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Mixed formulation for seismic analysis of shear critical reinforced concrete, steel and composite structures

Das, D. (2019). Mixed formulation for seismic analysis of shear critical reinforced concrete, steel and composite structures. (Unpublished Doctoral thesis, City, University of London)

Abstract

This study presents the formulation of new two dimensional frame finite element models for the analysis of shear-critical reinforced concrete, steel and steel concrete composite structural members considering the interaction of axial force, bending moment and shear force under monotonic and cyclic loading conditions. The elements are developed by following a variational approach with consistent linearization of the governing equations. Shear deformation is considered through the Timoshenko-based section kinematics. Distributed inelasticity at the element and section levels are considered through section integration points along the length of the element and material fibre discretization across the cross-section respectively. Multi-axial stress states due to crack-induced anisotropy in reinforced concrete fibres is simulated through a fixed crack smeared softened membrane model which is based on the stress equilibrium, the strain compatibility and the constitutive relationships of materials. 2d J2 plasticity and generalized plasticity models with radial return mapping algorithm are implemented for structural steel fibres under monotonic and cyclic loading conditions respectively to accommodate the interaction among the multiaxial stress states. Three types of frame elements are formulated, namely a shear frame element which is applicable for both shear critical reinforced concrete and steel members, a composite shear beam element considering coupling between bond-slip and shear deformation, and a shear critical frame element considering both material and geometric nonlinearity.

The new shear beam element formulations for reinforced concrete and steel members are based on a two-field mixed formulation where both section forces and displacements are simultaneously approximated within the element through independent interpolation functions. New displacement shape function has been developed, which can alleviate the shear locking issue for displacement-based formulation and also, satisfy the new stability criteria for two-field mixed-based formulation considering shear deformation. The element is validated through correlation studies with experimental results of shear-critical RC beams, columns, walls and steel beams for monotonic and cyclic loading conditions.

The new shear beam element formulations for steel-concrete composite members with deformable shear connectors are based on a displacement and two-field mixed formulations, where the transfer of forces between steel and concrete is modelled by distributed spring elements. New stability criteria has been proposed for shear critical inelastic composite mixed-based formulation with partial interaction. The element is validated through correlation studies with experimental results of shear-critical Steel Concrete (SC) composite beams for monotonic loading conditions.

This research work concludes with the development of a new shear beam element under large displacements which is based on two-field mixed formulations. The corotational formulation is used to describe the large displacement at the element nodal level and degenerated Green-Lagrange strain measures are used at the basic element level. Since the development of consistent state determination of fibre element formulation three decades ago, this is the first shear fibre beam element formulation which can reasonably reproduce the experimentally-observed post peak softening region of shear force-shear deformation curve of RC columns. The element is validated through correlation studies with experimental results of P-Delta dominated flexure-shear critical RC columns under monotonic and cyclic loading conditions.

Publication Type: Thesis (Doctoral)
Subjects: T Technology > TA Engineering (General). Civil engineering (General)
Departments: Doctoral Theses
Doctoral Theses > School of Mathematics, Computer Science and Engineering Doctoral Theses
School of Mathematics, Computer Science & Engineering > Engineering
Date Deposited: 12 May 2020 12:02
URI: https://openaccess.city.ac.uk/id/eprint/24180
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