Determination and Analysis of Flexure ∆_{𝑓𝑙𝑒𝑥𝑢𝑟𝑒} and Shear ∆_{𝑠ℎ𝑒𝑎𝑟} Displacements Displacements of Reinforced Concrete Walls of Civil Buildings

Introduction. To date, there have been extensive experimental data made available in both domestic and foreign scientific literature on the study of displacements and deformations of reinforced concrete walls under the combined action of horizontal load Q and vertical load N. However, there are not enough comprehensive works systematizing the obtained data to be used as an empirical basis for designing more accurate deformation models and engineering calculation methods for walls, allowing differentiated assessment of flexure ∆_{𝑓𝑙𝑒𝑥𝑢𝑟𝑒} and shear ∆_{𝑠ℎ𝑒𝑎𝑟} displacements. This article aims to look into this issue.

Materials and Methods. The object of the study is reinforced concrete walls of buildings and structures under the combined action of horizontal load Q and vertical load N. The subject of the study are the displacements and deformations of the walls. Materials include scientific articles on the topic by foreign authors. The methods being used are formal logic (analysis, synthesis, induction, deduction), graphical methods for constructing deformation schemes, and analytical methods of nonlinear structural mechanics.

Research Results. For wall aspect ratios 1.5 < H/B < 2.0, flexure ∆_{𝑓𝑙𝑒𝑥𝑢𝑟𝑒} displacements dominate in the total displacement structure ∆, while horizontal sliding displacements ∆_{𝑠𝑙𝑖𝑑} amount to about 1% of ∆ and can be neglected. The share of flexure ∆_{𝑓𝑙𝑒𝑥𝑢𝑟𝑒} is approximately 98% of ∆ at the initial loading stages. As horizontal load Q increases, the contribution of ∆_{𝑓𝑙𝑒𝑥𝑢𝑟𝑒} gradually decreases: to 90% at the moment of crack formation, to 85% at the yielding of vertical reinforcement, and to 80% at the failure stage (when compressed concrete spalls).

For wall aspect ratios 1.0 < H/B < 1.5, shear displacement ∆_shear has a significant influence on the total displacement ∆: its share at the initial loading stages is about 22%, while determining a protective concrete layer — 46%, and reaches 64% at failure. Using the graphs of relative displacements of walls with aspect ratios 1.5 < H/B < 2.0, it was found that at the failure stage, the shares of flexure and shear displacements are 88% and 12% of the total, respectively. Similar graphs obtained for walls with aspect ratios 1.0 < H/B < 1.5 confirmed that ∆_{𝑠ℎ𝑒𝑎𝑟} significantly affects the total displacement ∆. The share of ∆_shear at initial loading is about 22%, while determining a protective concrete layer — 46%, and reaches 64% at failure.

Discussion and Conclusion. The "X-diagonals" method implemented in a planar calculation scheme allows for highly accurate separation of components caused by flexure and shear deformations from the total displacements. Thanks to this the scheme is a promising tool for further experimental and theoretical studies. We assume that the height of the wall segment where the diagonals are designed should be arbitrary — H_i making this method more universal.

In addition to the planar calculation scheme, a rod (beam) scheme can also be used. The rod calculation scheme of the wall, with known patterns of stiffness parameter changes in the rod end sections (at the locations of plastic hinge formation), is convenient for engineering calculations of frame buildings and structures based on the finite element method in diverse computational complexes.

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