Strength Of Materials Book Pdf By Bhavikatti

[Leroy Turcios]

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In structural engineering systems, shear walls are two-dimensional vertical elements designed to endure lateral forces acting in-plane, most frequently seismic and wind loads. Shear walls come in a variety of materials and are typically found in high-rise structures. Because steel shear walls are lighter, more ductile, and stronger than other concrete shear walls, they are advised for usage in steel constructions. It is important to remember that the steel shear wall has an infill plate, which can be produced in a variety of forms. The critical zones in flat steel shear walls are the joints and corners where the infill plate and frame meet. The flat infill plate can be modified to improve the strength and weight performance of the steel shear walls. One of these procedures is Topology Optimization (TO) and this method can reduce the weight and also, increase the strength against the cyclic loading sequences. In the current research paper, the TO of the infill steel plate was considered based on the two methods of volume constraint and maximization of strain energy. Four different volumes (i.e., 60%, 70%, 80%, and 90%) were assumed for the mentioned element in the steel shear wall. The obtained results revealed that the topology configuration of CCSSW with 90% volume constraint presented the highest seismic loading performance. The cumulated energy for this type of SSW was around 700 kJ while it was around 600 kJ for other topology optimization configurations.

One of the key points in the field of strengthening the shear walls, is topology optimization. As a form optimization technique, topology optimization makes use of mathematical models to optimize material arrangement for a given set of loads, circumstances, and constraints inside a user-defined space19. By considering the topology optimization on the steel shear walls, the weight and strength can be reduced and improved, respectively. Therefore, topology optimization can be useful from a cyclic performance point of view.

In order to gain a better understanding of the seismic performances of shear walls, several researchers have recently attempted to investigate various techniques that may be effective against the seismic sequences. Some of the published articles about the aforementioned issues are included in the paragraph that follows.

Professional software is now made specifically for topology optimization thanks to the development of optimization techniques. Numerous research that optimizes the topology of structures has recently been reported. Topology optimization was utilized by Bagherinejad and Haghollahi25 to determine the optimal form of perforated steel plate shear wall in the moment frames. They used the maximizing of reaction forces as the objective function and carried out the optimization. Daryan et al.26 proposed an effective approach for the best design of frames with steel plate shear walls by utilizing bat optimization and modified dolphin echolocation techniques.

According to the above literature, using topology optimization to find the optimum shape of the infill plates of the steel shear walls can be useful in the presence of cyclic loading conditions. Thus, in this research article, three different connection types between the infill plate and the border elements (i.e., fully-connected, beam-connected, and column-connected) together with the two well-known methods of volume and strain energy were assumed for the analyses through the use of finite element analyses. Besides, four various volume constraints of 60%, 70%, 80%, and 90% were remarked for the infill plates of the steel shear walls. It is noteworthy that the selected assumption is considered for the first time and it can be stated that this paper considered comprehensive assumptions. Then, finite element analysis was implemented to figure out the optimum infill plate shapes and some critical characteristics of the steel shear walls including stress and strain distributions, hysteresis curves, strength, cumulated energy, and plastic dissipation energy.

As stated earlier, the current research paper used the topology optimization concept in the steel shear walls to obtain the optimum shape of the infill plate of the steel shear wall by utilizing finite element simulations. Thus, first, this concept is briefly described and then the implemented experimental data together with the studied steel shear walls in the current research paper are stated.

Here, the reported results by Emami et al.28 were considered as the main input data for the analyses. They tested three different types of shear walls; flat Steel Shear Walls (SSWs), vertically Corrugated Steel Shear Walls (CSSWs), and horizontal ones. The results revealed that the corrugated shear walls could present higher cyclic performance compared to the flat SSW. But from an economic issues point of view, the flat SSW was a good choice. The schematic representation and the real test specimen of the flat SSW are exhibited in Fig. 2.

Besides the mentioned consideration above, three other assumptions were also considered in the TO theories. Here, different zones in the infill plate were considered frozen areas, which meant that these areas were out of the optimization scope. The frozen areas and other areas as the targeted zones of the optimization are illustrated in Fig. 3.

After considering the mentioned assumptions, the TO theories together with the finite element analysis software were implemented to optimize the infill plate of the SSW. The procedure of the finite element analysis is briefly described in the next subsection.

Finite Element Analysis (FEA) is the process of modeling objects and systems in a computerized environment with the objective of locating and fixing potential (or existing) structural or performance issues31. Preprocessing, which gets the modeling data, processing, which puts the equations together and solves them, and postprocessing, which shows the analysis results, are the three primary steps in the finite element analysis process32. The automotive, aerospace, shipbuilding, and construction industries can all benefit greatly from the use of FEA33. It provides precise, efficient, and economical answers to engineering problems.

In the current research paper, the SSWs were modeled in the FEA software (Abaqus CAE) and then, the mechanical properties according to Table 3 were assumed as the material properties of the elements. After assembling the elements together, three different solvers were used; nonlinear static and dynamic explicit. It is noteworthy that in the current research paper, to obtain the optimized shape of the infill plate, the TOSCA34 plugin was used. Where the mentioned solvers were implemented to obtain the pushover curves, and hysteresis behavior, respectively. The loading and boundary conditions were applied based on Fig. 4 in the optimized SSWs.

The designed shear walls were meshed apart following the aforementioned processes (see Fig. 6). Also, after performing the TO procedures and implementing the mentioned plugin in the FEA, the optimized SSWs were also meshed apart. Figure 7 shows a representative illustration of the SSW with an optimized infill plate. The mesh convergence analysis was also used to determine the appropriate number and sizes of elements for the shear walls, with the element type being S8R that is based on the reduced integration method and with the order of two. In the end, a 5 cm mesh size was used for the frame parts and a 2.5 cm mesh size for the infill plate.

The von-Mises stress distributions in the different configurations of the SSWs are illustrated in this subsection. Figure 13 shows the stress distribution in the SSW with the flat infill plate. Based on this figure, the corners where the infill plate joined to the other elements resulted in higher amounts of stress. Thus, these zones are known as the stress concentration zones. Figures 14, 15, and 16 present the stress distributions in the FCSSW, BCSSW, and CCSSW configurations, respectively. The TO procedure could reduce the amounts of stress in the stress concentration zones and also, helped to good distribution of the stress over the infill plate of the SSWs. This claim was completely approved at the bottom of the columns of the optimized SSWs in Figs. 14 and 15.

When a loading sequence is applied to a structure cyclically, the mentioned structure experiences the hysteresis behavior. In the current research paper, the seismic loading condition was applied according to the curve plotted in Fig. 5, and then, the hysteresis responses of the SSWs were recorded in the FEA and plotted in a single curve. As stated earlier in the FEA section, the loading condition that was applied to the SSWs was displacement control, thus, the hysteresis curves presented constant values of displacement but the evaluated forces were different. The hysteresis curves of SSW with various configurations of FCSSW, BCSSW, and CCSSW are presented in Figs. 25, 26, and 27, respectively.

The hysteresis curves are loops and they have an inside area which means the absorbed energy by the SSWs. The hysteresis curve of a flat SSW is represented in Fig. 8. Considering this figure with those presented in the current subsection, confirmed that topology optimization could not expand the loops of hysteresis curves and consequently the absorbed exerted energies by the cyclic loading sequences. The highest value of the exerted force in the flat SSW (shown in Fig. 8) was around 600 KN but the optimized SSWs with three different configurations of FCSSW, BCSSW, and CCSSW and volume constraints resulted in lower forces.

Comparing the presented results gave a better inside into the seismic performance of the various types of studied SSWs. In each category of the SSW, the 80% and 90% volume constraints especially the 90% could result in the higher area inside the hysteresis loop in comparison to the other ones. As a matter of fact, the 90% volume constraint was similar to the 100% one (the fully flat SSW that was exhibited in Fig. 8) but the only problem with this volume constraint was the higher weight and costs of fabrication processes. However, in a single case of volume constraint (e.g., 90%) the CCSSW configuration of SSW presented the best response from a hysteresis curve point of view. The main reason for this issue was the frozen area in the TO procedure because, in a shear wall, the columns play a critical role in controlling the structure strength.

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