Journal of Engineering Mechanics

For concrete, two simple three‐dimensional failure conditions depending on the first invariant of the stress tensor as well as on the second and third invariant of the stress deviator tensor with two and four material parameters and a nonassociated flow rule are proposed in this paper. First, the basic equations like stress deviator tensor and invariants of the stress tensor and a stress deviator tensor are introduced. Then the proposed failure conditions are presented in a geometrically interpretable form. In the next step, the material parameters are determined by fitting the failure conditions to several test results. Finally, a nonassociated flow rule is introduced. An example illustrates the usefulness of the proposed constitutive equations in the failure state.

Active control of building structures has been extensively studied theoretically, using a variety of control schemes showing varying degrees of efficiency. The demand for experimental evidence of feasibility of control of structures subjected to severe transient loads leads to the present study. Structural control experiments are carried out in the laboratory using a 1:4‐scaled model structure simulating a three‐story frame building. The control experiments are performed using a system of prestressing tendons connected to a servo‐hydraulic system and linear optimal control algorithms. The model is subjected to base motions produced by a $12\mathrm{ft}\times 12\mathrm{ft}(3.6m\times 3.6m)$ shaking table, which include banded white noise and earthquake accelerograms. Results of the experiments show clearly that traditional algorithms can be implemented when proper adjustments are made. These include compensations for time delay and error accumulation in the online computation. Several new algorithms based on instantaneous optimal control are experimentally verified in this study, following new developments based on previous experiments of smgle‐degree‐of‐freedom structures. The efficiency of various algorithms is discussed along with comparisons of analytical and experimental results.

Characteristics of finite element solutions involving strain‐softening plasticity are discussed with reference to strain localization and stability for simple uniaxial problems. The stability of localized and nonlocalized solutions is evaluated with the aid of incremental potential energy expressions. An algorithm is devised for the incremental solution based on implicit integration, and it is demonstrated that a good predictor expression is absolutely essential in order to capture the most stable solution. It is shown that if the finite element space is increased in a regular manner, those solutions that were believed to be stable become unstable. A couple of alternative predictors are proposed along with an algorithm that is both reliable and efficient, when applied to simple test problems. The number of iterations that are required is small, and it is shown that the behavior of the scheme is quite insensitive to the size of the load steps. The algorithm can be generalized to multiaxial stress conditions. In order to enhance localization tendencies in the multiaxial case, it is noted that higher order approximations may be adapted within the elements, or the elements may be aligned with incipient discontinuities that are detected by bifurcation analysis, for example.

Panel‐type concrete structures are generally reinforced with more than one layer of steel in different directions. The response of the panels under general states of in‐plane stress is a function of cracking and the degree‐of‐tension stiffening between the cracks. In this paper, a tension‐stiffening model, which accounts for multiple generally oriented reinforcing layers and cracks, is developed. The model is based on an equivalent reinforcing ratio normal to the crack, which maintains strain compatibility with the actual layers. An equivalent stress‐strain relation is developed for the equivalent layer. This relation is used in turn to develop the tension‐stiffening contribution across the crack. The model is implemented in a smeared‐crack concrete constitutive relation of the rotating‐crack type. This model is used within computer program FEPARCS to simulate the response of various panel specimens for which test results are available.

The degrading effect of small shape imperfections on the buckling strength of certain nominally optimized structures is investigated. A general method for such problems is presented, which reduces the imperfection effect to an eigenvalue problem. As an example, the general method is applied to the optimization of a column on a linear elastic foundation. The random shape imperfections are simulated as a weakly stationary stochastic process, with an assumed autocorrelation function, leading to a reliability‐based optimal design. The significant effect of the shape imperfections on the optimal design is demonstrated.

This paper discusses the structural optimization problem of finding the optimal wall fhickness of an axisymmetric cylindrical shell so as to maximize the buckling load when the volume of material is fixed. An optimality condition is derived and then the method of truncated Fourier series is used to find an optimal design which indicates an 83% increase in buckling load over the classical critical buckling load for the case of uniform thickness.

The paper presents a new general constitutive law for creep in which the aging due to continuing hydration of cement is taken into account in a manner that is both simpler and physically better justified than in existing theories. Micromechanical analysis of the solidification process is used to show that the aging may be modeled as a growth of the volume fraction of load‐bearing solidified matter (hydrated cement), which itself is treated as nonaging and thus is describable as a nonaging viscoelastic material. The analysis shows that a history integral should be used to express the rate, rather than the total value, of the viscoelastic strain component. Material functions can be chosen in a way that yields previously established simple laws, i.e., the double power law, logarithmic law and log‐double power law, as special asymptotic cases. The creep strain is obtained as a sum of aging and nonaging viscoelastic strains and an aging viscous strain (flow). Nonlinearity is introduced by modifying the current creep rate as a function of the current stress. Verification by test results and numerical application is left to Part II, which follows.

The theory that was formulated in the preceding paper is verified and calibrated by comparison with important test data from the literature pertaining to constant as well as variable stress at no (or negligible) simultaneous drying. Excellent agreement is achieved. The formulation describing both elastic and creep deformations contains only four free material parameters, which can be identified from test data by linear regression, thus simplifying the task of data fitting. For numerical structural analysis, the creep law is approximated in a rate‐type form, which corresponds to describing the solidified matter by a Kelvin chain with nonaging elastic moduli and viscosities. This age‐independence on the microlevel makes it possible to develop for the present model a simple version of the exponential algorithm.

The response variability of statically indeterminate linear structures due to spatial variation of material or geometry properties, or both, is investigated. Utilizing a Green's function formulation or the more general flexibility method, the mean square response of statically indeterminate beams and frames (multistory/multibay) is determined without recourse to a finite element analysis. The response variability is expressed in terms of random variables even though the material or the geometric property, or both, (in this case the fiexibility) are considered to constitute stochastic fields. This makes it easier to estimate not only the response statistics but also the limit state probability, if the limit state conditions are given. The response variability can be estimated by various methods, including the first‐order second moment method and Monte Carlo simulation techniques. Finally, the safety index for the beam midspan deflection and end moment are evaluated using standard methods.

In specimens undergoing strain localization, applied forces and the corresponding measured displacements cannot be directly constraed as stress‐strain data, owing to the inhomogeneous character of the deformation. This complicates the interpretation of experimental data in materials which are prone to exhibiting localization prior to failure. However, we show that the true stress and strain paths inside a band in a localized specimen can be estimated simply from the measured data. Criteria are provided to determine when the proposed method may be expected to produce accurate results. Experimental records from concrete specimens are examined in the light of the method.

An effective procedure is developed for estimating the maximum response of a class of torsionally‐coupled, multistory buildings due to earthquake ground motion characterized by smooth response spectra. Several properties characterize this class of buildings, the most important of which is that all frames (spanning along either of two orthogonal directions) have proportional lateral stiffness matrices. It is demonstrated that the maximum response of such a torsionally‐coupled, N‐story building in its njth mode of vibration can be determined exactly by analyzing: (1) The response in the jth vibration mode $(j=1\text{,}2\text{,}\dots \text{,}N)$ of the corresponding torsionally‐uncoupled, N‐story system; and (2) the response in the nth vibration mode $(n=1\text{,}$ 2 for a one‐way symmetric plan) of an associated torsionally‐coupled, one‐story system. The total response is then determined by an appropriate modal combination rule.

In this paper, a single‐story, bilinear‐hysteretic structure, square in plan and supported on four columns, subjected to two horizontal ground motions is studied. The model is assumed to possess three degrees of freedom, viz., translational displacements along the two horizontal orthogonal directions and a rotation about the vertical axis. Interaction of the bending moments in the two perpendicular directions has been considered.

The analysis of beam‐column systems resting on a Winkler foundation is simplified using modern numerical techniques. Recently, finite elements based on the solution of the governing differential equation have been derived for efficient and accurate analysis of such systems. However, the existing elements cannot be applied to beams under high axial loads and resting on a weak foundation. To overcome this limitation, in this paper the shape functions, stiffness matrix, and nodal load vector of a new element are explicitly obtained using the solution of the governing differential equation. Also, for the determination of the displacements and internal forces anywhere along a beam, the complete solution of the differential equation corresponding to some common types of loading is provided. The explicit form of the various expressions provided lends them to easy implementation in existing frame analysis or finite element programs.

Three-dimensional reconstructions of cardiac ventricular chambers can be obtained from two-dimensional echocardiographic and ultrafast computed tomographic images. Using finite element analysis of the reconstructed geometry, the deformation of the ventricular chambers and the stress distribution in the myocardium can be predicted. By performing the finite element analysis on a simulated model of the ventricular chambers, the importance of the interaction of the right and left ventricular chambers on the resulting deformation and stress distribution is discussed. Consideration of interventricular interactions and physiologically realistic boundary conditions should improve finite element modeling of left ventricular mechanics.

The stability of frictional materials that display a nonassociated flow rule is discussed. Particular emphasis is put on an analysis of recent experiments conducted by Lade et al. (1987), where stable behavior was observed, when the material was expected to be ``unstable'' in the sense of Drucker's stability postulate. It was therefore concluded that Drucker's postulate regarding material stability is not valid for frictional materials. In the present paper, the writers present an analysis and describe features in the experiments by Lade et al. that show that the reported stability may be less surprising.