累积变形影响下的半刚性节点古建木柱正截面压应力及承载力解析解

引用本文

常鹏, 胡娅春, 王军舰, 王钊. 累积变形影响下的半刚性节点古建木柱正截面压应力及承载力解析解[J]. 北京交通大学学报, 2018,42(4): 44-50.
CHANG Peng, HU Yachun, WANG Junjian, WANG Zhao. Normal section’s compression stress and bearing capacity analytical solution of ancient wood column semi-rigid connection joints influenced by cumulative deformation[J]. JOURNAL OF BEIJING JIAOTONG UNIVERSITY, 2018,42(4): 44-50.
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累积变形影响下的半刚性节点古建木柱正截面压应力及承载力解析解

常鹏¹, 胡娅春², 王军舰¹, 王钊¹

1.北京交通大学土木建筑工程学院,北京 100044

2.郑州城市职业学院,郑州 452370

第一作者:常鹏(1979—),男,陕西泾阳人,副教授,博士.研究方向为古建结构安全保护.email:pchang@bjtu.edu.cn.

收稿日期: 2017-12-22

基金: 国家自然科学基金(51778045)

摘要

古建筑木结构在长期竖向荷载作用下会产生累积变形,针对累积变形古建筑木柱在竖向荷载作用下平面应力问题,运用弹性力学方法求解了应力与位移分量及屈服荷载解析解.结合半逆解求解方式和等效荷载法,将累积变形柱进行了等效简化,对于古建筑端部半刚性特性,运用位移和应力边界条件进行处理.研究结果表明:柱跨中侧向挠曲变形对截面压应力影响大,而端部侧移影响较小;半刚性节点的非线性对截面压应力影响显著.通过Ansys数值计算与理论公式进行了对比,讨论了累积变形对木柱屈服荷载的影响,解析解与数值解结果吻合良好.研究结果对长期竖向荷载作用下有累计残损变形的古建木柱力学状态评估有一定的借鉴意义.

关键词: 古建筑木结构; 木柱; 累积变形; 半刚性连接; 正交各向异性

中图分类号:TU366.2 文献标志码:A 文章编号:1673-0291(2018)04-0044-07

Normal section’s compression stress and bearing capacity analytical solution of ancient wood column semi-rigid connection joints influenced by cumulative deformation

CHANG Peng¹, HU Yachun², WANG Junjian¹, WANG Zhao¹

1.School of Civil Engineering, Beijing Jiaotong University, Beijing 100044,China

2.City University of Zhengzhou, Zhengzhou 452370,China

Fund:National Natural Science Foundation of China(51778045)

Abstract

The ancient wood structure subject to accumulative deformation under long-term vertical load. Aiming to solve the problem of plane stress for the ancient building’s wooden column under vertical load, analytical solutions of the stress, displacement component and the yield load are proposed by using elasticity mechanics. The semi-inverse solution is combined with the equivalent load method to get the equivalent simplification of the accumulative deformation column. For the semi-rigid characteristic of the ancient building’s terminal part, the displacement and stress boundary are adjusted to solve it. The results show that the lateral deflection of the column cross section has a great influence on the sectional compressive stress and a smaller influence on the lateral displacement at terminal part. At the same time, the semi-rigid joints’ nonlinearity characteristic affects the sectional compressive stress significantly. The influence of accumulative deformation on the yield load of the wooden column is discussed through comparing the numerical simulation by Ansys with the theoretical formula, which are mutually consistent. This paper has referential significance on the state evaluation of wooden column’s accumulative deformation under long-term vertical load.

Keyword: ancient wood buildings; wood column; accumulative deformation; semi-rigid connection; orthotropic

文章图片

木柱是古建筑中主要的受力构件, “ 立木顶千斤” 足以说明其在古建筑中的重要角色.木柱的健康与否关系到结构的寿命及安全, 因此, 木柱受力状态的理论研究具有重要意义.梁和柱理论是力学分析中的经典课题, 在一定程度上, 梁和柱除了受荷类型不同, 理论分析具有相似性.戴瑛等^[1]通过简化后的固定边界条件, 求出了均布载荷下两端固定短梁的平面应力解析解.黄德进等^[2]通过Airy应力函数法, 研究了均布载荷作用下正交各向异性固支梁的平面应力问题, 并与数值解进行对比.榫卯连接是古建筑木结构特色, 连接特性介于固接和铰接之间, 为半刚性连接.姚侃等^{[3, 4]}通过试验和数值相结合的方法研究了古建梁柱榫卯的连接特性.张雷等^[5]推导出榫卯连接古建木梁在均布荷载作用下的应力、位移分量解析解, 并通过实例进行了讨论.国外学者Aristizabal等^{[6, 7, 8]}在2008年推导了基于铁木辛柯理论和二阶效应, 考虑弯曲变形和剪切变形时半刚性连接的对称截面构件在轴力作用下的转角位移方程, 该公式考虑了在构件发生横向变形时轴力的剪切分量的影响, 并运用4个经典例子说明了所推公式的有效性; 在2010年推导了基于欧拉-伯努利理论和二阶效应, 考虑弯曲变形并忽略剪切变形时半刚性连接且具有对称截面的构件在偏心荷载作用下的转角位移方程; 在2011年运用弯矩分配法对静定梁和框架结构进行了稳定性和非线性二阶分析, 该分析过程均考虑了弯曲和剪切变形、轴向荷载和半刚性连接的影响, 并运用3个典型的例子证明了该研究的有效性.

综上, 国内外相关学者对于木梁构件的研究分为在各向同性的情况下引入变形或在各向异性的情况下不考虑变形影响, 而对于柱截面应力和承载力方面的研究未同时考虑正交各向异性和累积变形.

本文作者结合古建木结构特性, 选取西藏地区宫殿内古建木柱为研究对象, 考虑其细长形态及竖向荷载大的特点, 将线性阶段推进到非线性阶段, 考虑端部节点半刚性、端部侧移、跨中挠曲变形作为非线性因素, 研究了端部轴向荷载作用下累积变形木柱的解析解, 给出了累积变形对屈服荷载的影响.此处累积变形是指柱高方向的侧向挠曲变形和端部侧移.

1 累积变形下木柱解析解

1.1 计算简图

古建木柱在柱端约束比较弱, 弯矩作用较小, 所以假定木柱挠曲形状为半波余弦曲线, 即y₁(x)=δ ₁cos(π x/L).累积变形木柱计算简图如图1(a)所示.

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	图1 累积变形木柱等效计算简图Fig.1 Equivalent computing model of wooden column with accumulative deformation

对于受竖向荷载发生挠曲变形的木柱, 可通过附加一个等效虚荷载来近似考虑挠曲变形的影响, 即将挠曲变形在跨中截面产生的弯矩和近似等效成横向均布荷载单独作用时产生的弯矩, 计算简图如图1(b)所示; 其中:δ ₁为跨中挠曲变形值; L为柱高; Δ ₀为柱端侧移; P为端部轴向力; K_y为柱端部半刚性刚度值; h为截面长度.

1.2 均布荷载下理想构件解析解

为了求出均布荷载q, 需先求半刚性理想构件在q下的解析解.本文研究的柱为方柱, 截面为矩形, 荷载均匀分布, 且横截面尺寸不随x变化, 所以该问题为平面应力问题, 木材本构方程为

$[\begin{array}{l} ε_{x} \\ ε_{y} \\ γ_{xy} \end{array}] = [\begin{array}{l} \frac{1}{E_{x}} & - \frac{μ_{yx}}{E_{y}} & 0 \\ - \frac{μ_{xy}}{E_{x}} & \frac{1}{E_{y}} & 0 \\ 0 & 0 & \frac{1}{G_{xy}} \end{array}] [\begin{array}{l} σ_{x} \\ σ_{y} \\ τ_{xy} \end{array}] (1)$

式中:ε _x为x向正应变; ε _y为y向正应变; γ _xy为xy向切应变; E_x为x向弹性模量; E_y为y向弹性模量; μ _xy为xy向泊松比; μ _yx为yx向泊松比; G_xy为xy面剪切模量; σ _x为x向正应力; σ _y为y向正应力; τ _xy为xy向切应力.

几何方程表达为

$\{\begin{array}{l} ε_{x} = \frac{\partial u}{\partial x} = \frac{1}{E_{x}} σ_{x} - \frac{μ_{yx}}{E_{y}} σ_{y} = s_{11} σ_{x} + s_{12} σ_{y} \\ ε_{y} = \frac{\partial v}{\partial y} = \frac{1}{E_{y}} σ_{y} - \frac{μ_{xy}}{E_{x}} σ_{x} = s_{12} σ_{x} + s_{22} σ_{y} \\ γ_{xy} = \frac{1}{G_{xy}} τ_{xy} = s_{66} τ_{xy} \end{array} (2)$

应变协调方程为

$\frac{\partial^{2} ε_{x}}{\partial y^{2}} + \frac{\partial^{2} ε_{y}}{\partial x^{2}} = \frac{\partial^{2} γ_{xy}}{\partial x \partial y} (3)$

采用半逆解法求解, 设应力函数为φ (x, y), 联立式(2)和式(3)得到

$s_{11} \frac{\partial^{4} φ}{\partial y^{4}} + (2 s_{12} + s_{66}) \frac{\partial^{4} φ}{\partial x^{2} \partial y^{2}} + s_{22} \frac{\partial^{4} φ}{\partial x^{4}} = 0 (4)$

挤压应力σ _y主要是由均布荷载q引起的, 且q不随x的变化而变化, 所以先假设σ _y=f(y), 对σ _y进行2次积分得

$φ (x, y) = x^{2} f (y) / 2 + x f_{1} (y) + f_{2} (y) (5)$

应力边界条件为

$\{\begin{array}{l} (σ_{y})_{y = h / 2} = 0 \\ (σ_{y})_{y = - h / 2} = - q \\ (τ_{xy})_{y = \pm h / 2} = 0 \end{array} (6)$

结合正应力σ _x、σ _y、τ _xy的对称性, 得

$\{\begin{array}{l} σ_{x} = - \frac{6 q}{h^{3}} x^{2} y - \frac{2 q}{a h^{3}} y^{3} + 6 Hy + 2 K \\ σ_{y} = - \frac{2 q}{h^{3}} y^{3} + \frac{3 q}{2 h} y - \frac{q}{2} \\ τ_{xy} = - x (- \frac{6 q}{h^{3}} y^{2} + \frac{3 q}{2 h}) \end{array} (7)$

式中:H、K为待定参数; a为代表各向异性的参数, a=-s₁₁/(2s₁₂+s₆₆).

对式(2)两边积分得到位移分量

$\{\begin{array}{l} u = s_{11} (- \frac{2 q}{h^{3}} x^{3} y - \frac{2 q}{a h^{3}} y^{3} x + 6 Hyx + 2 Kx) + \\ s_{12} x (- \frac{2 q}{h^{3}} y^{3} + \frac{3 q}{2 h} y - \frac{q}{2}) + wy + u_{0} \\ v = s_{12} (- \frac{3 q}{h^{3}} x^{2} y^{2} - \frac{q}{2 a h^{3}} y^{4} + 3 H y^{2} + 2 Ky) + \\ s_{22} (- \frac{q}{2 h^{3}} y^{4} + \frac{3 q}{4 h} y^{2} - \frac{q}{2} y) + J (x) \end{array} (8)$

式中:u为x向位移分量; v为y向位移分量; u₀、v₀代表刚体运动; ω 为待定参数; J(x)=s₁₁ $\frac{q}{2 h^{3}}$ x⁴-3Hs₁₁x²- $\frac{3 q}{4 h}$ s₁₂x²- $\frac{3 q}{4 h}$ s₆₆x²-wx+v₀.

古建梁柱连接为半刚性连接, 设端部弯矩为M, 其中M=K_rot_z· θ _z, K_rot_z为端部绕z轴的转动刚度, 根据位移边界得

$\{\begin{array}{l} {(u)}_{x = \pm L / 2, y = 0} = 0 \\ {(v)}_{x = \pm L / 2, y = 0} = 0 \\ \frac{\partial v}{\partial x} - {\frac{\partial u}{\partial y}}_{x = \pm L / 2, y = 0} = \frac{2 M}{K_{rot z}} \end{array} (9)$

端部为小边界问题, 运用圣维南定理

$\{\begin{array}{l} \int_{-}^{h} σ_{x} d y = N \\ \int_{-}^{h} σ_{x} y d y = M \\ \int_{-}^{h} τ_{xy} d y = - qL / 2 \end{array} (10)$

式中:N为文献[5]中两端固支时的轴向力.结合式(8)、式(9)和式(10)得

$\{\begin{array}{l} H = \frac{q (10 L^{3} a K_{rot z} s_{11} + 5 L^{2} a h^{3} + 15 L h^{2} K_{rot z} s_{11} + h^{5})}{20 a h^{3} (6 L K_{rot z} s_{11} + h^{3})} \\ u_{0} = w = 0 \\ K = q s_{12} / 4 s_{11} \\ v_{0} = \frac{L^{2} (24 H h^{3} s_{11} - L^{2} q s_{11} + 6 h^{2} q s_{12} + 6 h^{2} q s_{66})}{32 h^{3}} \end{array} (11)$

将式(11)参数带到式(7)和式(8)中即可得到横向均布荷载作用下构件应力和位移分量解析解.

1.3 累积变形下等效柱解析解

用等效荷载法将侧向挠曲在跨中截面产生的弯矩近似等效横向等效均布荷载单独作用时产生的弯矩, 通过施加横向均布荷载近似考虑累积变形影响.

$q_{1} = \frac{40 P δ_{1} (h^{3} + 6 K_{rot z} s_{11} L)}{K_{rot z} s_{11} L^{3} b (10 + 9 h^{2} / a L^{2}) + 5 b h^{3} L^{2}} (12)$

式中b为截面宽度.

端部看成小边界, 在x=L/2处运用圣维南定理得

$\{\begin{array}{l} \int_{-}^{h} σ_{x} d y = - \frac{P}{b} \\ \int_{-}^{h} τ_{xy} d y = - \frac{q_{1} L}{2} \\ \int_{-}^{h} σ_{x} y d y = K_{rot z} θ_{z} = M \end{array} (13)$

端部位移边界条件为

$\{\begin{array}{l} {(u)}_{x = \pm L / 2, y = 0} = 0 \\ {(v)}_{x = \pm L / 2, y = 0} = Δ_{0} + \frac{q_{1} L}{2 K_{y}} \\ \frac{\partial v}{\partial x} - {\frac{\partial u}{\partial y}}_{x = \pm L / 2, y = 0} = \frac{2 M}{K_{rot z}} \\ {(v)}_{x = \pm L / 2, y = 0} = 0 \end{array} (14)$

结合式(13)和式(14)得到未知参数

$\{\begin{array}{l} u_{0} = - \frac{q_{1} s_{12} L}{4} - \frac{P s_{11} L}{2 b h} \\ v_{0} = \frac{2 Δ_{0} + 3 H L^{2} s_{11}}{4} + \frac{q_{1}}{4 K_{y}} + \\ \frac{q_{1} L^{2} [6 h^{2} (s_{12} + s_{66}) - s_{11} L^{2}]}{32 h^{3}} \\ K = - P / (2 b h) \\ H = \frac{q_{1} (λ_{1} + λ_{2}) + λ_{3}}{20 a h^{3} L K_{y} (6 L K_{rot z} s_{11} + h^{3})} \\ w = - Δ_{0} / L - q_{1} / 2 K_{y} L \\ λ_{1} = (10 L^{2} a + 15 h^{2}) K_{rot z} K_{y} s_{11} L^{2} \\ λ_{2} = K_{y} L h^{5} + 20 a h^{3} K_{rot z} + 5 a h^{3} L^{3} K_{y} \\ λ_{3} = 40 a h^{3} K_{rot z} K_{y} Δ_{0} \end{array} (15)$

将式(15)参数带到式(7)和式(8)中即可得到累积变形影响下木柱应力和位移分量近似解析解.

木材主要是顺纹方向的力学性质起作用, 在累计变形下跨中截面不仅承受力P, 同时跨中还承受最大的截面弯矩, 所以当跨中左侧截面边缘应力首次达到屈服压应力 $f_{t}^{cy}$ 时求得弹性屈服荷载.因此, 弹性屈服荷载表达式为

$P_{e} = - \frac{b [R_{1} + R_{2} + R_{3}]}{4 a h L K_{y} (6 K_{rot z} s_{11} + L h^{3})} (16)$

式中:R₁=4LK_yh⁵( $f_{t}^{cy}$ -0.1q₁); R₂=3ah³(q₁L³K_y+8K_rot_zK_yΔ ₀+4K_rot_zq₁); R₃=3L²K_rot_zK_yh²s₁₁(q₁+8 $f_{t}^{cy}$ a).

2 截面最大压应力影响因素分析

根据上述得到的解析解, 计算一根实例构件.按照《清式营造则例》^[9], 木柱截面高度为4.5斗口, 取360 mm; 宽为3.6斗口, 取288 mm; 构件长度取3 600 mm.此时P=600 kN, K_y=10⁵ N/m^[10], K_rot_z=1.8× 10⁵(N· m)/rad^[11], Δ ₀、δ ₁挠度限值取《古建筑木结构维护与加固技术规范》^[12]的L/250.红松材的弹性常数参照文献[13]取值, 见表1.

表1 红松材的弹性常数 Tab.1 Elastic constants of Korean Pine

木柱中间截面左侧边缘压应力最大, 得到柱端侧移Δ ₀、跨中挠曲变形值δ ₁对截面最大压应力σ _x 的影响如图2所示.由图2可见, 柱端侧移Δ ₀、跨中挠曲变形值δ ₁的相互作用均对截面最大压应力产生影响; 当Δ ₀为0, δ ₁达到限值L/250时, 使σ _x为7.28× 10⁶N/m², 增大了25.52%; 当δ ₁为0, Δ ₀增大到挠度限值L/250时, 使σ _x为6.16× 10⁶N/m², 仅增加了6.29%, 相比而言, Δ ₀影响较δ ₁小.

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	图2 Δ ₀和δ ₁对σ _x的影响Fig.2 Influence of Δ ₀ and δ ₁ on σ _x

梁柱连接处易受环境影响, 其半刚性程度不断变化, 假设Δ ₀=δ ₁=L/1000, K_y与P同上, 得到半刚性程度对截面最大压应力σ _x的影响, 见图3.

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	图3 半刚性对σ _x的影响Fig.3 Influence of semi-rigidity on σ _x

由图3可知, 半刚性对压应力影响为非线性, 且影响显著, 不能忽略.说明半刚性节点对结构节点受力状态评估影响很大, 需在性能评估时进行考虑.

3 有限元分析

采用Ansys建立模型, 柱的尺寸选用长度h× 宽度b=450 mm× 300 mm, 高度L=4 500 mm.单元选用Solid 45实体单元, 该单元是八节点六面体实体单元, 可定义各向异性材料.端部半刚性连接采用Matrix 27单元, 该单元可定义6个方向的刚度, 通过调整单元刚度矩阵中的参数模拟端部侧移和转动.

木材弹性参数参照文献[14]选取, 藏青杨的弹性常数如表2所示.

表2 藏青杨的弹性常数 Tab.2 Elastic constants of Tibetan cathay poplar

3.1 模型验证

木材具有正交各向异性, 这种特性体现在单元坐标系中.为了正确模拟这种特性, 选用半刚性连接的构件进行建模^[16], 施加均布面荷q=1 kN/m², 验证模型的计算简图如图4所示, 图4中K_a为A端节点刚度值, K_b为B端节点刚度值.理论与数值结果对比如表3所示.

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	图4 验证模型的计算简图Fig.4 Calculating diagram of verification model

表3 理论与数值结果对比 Tab.3 Comparison of theoretical and numerical models

对比发现, 理论计算结果和数值模拟计算结果非常接近, 误差在1%以内, 证明了模型的正确性.

3.2 数值解与解析解的对比分析

建立跨中挠曲变形值δ ₁为0, L/1000, 2L/1000, 4L/1000的实体有限元模型.结合式(16)得到跨中节点解析解与数值解的荷载-位移曲线.荷载-位移曲线对比图如图5所示.

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	图5 荷载-位移曲线Fig.5 Curves of load-displacement

由图5可知, 弹性阶段侧向挠曲变形对轴向荷载影响较大; 当跨中挠曲变形δ ₁为零时, 理想柱跨中位移v较小; 且轴向荷载p一定时, 随着跨中挠曲变形值δ ₁的增大, 跨中位移v增大; 解析解与数值解吻合良好.

为了进一步研究累积变形对屈服荷载的影响, 结合式(15)分别得到累积变形对屈服荷载的影响, 跨中侧向挠曲变形δ ₁影响下及柱端侧移Δ ₀影响下柱屈服荷载p_e及荷载曲线分别如表4和表5及图6和图7所示.

表4 跨中侧向挠曲变形影响下柱屈服荷载 Tab.4 Column yield load under midspan lateral deflection

表5 柱端侧移影响下柱屈服荷载 Tab.5 Column yield load under lateral displacement at the end of column

	Figure Option View Download New Window
	图6 跨中侧向挠曲变形影响下柱屈服荷载曲线Fig.6 Curves of column yield load under midspan lateral deflection δ ₁

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	图7 柱端侧移影响下柱屈服荷载曲线Fig.7 Curves of column yield load under lateral displacementΔ ₀ at the end of column

由图6、图7可知, 跨中侧向挠曲变形δ ₁和柱端侧移Δ ₀对木柱屈服荷载p_e的影响均呈线性, 但使其下降变化的梯度不同.当跨中侧向挠曲变形δ ₁累积变形值达到4L/1000时, 屈服荷载p_e降低39%; 当柱端侧移Δ ₀累积变形值达到4L/1000时, 屈服荷载p_e仅降低2%.因此, 跨中侧向挠曲变形δ ₁对木柱屈服荷载p_e的影响明显大于端部侧移Δ ₀的影响.说明在残损调查中, 相较于端部侧移Δ ₀, 更应关注跨中挠曲变形δ ₁, 力学评估中也更应关注这一因素, 其对构件承载力也有较大影响, 古建筑的维修保护中应重点关注.

4 结论

运用弹性力学方法结合半逆解求解方式和等效荷载法, 对累积变形下古建木柱的应力与位移分量及屈服荷载进行了解析求解并验证, 研究可为轴向荷载作用下存在累计残损变形的古建木柱力学状态评估提供依据.得出的主要结论如下.

1)综合考虑柱端侧移值、跨中侧向挠曲变形值以及半刚性节点的影响, 推导出了累积变形古建筑木柱在轴向荷载作用下的解析解.

2)通过算例对比分析验证了解析解的正确性.结果表明跨中侧向挠曲变形对截面压应力影响大, 柱端侧移影响较小, 同时, 半刚性节点的非线性对截面压应力影响明显.

3)建立了有限元模型, 进行数值解与解析解的比较, 得出弹性阶段跨中侧向挠曲变形对轴向荷载影响大; 当荷载一定时, 理想柱跨中位移很小, 而随着跨中侧向挠曲变形的增大, 跨中位移很大的结论.

4)跨中侧向挠曲变形对屈服荷载的影响明显大于端部侧移对屈服荷载的影响.当跨中侧向挠曲变形累积值达到L/250时, 屈服荷载降低39%; 而当柱端侧移变形累积值达到L/250时, 屈服荷载仅降低2%.

参考文献

文献列表

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2008

0.0

... 戴瑛等^[1]通过简化后的固定边界条件,求出了均布载荷下两端固定短梁的平面应力解析解 ...

2006

0.0

黄德进, 丁皓江, 王惠明. 均布载荷作用下正交各向异性固支梁的解析解[J]. 浙江大学学报(工学版), 2006, 40(3): 511-514.

HUANG

Dejin

, DING

Haojiang

, WANG

Huiming

. Analytical solution for fixed-end orthotropic beams subjected to uniform load[J]. Journal of Zhejiang University (Engineering Science), 2006, 40(3): 511-514. (in Chinese)

针对均布载荷作用下正交各向异性梁在两端固支条件下的平面应力问题，求解了应力和位移的解析解.在求解过程中,构造了一个含待定系数的应力函数,通过Airy应力函数解法,给出了应力和位移的表达式.对固支端边界条件采用两种处理办法,利用应力和位移边界条件,确定应力函数中的待定系数,得到了应力和位移的解析解结果.结果表明,该解析与由Nastran程序计算的有限元数值结果相比,解析解落在有限元数值的附近,两者较为吻合.该解析解对于跨高比较大的梁有较高的精度,并可退化到各向同性梁的结果.

... 黄德进等^[2]通过Airy应力函数法,研究了均布载荷作用下正交各向异性固支梁的平面应力问题,并与数值解进行对比 ...

2006

0.0

姚侃, 赵鸿铁, 葛鸿鹏. 古建木结构榫卯连接特性的试验研究[J]. 工程力学, 2006, 23(10): 168-173.

YAO

Kan

, ZHAO

Hongtie

, GE

Hongpeng

. Experimental studies on the characteristic of mortise-tenon joint in historic timber buildings[J]. Engineering Mechanics, 2006 , 23(10) : 168-173. (in Chinese)

The typical mortise-tenon joints in historic timber buildings were analyzed in mechanics. The low cyclic reversed loading tests were carried out. The semi-rigid characteristic of the joggle joint and the change rules of stiffness degradation were obtained. The moment-deflection angle hysteretic curves were tested. By simulating the state of mortise-tenon joint with the varied stiffness element, the relation between the varied stiffness and the relative flexibility was found. It is shown that the stiffness change of the mortise-tenon joint is nonlinear from 0.3062 to 23.6054 with the change of load. It may provide information, suggestions and theoretical base for seismic research, protection and maintenance of historic timber buildings.

1. Department of civil engineering, Xi'an University of Architecture and Technology, Xian, Shaanxi 710055, China;2. Unit 95022 of Chinese People's Liberation Army, Shantou, Guangdong 515800, China;3. China Northwest Building Design Research Institute, Xian, Shang Xi 710003, China

通过对典型榫卯连接的力学分析和模型低周反复荷载试验,研究了榫卯的半刚性连接特性和刚度退化的规律。试验得到榫卯连接的弯矩-转角滞回曲线和骨架曲线,并拟合出了榫卯节点恢复力模型。将榫卯连接比拟为变刚度杆单元,理论推导了变刚度和相对柔度之间的关系。结果表明,木结构的榫卯连接刚度随荷载变化而呈非线性变化,刚度在0.3062~23.6054之间变化。研究结果可为木结构古建筑的抗震性能研究和修缮加固提供理论基础。

... 姚侃等^[3,4]通过试验和数值相结合的方法研究了古建梁柱榫卯的连接特性 ...

2008

0.0

... 姚侃等^[3,4]通过试验和数值相结合的方法研究了古建梁柱榫卯的连接特性 ...

2017

0.0

... 张雷等^[5]推导出榫卯连接古建木梁在均布荷载作用下的应力、位移分量解析解,并通过实例进行了讨论 ...

... 式中:N为文献[5]中两端固支时的轴向力 ...

2008

0.0

... 国外学者Aristizabal等^[6,7,8]在2008年推导了基于铁木辛柯理论和二阶效应,考虑弯曲变形和剪切变形时半刚性连接的对称截面构件在轴力作用下的转角位移方程,该公式考虑了在构件发生横向变形时轴力的剪切分量的影响,并运用4个经典例子说明了所推公式的有效性 ...

2010

0.0

2011

0.0

1981

0.0

... 按照《清式营造则例》^[9],木柱截面高度为4 ...

2003

0.0

... 此时P=600 kN,K_y=10⁵ N/m^[10],K_rot_z=1 ...

2011

0.0

... m)/rad^[11],#cod#x00394 ...

1993

0.0

... ₁挠度限值取《古建筑木结构维护与加固技术规范》^[12]的L/250 ...

2011

0.0

... 红松材的弹性常数参照文献[13]取值,见表1 ...

2009

0.0

... 木材弹性参数参照文献[14]选取,藏青杨的弹性常数如表2所示 ...

2012

0.0

2017

0.0

... 为了正确模拟这种特性,选用半刚性连接的构件进行建模^[16],施加均布面荷q=1 kN/m²,验证模型的计算简图如图4所示,图4中K_a为A端节点刚度值,K_b为B端节点刚度值 ...