Showing papers by "Zdenek P. Bazant published in 1998"

Easy-to-Compute Tensors With Symmetric Inverse Approximating Hencky Finite Strain and Its Rate

Abstract: It is shown that there exist approximations of the Hencky (logarithmic) finite strain tensor of various degrees of accuracy, having the following characteristics: (1) The tensors are close enough to the Hencky strain tensor for most practical purposes and coincide with it up to the quadratic term of the Taylor series expansion; (2) are easy to compute (the spectral representation being unnecessary) ; and ( 3 ) exhibit tension-compression symmetry (i.e., the strain tensor of the inverse transformation is minus the original strain tensor). Furthermore, an additive decomposition of the proposed strain tensor into volumetric and deviatoric (isochoric) parts is given. The deviatoric part depends on the volume change, but this dependence is negligible for materials that are incapable of large volume changes. A general relationship between the rate of the approximate Hencky strain tensor and the deformation rate tensor can be easily established.

Measurement of time-dependent strains of concrete. Prepared by subcommittee 4: Standardized test methods for creep and shrinkage

Abstract: 1359-5997/98 © RILEM tion of long-term behaviour. At the same time, creep and shrinkage values appear in certain cases to be a material selection criterion. Shrinkage and creep tests thus have two possible purposes: • determination of the properties of the concrete of a given mix design, aimed to provide the input data for the time-dependent constitutive law of the material; in this case, the aim is to determine the inf luence of the main parameters by varying the test conditions (loading age, ambient environment, compression stress magnitude, age at unloading); • concrete mix design optimization (generally in relation with other mechanical or physical properties, and in particular compressive strength); in this case, it is normally feasible to test only some representative conditions (early age and 28-day loading, with and without drying, for example). In both situations, the pronounced hereditary behaviour of the material (i.e. the fact that the behaviour at a given instant depends on the entire history of preceding stress) calls for a rigorous definition of the creep test, which does not require any correction in the case of non-constant loading. The quality of the test consequently depends primarily on the ability of the device to keep the applied load constant, particularly at the very beginning of the test. Furthermore, an essential influencing factor is the evaporable water content in the material which, except in very special cases, is not uniform in the structures, owing to the ABSTRACT

Size effect in penetration of sea ice plate with part-through cracks. ii: results

Abstract: After development of the theory in the part I paper, systems of up to 300 nonlinear equations are solved in this paper by the Levenberg-Marquardt optimization algorithm. The maximum load is reached when the circumferential cracks begin to form. Numerical calculations show a typical quasi brittle size effect such that the plot of log σN versus log h (where αN= nominal stress at maximum load and h= plate thickness) is a descending curve whose slope is negligible only for h< 0.2 m and then gets gradually steeper, asymptotically approaching −1/2. The calculated size effect agrees with the existing test data, and contradicts previous plasticity solutions.

Triaxial composite model for basic creep of concrete

Abstract: This paper shows how the mechanics of elastic composite materials can be adapted to predict the basic creep of concrete with aging caused by hydration. The prediction is made on the basis of the given composition of concrete, the elastic constants of the aggregate, and the aging viscoelastic properties of the portland cement mortar. The triaxial action of the composite is approximated by Dvorak's transformation field analysis. To convert the aging creep problem to an elastic problem of a composite material with inelastic strains, Granger and Bazant's approach is used. This approach relies on Bazant's age-adjusted effective modulus method that reduces the integral-type stress-strain relation for linear aging creep with nonconvolution kernel to a quasi-elastic incremental stress-strain relation with inelastic incremental strain. Explicit expressions for the aging creep properties of concrete as a composite are deduced. The model is calibrated and verified by Ward and colleagues" and Counto's test data. The predictions obtained are almost as close as those recently obtained by Granger and Bazant's model. While the present model has the advantage of describing the triaxial composite action in a rational manner, it does not yet capture the effect of the deviation of the aggregate configuration from the case of a continguous aggregate skeleton of maximum possible compactness. Further refinements in this respect are needed. Another refinement might be needed to take into account possible enhancement of creep in the interface layers between the mortar and the aggregate.

Closure of "Inelastic Buckling of Concrete Column in Braced Frame"

Abstract: The paper proposes an improved method of analysis of reinforced concrete columns in braced (no-sway) frames, which is suitable as a simple computer solution for design practice and is more realistic than the existing ACI and CBB methods. The elastic restraint provided by beams adjacent to columns is described by rotational springs. The inelastic behavior of concrete is defined by a uniaxial stress-strain curve with postpeak softening in compression and a zero strength in tension. Plasticity of reinforcement is also considered. The deflection curve is assumed to be a sine curve. The improvement consists in considering the wavelength as unknown and variable during loading. The problem is reduced to a system of seven nonlinear algebraic equations, which are easily solved for small increments of axial displacement by a standard library optimization algorithm. The convergence always occurs and is fast if the increments are small enough. The influence of various param­ eters on the load-deflection curve, the path in the diagram of axial load P versus moment M, and the failure envelope are studied. Various phenomena, such as the possibility of a concave P(M) path at constant load eccentricity, are explained. It is shown that the ACI approach is slightly conservative in most cases, although situations exist in which the ACI approach is either grossly overconservative or slightly unconservative.