Experimental study on concrete beams without web reinforcement based on fractal theory
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Abstract: Based on the development and distribution of cracks, in order to explore the shear behavior of concrete beams without web reinforcement under different shear span ratios and longitudinal reinforcement ratios, the shear span ratio λ is 1.5, 2, 2.5 longitudinal reinforcement. The four sets of non-belt concrete beams with a rate of 1.28%, 1.62% and 1.99% were subjected to four-point loading shear test. The cracks on the surface of the test beam were analyzed by applying fractal geometry theory, and the graded load and limit were calculated by the box counting method. The fractal dimension D of the crack on the surface of the beam under load is used to investigate the relationship between the fractal dimension D of the beam surface and the ultimate load, the grading load and the mid-span deflection y. The results show that the shear span ratio λ is inversely proportional to the ultimate load and the cracking load, while the longitudinal reinforcement ratio ρ is proportional to the ultimate load, but its influence on the cracking load is small. The concrete beams without web reinforcement have obvious fractal characteristics under the action of step loading or ultimate load. The fractal dimension D under the step load is 0.964~1.449, and the fractal dimension D under the ultimate load is around 1.33. There is a good logarithmic relationship between the graded load, the mid-span deflection and the fractal dimension D. The variation curve of the graded load and the fractal dimension has certain regularity due to the shear span ratio λ and the beam longitudinal reinforcement ratio ρ. However, the mid-span deflection is less affected by the shear span ratio. Under the effect of the longitudinal reinforcement ratio, the curvature of the curve first increases and then decreases, but the relationship between the ultimate load and the fractal dimension D has With a certain difference, the ultimate load will increase first and then decrease with the increase of the shear span ratio λ, and the difference will be greater with the increase of the longitudinal reinforcement ratio ρ.