Journal of Engineering Mechanics

The equivalent force control (EFC) method has been developed for real-time substructure testing with implicit integration to replace the numerical iterative process with feedback control. This paper addresses two issues concerning the performance of this method. One is the determination of the force-displacement conversion factor (a key component of EFC) for nonlinear specimens. The analysis conducted here shows that the force-displacement conversion factor is largely governed by the properties of the numerical substructure and the numerical scheme when a small integration time interval is used. Otherwise, the factor has to be determined with the secant stiffness of the specimen and of the numerical substructure if a proportional-derivative controller is used for EFC. The other issue is the overshooting problem, which may arise for multidegree-of-freedom structures because of the relatively quick response feedback from the numerical substructure in the closed-loop EFC. This problem can be resolved by reducing either the EFC gains or the increment size of the equivalent force command. The analytical studies on these two issues are verified by numerical simulations and for real-time substructure tests conducted on structural models with buckling restrained braces. Furthermore, a real-time substructure test was conducted on an offshore platform with magnetorheological dampers in order to serve as an example of a practical application of the method.

The ability of a RC beam to rotate is extremely important at both the serviceability and ultimate limit states as it affects deflection, moment redistribution, and the absorption of energy. The rotation in a RC beam can be considered to have two components: the continuous rotation that occurs in the homogenous portions of the beam and that can be determined by straightforward integration of the curvature and the discrete rotation due to the rigid body displacement between crack faces. In this paper, generic closed-form solutions are derived for the discrete rotation across crack faces, which are limited by debonding or fracture of the reinforcement in tension, or softening of the concrete in compression. It is shown how closed-form solutions can be derived for the moment/discrete rotation for the simplest case of a RC beam with a single layer of reinforcement, which could be used as the starting position for much more complex scenarios. The technique developed is generic as it can cope with any type reinforcement and concrete.

Modeling errors, represented as uncertainty associated with the parameters of a mathematical model, inevitably exist in the process of constructing a theoretical model of real structures and limit the practical application of system identification. They are usually represented either in a deterministic manner or in a probabilistic way. However, if the available information is uncertain but of a nonprobabilistic nature, as it may emerge from a lack of knowledge about the sources and characteristics of model uncertainties, a third type of approach may be useful. Presented in this paper is an approach to treat modeling errors with the aid of intervals, resulting in bounded values for the identified parameters. Compared with the traditional identification procedures where model-based forward dynamic analysis is often involved, computing bounded time history responses from a computational model with interval parameters is avoided. Two required submatrices are firstly extracted from identified state-space models by applying a subspace identification method to the measurements, and then interval analysis is performed upon these two matrices to estimate the bounded uncertainty in the identified parameters. The effectiveness of the proposed methodology is evaluated through numerical simulation of a linear multiple–degree-of-freedom (MDOF) system when modeling errors in the mass and damping parameters are taken into account. The results show the ability of the proposed method to maintain sharp enclosures of the identified stiffness parameters.

In this paper, the response of two-dimensional framed structures made of rectangular cells to the sudden removal of columns is studied. A simulation algorithm based on the discrete-element method is employed, where the structural elements are represented by elasto-plastic Euler-Bernoulli beams with elongation-rotation failure threshold. The effect of structural cell slenderness and of topological hierarchy on the dynamic residual strength after damage $R_1$ is investigated. Topologically hierarchical frames have a primary structure made of a few massive elements, while homogeneous frames are made of many thin elements. It is also shown how $R_1$ depends on the activated collapse mechanisms, which are determined by the mechanical hierarchy between beams and columns, i.e., by their relative strength and stiffness. Finally, principles of robustness-oriented capacity design that seem to be in contrast to the conventional antiseismic capacity design are addressed.

A general method is found to obtain the exact solutions for an orthotropic plane beam subjected to arbitrary loads with various end-support conditions. Compared with the traditional trial-and-error method, the biggest advantage of this general method is that it does not need to guess and modify the form of the stress function but rather obtains the solutions directly. The unified equations to deal with the boundary value problem of an orthotropic plane beam are obtained by solving functional equations. Several examples show the correctness and generalization of this method.

Finite-element analysis is used to model the failure of thin-film butt-joint specimens of pure bitumen in tension for a wide range of test conditions (temperature and strain rate). The approach uses a powerful numerical scheme based on two components: a nonlinear viscous, temperature- and rate-dependent constitutive material model that describes the mechanical deformation behavior of bitumen, implemented into a special-purpose finite-element user material subroutine, and a cohesive zone model for simulating the fracture process. The finite-element model is validated by comparing computed fracture characterization parameters with experimental results. The predicted force versus displacement characteristics and the normalized toughness, $G/2h$, are found to compare favorably with experimental results in the ductile and brittle regimes, with the failure mode being accurately simulated.

Early-age cracking affects the structural integrity of concrete structures and, if not inhibited, would lead to a reduction in service life. Plastic cracks are observed in the first few hours after placing the concrete, a time period well within the initial stages when the drying process is controlled by the rate of evaporation of concrete surfaces, which is roughly constant and similar to the rate of evaporation from water surfaces. In the absence of a theoretical method, this rate is commonly estimated using a nomograph based on Dalton’s law. In this paper, a fluid mechanics–based approach for water evaporation based on the boundary-layer theory, mass transfer, diffusion, and convection is described. A parametric study is conducted on the effect of boundary-layer temperature, wind speed, relative humidity, and evaporation characteristic length on the calculated evaporation rates. Predicted evaporation rates are verified by recent experiments. Results show that given appropriate environmental parameters, evaporation rates can be predicted with a good degree of accuracy.

A differential model is presented to show the behavior of general hysteretic systems considering all relevant structural characteristics, including pinching, stiffness degradation, load deterioration, and sliding. This model is generated based on Mostaghel’s model, which already includes all of these characteristics except sliding. Thus, an attempt is made to develop the model to also cover sliding. A single-degree-of-freedom system is used to develop the hysteretic model by writing a system of ordinary differential equations. The proposed model captures the key features of the hysteretic cycles of any structure using some measurable system parameters through tests. A few examples of bilinear systems excited by harmonic loads are provided to show that the descriptions of the force-displacement performance of general hysteretic systems are realistic.

Although a number of the higher-order/refined beam theories had been proposed for the analysis of shear deformable beams, these beam theories cannot properly take account of the displacement boundary conditions of shear deformable beams, and they are not capable of characterizing the boundary layer effects resulting from the displacement boundary conditions. A new beam theory with the sixth-order differential equilibrium equations is employed in this paper to analytically solve the boundary layer solutions of three typical beams with clamped ends. The influences of the boundary layer solutions given by the new sixth-order beam theory on the deflections, shear forces and stresses are studied, and the resulting solutions are evaluated by the finite-element results. The accuracy assessment of the deflections given by various higher-order/refined beam theories is also carried out by comparing these analytical solutions of deflections with the numerical results. The numerical results show that the new sixth-order beam theory can properly deal with the displacement boundary conditions of shear deformable beams and yield accurate solutions of both displacements and stresses. Furthermore, the new sixth-order beam theory is also capable of properly characterizing the boundary layer effect induced by the displacement boundary conditions. The current study also shows that the boundary layer solutions at the zone of clamped ends do not considerably affect the deflections; however, they contribute significantly to the localized distributions of the shear force and the normal stresses at the zone of the clamped ends. In particular, the resulting normal stresses at the beam surfaces of a clamped end are much larger than those predicted by Timoshenko beam theory.