Journal of Engineering Mechanics

A numerical model is proposed for reinforced-concrete behavior that combines some commonly accepted ideas for modeling plain concrete, reinforcement, and interaction behavior (e.g., due to bond) in a consistent manner. The basic idea is that the total stress that exists in a reinforced-concrete element can be rigorously decomposed into individual contributions of the plain concrete, the reinforcement, and the interaction between these constituents. The behavior of plain concrete is governed by fracture-energy–based formulations both in tension and in compression. In this fashion, mesh-independent results can be obtained with respect to the limit load. In the presence of reinforcement, the fracture energy is assumed to be distributed over a tributary area that belongs to a crack. The crack spacing is estimated using accepted CEB-FIP recommendations. The reinforcement is modeled using a standard elastoplastic model, and for the stress contribution that results from the interaction between concrete and reinforcement a trilinear function is adopted. Although the model allows for inclusion of dowel action, this contribution proved unimportant in the structures considered. The application of the model to reinforced-concrete panels and shear walls gives good simulations of the failure behavior.

Twelve identical cantilever-type column specimens were subjected to load paths of cyclic uniaxial or biaxial flexure with axial load, to provide data for the development and calibration of mathematical models of columns subjected to biaxial bending. The specimens had a shear span ratio of 6.0 and were overdesigned in shear, so that their behavior and damage were controlled by flexure. The only test variable was the load path. In 10 of the tests the axial load was essentially kept constant and in the rest it varied, either simultaneously or independently of the transverse loads and/or displacements. Very strong coupling was observed between the two directions of bending and between these two directions and the axial direction. The coupling between the two transverse directions significantly increased the hysteretic energy dissipation. This increase was related to the phase lag of the vector of biaxial deflections relative to that of biaxial transverse loads, and to the relative rotation of the biaxial load path with respect to that of biaxial deflections. Cycling of the deflections had two effects on axial deformations: (1) gradual permanent shortening for low-to-medium axial loads, or a gradual extension, which turned into shortening when failure was approaching, for very low axial loads; and (2) a recoverable axial extension, approximately proportional to the vector resultant of deflections. Cycling of the axial force caused a ratcheting increase of deflections under constant transverse force.

Nonparametric identification techniques are used to process recorded data of nonlinear structural responses and to represent the constitutive relationship of the structure. When hysteretic systems are dealt with, attention must be given to the appropriate subspace of the state variables in which the restoring force can be approximated by a single-valued surface. Nonparametric models are investigated, defined by two different descriptions: the first, in which the restoring force is a function of displacement and velocity, is commonly used; and the second, in which the incremental force is a function of force and velocity is less adopted. The ability of the second variable space to better reproduce the behavior of hysteretic oscillators is shown by analyzing different cases. Meanwhile, approximation of the real restoring function in terms of orthogonal (Chebyshev) polynomials and nonorthogonal polynomials is investigated. Finally, a mixed parametric and nonparametric model that exhibits a very satisfactory behavior in the case of important hardening and viscous damping is presented.

To calculate the unit-impulse response matrix of an unbounded medium for use in a time-domain analysis of medium-structure interaction, the consistent infinitesimal finite-element–cell method is developed. Its derivation is based on the finite-element formulation and on similarity. The limit of the cell width is performed analytically, yielding a rigorous representation in the radial direction. The discretization is only performed on the structure-medium interface. Explicit expressions of the coefficient matrices for the out-of-plane (antiplane) motion are specified, which depend only on the geometry of the structure-medium interface and the material properties of the unbounded medium. For each time step, a linear system of equations is solved. The calculated unit-impulse response matrix is symmetric. In contrast to the boundary-element formulation, no fundamental solution is necessary, and the conditions on the boundaries extending from the structure-medium interface to infinity are incorporated automatically. Applications of the consistent infinitesimal finite-element–cell method to the semiinfinite wedge and the strip footing with rectangular cross section embedded in a half plane show excellent accuracy.

Test results on the size effect in the pullout strength of reinforcing bars embedded in concrete are presented. Attention is focused on failures due solely to interface slip, with no cracking in the surrounding concrete. This type of failure is achieved by using smooth round bars and a sufficiently large ratio of bar diameter to embedment length. Elimination of cracking in the surrounding concrete makes it possible to study the characteristics of the interfacial shear fracture between steel and concrete. The results of tests of geometrically similar specimens show that interfacial shear fracture causes a size effect on the nominal strength in pullout. The size effect is found to be transitional between plastic failure (the current approach of concrete design codes, for which there is no size effect) and linear elastic fracture mechanics (for which the size effect is the maximum possible). This transitional size effect can be approximately described by the size effect law proposed by Bažant in 1984 for quasibrittle failures in general. By fitting a theoretical formula obtained in a previous study (by Bažant and Desmorat in 1994) to the size effect data, the basic characteristics of the stress-slip law for interface fracture are determined. These include the interfacial fracture energy, the shear bond strength (debonding shear stress), and the residual frictional shear stress. The same method could be used for identifying the interfacial fracture characteristics of other materials, e.g., fibers in cementitious composites.

Experimental observations have shown that the dissipation per cycle in many materials does not depend on the deformation frequency over a wide frequency range. A linear model used frequently to represent this type of mechanical behavior is the concept of linear hysteretic damping. Also referred to as structural damping and complex stiffness in the literature, this noncausal model is characterized by storage and loss moduli independent of frequency. In the present paper, a consistent time-domain representation for linear hysteretic damping is presented using the Hilbert transform. This time-domain representation is a mathematically correct way to replace the complex-stiffness parameters or frequency-dependent damping coefficients commonly used in differential equations that model the dynamics of structures with linear hysteretic damping. A technique is proposed for the computation of the response of structures containing linear hysteretic elements in the time domain; the convergence of the iterative technique is analyzed; and simple numerical examples are developed to illustrate the application of the method.

The method of quasiconservative averaging, developed originally to treat the random vibration of a system with a strongly nonlinear stiffness and under white-noise excitations, is modified to apply to the case of nonwhite wide-band excitations. The excitations can be either additive, multiplicative, or both. The total energy of the system is approximated as a Markov diffusion process under the condition that the damping and excitations are weak. A general procedure is given for calculating the drift and diffusion coefficients of the energy process by using Fourier series expansions. The nonwhite characteristics of the excitations are taken into account in the modified version of quasiconservative averaging. For illustration, the procedure is applied to a Duffing oscillator under both additive and multiplicative excitations with nonwhite spectral densities. Monte Carlo simulations are performed to substantiate the accuracy of the proposed procedure.

An analytical study of the transverse shear strain effect on the lateral buckling of thin-walled, open-section fibrous composite beams is presented in order to derive a better estimate of load capacity. Uniformly distributed and transverse central point loads are applied, being two popular loading systems, on simply and clamped supported I-section beams. An analytic-numerical moment method is used as an effective approach for solving the coupled system of differential equations. The present study highlights the insensitivity of the shear factor for UDL (uniformly distributed load) systems in lateral buckling. However, the results show, in short-span composite beams under concentrated central loads, the shear factor causes a considerable drop in the buckling load.

A new constitutive model for predicting the undrained stress-deformation and pore water pressure response of saturated cohesive soils subjected to cyclic loading is developed using the disturbed-state concept (DSC). The model takes into account inelastic response during loading (virgin) and unloading-reloading (nonvirgin) behavior. Comprehensive laboratory tests have been performed on undisturbed soft (marine) clay samples procured from a site at Sabine Pass, near Houston, Tex. The tests include conventional cylindrical triaxial tests and cyclic triaxial tests in the multiaxial device with pore-water-pressure measurements. The model is verified with respect to the observed behavior of undisturbed clay samples.Verification is performed with respect to laboratory tests that were used, and the independent tests that were not used in the calibration of the model. Overall, the proposed model provides highly satisfactory predictions of the observed behavior during virgin and nonvirgin loading.