# Nonlinear Analysis of 2D and Shell Reinforced Concrete Structures Including Creep and Shrinkage

Jendele, Libor (1992) Nonlinear Analysis of 2D and Shell Reinforced Concrete Structures Including Creep and Shrinkage. PhD thesis, University of Glasgow.

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## Abstract

The work deals with the static analysis of plane stress, plane strain, axisymmetric and shell reinforced concrete structures subject to short and long term loading conditions. Nonlinear short term material properties and structural nonlinear geometric behavior is considered. The effect of time factors is adopted in a linear form because of the lack of well established nonlinear models for creep and shrinkage of concrete. The Total and Updated Lagrangian formulation of the problem is used to derive structural governing equations via the principle of virtual displacements. The adopted formulation is suitable for structures with large deflections, large rotations but small strains. Constitutive smeared-type equations for both 2D and 3D analysis of reinforced concrete are also considered. For the 2D analysis isoparametric elements with variable number of nodes (four to nine) with Lagrangian approximation of geometry and displacements are employed using a simple linear material model accounting for cracking, crushing as well as for smooth tension stiffening of concrete. The reinforcement is modeled by piece-wise linear elastic isotropic constitutive equations. For shell analysis, the degenerated Ahmad's shell element using Serendipity, Lagrange and Heterosis geometry and displacement interpolating hierarchical approach is adopted. Special attention is focused on the problem of shear locking and thus full, selective and reduced integration rules are dealt with. Constitutive equations are assumed which are elastic-plastic for both concrete and steel materials. Also tension stiffening and compression hardening and softening of concrete is included. Nonlinear solution techniques are comprehensively reviewed and consequently some of them are significantly improved. A new algorithm for the solution of nonlinear equations, which is based on Newton-Raphson, Arc-length and Line search methods, has been developed. Analysis considering shrinkage and creep has also been developed. The Step-by-step analysis using the Dirichlet series ap- proximation to the creep function was adopted and its problem of numerical instability has been overcome. The derived theory has been extensively tested for both short and long term loading conditions. Short term analyses focus especially on the accuracy of the material models being used and on shell behavior near the loss of stability. This type of analysis has been feasible only with the implementation of a very robust nonlinear equation solver, which is capable of dealing with structural snap through and snap back phenomena. The long term analyses concentrate on the accuracy of various simplified solution techniques, comparing these results with the Step-by-step method. The collective results show that full time analysis is necessary to assess serviceability structural conditions, whilst the time factor is negligible for the total structural strength with a failure mechanism being controlled mainly by time-independent reinforcement. The above conclusions are applicable for the structures investigated herein, (i. e. relatively thin and well reinforced), and should not be generalized for any arbitrary structure. All developments in the work have been programmed into the nonlinear program NONSAP (University of Berkeley, USA) and CONCRETE (University of Swansea, U. K.). In addition other software has been created, such as material preprocessing program, library with graphics accessible from the FORTRAN environment etc.

Item Type: Thesis (PhD) Doctoral Civil engineering 1992 Enlighten Team glathesis:1992-78405 Copyright of this thesis is held by the author. 28 Feb 2020 12:09 28 Feb 2020 12:09 https://theses.gla.ac.uk/id/eprint/78405