Introduction
The short-limbed wall (SLW) belongs to the shear wall structure system and is generally defined as a reinforced concrete shear wall with a ratio of section depth to width ranging from 5 to 8. The width of the section is no less than 200 mm, and the depth of the section ranges from 1000 mm to 2500 mm. In the former nonlinear FEM analysis, the finite model usually was the united model [
1,
2], which assumed that the steel distributes evenly in the concrete and is regarded as a united material and element. We can obtain the composite results from the ANSYS analysis but cannot obtain the stress-strain relation of the steels. In this paper, a nonlinear finite element analysis of some separate models are taken according to the SLW specimens. We investigated the stress distribution characteristics of the SLW structure in different section forms and the axial compression ratio of the section, especially when the steel yields.
Experiments
The FEM models in this paper are used according to the specimens in the horizontal cyclic loading experiments in Ref. [
3]. The experimental specimens were scaled to half of the actual size. All the 6 specimens were divided into 2 groups. The specimens in the first group were non-flanged ones, denoted as S1, S2, and S3; the specimens in the second group were flanged ones, denoted as FS1, FS2, and FS3. All the reinforcements were of Grade HRB400, with a crest-formed extrusion on the surface of the bar, and all the concrete was of Grade C20. Their dimensions and section reinforcement are shown in Figs. 1 and 2.
FEM models
In this paper, the models were constructed by separate models. The difference between the united model and the separate model is that the concrete elements and the steel elements are treated as two element types in the separate model; the concrete element is SOLID65, and the steel element is LINK8. The concrete and the steel are meshed into finite elements, and the rigidity matrixes of SOLID65 and LINK8 are calculated. The constitutive relation of the concrete is Multilinear Kinematic Hardening.
Load steps are necessary in load imposing. First, define a specific time range as the whole process of loading; then divide the duration of time into several even parts. Because the load imposing process corresponds to the time, the value of loading can be obtained according to the value of time. The order of load imposing is vertical loading first and then horizontal loading. The FEM models of the SLW and steel elements are shown in Fig. 3.
FEM analyses
Section form
In order to compare with the experiment, we constructed the FEM models in 2 section forms in this study, and the section dimensions are shown in Fig. 1. The axial compression ratio controlling the vertical load of the 6 models is 0.3, and the horizontal loads selected are large enough according to the theoretical values. The loads are determined by setting an appropriate time value and time increasing value in solve control. By using ANSYS, the principal stress and the principal strain equivalent line distribution of the models under different load steps can be obtained. The load-displacement curves of the FEM models are shown in Fig. 4. It is easy to get the crack load and displacement, yield load and displacement, and failure load and displacement of the 6 models.
It is shown in Fig. 4 that the load-displacement curves of the non-flanged wall models are not very smooth, and the curves change suddenly. The curves are nearly straight lines before the models yield, but their trend goes down immediately after the yield, displaying an obvious brittle characteristic. It shows that the non-flanged wall structure’s earthquake resistance performance is quite bad. On the contrary, the load-displacement curves of the flanged wall models are quite smooth. The load-displacement curves have an obvious turning point, generally along with the load enlargement, displaying a long rigidity degeneration process. It shows that the ductility of the flanged wall is better than the non-flanged one, and this conclusion supports the stipulation of limiting the use of non-flanged walls in the Reinforced Concrete Design Standard.
The skeleton curves of the specimens are shown in Fig. 5. Compared with the skeleton curves of the specimens obtained from the experiment, the load-displacement curves of the FEM models from the ANSYS finite element analysis do not match precisely in terms of the load and displacement value, but the curve trend agrees well.
Depth-to-width ratio
Ductility is very important for measuring a structure’s earthquake-resistant behavior. In this paper, dividing the yield displacement by the failure displacement is defined as the ductility coefficient. The ductility coefficient of the FEM models is shown in Table 1.
For not only the non-flanged models but also the flanged models, when the section depth-to-width ratio is 6.5, the model’s ductility coefficient is biggest. Either increasing or decreasing the section depth-to-width ratio may reduce the ductility coefficient and reduce the earthquake-resistant behavior of the structure. Therefore, in real-life engineering design, the SLW with a section depth-to-width ratio of 6 is suitable.
The ductility coefficients of the SLW models obtained from the ANSYS analysis are less than that from the result of the experiment, but the value trend agrees well.
Axial compression ratio
The effect of axial compression ratios on a structure’s earthquake resistance performance has been studied in some experiments. In this paper, the ANSYS finite element analysis on the model FS2 was selected for comparison with the experimental result. The axial compression ratios of the models are 0.1, 0.3, and 0.5, and the corresponding assign numbers are FS2a, FS2b, and FS2c, respectively. The load-displacement curves of the FEM models are shown in Fig. 6.
In Fig. 6, the load-displacement curves are quite smooth when the axial compression ratio is 0.3. It is shown that the model with an axial compression ratio of 0.3 has the best ductility and seismic resistance property, agreeing well with the result of the experiments. The conclusion proposes controlling the axial compression ratio to about 0.3 in the structure design.
In Ref. [
3], the experiment does not change the axial compression ratios; the conclusions of the ANSYS analysis are the supplements to the experiment.
Steel bar stress
The positions of the steel bars’ yield are different in the non-flanged models and in the flanged models. For the non-flanged models, the S1 steel bars’ initial yield position is the edge of the bottom of the limb; the S2 steel bars’ initial yield positions are the edge of the bottom of the limb and the end of the linking beam, while the S3 only yielded in the steel bars at the end of the linking beam. For the flanged models, the FS1 steel bars’ yield position is the edge of the bottom of the limb, while the steel bar yield positions of the FS2 and FS3 are the longitudinal bars at the bottom of the limb. The failure positions of the steel bars of the 6 models are all at the end of the linking beam, which agrees well with the experiment results. The contour plot of the yield stress of the models is shown in Figs. 7(a)-(f).
The positions of the steel bar yields obtained from the ANSYS analysis agree well with the experiment result, which is the merit of the separate model over the united model.
Conclusions
Some conclusions can be drawn from the nonlinear finite element analysis of the short-limbed wall.
1) Compared with the united model, the separate model can simulate the SLW structure more precisely, and the stress distribution of the SLW structure, especially the stress distribution characteristic of the bar, can be obtained. The separate model used in this paper is an important improvement in the FEM analysis of the SLW and is a supplement to the former united model analysis.
2) The load-displacement curves about the wall are different when the section forms are different. The load-displacement curves of the non-flanged wall models are not very smooth, and the curves change suddenly. On the contrary, the load-displacement curves of the flanged wall models are quite smooth. It shows that the seismic resistance property of the flanged wall is better than the non-flanged one, and this conclusion supports the stipulation of limiting the use of the non-flanged wall in the Reinforced Concrete Design Standard.
3) When the section forms of the SLW are the same, the SLW structures with a depth-to-width ratio of 6.5 exhibit the best comprehensive seismic-resistant property. So the use of a SLW with a depth-width ratio of 6.5 is advocated in actual project design.
4) In structure design, we propose controlling the axial compression ratio to about 0.3 because the structure has the best ductility and seismic resistance property with this ratio.
5) The yield positions of the structure are at the edge of the bottom of the limb and the end of the linking beam, while the failure positions of the structure are all at the end of the linking beam; improving the ductility of the linking beam is very important in the structure design.
Higher Education Press and Springer-Verlag Berlin Heidelberg
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