层状裂隙岩石顶板的失稳

Buckling Behaviors of Cracked Roof

采用无拉力岩石梁的力学解析模型，根据自由刚体法及卡氏定理建立了层状裂隙岩石顶板失稳问题的基本求解方程．分析考察了在不同荷载条件、梁轴向产生永久变形、以及不同支座条件下裂隙岩石顶板梁的失稳特性．结果表明：其弯曲失稳可用临界挠度δｍａｘ／Ｄ来描述．当不考虑梁轴向永久变形及支点位移条件影响时，顶板梁失稳的临界挠度为０．４．梁轴向永久变形将使失稳点的临界挠度及梁的承载能力降低．同时，梁的失稳还直接受两端支承条件的支配．其影响程度可用支点系数α来描述．α增大，梁的弯曲刚度降低，梁易于失稳．

A notension roof beam model is presented in this paper. The elementary equations for buckling of cracked roof beam are established by means of freebody method and Castigliano's principle. Buckling behaviors of cracked roof beam are analyzed and considered under the conditions such as permanent deformation of roof and the properties of supporting points. The results indicate that buckling of the roof beam can be expressed in critical deflection δmax/D. When permanent axial deformation of the beam and its supporting condition are neglected, the critical deflection is equal to 0.4. Both critical deflection and bearing capacity of the beam will decrease under influence of the permanent deformation. In addition, buckling behaviors of the beam is also affected by its supporting condition expressed in supporting coefficient α. When α increases, bending stiffness becomes low and the beam is easy of buckling failure.