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The research work presented in this thesis deals with the structural behavior of R.C. cores with regular and irregular cross sections under the effect of lateral loads. The simulation of these cores is addressed in this study, and an extensive parametric study is performed to investigate the behavior patterns of these lateral load resisting elements.
In this study, the common assumptions related to design of cracked sections used by commercial software packages, are investigated in relation to their application in estimating the ultimate capacity of reinforced core sections, in tall buildings under the effect of lateral loads, with an emphasis on the modeling of cores of irregular shapes, and cores which undergo torsional movements.
“ABAQUS” was selected from the finite element software packages to perform a non-linear analysis on the proposed configurations of regular and irregular cores under the effect of lateral loads. Two modeling elements, solid and shell, were tested to simulate the concrete and reinforcing steel for the R.C. cores. Verification of these modeling techniques with published experimental work had been performed and illustrated in thesis with a proof that the two techniques are adequate in modeling these cores. Other specimens of shear walls and T-shaped R.C cores from previous experimental work were selected to verify the
proposed modeling techniques; this verification shows a good agreement between analytical and experimental results.
In this research, an extensive study is conducted to investigate the actual structural behavior of cores of different section shapes, through the development of more accurate nonlinear finite element analysis models, taking into account steel yield, and concrete cracking. The parametric study includes analysis of symmetric and unsymmetrical core shapes, the effect of various degrees of torsional movements on the overall section capacity, width and thickness of flange connecting webs of cores section, and the longitudinal steel to concrete ratio.
Furthermore, analysis results of cores moment capacity were compared to those which were obtained by commercial programs and the differences were studied and highlighted.
A discussion of the finite element results of the parametric study was presented, and compared to the linear strain assumption in estimating the section moment capacity followed in design codes of practice. The findings of the study were used to develop general conclusions, and recommendations.
For symmetric regular R.C. core sections
• Analysis results obtained showed high agreement between the structural behavior of symmetric regular core sections (I-section, etc), and the full-height linear strain assumption specified by design codes, and applied in commercial software packages.
• Finite element analysis reveals that the structural behavior of symmetric regular core sections (I-section, etc) is almost the same regardless of the applied degree of torsional rotation because they achieve the same moment capacity under different proposed torsional rotations. Additionally, strain diagram along section height is the most adequate relationship among all studied sections to the full-height linear strain assumption specified by design codes of practice.
• Results obtained from parametric study proved that intermediate flange dimensions have a minimal effect on the moment capacity predicted for these sections. Thus, increasing or decreasing the rigidity of intermediate flange does not improve the behavior.
For irregular R.C. core sections
• In case of irregular core shapes, especially where the section web is discontinuous (Z section, etc), the structural behavior and the resulting stress and strain distribution are highly different from the common linear strain assumption. The effect on the ultimate moment capacity of the section is found to be significant, and reached up to 46% reduction in capacity for some sections. This reduction in capacity was found to be smaller when the core section is rotationally restrained, and was found to be largest for the case of rotationally unrestrained core sections.
• However, the proposed rotationally restrained degrees undergo an improved behavior with a smaller reduction factor. This means that if the building exhibit a small rotational value by fixing the rotation of the buildings using other lateral loads resisting elements, RC cores with irregular shapes will undergo a close
moment capacity to those or regular shapes with the same dimensions and reinforcing configuration. It is concluded that the maximum reduction factor for rotationally restrained sections is 9.3% compared to a symmetric section of same dimensions and reinforcement.
• Parametric study showed that irregular core shapes, especially where the section web is discontinuous, depend significantly on the rigidity of intermediate flange.
• Moment capacities of these sections increase by 22% in case of continuous webs and 21% in case of discontinuous webs by doubling the ratio of thickness to width. On the other hand, sections have a reduction up to 12.5% in case of continuous webs and 8% in case of discontinuous webs by decreasing the thickness to width ratio of intermediate flange to half of its value.
• The analysis results showed that commercial packages design routines produced the same results for regular and irregular core shapes, and the results also did not reflect the effect of torsional movements. This is caused by the fact that the linear strain assumption throughout the whole section height prevents any assessment of the effect of web discontinuity, and any other irregularity in shape. Moreover, commercial software packages calculate the total straining actions on the core section by accumulating the individual forces acting on all elements at the section. This prevents any consideration of the effect of the torsional movement which affects the stresses in the different flanges of the section differently. These observations indicate a
critical deficiency in the assumptions on which commercial software packages base their design routines.
• Sophisticated nonlinear finite element analysis performed in this study, reveals the inadequacy of the linear strain assumption throughout the whole section height which prevents any assessment of the effect of web discontinuity, and any other irregularity in shape.
• Non-linear analysis showed the inadequacy of uniform stress distribution for all points at the same line perpendicular to applied load owing to the shear lag. In some studied cases, a reduction of up to 40% in stresses occurred between points connected to web and free ones at the same flange. This means a smaller share in the moment capacity compared to the calculations done by the commercial software packages.
5.3 Recommendations for future work
The work presented in this research study provides researchers with an insight into the behavior of R.C. cores with regular and irregular sections under the effect of lateral loads. Several points of research can be of interest to researchers in the future,
• A main recommendation is reached in this study regarding the necessity for introducing capacity reduction factors to the computed ultimate moment capacity of core sections. An extensive parametric study including various common core shapes is required to reach adequate reduction factors for the accurate assessment of the ultimate capacity of core sections in high rise buildings.