林业科学 ›› 2022, Vol. 58 ›› Issue (8): 173-181.doi: 10.11707/j.1001-7488.20220818
王正,周宇昊,沈肇雨,何宇航
收稿日期:
2021-09-17
出版日期:
2022-08-25
发布日期:
2022-12-19
基金资助:
Zheng Wang,Yuhao Zhou,Zhaoyu Shen,Yuhang He
Received:
2021-09-17
Online:
2022-08-25
Published:
2022-12-19
摘要:
目的: 基于试验探究Timoshenko自由梁迭代法计算木材弹性模量和剪切模量的适用性,重点考虑木材弹性模量和剪切模量的测试精度,寻求梁试件合适的长厚比。方法: 通过山毛榉、云杉-松-冷杉(SPF)和单板层积材(LVL)试件截短试验,动态测试不同长厚比试件的频谱,从频谱图上读出自由梁的第一阶和第二阶弯曲频率;应用迭代程序计算木材和木质复合材料的弹性模量和剪切模量;采用自由杆件扭转振动法和自由板扭转振型法验证自由梁迭代法计算剪切模量的有效性。结果: 存在一个与树种有关的试件长厚比下限值,当试件长厚比小于该下限值时, 自由梁迭代法不能计算出正常的弹性模量和剪切模量或根本计算不出弹性模型和剪切模量;自由梁迭代法计算出的弹性模量高于Euler自由梁法计算出的弹性模量,其程度与试件长厚比有关,仅当试件长厚比大于24时其偏高值才在4%以内;自由梁迭代法计算出的剪切模量与矩形截面因子k取值有关,当k取0.833和0.913时,分别高于自由杆件扭转振动法(自由板扭转振型法)剪切模量测试值12.2%和2.3%(19.9%和9.3%)。结论: 为保证自由梁迭代法测试精度,推荐采用长厚比20~24的梁试件动态测试其第一阶和第二阶弯曲频率,并用矩形截面因子取0.913进行迭代计算木材的弹性模量和剪切模量。
中图分类号:
王正,周宇昊,沈肇雨,何宇航. Timoshenko自由梁迭代法计算木材弹性模量和剪切模量的适用性[J]. 林业科学, 2022, 58(8): 173-181.
Zheng Wang,Yuhao Zhou,Zhaoyu Shen,Yuhang He. Applicability of Timoshenko Beam Iterative Method to Calculate Wood Elastic Modulus and Shear Modulus[J]. Scientia Silvae Sinicae, 2022, 58(8): 173-181.
表1
梁试件基本参数"
试件 Specimen | 长 Length/mm | 宽 Width/mm | 厚 Thickness/mm | 数量 Quantity | 密度 Density/(kg·m-3) | 备注 Remark |
山毛榉 Fagus sylvatica | 600 | 28 | 24 | 8 | 708 | 径向 Radial |
600 | 24 | 28 | 8 | 708 | 弦向 Tangential | |
SPF | 578 | 26 | 24 | 6 | 458 | 径向 Radial |
578 | 24 | 26 | 6 | 458 | 弦向 Tangential | |
LVL | 1 002 | 46 | 46 | 4 | 573 | 顺纹 Grain |
960 | 30 | 30 | 4 | 591 | 顺纹 Grain | |
山毛榉 Fagus sylvatica | 768 | 24 | 24 | 4 | 720 | 弦向、径向 Tangential,radial |
SPF | 768 | 24 | 24 | 2 | 481 | 弦向、径向 Tangential,radial |
LVL | 760 | 45 | 45 | 4 | 591 | 横纹 Horizontal |
西加云杉 Picea sitchenrsis | 300 | 30 | 20 | 3 | 369 | 横向 Transverse |
表3
SPF、山毛榉和LVL采用自由梁迭代法计算的E/E0随梁长厚比(l/h)的变化"
试件 Specimen | 梁长厚比 Length-to-thickness ratio of beam(l/h) | ||||||||
32 | 28 | 24 | 20 | 16 | 14 | 12 | 10 | 8 | |
SPF | 1.030 | 1.029 | 1.030 | 1.041 | 1.080 | 1.108 | 1.139 | 1.225 | 2.758 |
山毛榉 Fagus sylvatica | 1.024 | 1.029 | 1.039 | 1.054 | 1.086 | 1.679 | 2.554 | - | - |
LVL | 1.020 | 1.028 | 1.037 | 1.050 | 1.079 | 1.103 | 1.140 | 2.969 | - |
表4
山毛榉、SPF和LVL采用自由梁迭代法计算的弹性模量和剪切模量①"
试件 Specimen | 取向 Direction | 梁长厚比 Length-to-thickness ratio of beam(l/h) | 弹性模量 Elastic modulus/GPa | 剪切模量 Shear modulus/MPa | |
k = 0.833 | k = 0.913 | ||||
山毛榉 Fagus sylvatica | 弦向 Tangential | 32~16 | 16.1(0.4%) | 1 114(7.1%) | 1 017 (7.1%) |
径向 Radial | 32~16 | 16.4(0.7%) | 1 417(4.6%) | 1 293 (4.6%) | |
SPF | 弦向 Tangential | 32~10 | 13.5(5.2%) | 690(9.9%) | 628(9.7%) |
径向 Radial | 32~10 | 13.6(3.5%) | 778(12.0%) | 719(12.5%) | |
LVL顺纹 LVL grain | 垂直胶层 Perpendicular to adhesive layer | 28~12 | 12.7(0.7%) | 957(9.3%) | 873(9.3%) |
平行胶层 Parallel to adhesive layer | 28-12 | 12.3(1.0%) | 928(4.5%) | 847(9.3%) |
表5
自由杆件扭转振动法和自由板扭转振型法测试的山毛榉、SPF和LVL剪切模量"
试件 Specimen | 试件数 Number of specimens | 板长宽比 Aspect ratio of plate | 取向 Direction | 剪切模量 Shear modulus/MPa | |
自由板扭转振型法 Free plate torsional mode method | 自由杆件扭转振动法 Free member torsional vibration method | ||||
山毛榉 Fagus sylvatica | 4 | 3.0~6.0 | 弦向 Tangential | 932(3.9%) | 994(3.0%) |
SPF | 3 | 3.0~5.5 | 弦向 Tangential | 580(7.2%) | 618(5.8%) |
LVL | 3 | 4 | 顺纹 Grain | 790(0.1%) | 848(0.3%) |
表6
矩形截面因子k取值对自由梁迭代法计算结果的影响"
试件 Specimen | 试件编号 No. | 长 Length/mm | 宽 Width/mm | 高 Height/mm | l/h | 密度 Density/(kg·m-3) | 一弯 First-order bend/Hz | 二弯 Second-order bend/Hz | k=0.833 | k=0.913 | ||
E/GPa | G/MPa | E/GPa | G/MPa | |||||||||
山毛榉径向 Fagus sylvatica, radial | 4-1 | 401 | 29.19 | 23.98 | 16.7 | 742 | 771.9 | 1 981.3 | 38.46 | 166 | 20.11 | 1 487 |
山毛榉弦向 Fagus sylvatica, tangential | 4-1b | 401 | 23.98 | 29.19 | 13.8 | 742 | 887.5 | 2 131.3 | 43.21 | 183 | 19.22 | 913 |
山毛榉弦向 Fagus sylvatica, tangential | 5-1b | 401 | 24.58 | 29.05 | 13.8 | 734 | 834.4 | 2 068.8 | 33.81 | 174 | 16.42 | 1 101 |
SPF径向 SPF, radial | 24-2 | 201 | 27.11 | 24.31 | 8.3 | 458 | 2 758.3 | 6 104.2 | 38.17 | 221 | 38.17 | 202 |
SPF径向 SPF, radial | 26-2 | 201 | 26.98 | 24.21 | 8.3 | 444 | 2 696.9 | 5 892.7 | 40.04 | 198 | 11.19 | 686 |
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