Journal of Engineering Mechanics

For long‐span bridges, the traffic load can be modeled as white‐noise‐load fields along the lanes. The mean and the intensity of the white‐noise field depend on the traffic situation. Theoretical expressions in terms of the traffic parameters are available for these white‐noise‐field characteristics covering the entire range from free Poissonian traffic to dense congested traffic that in the limit of zero vehicle velocity becomes a standing queue of vehicles. This paper presents a stochastic model for the load‐effect pulse process caused by the formation of queues of stopped vehicles. The key assumptions leading to the model are the following: (1) The probabilistic structure of the succession of cars and trucks in the queue is generated on the basis of the free Poissonian traffic situation; (2) the occurrences of standing queues are Poissonian and sufficiently rare to justify the neglect of the effect of within‐lane overlap; (3) the queue durations and lengths are exponentially distributed; and (4) the central‐limit theorem is effective implying asymptotic Gaussianity of the load effect from any given lane interval fully covered by a stochastically homogeneous traffic load. Assumption 3 is not in conflict with actual observations on a German freeway, whereas assumption 4 has been justified for specific examples by computer simulations using different truck‐weight distributions of given mean and standard deviation. Finally, it is shown by use of the model that the effect of queue overlap in the case of two‐way traffic on the bridge can be decisive for the reliability analysis of the considered component of the bridge.

Two different approaches are presented for the large‐deflection analysis of an inextensible elastic beam under moment gradient. One end of the beam is hinged and at a fixed distance away from this end is a frictionless support where the beam can slide freely. In the first approach, the differential equation based on elastica theory is formulated and solved by using elliptic integrals; which yield a closed‐form solution. In the second approach, the governing differential equations are solved numerically by the shooting‐optimization technique in which the fourth‐order Runge‐Kutta algorithm and an optimization algorithm are employed. Comparison studies of the results obtained from the two methods are made and the results are found to be in very good agreement.

An analysis of free vibrations of tall buildings, such as frame, shear‐wall, and frame‐shear‐wall structures, is proposed and discussed in this paper. Frame buildings are treated as shear beams with varying cross sections, the solutions of mode shapes of such buildings are expressed in Bessel's functions, and the parameter of determining the fundamental period can be found from a figure provided in the paper. Based on the fact that the shear deformation and bending deformation are all considered for shear wall and frame‐shear‐wall structures, the formulas for calculating free vibrations of such structures are presented. It is very simple and convenient to apply these formulas to dynamic analysis of tall buildings. The measurement results and statistical analysis of frame, shear‐wall, and frame‐shear‐wall structures in sites, and three examples of determining free vibrations of structures are also given in this paper. The examples show that the effect of shear deformation on the first natural frequency is not significant, but the effect of that on higher natural frequencies may not be neglected.

An elastoplastic model for concrete is presented that covers the nonlinear triaxial behavior of concrete under compressive and tensile loading, compressive failure, and tensile cracking. In all the states, the model is based on the same concept. For the description of the prefailure behavior, two different hardening functions are introduced that control the expansion and the transposition of the “yield surface.” To simulate tensile cracking, a “smeared‐crack approach” is chosen. The elastoplastic concept is extended, whereas the anisotropic behavior of cracked concrete is taken into account. By introducing a new combination of isotropic expansion and kinematic transposition of the “yield surface,” steady transitions between compression and tension zones are obtained both in cracked and uncracked states. Comparisons with test results show the very good capacity of the proposed model to cover the material behavior both in the pre‐ and postfailure regions. By applying the method of finite elements, the analysis of notched beams demonstrates that the model is very well suited to predict the response of concrete structures.

This paper presents a detailed finite‐element investigation into the axisymmetric failure behavior and strength of intersections of the large end of a cone and a cylinder subject to uniform internal pressure. The study considers shells of uniform thickness with cone‐apex half angles ranging from 10° to 85° and cylinder radius‐to‐thickness ratios from 10 to 1,000. Plastic limit loads from a small‐deflection elastic‐plastic analysis are first presented. A rationally based simple equation is then established, which approximates the finite‐element limit loads very closely and is suitable for future incorporation in pressure‐vessel design codes. The effect of large deflections on the load‐deflection behavior is examined extensively for the covered geometric parameters for three different yield stresses. An approximate equation to assess the beneficial effect of large deflections on failure strength is also developed.

A three‐dimensional plasticity model is developed for foams and honeycombs. The model accounts for the transverse isotropy of foams and the orthotropy of honeycombs by incorporating a shift on stress that provides a yield surface in the form of a sphere with the centroid shifted from the origin in the principal stress space. To model the extensive strains that occur at constant stress, an elastic‐perfectly plastic formulation is used until a critical plastic volumetric strain is reached. Then the initiation of lockup is represented as an isotropic hardening function of plastic volumetric strain. Both elastic and plastic constants are given as functions of the initial density of the cellular material. With lockup, the elasticity tensor transforms to that of the parent solid. To account for strain‐rate effects, the plateau stresses and the hardening parameter are taken as functions of volumetric strain rate. For each material, experimental data are given for various densities and illustrative plots are given to show how well the model represents these data.

An innovative finite‐element technique for the analysis of buckle propagation in cylindrical shells subjected to external pressure is presented. Advantage is taken of the steady‐state nature of propagation, permitting a robust and efficient formulation to be implemented within the framework of large displacement/rotation elastoplastic finite‐element analysis. The procedure relies on the fact that the history of deformation that any material point undergoes during buckle propagation can be traced by marching in the longitudinal direction, along the pipe generator through the point, from the front to the tail in a snapshot of the propagating profile. Thus, the state of deformation and stress everywhere in the pipe can be determined from the propagating profile. A scheme is described in which suitable initial estimates of the propagation pressure and the propagating profile are selected, and improved estimates are obtained by means of equilibrium iterations. The computational requirements are rather low, and parametric studies can be conducted easily for a wide range of values of the diameter‐to‐thickness ratio. In this paper, the technique, its implementation, and results for stainless steel pipes are presented. Excellent agreement is found between the analytical results and previously reported experimental data.

The paper analyzes the size effect, which is an inevitable consequence of softening in the relation of interface shear stress and slip displacement between a fiber or reinforcing bar and the surrounding matrix. The problem is simplified as one‐dimensional. Closed‐form solutions of pull‐pull and push‐pull failures are obtained for a linear softening stress‐slip law with residual strength, and for an exponential law without residual strength. The postpeak softening is shown to lead to localization of slip and interface shear fracture with a process zone of finite length. This zone propagates along the interface during the loading process, causing the distribution of interface shear stress to become strongly nonuniform. The larger the bar or fiber size, the stronger the nonuniformity. The size effect in geometrically similar pullout tests of different sizes is found to represent a smooth transition between two simple asymptotic cases: (1) The case of no size effect, which occurs for very small sizes and is characteristic of plastic failure; and (2) the case of a size effect of the same type as in linear elastic fracture mechanics, in which the difference of the pullout stress from its residual value is proportional to the inverse square root of the fiber or bar diameter. An analytical expression for the transitional size effect is obtained. This expression is found to approximately agree with the generalized form of the size effect law proposed by Bažant. The shape of the size effect curve is shown to be related to the shape of the softening stress‐slip law for the interface. Finally, it is shown how measurements of the size effect can be used for identifying the interface properties, and a numerical example is given.

The concept of variability response function based on the weighted‐integral method is extended to two‐dimensional plane stress/plane strain stochastic problems in order to calculate their response variability (in terms of second moments of response quantities) and reliability (in terms of the safety index) with great accuracy even when using relatively coarse finite‐element meshes. The concept of variability response function is used to establish spectral‐distribution‐free upper bounds of the response variability. In addition, the variability response function based on the local‐averaging method is introduced to reduce the computational effort associated with the weighted‐integral method. The two methods are compared to estimate the relative accuracy of the more approximate local‐averaging method. The response variability is calculated using a first‐order Taylor expansion approximation of the response quantities. The safety index is calculated using the advanced first‐order second‐moment approach. One of the most important findings is that the coefficient of variation of certain response quantities can be much larger than the coefficient of variation of the elastic modulus (the input quantity).

A constitutive formulation is presented that covers the triaxial load‐response spectrum of plain concrete in tension as well as in shear. The elastoplastic concrete model resorts to an isotropic‐hardening description of the prepeak behavior and to a fracture energy‐based isotropic‐softening description of the post‐peak response. To control inelastic dilatancy, a nonassociated plastic flow rule is adopted in regard to the inelastic volume change. The constitutive parameters are calibrated from a series of stroke‐controlled laboratory experiments that include the direct‐tension test and triaxial compression tests at three different levels of confinement. The predictive capabilities of the proposed model are assessed with a broad range of experimental data. The issue of failure on the constitutive level is addressed with the aid of the instability indicator for continuous material branching and the localization indicator for the formation of weak discontinuities. The relevance of these two failure diagnostics is evaluated with the experimental data of the wedge experiment on cylindrical concrete specimens when the stress path approaches the failure surface within the cone of instability.