非均布含水率梯度下圆木构件横截面湿度应力解析模型

doi:10.12068/j.issn.1005-3026.2025.20239050

摘要/Abstract

摘要：

建立木构件湿度应力解析模型是研究木材干缩开裂规律及其对承载力影响的基础.首先通过木构件横截面应力平衡分析建立了含水率梯度下横截面应力分布模型；其次借鉴温度应力弹性解析模型和温—热类比关系,建立了非均布含水率梯度下木构件的平衡条件、物理条件、几何条件和协调方程，得到了木构件横截面切向、径向湿度应力的解析解、开裂临界含水率和切向拉压临界点；最后通过数值模拟方法验证了本文解析解的正确性.以杉木圆柱构件为例，分析了不同参数（含水率差、构件直径、初末含水率值）对木构件横截面径向、切向湿度应力分布的影响.结果表明：木构件横截面湿度应力分布与木构件初末含水率值及构件尺寸大小无关，而主要与含水率差和材料性能有关.

关键词: 湿度应力, 木构件横截面, 含水率差, 非均布含水率, 解析模型

Abstract:

Establishing the moisture stress analytical model of wood members is the basis for studying the laws of wood shrinkage cracking and their impact on the bearing capacity. Firstly， the stress distribution model of cross-section under moisture content gradient was established by analyzing the stress balance in the cross-section of wood member. Secondly， the equilibrium conditions， physical conditions， geometric conditions and coordination equations for wood members under non-uniform moisture content gradient were established based on the temperature stress elastic analytical model and the thermo-analogy relationship. The analytical solutions of tangential and radial moisture stresses， critical moisture content of cracking and critical point of tangential tension and compression were obtained by solving the equations. Finally， the correctness of the analytical solutions was verified by numerical simulations. Taking Chinese fir members as an example， the influence of different parameters （moisture content difference， member diameter， initial and final moisture content values） on the radial and tangential moisture stress distributions of the cross-section of wood members was analyzed. The results show that the moisture stress distributions in the cross-section of the wood member is not related to the initial and final moisture content of the wood member and the size of the member， but is related to the moisture content difference and material properties.

Key words: moisture stress, cross-section of wood member, moisture content difference, non-uniform moisture content, analytical model

中图分类号:

TU 366.2

田盼盼, 邱洪兴, 韩建红, 韩霞. 非均布含水率梯度下圆木构件横截面湿度应力解析模型[J]. 东北大学学报（自然科学版）, 2025, 46(4): 144-150.

Pan-pan TIAN, Hong-xing QIU, Jian-hong HAN, Xia HAN. Analytical Model of Moisture Stress in the Cross-Section of Wood Member Under Non-uniform Moisture Gradient[J]. Journal of Northeastern University(Natural Science), 2025, 46(4): 144-150.

图/表 6

图1 木材开裂前应力分析（a）—变形协调条件；（b）—径向截面应力分布；（c）—微元应力分布.

Fig.1 Stress analysis before wood cracking

表1 有限元模型参数

Table 1 Parameters of finite element model

组号	模型形状	截面半径R	初始含水率	平衡含水率	含水率分布形式	约束位置	含水率差Δw
组号	模型形状	mm	%	%	含水率分布形式	约束位置	%
1	圆盘	100	25	10	抛物线Δw(t,ρ)=Δw[2ρ/R-(ρ/R)²]	圆心	15
2	圆盘	100	25	20	抛物线Δw(t,ρ)=Δw[2ρ/R-(ρ/R)²]	圆心	5
3	圆盘	100	25	0	抛物线Δw(t,ρ)=Δw[2ρ/R-(ρ/R)²]	圆心	25
4	圆盘	150	25	10	抛物线Δw(t,ρ)=Δw[2ρ/R-(ρ/R)²]	圆心	15
5	圆盘	100	15	0	抛物线Δw(t,ρ)=Δw[2ρ/R-(ρ/R)²]	圆心	15

表2 材料参数

Table 2 Material parameters

方向	弹性模量	抗压强度	抗拉强度	干缩湿胀系数	方向	剪切模量	泊松比
方向	MPa	MPa	MPa	%	方向	MPa	泊松比
R	E_R=1 048	f_c,R=3.07	f_t,R=3.07	α_R=0.139	RT	G_RT=232	v_RT=0.43
T	E_T=594	f_c,T=2.67	f_t,T=2.67	α_T=0.255	RL	G_RT=967	v_RL=0.03
L	E_R=12 888	f_c,L=36.25	f_t,L=36.25	α_L=0.019	TL	G_RT=773	v_TL=0.02

图2 有限元分析结果（a）—第1组；（b）—第2组；（c）—第3组；（d）—第4组.

Fig.2 Results of finite element analysis

图3 应力分布验证与对比（a）—不同含水率梯度差下径向应力；（b）—不同含水率梯度差切向应力；（c）—不同构件尺寸；（d）—不同初始和最终含水率值（同梯度）.

Fig.3 Verification and comparison of stress distribution

图4 不同含水率分布下应力对比（a）—切向应力；（b）—径向应力.

Fig.4 Comparison of stresses under different water content distributions

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