Résumé Le présent travail repose sur la détermination statistique de la rigidité en flexion de deux essences camerounaises dont
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| STATISTICAL DETERMINATION OF THE RIGIDITY IN FLEXION OF SOME CAMEROONIAN HARDWOODS. Pierre Kisito TALLA1*, J.C. CHEDJOU1, H.B. FOTSING1, ANJAH G. M2., Amos FOUDJET3 , UTAH4, Daniel GUITARD5 1 : Laboratoire de Physique, Université de Dschang, B.P. 67 Dschang, Cameroun. Tel (237) 45 15 97 Email : tapikisito@yahoo.fr 2 : Département de Biologie Végétale, Université de Dschang, B.P. 67 Dschang, Cameroun. 3 : CRESA Forêt-bois, Université de Dschang, B.P. 8390 Yaoundé, Cameroun. 4 : Department of Physics, University of Jos 5 : Laboratoire de Rhéologie du Bois de Bordeaux, B.P. 10F-33610 CESRAS GAZINET France. * Author to whom correspondence should be sent Abstract This work deals with the statistical study of the rigidity in flexion of some Cameroonian hardwoods. It is based on the statistical determination of the rigidity of the concerned woods from a series of bending measurements. Two Cameroonian hardwoods were used in the study, namely Moabi (Chlorophora excelsa) and Iroko (Milicia excelsa). 22 samples of each wood were selected. The samples had the following dimensions 340 cm x 2 cm x 2 cm as recommended by the norm NF B51 008. They were tested under bending. From the graph of load against displacement we determined the rigidity in flexion at different moisture rate, from which we calculated the Young modulus. Using the linear regression (R = 0.73 for Moabi and R= 0.76 for Iroko. We realised that there is a strong correlation between the Young modulus and the rate of moisture for each wood. RésuméLe présent travail repose sur la détermination statistique de la rigidité en flexion de deux essences camerounaises dont : Moabi (Chlorophora excelsa) et Iroko (Milicia excelsa) . A cet effet, 22 éprouvettes de chaque essence ont été testées en flexion. Chaque éprouvette avait pour dimension 34 cm x 2 cm x 2 cm, conformément à la norme NF B51 008. A partir du graphe de la charge en fonction du déplacement, nous avons, à chaque taux d’humidité, déterminé la rigidité en flexion correspondante. La méthode des moindres carrés est ensuite utilisée pour déterminer la relation entre la rigidité en flexion et le taux d’humidité. Utilisant la relation donnant la rigidité en flexion en fonction du module d’Young, nous avons établi une relation entre le module d’Young et le taux d’humidité. Les coefficients de corrélation qui en découlent (R = 0.73 pour le Moabi et R = 0.76 pour l’Iroko) montrent qu’il existe une corrélation forte entre le module d’Young et le taux d’humidité pour les deux essences concernées. Keywords: Moabi (Chlorophora excelsa)Iroko (Milicia excelsa) Bending Rigidity in flexion Guitard law on the rigidity in flexion. Introduction Wood is an hygroscopic material, that is, it retains some water in each state of equilibrium. Consequently, the mechanic constants of a wood is a function of the quantity of water present in its structure. It is therefore important when a wood is used to predict its behaviour at given moisture so as to avoid unwanted deformation due to the change of temperature. The aim of this work is an attempt to do such a prediction for two Cameroonian hardwoods, that is Moabi (Chlorophora excelsa) and Iroko (Milicia excelsa). Development The flexural rigidity of a wood can be approximate in many ways depending on the accuracy expected. So to speak, a gross approximation of the rigidity under flexion is given by the formula [2]:  (1)where, R is the rigidity under flexion, L the length of the sample, h its thickness, b its width and EL its Young modulus. A more accurate approximation based on variability principle show that, in bending experiment, where the load is normal to the grain, the deflexion can be approximated by [5]  (2)relations in which u is the displacement, h = 2 the thickness of the sample, L its length, EL the young modulus, LR and RL the corresponding poisson’s ratio. Thus the flexural rigidity is given by the relation  (3)The rate of moisture of a sample is the ratio  (4)where m is the actual mass of the sample and m0 its anhydrous mass, that is the mass of the sample when it stops loosing water in an oven at 103°C. Experimental set up 22 samples of each wood were weighed and introduced in an oven at constant temperature t = 103°C until the mass of each sample became constant. This constant mass m0 is the anhydrous mass. The samples were then removed from the oven so as to regain humidity. During this last process, they were weighed periodically in order to have their actual mass before testing under flexion. Samples had the dimension 34 cm x 2 cm x 2 cm as recommended by the norm NF B51 008 [1]. The experiments were carry out in “Laboratoire d’Analyse des Structures” in the Yaounde Polytechnic High School. Using these tests we determined from the deflexion-force curve the flexural rigidity. The results obtained are listed in tables 1 and 2. We then used the linear regression method to determine the best slope as indicated in figures 1 and 2. The related coefficients of regression are 0.73 for Moabi and 0.76 for Iroko. Those values indicate that there is a strong correlation between the flexural rigidity and the moisture. Thus the probable relation linking the two quantities are:
Table 1: Flexural rigidity as a function of moisture. The case of Moabi.
Table 1: Flexural rigidity as a function of moisture. The case of Iroko.
 Figure 1: Flexural rigidity against moisture. The case of Moabi.  Figure 2: Flexural rigidity against moisture. The case of Iroko. ConclusionFrom our analysis, it appears that there is a correlation between the flexural rigidity and the moisture rate for the different woods analysed in this study. The data obtained and the linear regression techniques used in this work show that the relation between the Young modulus and the moisture rate can be approached with a linear relation and with a coefficient of regression greater than 0.7 which indicates a strong correlation between the two quantities. References1: C.C. Gerhards : Effect of the moisture content and temperature on the mechanical properties of wood. Wood and Fiber 14 (1982) 1, pp. 4-36. 2: Duvaut G., Mécanique des milieux continus, Paris, Masson, 1990. 3 : Guitard D., Mécanique du matériau bois et composites, Cepadues, Collection Nabla, 1987. 4 : Lemaître J. et Chaboche J.L., Mécanique des matériaux solides, Paris, Dunod, 1985. 5 : J.A. Mukam Fotsing and A. Foudjet, Size effect of two Cameroonian hardwoods in compression and bendind parralel to the grain, Holzforschung 49(1995) pp 376-378. 6: Talla P. K., Contribution à l’élaboration d’une théorie asymptotique à une dimension du comportement en flexion des poutres multicouches à phases orthotropes (application à quelques essences du Cameroun), Thèse troisième cycle, UY1, 1994. 7 : Talla P. K., A. Foudjet, D. Guitard, The one dimensional, linear orthotropic beams, accepted for pulication in African Journal of Natural Science, Jos, 2000. 8: Charlot G., Statistique appliquée à l’exploitation des mesures, Paris, Masson, 1986. 9 : Destuynder P., Plaques minces en élasticité linéaire, Paris, Masson, 1986. 10 : Raoult A., Analyse mathématique de quelques modèles de plaques et poutres élastiques ou élastoplastiques, Université Pierre et Marie Curie, 1988. |
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