叠层梁理论在复合顶板受力分析中的应用

Application of laminated beam theory in stress analysis of composite roof

为分析复合顶板稳定性及锚杆组合作用,将叠层梁理论应用于复合顶板中,对叠层梁非共同曲率、共同曲率及整体梁模型进行对比,分析了不同模型下复合顶板梁的弯矩分配规律、拉应力大小与比值及其影响因素,得到了各模型适用条件。研究表明:3种模型计算的复合顶板稳定性差别较大,当高跨比大于1/3时,可将复合顶板叠层梁近似看作共同曲率模型来处理;当高跨比小于1/3时,应将叠层梁按照非共同曲率模型进行分析;当层间黏结力未发生破坏时,可用整体梁模型来处理。分析得出复合顶板锚杆主被动加固机理,主要是防止复合顶板由整体梁向共同曲率叠层梁及非共同曲率叠层梁转化,实现由非共同曲率叠层梁向整体梁转化,从而增强复合顶板抗弯能力及巷道稳定性。

In order to analyze the stability of composite roof and the effect of rockbolt combination,the laminated beam theory was applied to the composite roof,and the non-common curvature,common curvature and integral beam models of laminated beam were compared.The distribution law of bending moment,the magnitude and ratio of tensile stress and their influencing factors of composite roof beams under different models were analyzed,and the applicable conditions of each model were obtained.The research shows that the stability of composite roof calculated by the three models is very different,and when the height-span ratio is greater than 1/3,the composite roof laminated beam can be approximated as a common curvature model;when the height-span ratio is less than 1/3,the laminated beam should be analyzed according to the non-common curvature model;the integral beam model can be used when the interlayer bonding force is not destroyed.The analysis shows that active and passive reinforcement mechanism of composite roof rockbolt is mainly to prevent the transformation of composite roof from integral beam to common curvature laminated beam and non-common curvature laminated beam,realize the transformation from non-common curvature laminated beam to integral beam,so as to enhance the bending capacity of composite roof and roadway stability.