预应力混凝土梁斜裂缝倾角的概率计算模型

针对预应力混凝土(PC)梁剪切斜裂缝倾角的大小,各国规范建议公式差异较大,尚没有明确的理论模型。基于贝叶斯理论,引入马尔科夫链-蒙特卡洛(MCMC)高效采样方法,根据选定的预应力混凝土梁斜裂缝倾角计算公式作为贝叶斯先验模型; 通过收集到的45组剪切斜裂缝数据,考虑了箍筋配筋率、箍筋强度、混凝土抗压强度、剪跨比和有效预应力参数,建立了修正的斜裂缝倾角计算模型。结果表明:先验模型的预测值和试验值比值的均值和变异系数分别为0.68和0.26,后验模型的预测值和试验值比值的均值和变异系数分别为0.98和0.25,预测值更加接近试验值; 基于先张法预应力混凝土空心板梁实测斜裂缝倾角验证计算模型,先验模型的预测值和试验值比值的均值和变异系数分别为0.57和0.19,后验模型的预测值和试验值比值的均值和变异系数分别为0.81和0.21,后验模型的预测值更接近试验值,能够更加准确预测PC梁斜裂缝倾角。

Probabilistic Calculation Model of Inclined Crack Angle of Prestressed Concrete Beam

In view of the inclined crack angle of prestressed concrete(PC)beams, the formulas recommended by national codes are quite different, and there is no clear theoretical model. Based on the Bayesian theory and the introduction of Markov Chain-Monte Carlo(MCMC)efficient sampling method, the selected calculation formula of inclined crack angle of prestressed concrete beams was used as the Bayesian prior model. Based on the collected 45 groups of inclined crack data, considering stirrup reinforcement ratio, stirrup strength, concrete compressive strength, shear span ratio and effective prestress, the modified calculation model of inclined crack angle was established. The results show that the mean and coefficient of variation of the ratio of predicted and experimental values of the prior model are 0.68 and 0.26 respectively. The mean and coefficient of variation of the ratio of predicted and experimental values of the posterior model are 0.98 and 0.25 respectively, and the predicted value is closer to the experimental value. Based on the inclined crack angle measured by the shear test of PC hollow slab beam, the proposed posterior model is verified,and the mean and coefficient of variation of the ratio of predicted value and experimental value of the prior model are 0.57 and 0.19 respectively. The mean and coefficient of variation of the ratio of predicted value and experimental value of the posterior model are 0.81 and 0.21 respectively. The predicted value of the posterior model is closer to the experimental value, which can more accurately predict the inclined crack angle of PC beams.