simulation of residual stress in curved glulam beams - Engineered ...

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e found that larger the pressure and smaller radius of curvature of the neutral axis give rise larger residual stress perpendicular to grain. The effect of radius of curvature is more significant than that of pressure on the stress perpendicular to grain. For example, under the condition of µ=0.1, when p=0.5MPa, R=5.0m, the stress is 0.16MPa; while when p=0.5MPa, R=4.0m, the stress is 0.18MPa and when p=0.75MPa, R=5.0m, stress is 0.19MPa. Residual stress perpendicular to grain (MPa) 0.4 0.3 0.2 0.1 p=0.5MPa, R=3.0m p=1.0MPa, R=3.0m p=0.75MPa, R=3.0m p=0.5MPa, R=4.0m p=0.75MPa, R=4.0m p=1.0MPa, R=4.0m 0.0 p=0.5MPa, R=5.0m p=1.0MPa, R=5.0m p=0.75MPa, R=5.0m 0.0 0.1 0.2 0.3 0.4 0.5 Coefficient of friction Figure 5: Residual stress perpendicular to grain of beam (cross-section: 90mm×180mm; lamina: 90mm×15mm) Figure 6 shows the effect of different parameters on the longitudinal residual stress in curved Glulam beams. Only the radius of curvature affects the longitudinal residual stress in a curved beam. The smaller the radius of curvature of the neutral axis, the more severe the bending of the laminas and the larger the longitudinal stress in a lamina. While the coefficient of friction and the pressure pose little effect on the longitudinal stress. When radius of curvature R=5.0m, the longitudinal stress is about 13.2MPa; while when R=4.0m and 3.0m, the stress are about 16.5MPa and 22.2MPa, respectively. Longitudinal residual stress (MPa) 21 18 15 p=0.5MPa, R=3.0m p=0.75MPa, R=3.0m p=1.0MPa, R=3.0m p=0.5MPa, R=4.0m p=0.75MPa, R=4.0m p=1.0MPa, R=4.0m p=0.5MPa, R=5.0m p=0.75MPa, R=5.0m p=1.0MPa, R=5.0m 12 0.0 0.1 0.2 0.3 0.4 0.5 Coefficient of friction Figure 6: Longitudinal residual stress (cross-section: 90mm×180mm; lamina: 90mm×15mm) The effect of the parameters on the rebounding deformation of curved Glulam beams is shown in Figure 7. Parameters listed in Table 1 all affect the rebounding deformation. The smaller the coefficient of friction in Stage 1, the more the slippage and the less the composite action, thus the rebounding deformation is smaller. A smaller radius of curvature and the larger pressure mean more severe bending of lamina, resulting in larger rebounding deformation. Rebounding deflection (mm) 18 15 12 9 6 3 p=0.5MPa, R=3.0m p=0.75MPa, R=3.0m p=1.0MPa, R=3.0m p=0.5MPa, R=4.0m p=0.75MPa, R=4.0m p=1.0MPa, R=4.0m p=0.5MPa, R=5.0m p=0.75MPa, R=5.0m p=1.0MPa, R=5.0m 0 0.0 0.1 0.2 0.3 0.4 0.5 Coefficient of friction Figure 7: Rebounding deflection of curved Glulam beam (cross-section: 90mm×180mm; lamina: 90mm×15mm) The effect of thickness of lamina on the residual stress of curved Glulam beams is shown in Figure 8. Figure 8(a) shows the residual stress perpendicular to grain versus the thickness of lamina and Figure 8(b) shows the longitudinal residual stress versus the thickness of lamina. The residual stress during manufacturing is affected by the thickness of lamina. Larger stress either perpendicular to grain or longitudinal is formed in thicker laminas. It can be found that thick laminas are actually not suitable for manufacturing curved beam due to the large residual stress that could exceed the strength of wood. Residual stress perpendicular to grain (MPa) 1.0 0.8 0.6 0.4 0.2 R=5.0m R=4.0m R=3.0m 10 20 30 40 50 Thickness of lamina (mm) (a) The effect of thickness of lamina on the residual stress perpendicular to grain
Longitudinal residual stress (MPa) 80 60 40 20 R=5.0m R=4.0m R=3.0m 0 10 20 30 40 50 Thickness of lamina (mm) (b) The effect of thickness of lamina on the longitudinal residual stress Figure 8: The effect of thickness of lamina on the residual stress (p=0.5MPa, µ=0.1) 5 THE FORMULA FOR LONGITUDINAL RESIDUAL STRESS For a lamina in a curved member under pure bending, the maximum bending stress is Et σ = h−t 2( R − ) 2 (2) where, E is the MOE of the lamina; R is the radius of curvature of the neutral axis of beam; h is the depth of beam; t is the thickness of lamina. In a curved Glulam beam, the action of glueline, the normal stress and shear stress, induce bending of the lamina, which is different from pure bending. The bending stress can be expressed by Eq. (3) by introducing an adjustment factor K . Et σ max = K h−t 2( R − ) 2 (3) Through the parametric study, the adjustment factor is obtained as K =0.76, by regression of the maximum residual longitudinal stress with different radii of curvature and thicknesses of lamina. For different thicknesses of lamina commonly used in curved Glulam and different radii of curvature, the longitudinal residual stress from the FE modelling and Eq. (3) are given in Figure 9, which shows good correlation of the Equation and the numerical method. The longitudinal residual stress can thus be evaluated by Eq. (3). Longitudinal residual stress (MPa) 50 40 30 20 (R=5.0m) FE results Eq.(3) results (R=4.0m) FE results Eq.(3) results (R=3.0m) FE results Eq.(3) results 10 10 15 20 25 30 35 Thickness of lamina (mm) Figure 9: The longitudinal residual stress regressed by Eq. (3) 6 CONCLUSIONS A two-dimensional FE model was developed to simulate the residual stress and rebounding deformation of curved Glulam beams during manufacture. The residual stress perpendicular to grain is generally compressive except for some tension in the laminas around the end of curved beams. Quite significant longitudinal residual stress exists in the beam, and the longitudinal residual stress in the mid-length is larger than that at the end of the length. Each lamina has the similar stress distribution due to bending. The longitudinal residual stress can be evaluated by Eq. (3). The most important influencing factors on the longitudinal residual stress are the radius of curvature of the neutral axis and the thickness of lamina. As for the residual stress perpendicular to grain and the rebounding deformation, both are closely related to the radius of curvature, pressure, the time interval between adhesive applying and pressure applying and the thickness of lamina. In manufacturing the curved beams, smaller pressure, smaller thickness of lamina and quicker manufacturing lead to smaller residual stresses and rebounding deformation. Due to the behaviour of creep and relaxation of wood and adhesive, the residual stress from manufacturing will decrease. This is worth investigating in future study. ACKNOWLEDGEMENTS The writers acknowledge with gratitude the financial support of this study from the National Natural Science Foundation of China designated 50878067. REFERENCES [1] M. Gong, L. Li, Y. H. Chui, K. Li and N. Yuan.: Modelling of recovery of residual stress in densified wood. In 10th World Conference on Timber Engineering, 2008. [2] R. A. Shenoi and W. Wang. Through-thickness stresses in curved composite laminates and sandwich beams. Composites Science and Technology, 61:1501-1512, 2001. [3] L. De Lorenzis, J. G. Teng and L. Zhang. Interfacial stresses in curved members bonded with a thin plate.
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