environment into consideration, an emphasis is also deserved to make use of the school facilities constructed thereby in environmental education. From the point of view to provide with the essential knowledge and basic skills of ecological literacy, and focus teachings on reduce, reuse and recycle, as well as that wood is widely recognized as an ecological friendly material. Compared to other inorganic, mineral or petroleum materials, wood is not only a renewable and sustainable resource that reduces environmental impact effectively in facilities construction, updating and dismantling, but also known as a userfriendly material with superiority of characteristics over visual, fragrant, auditory, tactile and mental stable.

This study describes a wooden school chair made from curved sugi (Cryptomeria japonica D. Don) laminated veneer lumber which is converted from veneer residues of furniture manufacturer. As shown in Figure 1, the interior design and the lightness are the most advantages of this type of wooden school chair. As an environmental educational material for sustainable production and effective utilization of forest resources, it will be helpful for users to gain a better understanding of human-environment relationships, to appreciate immediate surroundings, and weigh the consequences of human interventions into nature systems.

To elucidate the mechanical performance of the chair under the loading condition according to Japanese Standard (Industrial Standard JIS S1021 for school furniture, 2002), a computer simulation by using a twodimensional finite element analysis was performed assuming a linear elastic plane strain state under the framework of Hoffman failure criterion (Hoffman, 1967). Consequently, the effectiveness on the improvement of the chair' s strength performance was assessed based on the calculated result of maximum failure index for each modification approach.

ANALYTICAL METHOD

A two-dimensional finite element analysis was conducted to simulate the mechanical performance of the chair, which is composed of 20-ply curved laminated veneer lumber with a cross sectional area of 21 mm wide and 40 mm thick. Due to the symmetrical geometry of the chair, the analytical model is focused on the side view of the chair.

A four-node element in the plane strain state was used. The element mesh divisions of the separated back and support frames of the chair are as shown in Figure 2, including 1132 elements with 1278 nodes in the model of the back frame, and 1910 elements with 2171 nodes in that of the support frame, respectively.

The constraint and loading conditions for individual models of the back and support frames of the chair were determined based on their assembly using bolt connections, and the applied load in accordance with Japanese Industrial Standard JIS S1021. For the back frame, the displacement of two nodes at bolt joints were restrained both in x and y directions, and 140 N of load were subjected to the two nodes jointed with cross rails, individually. As for the support frame of the chair, the constraint of displacement in y direction is set for all nodes located at the bottom of the frame; only excluding the node at the left corner whose translations along x and y axes were both constrained. The load subjected to the two nodes at bolt joints of the support were determined based on the strength testing for school chairs provided in Japanese Industrial Standard JIS S1021 as represented in Figure 3, where an offset of 100 mm for the load (1300 N) must be kept from the back (Case A) or front edges (Case B) along the center line of seat, respectively.

The frames of the chair were assumed to behave orthotropic, and the mechanical properties (Handbook of Wood Industry, 1982) of sugi (Cryptomeria japonica D. Don) are tabulated in Table 1.

The strength performance of the chair is evaluated by using Hoffman failure criterion (Hoffman, 1967) as shown in the following equation.

Where, F is defined as a failure index for orthotropic material that exhibits definitely different behavior in tension and compression; the numerators? σx, σy and τ are normal stresses parallel and perpendicular to grain, and shearing stresses; the denominators X, Y and S are their corresponding allowable value; the subscript letters t and c are used for the distinction of allowable values in tension and compression. If F is greater than 1 (100%), that means the material has been beyond its ultimate load, and the probability for failure to occur is higher at high value of F. Hence, the load bearing capacity of chair could be predicted from the calculated result of Hoffman failure index.

All computations were performed by using MSC.Marc Mentat programs.

RESULTS AND DISCUSSION

Hoffman failure index distributed in the back frame of the chair is as illustrated in Figure 4, which concentrates at the curved portion with the maximum value of 32.3%. As shown in Figure 5, the failure index of the support frame was found to concentrate at the bolt joints of the assembly for both loading case A and loading case B. Accordingly, the vulnerable portions in the chair could be figured out. Based on the fact that the maximum value of failure index for case B (31.0%) was much greater than that of case A (18.3%), it is evident that loading case B was severer than loading case A for testing the strength of the school chair provided in Japanese Industrial Standard S1021.

Table 2 itemizes the Hoffman failure index for the individual components of the chair. Where, Fmax is the sum of fa, fb, fc, fd, fe and ff as shown in Equation 1.

Significantly different from the other components, fb accounted over 86% of the maximum value of failure index, Fmax, either for the back and support frames of the chair, that means the stress perpendicular to grain is a dominant factor to the strength performance of the chair manufactured from curved laminated veneer lumber. However, as all calculated maximum values of Hoffman failure indexes were lower than 100%, which ensures that all the components of the existing wooden school chair qualifies to the standard.

For the further improvement of chair' s performance, the effectiveness of the following approaches for the curved laminated veneer lumber were verified by computer simulation.
Modification I: Replace the three layers of sugi veneers, where the maximum failure index located at, by akamatsu (Pinus densiflora Sieb. et Zucc.) veneers for the back and support frames. Table 3 shows the mechanical properties (Handbook of Wood Industry, 1982) of akamatsu veneer, which counts at least 30% higher than those of sugi.

Modification II: Increase five layers (10 mm thick) of veneers for the back frame
Modification III: Widen the laminated veneer lumber in an additional 10 mm for the back frame

Figure 6 demonstrates the improvement quantitatively in the strength performance of the chair with comparison of the maximum failure index for each modification.

The reinforcement to replace the three layers of sugi veneers by akamatsu ones, would result in 15% and 18% improvement in strength for the chair' s back and support frames, respectively. Increasing five layers of veneers for the back frame would be estimated at 19% increase in strength for the chair' s back frame, if a slight change in design is tolerable. The highest improvement in strength records up to 28% for the modification by widen the laminated veneer lumber of the back frame, but one disadvantage to it is the obvious need to introduce a new high frequency heating press machine for manufacturing the wider laminated veneer lumber.

CONCLUSIONS

This study focuses on an effort of Eco-School promotion through the effective utilization of wood resources for school furniture as well as a material for the environmental education. The objective of this study is to assess load carrying capacity of a wooden school chair produced from curved laminated veneer lumber converted from veneer residues of furniture production. Based on the finite element analytical results of Hoffman failure indexes distributed in the components of the chair under the loading condition provided in Japanese Industrial Standard S1021, the mechanical performance of the chair has been ensured. For the further improvement, several modification approaches have also been discussed in this study. As a result, the modification of reinforcing the vulnerable layers in the back and support frames of the chair by substituting akamatsu veneers for sugi ones would be an available and effective modification approach. That way, the strength improvement would be reached at least 15% compared with the existing chair.

REFERENCES

Japanese Ministry of Education, Culture, Sports, Science and Technology: http://www.mext.go.jp/, 2002
Japanese Industrial Standard S1020, School furniture - Desks and chairs for general learning space, 2004
O. Hoffman, Journal of Composite Materials, Vol.1, pp.200-207, 1967
Forestry Experimental Station, Handbook of Wood Industry, Maruzen, pp.131-132, 1982

From < the Third International Symposium on Veneer Processing and Products >