Journal of Engineering Mechanics

A submerged, vertical, turbulent plane jet impinging onto a free water surface will be self-excited into a flapping oscillation when the jet velocity, exiting the jet orifice, exceeds a critical value. The dependence of the critical velocity W_0c and the flapping frequency f₀ on the water depth H and the jet orifice width d was investigated in detail in this study. The jet flapping motion was visualized by a laser induced fluorescence technique and measured with a laser Doppler velocimeter; a supplemental measurement of the displacement of water surface by a surface wave gauge was made. The jet flapping characteristics are interpreted in terms of the effective water depth given by H_e = H-z₀, where z₀ is the virtual origin of the jet. The critical jet exit velocity was found to increase linearly with the effective water depth and to decrease with the square root of the jet orifice width. The flapping frequency decreased with the root square of the effective water depth and independent of the jet orifice width. These results led to a critical condition for the onset of instability as St = 0.929[(H − z₀)/d]^−3/2, where St is the critical Strouhal number defined by St = f₀d/W_0c.

Homogenization is one of the most important steps in the numerical analysis of masonry structures where the continuum method is used. In the present study, equivalent elastic properties, strength envelope, and different failure patterns of masonry material are homogenized by numerically simulating responses of a representative volume element (RVE) under different stress conditions. The RVE is modeled with distinctive consideration of the material properties of mortar and brick. In the numerical simulation, various displacement boundaries are applied on the RVE surfaces to derive the stress-strain relation under different conditions. The equivalent overall material properties of the RVE are averaged by integrating the stresses and strains over the entire area. Failure of masonry is defined by three different modes, namely, tensile failure of mortar (Mode I), shear failure of mortar or combined shear failure of brick and mortar (Mode II), and compressive failure of brick (Mode III). The homogenized elastic properties and failure model can be used to analyze large-scale masonry structures.

Modal transformation techniques are usually adopted in structural dynamics with the aim of decoupling the equations of motion. They are based on the search for an abstract space in which the solution of the problem results simplified. Analogous transformation techniques have recently been developed with the aim of defining a space where a multivariate stochastic process is expressed by a linear combination of one-variate uncorrelated processes. This paper proposes a method, called double modal transformation, by which the dynamic analysis of a linear structure is carried out through the simultaneous transformation of the equations of motion and the loading process. By adopting this technique, the structural response is obtained through a double series expansion in which structural and loading modal contributions are superimposed. Its effectiveness and application are discussed with reference to two classic wind engineering problems—the alongwind response and the vortex-induced crosswind response of slender structures—which provide a wide panorama of the most relevant properties of this procedure.

A Lagrangian reproducing kernel formulation is introduced as an approximation of field variables under the Galerkin meshfree framework of geomechanics. The reproducing kernel approximation is formulated with reference to the material coordinates, yielding an approach that is applicable to both total and updated Lagrangian formulations. In the method presented, geotechnical materials described by pressure-sensitive multisurface plasticity with a cap hardening rule are considered in the meshfree formulation. The solution obtained from the meshfree method with linear basis was compared to that of bilinear finite elements for elastoplastic analysis of geotechnical materials.

A Ritz-based static analysis procedure is described for fiber-reinforced plastic, skew bridge superstructure, or deck, with a parallel grid core. This is a simplified analysis method based on a transformed plate formulation and the classical Ritz method. The rib core bridge superstructure, or deck, is idealized as a homogeneous, orthotropic skew plate to which the Ritz method is applied to discretize the resultant, equivalent orthotropic skew plate. Three laminated skew plate examples are presented; the results are compared with finite-element solution to verify the validity of the simplified method. A practical demonstration of a rib core skew bridge superstructure is investigated using the simplified method. The procedure provides a useful analysis tool that can be used in the preliminary design stage without the use of finite-element analysis.

Flood wave movement in an open channel can be treated as disturbances imposed at the upstream and downstream boundaries of a channel to an initially steady uniform flow. Linearized, cross sectionally integrated continuity and momentum equations are introduced to describe one-dimensional, unsteady, gradually varied flow in open channels. The Laplace transform method is adopted to obtain first-order analytical spatio-temporal expressions of upstream and downstream channel response functions. These expressions facilitate a critical comparison among different wave approximations in terms of their mathematical properties and physical characteristics. One or two families of characteristic waves, parameterized by an attenuation factor and a wave celerity, are found for various wave approximations. The effects of the downstream boundary condition on different wave approximations are discussed and compared. Wave translation, attenuation, reflection, distortion, and configuration from the analyses are further investigated and interpreted; thus, the differences and similarities in the propagating mechanism among the various wave approximations are revealed.

This paper examines in depth the transient rocking response of free-standing rigid blocks subjected to physically realizable trigonometric pulses. First, the expressions for the dynamic horizontal and vertical reactions at the pivot point of a rocking block are derived and it is shown that the coefficient of friction needed to sustain pure rocking motion is, in general, an increasing function of the acceleration level of the pulse. Subsequently, this paper shows that under cycloidal pulses a free-standing block can overturn with two distinct modes: (1) by exhibiting one or more impacts; and (2) without exhibiting any impact. The existence of the second mode results in a safe region that is located on the acceleration-frequency plane above the minimum overturning acceleration spectrum. The shape of this region depends on the coefficient of restitution and is sensitive to the nonlinear nature of the problem. This paper concludes that the sensitive nonlinear nature of the problem, in association with the presence of the safe region that embraces the minimum overturning acceleration spectrum, complicates further the task of estimating peak ground acceleration by only examining the geometry of free-standing objects that either overturned or survived a ground shaking.

This paper examines the transient rocking response of anchored blocks subjected to physically realizable horizontal pulse-type motion. Restrainers with elastic-brittle and elastic-plastic behavior are considered. Under one-sine pulse, anchored blocks can overturn with two distinct modes of overturning: (1) by exhibiting one impact; and (2) without exhibiting any impact. It is found that restrainers are more efficient in preventing overturning of small slender blocks subjected to low frequency pulses. This study uncovers that, although for most of the frequency range anchored blocks survive higher accelerations than free-standing blocks, there is a finite frequency range where the opposite happens. This paper examines this counterintuitive behavior and explains the destructive effect that increased strength and increased ductility of restrainers have on the rocking stability of rigid structures when excited by certain ground motions.

The characterization of the fracture process zone inside a cracked concrete specimen is investigated through optical fiber technology. Fiber Bragg gratings are used to measure the strains in the close vicinity of the crack front, thus enabling us (for the first time) to directly measure those deformations inside the concrete specimen. A detailed discussion of the experimental technique is first provided. Then, following the experimental measurements, test results are presented and discussed. Preliminary results indicate that there is a narrow zone on each side of the crack front with inelastic residual strains, and another where strains increase only in the presence of a neighboring crack tip. The width of the process zone is found to be about three times the maximum aggregate size.

The dynamic indentation of structural elements such as beams and plates continues to be an intriguing problem, especially for scenarios where large area contacts can occur. Standard methods of indentation analysis typically use a dynamic beam theory solution to obtain an overall load-displacement relationship and then a Hertzian contact solution to determine local stresses under the impactor. However, previous static and dynamic modeling efforts have shown that the stress distribution in the contact region will differ significantly from a Hertzian one when the contact length exceeds the thickness of the beam. In such cases point contact can no longer be assumed and Hertzian relationships are no longer valid. The dynamic indentation model presented herein is a first effort to model the asymmetric (i.e., off-center) low-velocity impact problem for elastically supported beams. Numerical results obtained are compared with elementary beam theory solutions for model validation.

The risk of early-age concrete cracking depends on the capacity of hardening concrete to support the thermal stresses caused by the exothermic nature of the hydration process. This has been recognized for “massive” concrete structures. However, with the increasing use of high performance concretes, it is apparent that this problem also concerns traditionally “thin” structural members (columns, beams). The definition of a “massive” concrete structure, and how the structural dimension affects intensity and occurrence of chemically-induced strucctural degradation is the main focus of this paper. Based on dimensional analysis of the governing equations, a characteristic length scale, the hydration heat diffusion length, is derived; beyond this length the structure needs to be considered as “massive,” and latent hydration heat effects affect the long-term structural integrity. From experimental data of normal strength concrete and high performance concrete, it is shown that this hydration heat diffusion length of high performance concrete is of the order of ℓ_h = 0.2 m, and l_h = 0.3 m for normal strength concrete. Through a number of case studies, the relevant similarity parameters of the risk of early-age concrete cracking are identified, which allow's the monitoring of the structural performance of early-age concrete structures.

Criteria for the incipient motion of a rigid body initially resting on a rigid surface are formulated from first principles in this work. A modified Coulomb friction model and an associated distribution of reaction forces are proposed. There exists a surprisingly large category of general motions, however, that subscribe to a more conventional analysis, an analysis made possible by identifying so-called “significant reaction surfaces.” In this way a model that caters for the majority of combined translations and rotations is devised. Some introductory results demonstrate the accuracy with which fluids can be numerically modeled for the purposes of entrainment. This work is an extension of previous work by the same writer.