Timoshenko自由梁迭代法计算木材弹性模量和剪切模量的适用性

doi:10.11707/j.1001-7488.20220818

Abstract

Abstract:

Objective: When Timoshenko free beam iteration method is used to dynamically test the elastic modulus and shear modulus of wood, its test accuracy is greatly affected by the different length thickness ratios of the specimen. Therefore, this paper was implemented to explore the applicability of calculating wood elastic modulus and shear modulus according to the iterative method of Timoshenko beam, and further focus on the test accuracy. Method: Through the truncated test of beech, SPF(spruce, pine and fir) and LVL(laminated venner lumber) specimens, the spectrums under different length thickness ratios were dynamically measured, and the first and second-order bending frequencies of free beam were read out from the spectrum. At the same time, the elastic modulus and shear modulus of wood and wood composites were calculated by iterative program. The effectiveness of the iterative method to calculate the shear modulus was verified by the free member torsional vibration method and the free plate torsional vibration mode method. Result: There was a lower limit value of length thickness ratio related to tree species. When the length thickness ratio of the specimen was less than the lower limit value, the elastic modulus and shear modulus could not be iterated by the iterative method. The elastic modulus determined by iterative method was higher than the elastic modulus test value of Euler beam. The iterative method also could give a too high calculated value of shear modulus. The elastic modulus calculated by iterative method might be higher than the elastic modulus test value based on Euler beam, and its degree is related to the length thickness ratio of the specimen. Only when the length thickness ratio of the specimen is greater than 24, the high value is less than 4%. The calculated value of shear modulus given by iterative method is related to the value of rectangular section factor k. When the rectangular section factor k is equal to 0.833 and 0.913, the calculated value of the shear modulus obtained by the iterative method is 12.2% and 2.3% (19.9% and 9.3%) higher than the measured value of the free member torsional vibration method (free plate torsional vibration mode method), respectively. Conclusion: In order to ensure the test accuracy, it is recommended to use beam specimens with length thickness ratio of 20-24 to dynamically test the first and second-order bending frequencies, and iteratively calculate the elastic modulus and shear modulus of wood with rectangular section factor of 0.913.

Key words: natural frequency, Timoshenko free beam iterative method, modulus of elasticity, shear modulus, applicability, test accuracy

CLC Number:

S781.2

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.

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References 0

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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
山毛榉 Fagus sylvatica	600	24	28	8	708	弦向 Tangential
SPF	578	26	24	6	458	径向 Radial
SPF	578	24	26	6	458	弦向 Tangential
LVL	1 002	46	46	4	573	顺纹 Grain
LVL	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

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	552	92	10	4	665	弦向 Tangential
SPF	486	89	10	3	439	弦向 Tangential
LVL	960	240	30	3	580	顺纹 Grain

试件 Specimen	梁长厚比 Length-to-thickness ratio of beam(l/h)
试件 Specimen	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	－

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
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	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%)
山毛榉 Fagus sylvatica	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%)
SPF	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%)
LVL顺纹 LVL grain	平行胶层 Parallel to adhesive layer	28-12	12.3(1.0%)	928(4.5%)	847(9.3%)

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
试件 Specimen	试件数 Number of specimens	板长宽比 Aspect ratio of plate	取向 Direction	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%)

Applicability of Timoshenko Beam Iterative Method to Calculate Wood Elastic Modulus and Shear Modulus

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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
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	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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