水平彈性支承圓弧鋼拱的幾何非線性穩(wěn)定研究
黃山1,楊洋2
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(1 浙江大學(xué)建筑設(shè)計(jì)研究院, 杭州 310028; 2 浙江綠城東方建筑設(shè)計(jì)有限公司, 杭州 310012)[摘要]鋼拱常支承于其他結(jié)構(gòu)上,拱腳在水平方向很難做到完全的剛性支承,拱的支座約束可以用拱腳處的水平彈簧進(jìn)行等效替代。利用ANSYS有限元程序,采用大撓度變形理論對(duì)水平彈性支承拱進(jìn)行了研究,分析了其平面內(nèi)屈曲模態(tài)和失穩(wěn)特征,對(duì)影響失穩(wěn)的支座約束剛度、長細(xì)比、圓心角和幾何初始缺陷等因素進(jìn)行了深入的探討。通過構(gòu)造反映支座約束程度的彈性柔度系數(shù),擬合得到了非線性極限荷載及支座水平位移的計(jì)算表達(dá)式,并具有良好的精度。理論分析結(jié)果表明,在工程設(shè)計(jì)中應(yīng)考慮支座約束對(duì)拱的影響,并可以利用彈性柔度系數(shù)對(duì)承載力和支座位移進(jìn)行定量分析。[關(guān)鍵詞]圓弧拱; 幾何非線性; 屈曲模態(tài); 極限荷載; 彈性約束中圖分類號(hào):TU311.2 文獻(xiàn)標(biāo)識(shí)碼:A 文章編號(hào):1002-848X(2013)15-0131-05Study for geometric non-linear stability of steel circular arches with horizontal spring supportsHuang Shan1, Yang Yang2(1 Architectural Design and Research Institute of Zhejiang University, Hangzhou 310028, China; 2 Zhejiang Greentown Oriental Architecture Design Co., Ltd., Hangzhou 310012, China)Abstract: Arches which are supported by other structural members can be considered to be supported elastically at both ends by horizontal springs. An elastic finite element model was established to study the in-plane modes of buckling and characteristic of stability of steel circular arches with horizontal spring supports using large deformation theory by ANSYS. The effects of stiffness of the horizontal end restraints, slenderness, angle and geometric initial defect on the stability of arches with I-sections are investigated. A dimensionless elastic softness factor which respects the restraint of supports is advanced. Based on the numerical results, formulas with good accuracy for non-linear ultimate load and displacement of supports under ultimate strength in terms of the stiffness of ends are proposed. It is pointed out that stiffness of the horizontal end restraints shall not be neglected in the engineering design, and ultimate load and displacement of supports can be calculated by elastic flexibility factor.Keywords: circular arches; geometric non-linear; modes of buckling; ultimate load; elastic restraints作者簡介:黃山,碩士,助理工程師,Email:tanoshii@163.com。參考文獻(xiàn)[1]RAYMOND H P. Buckling of shallow arches with supports that stiffen when compressed [J]. Journal of Engineering Mechanics, 1990, 116(4): 973-976.[2]PI Y L, BRADFORD M A, TIN-LOI F. Non-linear in-plane buckling of rotationally restrained shallow arches under a central concentrated load [J]. International Journal of Non-Linear Mechanics, 2008, 43(1): 1-17.[3]PI Y L, BRADFORD M A, TIN-LOI F. Nonlinear analysis and buckling of elastically supported circular shallow arches [J]. International Journal of Solids and Structures, 2007, 44(7-8): 2401-2425.[4]BRADFORD M A, WANG T, PI Y L, et al. In-plane stability of parabolic arches with horizontal spring supports,I:theory[J].Journal of Structural Engineering,2007, 133(8): 1130-1137.[5]PI Y L, BRADFORD M A, TIN-LOI F, et al. Geometric and material nonlinear analyses of elastically restrained arches [J]. Engineering structures, 2007, 29(3): 283-295.[6]楊洋,童根樹. 水平彈性支承圓弧鋼拱的彈性屈曲分析[J]. 工程力學(xué),2011, 28(3): 9-16.[7]楊洋,童根樹. 水平彈性支承圓弧鋼拱的平面內(nèi)極限承載力研究[J]. 工程力學(xué),2012, 29(3): 45-54.[8]童根樹. 鋼結(jié)構(gòu)的平面內(nèi)穩(wěn)定[M]. 北京:中國建筑工業(yè)出版社,2005.
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