Fiber Reinforced Concrete (FRC) with Applications in Civil Engineering 2020
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Jianmin Wang, Chengfeng Zhu, Ziqiang Xiao, Qijun Zhao, Junzhe Liu, "Numerical Analysis on the Bending Performance of Prestressed SuperposingPoured Composite Beams", Advances in Civil Engineering, vol. 2020, Article ID 8897621, 10 pages, 2020. https://doi.org/10.1155/2020/8897621
Numerical Analysis on the Bending Performance of Prestressed SuperposingPoured Composite Beams
Abstract
Aiming at the bending performance of the prestressed superposingpoured concrete beam, the numerical simulation on the composite beams poured with the normal weight concrete (NWC) superposed on the fibred ceramsite lightweight aggregate concrete (LWAC) was conducted. Three kinds of prestressing schemes, straight linear prestressing force, curved prestressing force not across the casting interface, and curved prestressing force across the casting interface, were simulated for comparison, and the influence of the casting interval time was also considered. Results indicate that the stiffness of the superposingpoured beam can be effectively strengthened by considered schemes of the prestressing force; in addition, there are certain increases on the ultimate load except imposing the straight linear prestressing force. As the curved prestressing force is imposed across the casting interface, the maximal interlayer slip of the casting interfacial transition zone (CITZ) approximately equals to that without the prestressing force. The scalar stiffness degradation (SDEG) of the CITZ for the casting interval time being 14 days is obvious because of the weakening on the bonding performance of the CITZ. Comparatively, the SDEG variation of the CITZ in the model with the curved prestressing force across the casting interface is smoother and smaller on the whole than the other two prestressed schemes for the case of the casting interval time being 14 days.
1. Introduction
Ceramsite lightweight aggregate concrete (LWAC) possesses the merit with higher strength relative to lighter density, which benefits from the ceramsite characterizing lighter apparent density and rough surface with many small opening holes. The density of LWAC is lighter than that of the normal weight concrete (NWC) for about 25%–30%. In addition, LWAC shows good performance such as the thermal insulation [1–3]. The developing of the prefabricated building technology puts forward higher requirements to the composite concrete members and the functionally graded concrete (FGC) members. Generally, the composite concrete members are composed of the precast and the cast insitu components. For the composite concrete and FGC, the interfacial bonding performance is prominent to guarantee the integration and compatibility of whole members. Lightweight aggregate can effectively improve the microstructure of the interface in concrete and make the interfacial transition zone (ITZ) more compact because of its own morphological structure and apparent pores [4]. Akmaluddin and Murtiadi [5] discussed the connection behaviour of the composite concrete precast column and the sandwich beam under the static loading. Campi and Monetto [6, 7] proposed a closed solution of twolayer beams considering the interlayer slip, in which a linear and nonproportional law relating interfacial shear tractions and slips was chosen to describe the interfacial behaviour. Iskhakov et al. [8, 9] studied the mechanical property of prestressed composite beams and proposed a new concept that considers the interlayer deformation of concrete in the tension and compression zones. Ji et al. [10] analyzed the change rule of the midspan deflection of prestressed reactive powder concrete (RPC) and the NWC composite beams considering the influence of the prestressing degree, the RPC height, and the NC strength; the higher the prestressing degree is, the longer the elastic stage before crack is, and the faster the stiffness in strengthening stage after the yielding decreases. Study indicates that the application of prestressing can improve the rigidity of composite beams and reduce the cracks [11, 12]. Wu et al. [13] studied the failure mechanism, flexural capacity, shortterm stiffness, and crack distribution of Ushaped and inverted Tshaped prestressed composite beams and pointed out that composite beams with natural rough surface can be analyzed as whole beams not considering the relative slip. Li and Ji [14] analyzed the developing law of the crack during the loading of prestressed composite beams considering different prestressing degrees and prefabricated component heights. Li et al. [15] studied the interfacial bonding performance of the prestressed composite beams with different stirrup spaces and pointed out that the smaller the stirrup spacing is, the less possible the bonding slip occurs on the casting interface.
The related research are mainly focused on the overall performance of composite members composed of NWC without prestressing or only with straight linear prestressing force. Moreover, different casting interval times are necessary to suit the constructional variety of the superposingpoured composite members. The imposing of the prestressing force can effectively increase the stiffness of the concrete beams. Because of the existing of the casting interfacial transition zone (CITZ) in the superposed composite beams, the mechanism and performance of the composite beams after exerting the prestressing force is complicated. Besides, the arrangement of the prestressed bars and the casting interval time are great importance to the performance of the composite beams [16]. In this paper, the numerical simulation was conducted on the mechanical performance of the composite beams poured with the NWC superposed on the ceramsite LWAC. Different arrangement ways of prestressed bars and casting interval times were specially discussed on the influence of the overall performance of the superposingpoured beams.
2. Simulation Modelling
2.1. Modelling Scheme
The simulation analysis is based on the bending experiment of the simplified supported superposingpoured beams composed of the ceramsite LWAC and NWC. The precast ceramsite LWAC component at the bottom of the beam mainly bears the tensile force under the experimental load, and the NWC is casted on the LWAC component late. The detailed parameters of the superposingpoured beams are shown in Figure 1, in which the sectional casting height are determined according to the neutral axis in the section of the composite beams. The description on the prestressing schemes and the casting interval time are listed in Table 1. There are eight superposingpoured beam models designed for simulation, in which six models are prestressed superposingpoured beams, and the other two ordinary beams models are based on the experiment used for comparison. The grades of the longitudinal bars and the stirrups bars are HRB400 and HRB300, respectively. The prestressing bars are 1860 grade 1 × 7 stranded wire, and the prestressing force is 30 kN.
 
For modelling comparison based on the experiment. 
2.2. Material Constitutive Relationship in the Model
The concrete damaged plasticity model (CDP) is used to simulate the mechanical properties of superposingpoured concrete beams in this paper. It describes the inelastic performance of concrete based on the isotropic damage elasticity together with the isotropic stretching and compression damage plasticity. Besides, the CDP model can effectively simulate the dynamic and static mechanical behaviour of the concrete [17, 18]. The mix ratio of the two kinds of concrete in the experimental members B11 and B12 are listed in Table 2, and the basic mechanical properties of the concrete and reinforced bars are listed in Tables 3 and 4.


 
Referring to the code for design of concrete structures (GB 500102010). 
The CITZ is a typical part zone in the composite beams, which has significant influence on the overall performance of the composite beams. The mechanical property of the CITZ is related to the treatment method of the casting interface, the casting interval time, two kinds of concrete materials, and so on. The manual chiselling method was adopted to handle the casting interface in the referring experiment [19]. The cohesive element is used in the model to simulate the CITZ in the superposingpoured beam model. The basic mechanical parameters of the cohesive element listed in Table 5 are determined according to the experimental data [16] and the relevant formula [20, 21].

2.3. Model Building
In the model, the concrete and reinforced bars are modelled using the solid element and link element, respectively. Among them, the reduced integral element C3D8R is assigned to simulate the concrete, and the T3D2 truss element is assigned to simulate the reinforced bars in the model. The CITZ between the LWAC and NWC in the stackpoured beams are simulated by the cohesive elements. The local rigid bodies are modelled at the loading point and bearings to avoid the stress concentration during the simulation. The boundary constraints and loading scheme are shown in Figure 1 and are identical to the experiment [19].
The application of the prestressing force in the model is realized by the cooling method in the temperature field corresponding to the initial state. In the subsequent analysis step, the prestressing strand shrinks as the temperature reduces to generate the pretension force. The temperature cooling value is determined according to the following formula [22]:in which F is the prestressing force, σ is the prestressing stress, A is the crosssectional area, E is the elastic modulus, and α is the linear expansion coefficient.
3. Simulation Results
3.1. Modelling Verification
The effectiveness of the modelling was first verified by comparing the simulation results of B11 and B12 with that of the experiment. The loadmidspan deflection is shown in Figure 2. The modelling results fit well with that from the experiment before the yielding except that the deflection is a little smaller than that of the experiment. This difference becomes obvious during the loading late stage. It is mainly because of the typical influence of the generation of macrocracks in the experiment members as the load increases. Besides, the yielding loads are a little lower than that of the experiment. Considering the variation of the casting interval times, the ultimate load of model B12 is lower than that of B11 whether from the experiment or from the simulation. It is because the bonding performance of CITZ in the superposingpoured beams is weakened as the casting interval time increases. The emerging and developing of the cracks in the model can be represented by the compressive and tensile damage factors of the concrete element, which are shown in Figure 3. The cracks distribution result from the simulation coincides well with that of the experimental result.
(a)
(b)
(a)
(b)
At the loading beginning stage, the vertical bending cracks first emerge in the midspan bottom bending zone. The bending cracks develop upward with the loading. At the same time, diagonal cracks also emerge near both two foot bearings and incline upward to the loading points. One important characteristic is that most cracks have a brief stop as they develop close to the CITZ. This can be verified both by the experimental and the simulating results. Subsequently, only some cracks develop across the CITZ as the load continually increases. Finally, the beam failures due to the yielding of the longitudinal reinforcement and the concrete crack are at the top of the midspan.
In addition, the simulation on the prestressing is verified by comparing the simulation results of B21, B31, and B41 with results from the corresponding calculation method and design codes. The prestressing effect can be represented by the equivalent load method: The effect of straight linear prestressing and curved prestressing are equivalent to the pure bending and uniformly distributed load, respectively. Due to a certain difference existing in the elastic module between LWAC and NWC, the ceramsite LWAC is first converted into NWC by the equivalent section converting method. The inverse arch deflections of the superposingpoured beam model are calculated according to the bendingmomentarea method. At the same time, the inverse arch deflections of the straight prestressing and the curved prestressing are calculated [23, 24]:where N_{po} is the effective prestressing force, e is the eccentricity from the center of prestressed bars to the neutral axis of the converted section, L is the span length, E_{c} is the elastic modulus, and I_{o} is the inertial moment of the converted section.
The comparison of the results is listed in Table 6. The simulation results are close to that from the referring calculation method and design codes on the whole. Compared with the bendingmomentarea method and ACI31899, it is shown that the result from GB500102002 is more reliable due to the stiffness reduction during calculating.

3.2. LoadDeflection Relationship
The loaddeflection curves of the superposingpoured beams are shown in Figure 4. Compared with B11 and B12 without the prestressing force, the midspan deflections of beams with different arrangement modes of prestressed bars are all lower before the yielding load. In addition, there are observable increases on the ultimate loads of beams with prestressed bars except that of B21 and B22. Compared with the straight linear prestressing scheme at the bottom of the beam, the increases on the ultimate loads of beams with curved prestressed bars are more obvious for different casting interval times.
(a)
(b)
The simulation results are listed in Table 7. For B21 and B22 exerting the straight linear prestressing force at the bottom of beams, there is no obvious increasing on the ultimate load compared with B11 and B12, respectively. But the midspan deflection is clearly smaller than that of B11 and B12, respectively. The reduction of the deflection is about 23% and 19.9% that of B11 and B12, respectively. At the same time, the induced inverted arch deflection at the midspan are largest among the three kinds of prestressing schemes.

For the scheme with curved prestressed bars not across the CITZ, the ultimate load of B31 is clearly increased about 8.7% compared with B11 while the deflection is reduced about 8.0%. Comparatively, the ultimate load of B32 is increased about 12.5% compared with that of B12 with the midspan deflection reduced about 7.0%. It is due to the weakening of the bonding performance of the CITZ in the superposingpoured beams, which has significant influence on the deformation of the beam as the load increases. Because the bonding shear performance of the CITZ in the superposingpoured beams decreases quickly as the casting interval time increases, and the remaining shear strength with the casting interval time being 14 days is about 40% that casting at the same time [24].
As the curved prestressed bars in the superposingpoured beam models are located across the CITZ for the model B41 and B42, the increase extent of the ultimate loads is 12.0% and 19.9%, respectively, compared with B11 and B12. At the same time, the midspan deflections are similar to that of B31 and B32, respectively.
3.3. Relative Slip in the CITZ
The cohesive element are adopted to simulate the performance of CITZ in the superposingpoured beams. The relative longitudinal slip of the CITZ outside the loading point is extracted as shown in Figure 5 for discussion. Whether there is or no prestressing force, the relative slip of CITZ in the beam that the casting interval time is 45 minutes is much smaller than that with the casting interval time being 14 days as the load increases. The final maximal relative slip value for all models is listed in Table 8.
(a)
(b)
(c)
(d)

For B21 and B22 exerted the straight linear prestressing force, the final relative slip value is 1.8 times and 2.05 times as large as that of B11 and B12, respectively, and the relative slip in the CITZ both of B12 and B22 characterizes continual and accelerated increasing with regards to the loading until the final failure.
As imposed, the curved prestressing force with the casting interval time being 45 minutes, the overall variation of the relative slip with regard to the loading for B31 and B41 is similar to that of B11. The final maximal relative slip of B31 is about 125% that of B11. Comparatively, this value of B41 is almost similar to that of B11. For the casting interval time being 14 days with the curved prestressing force, a significant characteristic for the variation relation of the relative slip with the loading is that the increase of the relative slip eases up after yielding both for B32 and B42. The possible reason is that the moment distribution generated by the curved prestressing force in the beam is similar to that from the experimental load. After the yielding of the longitudinal bars, the existing of the curved prestressing force effectively slow down the developing of the relative slip in the CITZ. Finally, the maximal relative slip value of B32 is about 156% that of B12. Comparatively, the maximal relative slip value of B42 is almost similar to that of B12.
3.4. Stiffness Degradation of the CITZ
The key for superposingpoured beams to perform with wellcollaborative behaviour is whether there is excellent working compatibility and adhesion in the CITZ. The performance of the CITZ is influenced by the constructional method of the casting interface, the difference in the elastic module and strengths between the two kinds of concretes together with the casting interval time, and so on. The scalar stiffness degradation (SDEG) of the cohesive elements in the modelling can be extracted to symbolically characterize the damage variation in the CITZ. SDEG equaling 0 indicates that there is no damage, and SDEG equaling 1 means the cohesive elements are in full failure. The SDEG diagrams of cohesive elements to simulate the CITZ in the modelling at the ultimate load state are shown in Figure 6. The mainly prominent region is located in the shear span near the loading point. For cases of the casting interval time being 45 minutes, there is a larger region with higher SDEG values emerged in B21 compared with B11, B31, and B41. The possible reason is the arrangement of the curved prestressing force in B31 and B41 approximate the bending moment diagrams under the designed load, which make the coordinated performance of the superposingpoured beam model better than that of B21.
(a)
(b)
Compared with the situation of the casting interval time being 45 minutes, the region with higher SDEG values are more obvious for all beam models with the casting interval time being 14 days. It is due to that the bonding shear strength of the CITZ decreases to 40% with the casting interval time being 45 minutes. Results indicate that the distribution range and the SDEG values of B42 are generally similar to that of B12 from Figure 6(b). In addition, the distribution of SDEG values in B42 is smoother than that in B12. Comparatively, the area range with higher SDEG values in B32 and B22 are larger, especially for B22. Similarly, the SDEG values of B22 are generally larger than that in B32 and B42.
The SDEG variation of the CITZ corresponding to the loading is shown in Figure 7, in which the data are extracted and averaged from the SDEG distribution area with relatively higher values. The increase of SDEG in B21 is much larger than that of B11, B31, and B41 for cases with the casting interval time being 45 minutes. Comparatively, the SDEG variation of B41 with regard to the loading is similar to that of B11.
(a)
(b)
For the casting interval time being 14 days, the variation of the SDEG of B22, B32, and B42 with regard to the loading are similar. The midspan deflection of B22, B32, and B42 as the SDEG begin to increase clearly is smaller than that of B12 due to the effect of the inverse arch from the prestress. Comparatively, the SDEG of B42 changes smoothly, and it is smaller than that of B22 and B32 on the whole.
The slipping load of the beam model is defined here as the load when the SDEG value of the CITZ is not zero and begins to change obviously. The slipping load of all beam models is listed in Table 9 together with the ratio of the slipping load to the ultimate load L_{R}. After exerting the prestressing force, the slipping loads and the ratio L_{R} all increase for all beam models. As the casting interval time changes from 45 minutes to 14 days, the slipping load all decrease whether there is or no prestressing force. In addition, the ratio L_{R} also decreases. For both two casting interval time cases, the increased degree of the slipping load and the ultimate load for the curved prestressing force across the casting interface are larger than that of the other two considered schemes of the prestressing force.

4. Conclusions
The bending performance of the superposingpoured composite concrete beams was analyzed considering the influence with different prestressing schemes and different casting interval times.(1)For the schemes imposing the straight linear prestressing force, the stiffness of the superposingpoured beam can be effectively strengthened, but there is little influence on the ultimate load. Comparatively, with the curved prestressing force imposed, there is observable increase on the ultimate load of the superposingpoured beam at the time of the stiffness effectively strengthened.(2)The relative slip of the CITZ is obvious as the casting interval time changes from 45 minutes to 14 days because of the weakening on the bonding performance of the CITZ. Imposing the straight linear prestressing force further obviously increases the relative slip. Comparatively, the variation relationship of the relative slip with regards to the loading as imposing the curved prestressing force across the CITZ is more rational, which eases up after the yielding load of the beam. And the final maximal relative slip is similar to that with no prestressing force whether the casting interval time is 45 minutes or 14 days.(3)When the casting interval time changes from 45 minutes to 14 days, the region with higher SDEG value at the ultimate state expands obviously whether there is or no prestressing force imposed. As imposed the straight linear prestress or the curved prestress but not across the casting interface, the region with higher SDEG value in the CITZ is larger than that with no prestress. Comparatively, when the curved prestressed bars are arranged across the CITZ, the region with higher SDEG value is similar to that with no the prestress; and the distribution of the SDEG are relatively uniform.
It is shown that more rational effect and performance can be obtained with the curved prestressing force across the casting interface exerted in the composite beams if it is practicable in the real construction. There is important influence on the mechanical performance of the superposingpoured composite beams as imposing the prestressing force. The possible interlayer slip and the stiffness degradation in the casting interfacial zone need further experimental analysis based on the numerical simulation.
Data Availability
The data used to support the findings of this 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
This work was supported by the National Natural Science Foundation of China (Nos. 51878360 and 51778302), Natural Science Foundation of Zhejiang Province (LY18E080008), and Ningbo Science and Technology Project (202002N3117).
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Copyright © 2020 Jianmin Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.