木材由於具有收縮異方性及其它性質如節、未成熟材、年輪的曲率半徑和螺旋木理等，會因吸脫濕而變形。平衡結構的合板會因為含水率分佈不均而產生翹曲。本研究的目的在探討合板中的單板，因含水率差異所引起的翹曲，並利用層合板理論分析層合板的中心翹曲，除改變含水率的變化外，也改變厚度、波松比，層板方向以及彈性模數 ( MOE ) 等對合板翹曲的影響。實測方面，將各層單板泡水使含水率達到 30% 以上，使其含水率達到飽和後，將單板依不同的木理方向以非水溶性的膠予以膠合成合板，並置於三種不同相對濕度的環境下，進行調濕後，觀察並量測其翹曲變化。
數值分析結果顯示，就含水率變化的影響，層合板的中心翹曲值會隨著各層之間含水率差的增加而增加；就層合板厚度增加的影響，層合板的中心翹曲值會隨著板厚度的增加而減小；就表層或底層單板MOE 增加的影響，發現層合板的中心翹曲值同樣會隨著 MOE 的增加而增加；就波松比改變的影響，層合板的中心翹曲值會隨著表層單板波松比的增減而增減；就表層單板方向改變的影響，層合板的中心翹曲值會以 135 度時為最高，而以 45 度時為最小。
實驗結果顯示當四塊單板均泡水達飽和後，將其膠合好之合板置於三種不同相對濕度下所測結果發現，層合板的中心翹曲值，其最終平衡含水率為 12.31 % 時的翹曲為最低；而在平衡含水率為 7.38 % 時有最高翹曲量。

Due to anisotropic shrinkage and other characteristics such as knot, juvenile wood, annual ring curvature, spiral grain angle, and so on, wood warps when its moisture content change. Plywood, structurally balanced, warps mainly because of non-uniform moisture content distribution. The objectives of this study is to analyze wood hygroscopic warping with the laminated plate theory to calculate the effect of variations in moisture content, plywood thickness, Poisson’s ratio, grain orientation and modulus of elasticity (MOE) on warping at the plywood center. Regarding to the experimental test, plies were glued according to their grain orientation with epoxy resin after plies were conditioned to the set moisture content level, placed in three chambers with different relative humidity, and the warp that ensued was measured.
The results were shown in the following.
The numerical analysis showed the central plywood warping increased with the increase of moisture content difference, the top layer MOE, the bottom layer MOE, and the Poisson’s ratio. The central plywood warping decreased with the increase of thickness of the plywood. The central plywood warping is the highest at 135o, and the lowest at 45o, when only the grain orientation of the face ply changed from 0 o to 180 o.
The experimental data showed that central plywood warping was minimum value and maximum value at the 12.31% and 7.38% equilibrium moisture content of plywood, respectively, when the four plies were saturated with water, glued together and placed in three chambers with different relative humidity conditions.

目 次
I.前言.....................................................1
（Ⅰ）合板.................................................1
（Ⅱ）影響合板翹曲之因子...................................4
（Ⅲ）研究動機與目的.......................................7
II.合板翹曲的層合板理論分析................................8
（Ⅰ）引言.................................................8
（Ⅱ）一般層合板的剛度....................................11
（Ⅲ）對稱層合板的彎曲剛度................................22
（Ⅳ）正交對稱層合板的彎曲剛度............................28
（Ⅴ）單板的濕熱變形......................................32
（Ⅵ）層合板的濕熱應變....................................32
（Ⅶ）層合板的中心翹曲....................................37
III..材料與方法...........................................38
（Ⅰ）材料................................................38
一、單板.............................................38
二、膠合劑...........................................38
（Ⅱ）方法................................................38
一、合板製作及翹曲量測 ..............................38
二、層合板理論探討合板翹曲的因子.....................39
(一) 單板含水率的變化............................40
(二) 環境的相對濕度..............................41
(三) 板厚度的變化................................42
(四) 彈性模數....................................43
(五) 波松比......................................43
(六) 上層層積方向................................44
（Ⅲ）層合板理論分析步驟..................................46
IV.結果與討論.............................................50
（Ⅰ）層合板理論的數值分析................................50
一、含水率變化之影響.................................50
二、板厚度之影響.....................................51
三、彈性模數之影響...................................53
四、波松比之影響.....................................56
五、上層層積方向之影響...............................57
（Ⅱ）實測值..............................................59
V.結論....................................................61
VI.參考文獻...............................................63
附錄......................................................66

表 目 次
表1 對稱層合板的標記......................................11
Table 1 code of a symmetric laminate.
表2 對稱層合板的加權因子表................................27
Table 2 Weighting factors for the flexural modulus of a symmetric laminate.
表3 雲杉的材料性質 .......................................40
Table 3 Material properties of Black spruce.
表4 單板之含水率..........................................41
Table 4 The moisture contents of veneers
表5 合板在三種不同環境下的平衡含水率......................42
Table 5 The EMC of plywood in three different environments.
表6 試驗條件..............................................45
Table 6 Experimental conditions
表7 軸上至偏軸的應力轉換公式..............................47
Table 7 Transformation of stiffness from on-axis to of axis ply.
表8 合板於三種不同平衡含水率下之中心翹曲..................51
Table 8 The central warping of plywood in three different equilibrium moisture content.
表9 厚度對翹曲的影響......................................52
Table 9 Thickness effect on warp.
表10 改變上或下層MOE值之中心翹曲..........................53
Table 10 The central warping when only MOE values of top and bottom ply change.
表11上層 MOE 對彎曲力矩、彎曲剛度係數和曲率的影響.........55
Table 11 Effect of MOE of the top on moment resultant, stiffness coefficient and curvature.
表12 波松比對翹曲的影響...................................56
Table 12 Effect of Poisson’s ratio on warp.
表13 上層層積方向對翹曲的影響.............................58
Table 13 Effect of the top ply orientation on warp.
表14 放射松合板於三種不同平衡含水率下之翹曲...............59
Table 14 The warping of Radiata pine plywood in three different equilibrium moisture content.

圖 目 次
圖1 平衡的層積構造：(a)層積方向，(b)對稱平面...............2
Fig. 1 Balanced laminated construction：(a) orientation of laminate , (b) plane of symmetry.
圖2 平衡的合板結構：(a)奇數層合板，(b)偶數層合板...........2
Fig. 2 Balanced plywood construction：(a) odd number of laminate , (b) even number of laminate.
圖3 不同結構的合板斷面.....................................3
Fig. 3 The plywood sections of different construction.
圖4 各種板的翹曲...........................................5
Fig. 4 A variety of wood warpings.
圖5 層合板的標示圖：(a)層合板,(b)奇數層合板,(c)偶數層合板.........................................................8
Fig. 5 Nomenclatures of laminates : (a) laminate, (b) odd number of laminate, (c) even number of laminate.
圖6 對稱層合板的鋪設順序：(a) 典型的鋪設順序,(b) z軸的層積方向.........................................................9
Fig. 6 Stacking sequence of a symmetric laminate： (a) Typical stacking sequence of a symmetric laminate, (b) Ply orientations as a function of z.
圖7 單元體上的應力 .......................................15
Fig. 7 Stresses on the unit.
圖8 單元體上的內力 .......................................15
Fig. 8 Forces on the unit.
圖9 4層對稱層合板.........................................28
Fig. 9 A Four-ply symmetric laminate.
圖10 濕熱引起殘餘應變和殘餘應力的機理：(a)初始無應力狀態；(b)假設無約束的最終狀態；(c)實際的最終狀態................33
Fig. 10 Build-up of residual stresses after hygrothermal behavior：(a) initial, stress free state, (b) hypothetical unconstrained final state, (c) actual final state.
圖11 合板翹曲的量測.......................................39
Fig. 11 The measurement of plywood warping.
圖12 厚度對翹曲的影響.....................................52
Fig. 12 Thickness effect on warp.
圖13 上層MOE改變的中心翹曲................................54
Fig. 13 The central warping when only MOE values of the top change.
圖14 下層MOE改變的中心翹曲................................54
Fig. 14 The central warping when only MOE values of the bottom change.
圖15 波松比對翹曲的影響...................................57
Fig. 15 Effect of Poisson’s ratio on warp.
圖16 上層層積方向對翹曲的影響.............................58
Fig. 16 Effect of the top ply orientation on warp.
圖17 放射松合板於三種平衡含水率下之翹曲...................60
Fig. 17 The warping of Radiata pine plywood in three different equilibrium moisture content.

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