Quality of Corner Joints of Beech Chairs under Load

This paper presents quality criteria for corner joints of beech chairs by comparison of break moments during static and dynamic testing of the most frequently used type of construction joints: round mortise and tenon. Laboratory joint testing using discursive construction methods showed a statistically supported value of the achieved results. The purpose of this paper is to investigate the possibility of shortening the testing procedure of fi nal products and evaluate the quality of fi nal products by segment testing of components in the design phase. The results showed that there is a signifi cant dependence between the Md/Ms coeffi cient and the number of testing cycles. This opens the possibility of a new, different approach to testing the strength of constructions, using methods for testing assemblies instead of entire fi nal products in accordance with the applicable standard working methods.


INTRODUCTION 1. UVOD
Research in the fi eld of sitting furniture durability was carried out by testing actual products subjected to dynamic loads, as prescribed by the valid standards.On 48 different chair models (Jeršić et al. 1978), the joint between the rear legs and side frame was determi-ned as a critical place.In the research (Dzigielewski et al. 1983), the infl uence of the frame position on the achieved number of cycles subjected to a static load of 40, 60 and 80 % was tested.In doing so, the authors mainly investigated the factors affecting construction strength.Due to the high cost of the experiment, the parts exposed to the heaviest loads were investigated, 63 (3) 205-210 (2012) by determining the interdependence between results of static and dynamic testing of samples of chair'corner joints.

MATERIJAL I METODE
Construction durability testing was carried out on 72 identical chair samples.Samples were grouped into seven classes defi ned by the effect of force moment of (38.43 Nm,47.7 Nm. 57,69 Nm,68.94 Nm,76.5 Nm,87.57 Nm and 96.84 Nm).
Test samples were chosen in line with previous studies of sitting furniture and their assemblies, and were determined by establishing the product critical element (Eckelman and Hincz, 1977;Smardzewski, 1998;Smadzewski and Papuga, 2004;Tkalec, 1985;Wilczynski and Warmbier, 2003), made up of the joint between the rear legs and chair frame, as shown in Figure 1.
Polyvinyl acetate glue Wegocoll HTF (Ehrengruber No. 117461 series 0243B 9K038) was used for experimental gluing of test samples.The glue and wood species (beech) represent constant parameters during the study.Due to the specifi c characteristics of wood as a material, the quality criteria of material and elements (Prekrat at al., 1998) comprising the joint were checked prior to gluing.These characteristics are presented in Tables 1 and 2.
Sample dimensions were adapted to the most frequently produced chairs in accordance with previous studies dealing with similar issues in order to obtain comparable results.
Any corner joint assembly consists of three constituents: legs, side and rear chair frame.Dried con-namely the rear legs assembly and chair frame.The investigations (Eckelman, 1997;Eckelman, 1989;Tkalec and Prekrat, 1997), were carried out under real conditions.Although computer modelling methods for determination of the quality of chairs or critical joints is not new (Eckelman and Fergus, 1976), this research method has been frequent applied in recent years, (Smardzewski and Papuga, 2004;Warmbier, 1999).There are a large number of papers investigating construction quality; however, only a few deal with the dependence between static and dynamic testing of construction strength.
This paper deals with wooden chairs as the most numerous type of construction in fi nal production, and which are especially signifi cant in terms of their production value and share of lumber and construction elements.
Evaluation and marketing of chairs on the domestic and global markets depends primarily on their quality.One of the quality factors is durability of the glued construction under static and dynamic load during use, as specifi ed by the Croatian sitting furniture standard HRN.D.E2.201.According to this standard, three samples of fi nal products must be taken from regular serial production.The high costs incurred in establishing negative results could be avoided through faster and simpler quality testing.Furthermore, the use of new unconventional design solutions and new materials has become quite common, thereby increasing the need for using discursive methods in furniture construction testing.
The aim of this paper is to determine the possibilities of shortening the quality testing procedure for chairs defi ned by the existing standards and predicting the degree of construction durability in the design phase.The assumption is that this aim could be achieved struction elements were sawn from beech, and then planed to the fi nal dimensions using a four-sided plane.
Cross-cut dimensions of chair legs were 42 x 28 mm, and the dimensions of the chair frame were 50 x 20 mm.Lengthways holes were made on the leg elements, and round-head mortises on the frames.The elements were glued into a system as shown in Figure 1.Upon applying the glue on both mortise and tenon adhesion surfaces, the samples were tightened by a force of 3900 N for four minutes in accordance with the manufacturer's recommendation and then air conditioned at a temperature of 19.2 °C and relative humidity of 52.2 %.The average moisture content of samples was controlled using a calibrated electro-resistant moisture metre, and ranged from 9.56 and 11.65 %.
Testing of dynamic strength is carried out on constructions subjected to varying dynamic loads, which is the reason why such constructions are considerably less strong then those subjected to a uniform load.In Croatia the procedure for testing sitting furniture (stools, chairs and semi-armchairs) is standardised by the standard HRN.D.E2.201.which is quite similar as EN 1728 and The effect of alternating load on the horizontal frame of the chair seat, i.e. on the arm of the presented model is shown in Figure 4.According to this regime, these chair assemblies are subjected to an alternating load every 2.5 seconds.
For the purpose of dynamic strength testing, a pneumatic device was produced with the appropriate instruments for adjusting force and number of impulses per unit of time (Figure 5).Testing was carried out at seven levels of operating moments ranked accordingly.All seven groups subjected to testing of specifi c force moments defi ned in Table 4. Due to the effect of the pulling strength, the occurring deformation or deviation was designated as f 1 and the deformation caused by pressure force or deviation was designated as f 2 (Figure 3).
The break moment is obtained by multiplying break force, arm length and a cosine angle of 19.68 o .The break moment results are expressed in Nm.The expression for calculating the break moment is as follows: (1)

REZULTATI
In order to apply the Md/Ms coeffi cient, a comparison was made of the results of static testing of the same samples used in (Prekrat at al. 2004).Table 3 shows the results of static break moment testing stated in the above paper for the samples corresponding to those used in this study.
As in Prekrat at al. (2004), where the break moment distribution was tested, in this paper testing was also carried out of the normality of distribution of the achieved number of cycles for all seven groups subjected to testing of specifi c force moments defi ned in Table 4.
The Kolmogorov-Smirnov test showed that the distribution for the analysed joint was not normally distributed (p<0.05).The type of error I of 5 % was considered statistically signifi cant.

DISKUSIJA
Many authors have investigated the infl uence of construction factors of different corner joints used in chair production, and a considerable dependence between gluing strength and the adhesion surface has been established (Wang and Yuang 1994).There are also signifi cant studies that determine the position of corner joints in testing the effects of force (Warmbier 1999).The greatest problem in comparing results is incomplete data on samples or the material they are made from.Joint strength depends on specifi c sample mass (Wang and Yuang, 1994), and variation was reported in large data dispersion of volume mass of beech wood (Fagus Sylvatica L.) from different stands (Tkalec, 1985).(Tkalec, 1985) reported the infl uence of seat and pressing extent of mortise not stated in the papers of other authors.Furthermore, the infl uence of technological factors is also signifi cant for comparing results, as seen in (Biniek and Smardzewski 1987), where the impact of moisture on joint strength was examined.In the study (Dziegielewski, 1991), dependence between the manner of glue application on the adhesion surfaces and joint strength is outlined as a highly signifi cant technological factor.Furthermore, it is necessary to give a detailed defi nition of the material and design in standardising the forces of static testing that correspond to a specifi c number of dynamic testing cycles.
In order to determine the interdependence between static and dynamic testing methods, a previous study (Prekrat at al., 2004) was used to calculate the coeffi cient equal to the quotient of dynamic and static moment of force.Due to insuffi ciently defi ned material parameters, there are diffi culties in comparing the results with the results listed in the literature.For this reason, the comparison was made on the basis of the said research, whose samples were made under the same conditions and from the same material.The coeffi cient was calculated for each level of moment of force.The dependence between the results of static and dynamic testing methods was determined by the correlation between the Md/Ms coeffi cient and the number of achieved cycles for each of the seven different values of moment of force.Table 5 presents the moment values to which the sample was subjected during testing, static and dynamic moments of force, number of achieved cycles until breaking and the calculated coeffi cient.The correlation is shown in Figure 6.
The high correlation coeffi cient (R 2 =0.9167) indicates a high dependence between the static and dynamic testing of samples.This dependence indicates the possibility of shortening the long dynamic testing prescribed under the current standards.Figure 6 shows the dependence curve of coeffi cient k ds and the number of achieved cycles until breakage.

ZAKLJUČAK
Based on the corner joints tested in this paper, the following can be concluded: a signifi cant correlation was established between the results of static and dynamic testing of joints, using the expressed Md/Ms coeffi cient and the number of cycles of joints dynamically tested in this paper and in comparison with the results of previous studies; the results are applicable to further research in in-novating design solutions and in practical application in testing chair quality;  there are other possibilities in the approach to che-cking quality through the partial testing of key assemblies for the durability of sitting furniture; this procedure can considerably contribute to suc-cessful planning and manufacturing of industrial products.

Figure 6
Figure 6 Dependence of the Md/Ms coeffi cent and cycle number for sample Slika 6. Ovisnost koefi cijenta Md/Ms o broju ciklusa za skupinu uzoraka

Table 3
Descriptive statistics of static break moment data (Nm)