不同半橢圓形栓孔對木材拉伸構件應力集中之影響

Abstract

一般而言，木材在平行木理方向的拉伸強度（Tensile strength）比壓縮強度（Compression strength）較佳。而因為木材用於連接件時，易因金屬連接件或扣件形成損傷，應力集中（Stress concentration）也多半發生於木材和金屬之間的接合處。這就是為何木材的拉伸能力在接合件無法明顯發揮其優勢，在結構設計時，拉伸設計強度時常很接近甚至比壓縮強度還要來得低。 在過去的研究中，許多前人應用有限元素法（Finite element analysis, FEA）進行電腦分析，模擬木材在受力時的應力分布情況，甚至破壞模式。但這些模擬研究中多將木材設定為等方性（Isotropic）均質材料，然而木材事實上是異方性（Anisotropic）材料，更進一步說，是正交性（Orthotropic）材料，因此模擬結果和事實仍有些差距。 本研究中主要應用有限元素法，透過軟體Solid Works2008進行電腦模擬，研究新的銷栓連結方法，並探討如何降低應力集中；同時亦進行實體試驗。試驗材料，板材為花旗松（Pseudotsuga menziesii）；金屬扣件則選用一般鋼材。模擬過程，金屬扣件設定為均質材料，而木材則具備三方向相異物理性質的正交性材料。卡氏座標（Cartesian coordinate）中，x方向給定於平行木理方向（縱向，Longitudinal direction），而徑向（Radial direction）及弦向（Tangential direction） 則分別指定為y、z方向。 板材長250 mm，寬60 mm，厚12 mm。栓孔中心位於板材正中央，孔右半側為固定半徑a = 9.5 mm之半圓孔，孔左半側則隨著模型的改變，而有不同比例軸長b之半橢圓。定義半橢圓兩軸長比例R = b/a = b/9.5 。自R = 0.75起，每隔0.25建一模型，並進行模擬分析。金屬扣件和栓孔左半側之半橢圓形狀相同，栓孔右半側留空，為銷施加荷重處。 外力荷重為980.67 N（100 kgf）的集中力，向左施加在金屬扣件上。板材右側端部為固定端，不可發生位移（Displacement）及形變（Deformation）。木材和板材間無塗布任何膠合劑，故施力後，允許元件彼此間發生間隙；摩擦力忽略不計。 比較異方性材料模擬結果，和以往均質材料所模擬的結果，其應力分布有明顯的差異。但應力集中仍存在，且發生處和均質材料及理論相近。 為了提高木材的有效利用，必需注意木材所擁有良好拉伸強度的特性。但往往因應力集中使得該特性效益降低。雖然傳統圓型栓孔對於其他大部分形狀，能降低不少應力集中，並認為圓型為目前較佳且使應力集中最小的形狀；而本研究發現，調整R值確實能改變應力分布的情況，並使應力極大值再降低，最大拉伸應力亦可減少。模擬結果顯示，當R值約為1.2∼1.25時有最佳效果。 實體試驗，利用應變規（Strain guage）及萬能強度試驗機（Universal testing machine）進行拉伸試驗，透過撰寫程式量測並處理應變（Strain）訊號。初步顯示，在應力集中發生的位置，該應變變化趨勢大致和電腦模擬相似，在荷重一定下，栓孔兩側拉伸處隨R值上升而應變下降，壓縮處則隨R值上升而應變絕對值上降。然而因實際木材的節、木理等缺點，及模型尺寸、應變規受破壞等問題，使得部分訊號並非精確。

Generally, the tensile strength of wood is larger than that of compression strength in longitudinal direction. Because wood tissue could be damaged by metal connector or fastener, stress concentration always occurred at wood near the interface between wood and metal. This is the reason why the tensile strength value is almost close to or even lower than compression value in structural design. In previous reviews, pioneers usually solved many problems by finite element analysis (FEA) simulation and assumed that the wood was isotropic. However, the wood is a kind of anisotropic material rather than isotropic. In fact, it is orthotropic. In this study, a software called Solid Works2008 was used to find the results by FEA. The computer simulation is a tool that an assumed force can apply on a new type of bolt connection in order to reduce stress concentration. Douglas fir (Pseudotsuga menziesii) was selected as the wood member. The material of the bolt was common steel. In this computer simulation, steel was set as an isotropic material. In Cartesian coordinate, the x-direction was assumed in longitudinal direction of the wood. The y- and z-direction represented radial and tangential directions of the wood respectively. The total length of the member is 250 mm, and the width and the thickness are 60 and 12 mm. The hole is drilled in the central. The right side of the hole is a semicircle with 9.5 mm radius a, and the left side is a semiellipse with b mm semimajor axis (or with semiminor axis, if b<a). All the initial sizes are constant, but the length of the semi axis of the semiellipse is variable, so that the definition of the axis ratio R is b/a, where a is the radius of the semicircle. R is set starting from 0.75, and each model with an increment of 0.25 for R was built and analyzed. The applied load was a concentrated force of 980.67 N（100 kgf） on the metal bolt towards the left. The right side of the member would be fixed and could not be moved and there was no deformation or displacement at the end surface. The interface between the wood and the metal bolt was set to free. There was neither glue nor adhesive between them, so there was a clearance while the deformation and displacement happened. Friction was neglected, however. Compared with simulation results, it is evident that the distribution of stress is quite different between isotropic and orthotropic member. But stress concentration still exists in both models at same locations. To enhance the utilization of wood material, the good property of tensile strength of wood should be considered. But stress concentration around the hole will reduce this property. Adjusting the ratio of the axes of R can find a way to reduce the stress concentration. One of the concentrated stresses must be increased while another must be decreased whether the ratio increases or decreases. The simulation show that a good result can be obtained when the ratio R is about 1.2 to 1.25. In the experiment, strain gauges and the universal testing machine were used. Signals were measured and converted through the written computer program. Basically, some of the results are similar with computer simulations. While the applied load is constant, the value of strain at the tensile area by the bolt hole decreases with R increasing, and the value of strain at the compression area by the bolt hole increases with R increasing. However, there were some disadvantages for mechanism such as nodes of wood, grain. And the dimension of the models was too small (limited by the testing machine) that the disadvantages appeared obviously. Because of the small dimension, the scale of strain gauges was enlarged, so that a part of the results were not so accuracy.