Mario M. Attard

Experimental Tests on Eccentrically Loaded High Strength Concrete Columns

Reported in this paper are the test results for 68 eccentrically loaded conventional and high-strength concrete columns. The columns were 150 x 150 mm (5.91 x 5.91 in) at the mid-section and haunched at the ends to apply the eccentric loading and prevent boundary effects. Concrete strengths used were 40, 55, 75, and 90 M.B.A. (5800, 8000, 10,900, and 13,100 psi) with load eccentricities of 8, 20, and 50 mm (0.32, 0.79, and 1.97 in). The columns had either 2 or 4 percent longitudinal reinforcement and tie spacings of 30, 60, or 120 mm (1.81, 2.36, or 4. 72 in). The ultimate strength of the columns is compared to the strength predictions based on the ACI 318-89 rectangular stress block parameters. The predictions compare reasonably well, although lower strengths than predicted occurred for some high-strength concrete specimens. Ductilities are calculated based on the area under the load versus average strain plus curvature times eccentricity relationship. This measure showed a weak correlation with the confinement parameter adopted. Strains in the tie reinforcement were measured at the side face for some of the medium and high- strength concrete columns. The measured strains were not at yield when the peak load was reached.

Nonlinear analysis of thin-walled members of variable cross-section: Part I. Theory

Abstract The majority of analyses of thin-walled beam-columns in the linear and nonlinear ranges of structural response have been for prismatic sections. This paper presents a theory for the nonlinear axial strain and Kirchhoff stress resultants for a thin-walled beam-column whose cross-section is tapered. An expression for the first variation of the Total Potential is derived, that may be used in a nonlinear equilibrium analysis, and an expression for the second variation of the Total Potential is derived, that may be used in a stability analysis. These variations are used as the basis for a finite element analysis, as described in the companion paper. The results are discussed in light of a previous study of tapered monosymmetric I-beams, and for a linear analysis it is shown that the results of this independent study agree with those presented in this paper.

Finite strain¿¿isotropic hyperelasticity

Abstract This paper presents a strain energy density for isotropic hyperelastic materials. The strain energy density is decomposed into a compressible and incompressible component. The incompressible component is the same as the generalized Mooney expression while the compressible component is shown to be a function of the volume invariant J only. The strain energy density proposed is used to investigate problems involving incompressible isotropic materials such as rubber under homogeneous strain, compressible isotropic materials under high hydrostatic pressure and volume change under uniaxial tension. Comparison with experimental data is good. The formulation is also used to derive a strain energy density expression for compressible isotropic neo-Hookean materials. The constitutive relationship for the second Piola–Kirchhoff stress tensor and its physical counterpart, involves the contravariant Almansi strain tensor. The stress stretch relationship comprises of a component associated with volume constrained distortion and a hydrostatic pressure which results in volumetric dilation. An important property of this constitutive relationship is that the hydrostatic pressure component of the stress vector which is associated with volumetric dilation will have no shear component on any surface in any configuration. This same property is not true for a neo-Hookean Green’s strain–second Piola–Kirchhoff stress tensor formulation.

A TWO PARAMETER STRESS BLOCK FOR HIGH-STRENGTH CONCRETE

The rectangular stress block parameters in the current ACI Code are limited to concrete strengths in the range 20-50 MPa (2,900-7,250 psi). This paper looks at the applicability of the ACI rectangular stress block parameters to high-strength concretes. New rectangular stress block parameters are proposed that are based on a probabilistic analysis using a stress-strain relationship for high-strength concrete and that include estimates of variability and distribution of the input properties. A sensitivity analysis is also carried out to ascertain the effect of parameter uncertainty. The probabilistic models proposed can be used in a code calibration of design formula for high-strength concrete. It is shown that for a ductile singly reinforced rectangular section, the ultimate moment capacity is relatively insensitive to the stress block model. Estimates of the ductility level at both ultimate and column capacity in primary compression failure, however, are significantly affected by the choice of the stress block model.

Lateral buckling analysis of beams by the fem

Abstract Two new finite element formulations for the calculation of the lateral buckling load for elastic straight prismatic thin-walled open beams under conservative static loads, are presented. The stability criterion used is based on the positive definiteness of the second variation of the total potential energy. One formulation is suitable for sections where the initial bending is about a dominant major axis. The other finite element formulation takes account of initial bending curvature and essentially takes the form of a quadratic eigenvalue problem. Both formulations are tested with problems that have classical solutions or experimentally determined results and are shown to be accurate.

Nonlinear theory of non-uniform torsion of thin-walled open beams

Abstract A nonlinear theory of non-uniform torsion based on finite displacements is developed. Expressions for the finite nonlinear strains in Lagrangian coordinates and the Kirchhoff stresses for thin-walled open beams are presented. Using the principle of stationary total potential, the dual forms of the beam equilibrium equations are derived. For conservatively loaded thin-walled open beams a static stability criterion, based on the positive definiteness of the second variation of the total potential, is presented. The criterion developed takes into account the effects of changes in beam geometry such as initial bending curvature, prior to instability.

Finite strain beam theory

Abstract An appropriate strain energy density for an isotropic hyperelastic Hookean material is proposed for finite strain from which a constitutive relationship is derived and applied to problems involving beam theory approximations. The physical Lagrangian stress normal to the surfaces of a element in the deformed state is a function of the normal component of stretch while the shear is a function of the shear component of stretch. This paper attempts to make a contribution to the controversy about who is correct, Engesser or Haringx with regard to the buckling formula for a linear elastic straight prismatic column with Timoshenko beam-type shear deformations. The derived buckling formula for a straight prismatic column including shear and axial deformations agrees with Haringx’s formula. Elastica-type equations are also derived for a three-dimensional Timoshenko beam with warping excluded. When the formulation is applied to the problem of pure torsion of a cylinder no second-order axial shortening associated with the Wagner effect is predicted which differs from conventional beam theory. When warping is included, axial shortening is predicted but the formula differs from conventional beam theory.

Nonlinear analysis of thin-walled members of variable cross-section. Part II: Application

Abstract The equilibrium equations of a tapered member may be structured into finite element format by vanishing of the first variation of the Total Potential, while the stability equations may be presented in finite element format when the second variation of the Total Potential vanishes. These variations have been developed in a companion paper, and are recast into finite element format in this paper. The finite element program is used to investigate the linear stiffness behaviour of a tapered beam subject to a torque, classical stability analyses of tapered members and the stability of tapered members when subjected to the effects of initial bending curvature. Where possible, comparisons are made with other solutions in the literature, and it is shown that the numerical model presented in this paper is very accurate.

ULTIMATE STRENGTH OF CONFINED VERY HIGH-STRENGTH CONCRETES

Results are presented from an experimental investigation into the ultimate strength of concrete under triaxial laoding. Several mixes are used with strength ranging from normal strength concrete to very high-strength concrete. Other parameters in the mixes were the use of silica fume and type of crushed coarse aggregate with the 3 types of aggregates studied. A 2-parameter model for the failure envelope for confined concrete was adopted. Empirical expressions for the failure envelope were derived for normal strength concrete and very high-strength concrete with and without silica fume. A simple lower bound expression for the ultimate strength of concrete under confinement is presented for any grade of concrete.

STRENGTH OF TIED HIGH-STRENGTH CONCRETE COLUMNS LOADED IN CONCENTRIC COMPRESSION

The research described in this paper deals with the strength of reinforced concrete columns loaded in concentric compression, with particular emphasis on the issue of early spalling of the concrete cover. To investigate the behavior of tied reinforced concrete columns, a test program was established. Twelve columns were tested in three series under axial compression. The study shows that the longitudinal reinforcement is at yield at the spalling load, while the tie steel is not at yield at the point of cover spalling. After cover spalling, microcracking of the core leads to expansion of the core and activation of the confinement provided by the ties. The ultimate capacity of a concentrically loaded high-strength concrete (HSC) column is the maximum of the spalling load and the capacity of the confined core. Design recommendations are given.