Abstract
In this paper, a model to predict the residual shear capacity of RAC beams with corroded stirrups was established, and the simulation analysis was conducted on recycled concrete beams with different corrosion level using ANSYS. The reliability of the finite element analysis model was verified by comparing the finite element results with experimental results.
1. Introduction
Recycled concrete refers to a new type of concrete that is made by using waste concrete, and it can also be called recycled aggregate concrete (RAC). RAC beam is an important structural member, and scholars have carried out a lot of research on its shear behavior. Zhang [1] studied the influencing factors of the cracking load of the inclined section of recycled concrete beams and fitted the calculation formula of the cracking load of the inclined section of recycled concrete beams. The authors in [2–15] studied the influencing factors of shear capacity, and the conclusions are basically consistent: the shear capacity of recycled concrete beams decreases with the increase of shear span ratio and aggregate replacement ratio and increases with the increase of stirrup ratio and concrete strength. Zhang [1] also fitted the shear capacity formula of recycled concrete beams through the shear static test of 8 recycled concrete beams.
Numerical analysis methods have a wide range of applications in engineering structural analysis. Finite element method is a very useful numerical analysis method for the analysis of reinforced concrete structures, which can provide a large amount of structural information, such as structural displacement, stress, strain, bond slip, and failure load [16].
In this paper, the calculation model to predict the residual shear capacity of RAC beams with corroded stirrups is established, and the ANSYS finite element software was used for structural nonlinear analysis and modeling; a separate model is selected to analyze the reinforced corroded recycled concrete beam, and the reliability of the calculation model is verified.
2. Analysis of the Residual Shear Capacity of Corroded RAC Beams
Based on results of the shear behavior experiment of RAC beams with corroded stirrups in laboratory, the relationship between the measured shear capacity Vu and the corrosion levels is shown in Figure 1, which illustrates that the measured shear capacity of RAC beams increases first and then decreases with the increase of corrosion level of stirrups.
The limit equilibrium method for the residual shear capacity of the oblique section of a beam is a method to solve the problem by establishing the equilibrium of the shear failure limit state of the structure through the study of the shear mechanism. The theory solves the unknown quantity by establishing the internal force balance equation and deformation equation through the stress analysis of the isolation body. The total shear ultimate capacity of the corroded stirrup can be expressed by the following equation:where Vc is the shear force borne by concrete in shear compression zone; Vd is the total pin force of longitudinal reinforcement; Vay is the vertical part of the bite force of the inclined section aggregate; is the shear force borne by stirrup; and Vcu = Vc + Vd + Vay.
Xu and Niu [17] summarized and proposed the calculation method of Vcu and , as shown in the following equation:where λ is the shear span ratio; s is the stirrup spacing; is the yield strength of stirrups; As/bh is the longitudinal reinforcement ratio; is Area of stirrup after corrosion; and .
In this study, the relationship between axial compressive strength and cubic compressive strength of recycled concrete is fc = 0.76fcu [18]. Assuming that the stirrup is uniformly corroded and the average corrosion rate is adopted, the geometric relationship after the stirrup is as follows:where L is the length of stirrup, mL is the weight of stirrup, ρs is the corrosion level of stirrups, d is the diameter of stirrup after corrosion, ω is the iron density, and D is the diameter of stirrup before corrosion.
The theoretical calculation formula of residual shear capacity of recycled concrete beams obtained from simultaneous equations (1), (2), and (3) as (4).where is is area of stirrup, h is the cross-sectional height of the beam, and h0 is the effective cross-sectional height of the beam.
The relationship between the measured shear capacity Vu and the calculated value of (4) is shown in Figure 2.
Figure 2 illustrates that the measured value is close to the calculated value of (4) but not completely consistent, which is also because the geometric relationship of corroded reinforcement in (3) is obtained under the ideal condition of uniform corrosion. To make the theoretical value of (4) satisfied with measured value, the corroded influence coefficient is introduced, and the fitting relationship between theoretical value and measured value can be expressed as follows:
According to (5), the relationship between calculation value of and the corrosion levels is shown in Figure 3, and it illustrates that the fit degree is better. Therefore, the residual shear capacity of corroded RAC beams can be calculated as follows:
3. Finite Element Analysis of Recycled Concrete Beams with Corroded Stirrups
3.1. Establishment of Finite Element Model
Solid65 solid elements are used for the concrete unit. The Solid65 element has eight nodes, each with three degrees of freedom, which can consider the cracking and crushing of concrete. The reinforcement unit adopts Link180 rod unit. This unit has two nodes, each with three degrees of freedom, does not bear bending moments, and has the function of large deformation. The concrete and steel elements established are shown in Figure 4.
(a)
(b)
Considering the impact of corrosion on the mechanical properties of beams, this paper simulates the bond slip relationship between steel and concrete using a nonlinear spring element Combin39. This unit has two nodes. Three mutually perpendicular nonlinear springs with different stiffness and no geometric volume are set at each steel and concrete element node.
After establishing different elements, the element nodes are merged and then constraints in the X and Y directions are applied, perpendicular to the beam length direction at the support, while freely deforming along the beam length direction. Using displacement loading mode, vertical load is applied at the loading point of the beam.
During the modeling process, the smaller the unit size division, the closer it is to the real component. However, during the simulation process, it is easy to cause stress concentration, which makes the calculation difficult to converge. It is necessary to determine a reasonable grid density by dividing the grid multiple times and comparing it with experimental results.
Concrete components often work with cracks during the stress process, and during the cracking process, cracks may close and new crack surfaces may be generated. In the computer simulation process, when internal forces act on the surface of cracks, the program can use the shear transfer coefficient of open cracks to simulate stress loss, or the shear transfer coefficient of closed cracks. The values of both variables are 0-1, and the analysis is generally based on experience.
Adopting the displacement convergence criterion, the convergence tolerance value has a certain impact on the simulation results. Convergence tolerance has no fixed value range in theory, and by appropriately relaxing, it can accelerate convergence, but by relaxing, it may result in incorrect results.
Based on the abovementioned analysis of influencing factors, several models were established using a single parameter change method to analyze the impact of each parameter change on the finite element simulation results (displacement and failure load) and compared with the experimental results to analyze the degree of influence of each factor. In order to reduce stress concentration, surface loading is used at the loading point. The reinforcement adopts a dynamic strengthening model, the constitutive relationship of concrete adopts an elastic-plastic MISO type curve, and the failure criterion adopts the William Warner five parameter failure criterion. The cracking option is turned on, and the crushing option is turned off. In order to obtain the sensitivity of each parameter to the simulation results, the parameter change amplitude should not be too large. The different model parameter settings are shown in Table 1.
3.2. Verification of the Reliability of Equation (6) for the Shear Capacity
The fitting formula for shear capacity in Section 2 was obtained when the corrosion rate was less than 13%. To verify the reliability of the fitting formula, a finite element analysis software was used to increase the corrosion rate of steel bars to establish a model.
In the design of finite element software simulation, the corrosion rates of stirrups are 15%, 19%, 23%, 27%, and 30%. The strength grade of recycled concrete is designed to be C50, and the other parameters are the same as those in the experiment. The comparison between the simulated results and equation (6) is shown in Figure 5.
From Figure 5, it can be seen that the calculated value of the shear capacity fitting formula is still in good agreement with the finite element simulation value after increasing the corrosion level of the stirrup, so fitting equation (6) is effective.
3.3. Model Parameter Analysis
The main influencing factors on the shear capacity of inclined sections are cross-sectional size, shear span ratio, etc. This section analyzes the shear capacity of recycled concrete beams by simulating changes in cross-sectional size and shear span ratio.
3.3.1. Influence of Cross-Sectional Dimensions on Shear Capacity
To determine the effect of section size on the shear capacity of recycled concrete beams, three sets of models were selected for calculation. The corrosion level of the stirrups was 0%, and the parameters of the stirrups and concrete were the same as those measured in the experiment in this paper. The results of simulation calculation using finite element software are shown in Table 2.
From Table 2, it can be seen that the shear capacity of recycled concrete beams increases with the increase of width and decreases with the increase of height. It can also be seen that the decrease in shear capacity is nonlinear with the increase of height. This is mainly because when the beam height is large, the tearing cracks are more obvious, the pin bolt effect is greatly reduced, and the width of oblique cracks is also large, weakening the interlocking effect of aggregates, thereby accelerating the speed of reducing shear capacity.
3.3.2. Influence of Shear Span Ratio on Shear Capacity
Through finite element method, the loading point and support position were changed to simulate beams with shear span ratios of 2 and 3. The relationship between shear capacity and shear span ratio was obtained as shown in Figure 6. From Figure 6, it can be seen that under the same corrosion level, the ultimate shear capacity decreases with the increase of shear span ratio, which is also because the increase of shear span ratio reduces the number of stirrups per unit volume.
4. Conclusions
Based on the results of the experiment, the following conclusions are presented:(1)A new calculation model to predict the residual shear capacity of RAC beams with corroded stirrups is established, and the calculated value of the shear capacity fitting calculation model is still in good agreement with the finite element simulation value after increasing the corrosion level of the stirrup.(2)Several models were established using a single parameter change method to analyze the impact of each parameter change on the finite element simulation results and compared with the experimental results to analyze the degree of influence of each factor.(3)In the finite element, the shear capacity of recycled concrete beams increases with the increase of width and decreases with the increase of height, and the ultimate shear capacity decreases with the increase of shear span ratio under the same corrosion level.
Data Availability
The data used to support the study are available from the corresponding author upon request.
Conflicts of Interest
The authors declare that there are no conflicts of interest regarding the publication of this paper.
Acknowledgments
The work carried out in this study was supported by the Science and Technology Research Project of Jiangxi Provincial Department of Education (Grant no. GJJ2201742).