Mogens Peter Nielsen

Limit analysis and concrete plasticity

Introduction The Theory of Plasticity Constitutive Equations Extremum Principles for Rigid-Plastic Materials The Solution of Plasticity Problems Reinforced Concrete Structures Yield Conditions Concrete Yield Conditions for Reinforced Disks Yield Conditions for Slabs Reinforcement Design The Theory of Plain Concrete Statical Conditions Geometrical Conditions Virtual Work Constitutive Equations The Theory of Plane Strain for Coulomb Materials Applications Disks Statical Conditions Geometrical Conditions Virtual Work Constitutive Equations Exact Solutions for Isotropic Disks The Effective Compressive Strength of Reinforced Disks General Theory of Lower Bound Solutions Strut and Tie Models Shear Walls Homogenous Reinforcement Solutions Design According to the Elastic Theory Beams Beams in Bending Beams in Shear Beams in Torsion Combined Bending, Shear, and Torsion Slabs Statical Conditions Geometrical Conditions Virtual Work, Boundary Conditions Constitutive Equations Exact Solutions for Isotropic Slabs Upper Bound Solutions for Isotropic Slabs Lower Bound Solutions Orthotropic Slabs Analytical Optimum Reinforcement Solutions Numerical Methods Membrane Action Punching Shear of Slabs Introduction Internal Loads or Columns Edge and Corner Loads Concluding Remarks Shear in Joints Introduction Analysis of Joints by Plastic Theory Strength of Different Types of Joints The Bond Strength of Reinforcing Bars Introduction The Local Failure Mechanism Failure Mechanisms Analysis of Failure Mechanisms Assessment of Anchor and Splice Strength Effect of Transverse Pressure and Support Reaction Effect of Transverse Reinforcement Concluding Remarks

Application of plastic theory to shear strength prediction of external prestressed concrete beams

This paper investigates the applicability of plasticity based models for shear strength prediction of reinforced concrete members with external prestressing. Shear tests collected from the literature are compared with calculations according to the Variable Strut Inclination Method as well as the upper bound Crack Sliding Model. Reasonably agreements with test results have been found, especially when the effectiveness factor proposed in the Eurocode 2 is used.

Simplified Non-linear Time-history AnalysisBased On The Theory Of Plasticity

This paper aims at giving a contribution to the problem of developing simplified non-linear time-history (NLTH) analysis of structures for which dynamical response is mainly governed by plastic deformations so as to be able to provide designers with sufficiently accurate results. The method to be presented is based on the Theory of Plasticity. Firstly, the formulation and the computational procedure to perform time-history analysis of a rigid-plastic single degree of freedom (SDOF) system are presented. The necessary conditions for the method to incorporate pinching as well as strength degradation are outlined. The procedure is applied to a typical SDOF system and results are compared with NLTH analysis commonly used for design purposes. Secondly, by means of the Virtual Work Principle, the definition of the equation of motion of a desired collapse mechanism of a multi degree of freedom (MDOF) system is presented. This equation is of the same type as in the SDOF case, and therefore the procedure presented in the first part of the paper may be used. The method is applied to a 4-story reinforced concrete frame structure. Results are compared to those derived by a conventional NLTH analysis and found to be encouraging.