Linh Cao Hoang

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

Strength of Loop Connections between Precast Bridge Decks Loaded in Combined Tension and Bending

Abstract The paper presents a study of the load-carrying capacity of loop connections subjected to combined tension and bending. For such connections, the main design challenge in practice is to obtain a load- carrying capacity that is governed by yielding of the looped reinforcing bars (i.e., the U-bars) and not by fracture of the joint concrete. Unfortunately, reliable design models serving this purpose have not yet been published. Therefore, in this paper, a design-oriented plasticity model is proposed for the calculation of the N–M interaction diagram accounting for both failure modes. The work is an extension of a model previously developed by the authors for the case of pure tension. In addition to the theoretical work, test results of connections subjected to combined tension and bending are also presented. Calculations according to the model have been compared with tests. Satisfactory agreements have been found.

Shear Strength of Reinforced Concrete Slender Beams with or without Axial Forces: A Generalized Theory

A theory for the shear strength of reinforced concrete rectangular and T-section beams, with or without axial forces, is described. This theory is an extension of the theory for slender rectangular and T-beams without axial forces described in previous work. This generalized theory results in a simple expression for the shear strength, which is equally applicable to rectangular and T-beams with or without axial forces. An effective width suitable for predicting the shear strength of T beams is used in this expression. The effect of the action of axial forces is taken into account by a suitable determination of the depth of the compression zone. A correction factor to account for the size effect is also included. The proposed generalized formula has been verified in previous works for slender rectangular and T beams without axial forces. Now, it is verified for rectangular and T-beams with axial forces. The comparisons of the theoretical results with the experimental results from the literature obtained on slender rectangular and T beams with various magnitudes of axialforces-compressive and/or tensile-are in very good agreement.

Shear Strength of Reinforced Concrete Piers and Piles with Hollow Circular Cross Section

Substructures in bridge engineering may be comprised of reinforced concrete piers and piles with hollow, circular cross section. Such members normally have a larger flexural strength to weight ratio than similar solid members. They are, however, more shear critical owing to the hollow core. Guidelines and code rules for shear strength evaluation of such members are almost non-existent. This paper deals with the problem using a plasticity approach. It is assumed that the shear strength of the member will, depending on the compressive normal force, be governed either by shear failure in cracked concrete or by shear failure in uncracked concrete. This distinction makes it possible to calculate the enhancement effect of axial compression on the shear capacity. To distinguish between the two types of failure, it is proposed to combine a classical upper bound model with the so-called crack sliding model. Results obtained from the model are compared with test results found in the literature. Good agreement has been found.

Shear Test on RC Elements with Circular Cross Section

Reinforced concrete members with circular cross section are widely used in bridge engineering, either as piers or as piles to support pile caps. In codes, guidelines for shear design of circular concrete members are almost none-existing. Some codes specify rules based on shear models for rectangular members. The shear behaviour of members with circular cross section is, however, quite different from that of rectangular members. The published experimental research on the shear behaviour of circular members contains only test results with very low shear reinforcement percentages. In this paper shear tests on a series of heavily confined concrete members are reported. The specimens have shear reinforcement percentages (hoops) up to more than three times the maximum percentage found in existing tests. The test results are compared with a recently developed shear design model for circular members Good agreement has been found.

Influence of High Axial Tension on the Shear Strength of non-shear RC Beams

This paper deals with the influence of high axial tension on the shear strength of beams without shear reinforcement. An experimental program with shear-tension tests was carried out. The experimental results have been used to evaluate the applicability of the Eurocode 2 (EC2) design formula in cases with large normal forces. In addition, the experiments have been used to evaluate an extension of the plasticity based Crack Sliding Model (CSM) to cover cases with large normal forces. The test results show, that even in the present of very high axial tensile stresses and strains, the member is still able to carry significant shear stresses. The analysis reveals that the EC2 formula is over conservative in this regard.

Ship collisions with pile-supported structures-estimates of strength and ductility requirements

Abstract This paper describes an analytical approach for design of pile-supported structures subjected to ship collisions. The main problem being addressed is how deformation of both ship and structure, in a simple way, can be taken into account when determining the collision force. Such an approach will lead to more accurate calculations of the maximum collision force as compared to methods, which assume the impact energy to be absorbed solely by ship deformations. The approach described here requires knowledge about the load-deformation characteristics of the structure and the ship. A major challenge in this context is to establish the so-called load-indentation curves for ships. The paper demonstrates a principle to establish load-indentation curves, which, in a mechanically consistent way, are linked to the Eurocode collision force formula. The obtained load-indentation curves have been used to develop analytical criteria for strength and ductility assessment of pile-supported structures. Calculations based on the outlined approach show that the maximum collision force reduces significantly as compared to calculations, where the deformation capacity of the structure is disregarded. The reduction of the maximum collision force can be transformed into similar reduction of the required number of piles.

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.

Serviceability Performance of Material Efficient Concrete Structures

This paper deals with some basic features of optimized reinforced concrete structures. For orthogonal mesh reinforced panels with given boundary conditions and given outer geometry, the theoretical criterion for a material efficient (optimized) structural layout is established. The criterion is based on a lower bound plasticity design approach. Subsequently, by using the principle of minimum complementary elastic energy, it is shown that for optimized panels, there is a close relationship between the stress distribution in the fully cracked elastic state and the stress distribution used in the ultimate limit state. It is discussed how this finding may be used for serviceability analysis of optimized structures.