Showing papers in "Journal of Engineering Mechanics-asce in 1987"

Nonlocal damage theory

Abstract: In the usual local finite element analysis, strain softening causes spurious mesh sensitivity and incorrect convergence when the element is refined to vanishing size. In a previous continuum formulation, these incorrect features were overcome by the imbricate nonlocal continuum, which, however, introduced some unnecessary computational complications due to the fact that all response was treated as nonlocal. The key idea of the present nonlocal damage theory is to subject to nonlocal treatment only those variables that control strain softening, and to treat the elastic part of the strain as local. The continuum damage mechanics formulation, convenient for separating the nonlocal treatment of damage from the local treatment of elastic behavior, is adopted in the present work. The only required modification is to replace the usual local damage energy release rate with its spatial average over the representative volume of the material whose size is a characteristic of the material. Avoidance of spurious mesh ...

Second-Order Reliability Approximations

Abstract: A simple method is presented for a second‐order structural reliability approximation. The method is based on an approximating paraboloid which is fitted to the limit‐state surface at discrete points around the point with minimal distance from the origin. An expression for the second‐order error in the approximation is derived, and the error is shown to be small, even for large dimensions and dispersed curvatures. In comparison to the existing approximation method, the proposed method is simpler and requires less computation. It is insensitive to noise in the limit‐state surface, approximately accounts for higher‐order effects, and facilitates the use of an existing formula for the probability content of parabolic sets.

New Optimal Control Algorithms for Structural Control

Abstract: A critical review of classical optimal control algorithms is made with respect to the specific application of structural control under seismic excitations With the earthquake ground acceleration being the major source of continuous external disturbances, the Riccati closed‐loop control does not satisfy the optimal condition New optimal control algorithms are proposed herein, including the instantaneous optimal open‐loop control, instantaneous optimal closed‐loop control, and instantaneous optimal closed‐open‐loop control These new control laws are developed for providing feasible control algorithms that can easily be implemented for applications to seismic‐excited structures Numerical examples are worked out to demonstrate the control efficiency of the proposed control algorithms Experimental verifications have been carried out

Closure of "Rocking of Rigid Blocks Due to Harmonic Shaking"

Abstract: The dynamic behavior of rigid-block structures resting on a rigid foundation subjected to horizontal harmonic excitation is examined. For slender structures, the nonlinear equation of motion is approximated by a piecewise linear equation. Using this approximation for an initially quiescent structure, safe or no-toppling and unsafe regions are identified in an excitation amplitude versus excitation frequency plane. Furthermore, several possible modes of steady-state response are detected, and analytical procedures are developed for determining the amplitudes of the predominant modes and for performing stability analyses. It is shown that the produced stability diagrams can be beneficial to assessing the toppling potential of a rigid-block structure under a given amplitude-frequency combination of harmonic excitation; in this manner the integration of the equation of motion is circumvented.

New Algorithm for Structural Reliability Estimation

Abstract: An efficient and accurate method for computing probabilities of failure, pf, of structural and mechanical components is presented. Limit state equations can be of any continuous functional form, and the basic variables can have any distribution. The algorithm that is an extension of the Rackwitz‐Fiessler and Chen‐Lind methods has the following qualities: (1) It employs an optimization routine to approxirhate nonnormal variants as equivalent normals; (2) approximates the limit state by a quadratic at the design point; and (3) transforms the quadratic form to a linear one, thereby approximating the limit state as linear in normal design factors. Exhaustive testing of the algorithm has indicated not only that computational time is “negligible,” but also that errors in pf are consistently less than 10% in all realistic physical problems and are usually much less. Examples are presented to illustrate the performance of this fast probability integration method.

Japanese Activities on On‐Line Testing

Abstract: The on-line computer test control method (the on-line test) is a new experimental technique to directly simulate the earthquake response behavior of structural systems without using a shake table device. This paper presents a review of Japanese activities in the development and application of the on-line test. First, the history of the development of the on-line test and its software and hardware algorithms are described, and 27 previous on-line tests conducted by Japanese researchers are summarized. Second, the reliability of the on-line test is discussed. Sources that may bring errors in the response are defined, and efforts to examine their effects on the response and to control the response error growth are introduced. Third, two extensions of the on-line test concept are presented: the fast on-line test and the substructure on-line test.

Analysis of Mixed‐Mode Fracture in Concrete

Abstract: A smeared crack model that covers tensile softening in mode I and shear softening in mode II fracture is described. In addition, the model provides for unloading and reloading and for multiple crack formation. Particular forms of tension and shear softening functions and relations with more conventional models are discussed. Two examples involving mixed-mode fracture in notched, unreinforced concrete beams have been included to demonstrate the versatility of the model. The results indicate that the addition of shear softening is essential to obtain realistic results in the post-peak regime since the classical approach based on a constant shear retention factor then results in a too stiff behavior. The results furthermore demonstrate that snap-back behavior may occur in strain-softening concrete under quasistatic loading conditions. Attention is also given to the possibility of hour-glass formation when constitutive laws involving softening are deployed in a finite element model.

Nonassociated Flow and Stability of Granular Materials

Abstract: Materials exhibiting nonassodated flow should, according to Drucker's stability postulate, become unstable when exposed to certain stress paths inside the failure surface. Results of a series of triaxial tests designed to expose the type of behavior displayed by granular materials are presented and discussed. The sand dilates during shear, it exhibits nonassociated flow, and when exposed to stress paths in the region of potential instability, none is observed. The reliability of the test results, the possible influence of viscous effects on the stability, and the effect of release of elastic energy are studied and discussed in detail. Thus, Drucker's stability postulate is not applicable to granular materials. The type of volume‐change behavior displayed by the material is of great importance in the question of stability of granular materials.

Interface element modeling of fracture in aggregate composites

Abstract: A brittle aggregate composite such as portland cement concrete or mortar is modeled in two dimensions as a system of perfectly rigid particles of various sizes separated by interface layers that are characterized by a given force-displacement relation for the normal and tangential components. The force-displacement relation exhibits for the normal component a tensile strength limit followed by a sudden drop of force to zero. The system of rigid particles is generated randomly. The particles are not allowed to overlap and are generally not in contact; however, when the distance between the particles is less than a certain limit, a deformable interface layer is introduced. Numerical simulation of a fracture specimen with a notch shows that the fracture front consists of an irregular band of interparticle cracks the width of which is about three maximum particle sizes. The interparticle cracks remain continuous and do not coalesce into a continuous line fracture until the deformation is very large. The load-displacement relation exhibits gradual softening after the peak force, with a rapid force decrease followed by a long tail of slowly decreasing force. These features qualitatively agree with observations of concrete.

Structural Response Variability III

Abstract: Dealing with the issues of response variability for statically determinate structures, this study analyzes the response variability in two cases in which the spectral density function of the stochastic field takes limiting shapes. In these limiting cases, the spectral density, having a constant total area, concentrates sharply around the origin in one case and spreads thinly throughout in the other. Also, the present study derives the upper and lower bounds on the response variability. These results provide important physical as well as numerical insight into the response variability issue, whether we solve the problem by exact or numerical integration of equations of equilibrium or motion, or by other numerical methods. It is rather difficult to estimate experimentally the autocorrelation or spectral density function for the stochastic variation of material properties. In view of this, the upper bound results are particularly important, since the bounds derived here do not require knowledge of the autoco...

Tensile Failure of Steel Fiber‐Reinforced Mortar

Abstract: Results are discussed from experimental and theoretical studies on the tensile failure of short, steel fiber-reinforced mortar/concrete SFRC composites. A displacement-controlled test method for conducting stable fracture tests on tension-weak brittle materials developed in an earlier study has been used for conducting uniaxial tension tests. Several concrete, mortar, paste, and SFRC mixes were tested. Fracture of SFRC in tension is observed to be influenced largely by the matrix softening behavior, the fiber-matrix interfacial response, and its composition parameters. The theoretical model proposed for the idealized SFRC composite takes into account these two primary nonlinear aspects of the failure mechanism in such composites, i.e., (1) the inelastic behavior of the fiber-matrix interface, and (2) the softening characteristics of the matrix. The model, in addition, is realistically sensitive to the reinforcement parameters like fiber volume content, aspect ratio, and the elastic properties of the fiber.

Evolutionary Kanai‐Tajimi Earthquake Models

Abstract: A versatile mathematical framework based on the concept of random pulse train is proposed for the modeling of hypothetical ground acceleration in a future earthquake for engineering design purposes. This framework is potentially capable of incorporating various physical features arising from the propagation, reflection and refraction of seismic waves in the ground. Three specific simplified models are then investigated: an evolutionary Kanai-Tajimi model, a one-dimensional elastic model, and a one-dimensional Maxwell model. Artificial seismograms are generated from these models to simulate the 1985 Mexico earthquake, and the results are compared with an actual record. It is shown that all the random pulse train models have an evolutionary spectral representation that permits variation of both mean-square intensity and frequency contents, and that the random vibration analyses of linear and nonlinear structures under such excitations can be simply formulated.

Modeling of Combined Thermal and Mechanical Action in Concrete

Abstract: To describe the response of concrete under combined thermal and mechanical action it is necessary to abandon the usual assumption that thermal strain and mechanical strain can be treated as mutually independent, additive components. A generalized model which accounts for the thermomechanical interaction observed in tests is discussed. The basic feature of the formulation is that the thermal strain rate is considered to be a function of both rate of temperature change and the current state of stress. The problems dealt with in the paper are of great practical interest in the design of concrete structures exposed to severe thermal loading.

Stress-induced thermal and shrinkage strains in concrete

Abstract: A previous material model for the increase of creep of concrete caused by simultaneous drying is extended to describe the effect of both drying and wetting, as well as the increase of creep caused by temperature changes, both heating and cooling. By theoretical arguments and comparisons with numerous existing test data, it is shown that the creep increase due to temperature changes, sometimes called the transitional thermal creep, is physically the same phenomenon as the increase of creep due to humidity changes, known as the Pickett effect (or the drying creep effect). In accord with the previous model for drying creep alone, the present extended model explains the increase of creep due to humidity or temperature changes as a consequence of principally two effects: (1) Stress-induced shrinkage (or swelling) or stress-induced thermal expansion (or contraction); and (2) the distributed tensile cracking (or strain-softening) of concrete. The former effect is explained by the previously advanced hypothesis that the creep viscosity depends on the pore humidity rate. The latter effect reduces measured overall deformations, and thus results in the true thermal expansion or shrinkage of uncracked material being considerably larger than observed on load-free companion specimens when significant nonuniformly distributed self-equilibrated stresses are produced by the temperature or humidity change. The proposed material model is suitable for finite-element programs.

Tensile behavior of concrete

Abstract: Under tensile stress, concrete fails at low average strain but a high local strain due to nonuniform strain distribution. It is demonstrated that the use of optical interferometry with laser light both provides adequate sensitivity and allows measurement of strain over a wide field. The measurement is continuous and capable of detecting the localization of strain in zones of very small width. It is shown also that while the use of strain gages would lead to unobjective constitutive stress‐strain relations, interferometric measurement on notched specimens allows art indirect determination of the local stress‐strain and stress‐separation relations. From the knowledge of these and of the strain path in the fracture zone, the value of the fracture energy of concrete can be calculated. It is shown that the energy dissipated in the microcracked zone is a small fraction of the energy dissipated in the final separation of concrete.

Rigid Body Motion Test for Nonlinear Analysis with Beam Elements

Abstract: A rigid body motion test is proposed for verifying the legitimacy of a finite element to be used in a geometrically nonlinear analysis. The test requires that the initial forces acting on an element rotate or translate with the rigid body motion while the magnitudes of the initial forces remain unchanged, so as to preserve the equilibrium of the element during the rigid body motion. Such a test is consistent with basic physical laws, and is, therefore, more rational than previous considerations on rigid body motions. This paper also demonstrates the significance of using a consistent procedure for calculating the member forces in an incremental nonlinear, solution process. When a consistent element is used along with a consistent force calculation procedure, convergent and accurate solutions can be obtained for various nonlinear problems.

Elastodynamic response of pile under transverse excitations

Abstract: The dynamic response of a finite flexible pile, partially embedded in an elastic half‐space and under transverse loadings, is discussed. The loadings are applied at the unembedded end of the pile and may, in general, be a combination of time‐harmonic lateral shear force and moment. By treating the pile as a one‐dimensional structure and the half‐space as a three‐dimensional elastic continuum, the interaction problem is formulated as a Fredholm integral equation of the second kind, which is solved by an appropriate numerical procedure. Selected results are presented to illustrate the basic features of the solution. Examples of the compliance functions of the system are also included.

Stability of Beams with Tapered I‐Sections

Abstract: The purposes of the paper are: (1) To derive differential equations of equilibrium for a tapered I‐beam; and (2) to formulate a finite element for the beam that takes into account the effect of nonuniform torsion. In the virtual work formulation, the updated Lagrangian approach is adopted, in which the effect of geometric nonlinearity is considered. The present formulation requires obtaining a rigorous expression for the strains based on the membrane theory of shells, through which the effect of tapering is considered. The displacements of each cross section are determined with Vlasov's thin‐walled beam assumptions. The derived finite element model, in terms of the linear and geometric stiffness matrices, is useful in a buckling or an incremental large displacement analysis. Using the present theory, one is able to investigate various torsional‐flexural instability problems. Examples are prepared and comparisons are made with existing solutions.

Predictive Control of Structures

Abstract: Different continuous‐time approaches have been proposed in recent years to formulate active control algorithms to reduce the response of civil engineering structures under dynamic excitations In this paper, a general formulation of a new discrete‐time control methodology is presented and applied to structural control This methodology, based on the concept of predictive control, is discussed and compared to the optimal control methodology by means of numerical examples

Time-delay effects on actively damped structures

Abstract: This paper shows the time-delay effect on the distributed parameters structures controlled using direct velocity feedback. It is shown how the stability of the structure could be lost due to time delay. Two ways of time-delay compensation are suggested. The first way is to redesign the gain matirx considering the presence of the time delay. In this case, however, the structure could remain unstable when using control moments as control actions. The other way is to use low-pass filters to filter the velocity measurements from the frequency components of the high order modes. In this case, one can control and compensate for time delay a number of vibrational modes equivalent to the number of control actions. However, the higher order modes remain uncontrolled.

Rocking Response of Liquid Storage Tanks

Abstract: A comprehensive analysis is made of the dynamic response of liquid containing, upright circular cylindrical tanks to a rocking base motion of arbitrary temporal variation. Both rigid and flexible tanks are examined. Critical response quantities for rigid tanks are evaluated over wide ranges of the parameters involved and the results presented in a form convenient for use in practical applications. The interrelationship of the responses of the system to rocking and lateral base motions of the same temporal variation is established, and it is shown that some of the effects of base rocking may be determined from available data concerning the response of laterally excited tanks. Additionally, the well‐known mechanical model for a laterally excited tank is generalized to permit consideration of the effects of base rocking. The influence of tank flexibility is evaluated by an extension of a simple approximate technique proposed previously for laterally excited tanks.

Active control of inelastic structures

Abstract: This work presents a methodology for the shape control of structures undergoing inelastic deformations through the use of an active pulse/force system. Large flexible structures such as tall buildings, long bridges, and offshore platforms tend to develop large deformations under the action of intense dynamic loads such as wind, waves, or earthquakes. Unless these deformations are controlled in some fashion, the structure will sustain extensive damage that may lead to total collapse. One possible solution to this problem is to apply external forces to the structure through cables, air jets, or other devices in order to assure that the deformations are kept below the limits set for serviceability at all times. The methodology presented herein is based on an active control algorithm derived from standard numerical integration methods that uses corrective pulses or forces to limit the response of a structure that has already entered the inelastic range. Material nonlinearities are accounted for by use of stan...

Beams on Variable Two‐Parameter Elastic Foundation

Abstract: Two methods for the solution of beams on variable two-parameter elastic foundation are presented. The first is based on using the exact shape functions for beams on variable two-parameter foundation, in order to obtain the stiffness, consistent mass, and geometric stiffness matrices. The second is based on using the cubic shape functions of a regular beam element and adding the contribution of the foundation as element foundation stiffness matrices. The two solutions are compared in an example that includes static, buckling, and vibration frequency analyses.

Constitutive modeling in analysis of concrete structures

Abstract: Although significant progress on the modeling of concrete behavior has been made in recent years, no unified treatment of the existing mathematical models from which a comprehensive three-dimensional constitutive model can be formulated, has been attempted. This paper summarizes our recent efforts in developing a relatively comprehensive and sophisticated model for progressive failure analysis of concrete structures. The main features of the proposed short-term, time-independent constitutive model include the most sophisticated Willam-Warnke five-parameter or Hsieh-Ting-Chen four-parameter failure surface, the nonuniform hardening rule, the nonassociated flow rule with changing dilatancy factor, linear softening for post-cracking in tension, and multiaxial softening for post-failure in compression. The present model accounts for the hydrostatic pressure sensitivity and Lode angle dependence behavior of concrete, not only in its strength criterion, but also in its hardening characteristics. The model is suitable for any stress range (tension, compression, or mixed), and covers the whole deformation process (elastic, hardening plastic, and softening). Good agreement with a wide range of experimental data has generally been observed. The proposed model has been coded in a nonlinear finite element program available for concrete structural analysis. A numerical example is also given.

Interpreting Aeroelastic Models of Cable‐Stayed Bridges

Abstract: Wind‐tunnel models of long‐span bridges have been exploited in various forms since the late 1930s, and the state of the art has progressed in a parallel fashion. With the rapid increase in the number of new cable‐stayed designs worldwide, new occasions to review the aeroelastic theory and practice of bridge wind‐tunnel modeling have arisen. In particular, the new cable‐stayed bridges have distinct vibration modal forms that are a direct reflection of the design philosophy behind this type of structure. The new modal forms present new challenges to modeling and its interpretation. In this context, the present paper offers a critical examination of the mechanisms involved in the windtunnel modeling of bridges. The method employed is based on flutter derivatives obtained experimentally from deck section models.

Aerodynamic Devices for Tall Buildings and Structures

Abstract: Wind tunnel tests were conducted to investigate the effects of some aerodynamic devices on the wind‐induced responses of tall buildings and structures. It was found that the fitting of small fins or vented fins to a square tower caused an increase in the along‐wind response, while reduction in cross‐wind response occurred only for a limited range of reduced wind velocities. The use of slotted corners resulted in significant reductions in both the along‐wind and cross‐wind responses over an extended range of reduced wind velocities. The concept of slotted corners is practical and could be useful in the design of modern tall buildings and structurees.

Nonstationary Random Critical Seismic Excitations

Abstract: A method is presented to find nonstationary random seismic excitations with a constraint on mean square value such that the response variance of a given linear system is maximized. It is also possible to incorporate the dominant input frequency into the analysis. The excitation is taken to be the product of a deterministic enveloping function and a zero mean Gaussian stationary random process. The power spectral density function of this process is determined such that the response variance is maximized. Numerical results are presented for a single-degree system and an earth embankment modeled as shear beam.

Beam on tensionless elastic foundation

Abstract: An infinitely long elastic beam rests under gravity on a tensionless elastic foundation and is acted upon by a pair of moving loads. This action results in the creation of lift‐off regions between the beam and the foundation that effect the character of the response. The solution includes the determination of the location, magnitude, and extent of the lift‐off region(s) as well as the beam deflection at any point. Sample calculations for parameters relevant in railroad systems show that the effect of lift‐off is substantial. Also included in this analysis is the effect of constrained thermal expansion.

Active Control of Nonlinear Oscillations in Bridges

Abstract: This paper shows how to design the parameters of a passive control mechanism in order to keep bridges safe at all possble resonant frequencies caused by nonlinear effects due to midplane stretching. The control mechanism is a king-post truss tendon mechanism. It is basically chosen to shift the natural frequencies of the bridge away from possible resonances. However, the structural parameters of this mechanism can be designed to eliminate or reduce the nonlinear effects on the primary-resonant responses of bridges. The design has been made using a perturbation technique for hinged-hinged single-span bridge.

Response of circular foundation to spatially random ground motion

Abstract: A method to obtain the response of a rigid circular foundation resting on a uniform elastic half‐space and subjected to a spatially random ground motion is presented. The solution of the resulting mixed boundary‐value problem is based on the use of an integral representation of the response of the foundation in terms of the free‐field ground motion and of the contact tractions between the foundation and the soil obtained in the course of calculating the dynamic compliance functions for the foundation. The results obtained indicate that the effects of the spatial randomness of the ground motion on the response of the foundation are qualitatively similar to deterministic wave passage effects. Both effects involve a reduction of the translational components of the response at high frequencies and the creation of rotational response components.