Chapter 5 Conclusion and Recommendations
5.1 Conclusion
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86 5.1.2 Numerical Experiment 2
Like Numerical Experiment 1, the results attained for Numerical Experiment 2 indicate that most of the damage caused by the static load occurs after load step 2, the horizontal displacement loading. Majority of the deformation occurs along the x-axis, though Numerical Experiment 2 shows a much higher proportion of deformation in the y-direction as compared to Numerical Experiment 1. Areas of high deformation include the entire top course of the wall and regions above the door and window opening. Areas of high equivalent stress include the bottom left and top right corner of the door and window opening and the bottom right corner of the wall. Relatively high shear stresses develop in the XY plane, above the door opening and across the middle of the wall. The non-linear behavior of masonry is proven through damage showing plastic strain and the shape of the force vs displacement diagram. Four regions of high plastic strain are identified.
5.1.3 Numerical Experiment 3
Numerical Experiment 3 is a dynamic analysis of Geometry 2, consisting of Modal and Response Spectrum analysis. The Modal analysis is limited to 6 Modes with natural frequencies ranging from approximately 6Hz to 40 Hz. Results from the Modal analysis identify areas of high stresses and deformations in the low-cost house wall. High deformations occur at the top of the wall, in the z-direction while relatively high stresses develop at the top corners of the door opening, the bottom left corner of the door opening and the bottom right corner of the wall. The Response Spectrum analysis is done by creating a design response spectra graph using (SANS 10160-4, 2009). The results from the Response Spectrum analysis show relatively high deformations at the top of the wall. The highest equivalent stresses and shear stresses are found at the bottom corner of the window opening. The results attained from the Response Spectrum analysis indicate that it is not the crucial load factor compared to the static structural loading.
5.1.4 Summary of results
The results compare well in a qualitative sense with existing literature found in (Agüera, et al., 2016), (Drosopoulos & Stavroulakis, 2018), (Elvin, 2009), (Khoyratty, 2016) and (Kömürcü & Gedikli, 2019). In the case of the 1-meter square wall, high stress concentrations are found at the bottom corner of the wall, indicating flexural failure as mentioned in (Tomaževič, 2016). These high stresses are shown to propagate upwards in a diagonal manner, indicating possible shear failure which is also mentioned in (Tomaževič,
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2016). Considering the static structural analysis for Geometry 2 (low-cost house wall), high stress concentrations are found around the door and window openings, similar findings are shown in (Drosopoulos & Stavroulakis, 2018) numerically and by field inspection in (Khoyratty, 2016). High stresses are also found at the bottom corner of the wall and propagate diagonally upwards, this is also mentioned in (Drosopoulos & Stavroulakis, 2018). For both geometries, plastic strain develops predominately in the mortar under static structural loading, with high plastic strain developing in the bottom most layer of mortar for Geometry 1, similar results are found in (Agüera, et al., 2016) qualitatively. Four zones of high plastic strain are observed for Geometry 2. These zones include regions at the bottom of the wall, above and around window and door openings and sections of the wall between the door and window opening.
The dynamic analysis is performed using both Modal analysis and Response Spectrum analysis. Results from the modal analysis indicate that high deformations occur at the top of the wall while relatively high stresses develop at the top corners of the door opening, the bottom left corner of the door opening and the bottom right corner of the wall. These problem areas are consistent with evidence shown in (Khoyratty, 2016). The Response Spectrum analysis is connected to the Modal analysis. The results from the Response Spectrum analysis show relatively high deformations at the top of the wall. The highest equivalent stresses and shear stresses are found at the bottom corner of the window opening. The results generated from the dynamic analysis in Numerical Experiment 3 show smaller deformations and stresses when compared to the static analysis in Numerical Experiment 2. It should be noted that the static loads used in Numerical Experiment 2 are exaggerated loads used to bring the structure to failure, whereas the Response Spectrum analysis uses realistic values based upon historical seismic data, which is region dependent. Therefore, in this study, the dynamic load is not the crucial load factor.
6.1.5 Propositions for improvement of design
Major points of weakness in the static and dynamic analysis of Geometry 2 include regions above and around the door and window openings. Reinforcement lintel beams placed above door and window openings will counter larges stresses and stop large deformations from developing around these openings. Steel lintel beams offer the greatest strength but are not of a suitable cost to be used in low-cost housing. Timber lintel beams offer good affordability but are susceptible to environmental conditions. Reinforced concrete lintels would be the ideal reinforcement to be used above door and window openings, considering
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durability, strength and cost (Sattar, 2014). Bed-joint reinforcement could be incorporated to provide additional resistance to lateral loads. To reduce cost, bed-joint reinforcement can be added to every third or fourth course. Steel reinforcement can be added at key areas to increase ductility and resistance to flexural forces. These key areas include the bottom corners of the wall and the center panel between the door and window opening in Geometry 2.