基于分形理论无腹筋混凝土梁的受剪性能

Experimental study on concrete beams without web reinforcement based on fractal theory

  • 摘要: 基于裂缝的发展及分布形态,探究无腹筋混凝土梁在不同剪跨比和纵筋配筋率作用下的剪切性能,采用剪跨比分别为1.5、2、2.5和纵筋配筋率分别为1.28%、1.62%、1.99%的9组无腹筋混凝土梁进行四点加载受剪试验,通过应用分形几何理论对试验梁表面的裂缝进行分析,使用盒计数法计算得到分级荷载及极限荷载作用下梁表面裂缝的分形维数,探讨了梁表面分形维数与极限荷载、分级荷载及跨中挠度之间的关系。结果表明:剪跨比与极限荷载及开裂荷载成反比,而纵筋配筋率与极限荷载成正比,但其对于开裂荷载的影响较小。无腹筋混凝土梁不论在分级加载作用下还是极限荷载作用下都具备明显的分形特征,在分级荷载作用下的分形维数在0.964~1.449,在极限荷载作用下的分形维数在1.33附近。分级荷载、跨中挠度与分形维数之间呈现较好的对数关系,分级荷载与分形维数的变化曲线受剪跨比及梁纵筋配筋率的影响具有一定的规律性,而跨中挠度受剪跨比的影响较小,在纵筋配筋率作用下,其曲线的曲率呈现出先增大后减小的趋势,但极限荷载与分形维数之间的关系具有一定的差异性,极限荷载会随着剪跨比的增大呈现出先增大后减小的趋势,随着纵筋配筋率的增大呈现出的差异性较大。

     

    Abstract: Based on the development and distribution of cracks, we explored the shear performance of concrete beams without web reinforcement under different shear span ratios and longitudinal reinforcement ratios. Nine groups of concrete beams without web reinforcement with shear-span ratios of 1.5, 2, 2.5 and longitudinal reinforcement ratios of 1.28%, 1.62%, and 1.99% were used for four-point loading shear tests. The cracks on the surface of the test beam were analyzed by applying fractal geometry theory, and the box counting method was used to calculate the fractal dimension of the cracks on the surface of the beam under the effect of the graded load and the ultimate load. The relationship among the fractal dimension of the beam surface, the ultimate load, the graded load and the span was discussed. The results show that the shear-span ratio is inversely proportional to the ultimate load and cracking load, while the longitudinal reinforcement ratio is directly proportional to the ultimate load and exhibit a small influence on the cracking load. Concrete beams without web reinforcement have obvious fractal characteristics under the effect of graded loading or ultimate load. The fractal dimension under the effect of graded load is 0.964–1.449, and the fractal dimension under the effect of ultimate load is around 1.33. The graded load, mid-span deflection and fractal dimension show a good logarithmic relationship. The change curve of graded load and fractal dimension is affected by the shear-span ratio and the beam longitudinal reinforcement ratio. The intermediate deflection is less affected by the shear-span ratio. Under the effect of the longitudinal reinforcement ratio, the curvature of the curve shows a trend of first increasing and then decreasing, but the relationship between the ultimate load and the fractal dimension has certain differences. The ultimate load first increases and then decreases with the increase of the shear span ratio, and the difference is greater with the increase of the longitudinal reinforcement ratio.

     

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