Strength and stiffness of 3D-printed connectors compared with the wooden mortise and tenon joints for chairs

Figures & data

Figure 1. Proposed chair construction and L-shaped mortise-and-tenon joint made with 3D-printed connectors. The dimensions of the chair were as follows: seat height 435 mm, seat width 420 mm, total height 762 mm, angle of backrest 97°. The cross section of the legs was 35 × 35 mm and that of the rails 30 × 50 mm.

Figure 2. 3D-printed connectors A, B, C, D with dimensions.

Figure 3. Joint testing: (a) the diagram of joint loading, (b) working diagram of joint strength testing.

Figure 4. The physical model and mesh of the joints: (a) connector - type 1 (A- without inner wall), (b) reinforced connector – type 2 (C – without inner wall).

Table 1. Elastic properties of beech wood (Smardzewski 2008).

Modulus of elasticity (GPa)			Modulus of rigidity (GPa)			Poisson's ratio
EL	ER	ET	GLR	GLT	GRT	νLR	νLT	νRT	νTR	νRL	νTL
13.969	2.284	1.160	1.645	1.082	0.471	0.450	0.510	0.750	0.360	0.075	0.044

Figure 5. Average failure load (N) for the various 3D-printed connectors and wood mortise-and-tenon joints.

Figure 6. Typical failures for the 3D-printed connector (connection between front leg and side rail): connector type A (top three photos), vertical sections of connector type A (bottom left) and vertical sections of connector type B (bottom right).

Figure 7. Deformation of joints obtained by numerical calculation: (a) connector A – I mod (left) and III mod (right), (b) (a) connector C – I mod (left) and III mod (right).

Figure 8. Distribution of von Mises stress of the first type of connectors: (a) connector A – I mod (left) and III mod (right), (b) (a) connector B – I mod (left) and III mod (right).

Figure 9. Distribution of von Mises stress of the second type of connectors: (a) connector C – I mod (left) and III mod (right), (b) (a) connector D – I mod (left) and III mod (right).

Table 2. Normal stress ${\sigma }_{\mathrm{x}}$ in the cross section of the rail at a distance of 80 mm from the applied load.

Connector	$F$, N	Normal stress ${\sigma }_x$, MPa							$F_{max}$, N	Normal stress ${\sigma }_x$, MPa
		I	II		III*		IV*	V*		I	II		III*		IV*	V*
			ABS	wood	wood	ABS					ABS	wood	wood	ABS
A	400	0.34	0.30	3.88	3.88	0.30	0.34	–	905	0.77	0.68	8.78	8.78	0.68	0.77	–
B									741	0.63	0.56	7.19	7.19	0.56	0.63	–
C	400	0.33	0.29	3.77	3.67	0.28	–	0.36	861	0.71	0.63	8.12	7.91	0.61	–	0.78
D									790	0.65	0.57	7.45	7.26	0.56	–	0.71

* Negative normal stress

Figure 10. Cross section of a composite part of the joint (length $a$) and distribution of normal stress: (a) first type of connector (connectors A and B), (b) second type of connector (connectors C, D).

Figure 11. Distribution of normal stress ${\sigma }_x$ of the first type connectors: (a) III mod of connector A – connector (left) and wooden rail (right), (b) (a) III mod of connector B – connector (left) and wooden rail (right).

Figure 12. Distribution of normal stress ${\sigma }_x$ of the second type of connectors (reinforced): (a) III mod of connector C – connector (left) and wooden rail (right), (b) (a) III mod of connector D – connector (left) and wooden rail (right).

Figure 13. Stiffness coefficient K of the joints with connectors.

Table 3. The experimental and numerical stiffness coefficient K of the joints with connectors.

Connector	Experimental results, N/mm	Numerical results, N/mm			exp./I mod	exp./II mod	exp./III mod
		I model	II model	III model
A	172.0	683.0	654.6	492.5	0.25	0.26	0.35
B	157.0	664.6	686.1	532.1	0.24	0.23	0.30
C	187.0	708.6	675.3	515.6	0.26	0.28	0.36
D	151.0	696.0	646.2	510.5	0.22	0.23	0.30

Table 4. The ratios of the stiffness coefficients K of the joints with four different connectors.

Ratio of stiffness coefficients for the joints with different connectors	Experimental results	Numerical results
		I model	II model	III model
A/B	1.10	1.03	0.95	0.93
C/D	1.24	1.02	1.05	1.01
A/C	0.92	0.96	0.97	0.96
B/D	1.04	0.95	1.06	1.04

Figure 14. From left to right: seat loading test, seat and back loading test, front edge forward loading test.

Smardzewski, J. (2008) Effect of wood species and glue type on contact stresses in a mortise and tenon joint. Journal of Mechanical Engineering Science, 222(12), 2293–2299. doi:10.1243/09544062JMES1084

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