Journal of Engineering Mechanics

The responses of two, low-rise, 2-degree-of-freedom base isolated structures with different isolation periods to a set of near-field earthquake ground motions are investigated under passive linear and nonlinear viscous damping, two pseudoskyhook semiactive control methods, and optimal semiactive control. The structures are isolated with a low damping elastic isolation system in parallel with a controllable damper. The optimal semiactive control strategy minimizes an integral norm of superstructure absolute accelerations subject to the constraint that the nonlinear equations of motion are satisfied and is determined through a numerical solution to the Euler–Lagrange equations. The optimal closed-loop performance is evaluated for a controllable damper and is compared to passive viscous damping and causal pseudoskyhook control rules. Results obtained from eight different earthquake records illustrate the type of ground motions and structures for which semiactive damping is most promising.

The degradation of concrete structures is always accompanied by the formation of cracks. Crack monitoring is hence useful in assessing the “health condition” of the structure. In our previous investigation on an optical-fiber crack sensor, we have successfully demonstrated the possibility of crack detection and monitoring without requiring prior knowledge of crack locations. Also, a single fiber can be employed to monitor a number of cracks. In practical applications, the signal loss versus crack opening relationship of the sensor needs to be properly “designed” to satisfy performance requirements on sensitivity to small cracks and/or the total number of detectable cracks (which is limited by the maximum loss at each crack). In this paper, a theoretical model for the signal loss versus crack opening relationship is developed through a combination of mechanical and optical analyses. Using concrete beams with embedded sensors, crack monitoring experiments are conducted. Test results are found to be in reasonably good agreement with predictions from the model. With the verified model, simulations are carried out to study the effect of various parameters on sensor performance. The potential application of the theoretical model to generate sensor design guidelines is hence demonstrated.

Implicit integration schemes for elastoplastic constitutive equations have been developed in recent years as an alternative to explicit schemes. The consistent tangent constitutive matrix ${\mathbf{D}}^{\mathrm{con}}$ that results from implicit schemes makes the global stiffness matrix consistent with the implicit integration procedure and differs from the traditional continuum tangent constitutive matrix ${\mathbf{D}}^{\mathrm{ep}}$ that results from explicit schemes. Onset of strain localization and shear banding has been traditionally predicted using the continuum tangent constitutive matrix. It is shown that different criteria for onset of shear-band formation are obtained depending on whether ${\mathbf{D}}^{\mathrm{con}}$ or ${\mathbf{D}}^{\mathrm{ep}}$ is used. It is shown that shear band prediction using ${\mathbf{D}}^{\mathrm{con}}$ is step-size dependent, and that the use of ${\mathbf{D}}^{\mathrm{con}}$ influences the predicted onset of strain localization in frictional materials. An analytical equation for prediction of the onset of shear-band formation using ${\mathbf{D}}^{\mathrm{con}}$ for the Mohr–Coulomb model is developed, and a numerical example is presented.

By observing that the optimal basis for the proper orthogonal decomposition (POD) can be obtained from the cross power spectral density (XPSD) matrix of a multivariate stationary Gaussian stochastic process, the computational efficiency, in both time and memory consumption, of simulations of this process is improved by using a hybrid spectral representation and POD approach with negligible loss of accuracy. This hybrid approach actually simulates another multivariate process with many fewer variables in an optimal subspace obtained by the POD. This approach is straightforward, effective, and does not place any conditions on the XPSD matrices. Furthermore, the error induced by the reduction of variables is predictable and controllable prior to the simulation procedure. The spectral representation method (SRM) is discussed in a heuristic way. In this paper, a specific POD theorem is formally stated, proved, and related to XPSD matrices. A numerical example is given to demonstrate the effectiveness of this hybrid approach. This approach may also have potential applications for simulations of nonstationary non-Gaussian processes.

A large-deflection mathematical analysis of rectangular plates under uniform lateral loading is presented in this paper. The analysis is based on solving two fourth-order, second-degree, partial differential Von Kármán equations relating the lateral deflections to the applied load. This paper provides a mathematical procedure which benefits from the software and hardware computing capabilities that were unavailable when mathematical modeling was last attempted. The solution is presented in a simple form suitable for direct practical use and can be easily implemented in common spreadsheet packages. Plates with two boundary conditions, namely, simply supported edges and held edges, are considered. Comparisons are held against earlier exact and approximate solutions, including results of finite element analyses. The results show close agreement with other exact analysis methods. The solution is able to produce the same results as other exact solutions, but with a much simpler and a more practical approach.

In this paper, an analytical solution for linear long-wave reflection by an obstacle of general trapezoidal shape is explored. A closed-form expression in terms of first and second kinds of Bessel functions is obtained for the wave reflection coefficient, which depends on the relative lengths of the two slopes and top of the obstacle as well as the depth ratios in front of and behind the obstacle versus that above the obstacle. The analytical solution obtained in this study finds a few well-known analytical solutions to be its special cases, which include the wave reflection from a rectangular obstacle, an infinite step, and an infinite step behind a linear slope. The present analytical solution, however, covers a much wider range of problems. It is found that the periodicity of the wave reflection coefficient as the function of the relative length of the obstacle remains when two slopes are present but with a reduced magnitude. The phenomenon of zero wave reflection from the structure is special to a rectangular obstacle only, which disappears with the addition of a slope in front or at the rear. The new solution may be very useful in some engineering applications, for example, the design of a submerged breakwater of trapezoidal shape.

In developing a one-dimensional analysis and design procedure for reinforced concrete structures, research is generally based on yield phenomena and the plastic flow of steel in tension and concrete in compression. The ability of concrete to resist tension is considered in the form of tension stiffening or is completely disregarded. This procedure does not account for the influence of structural size in changing the failure mode and the stress distribution across the uncracked or cracked ligament. The key factor affecting this stress distribution is found to be the strain-softening modulus. This paper presents an improved model that is based on the fundamental equilibrium equation for the progressive failure of plain concrete beams. The concrete stress-strain relationship in tension is derived by calculating the peak tensile stress and softening modulus for different depths of beams on the basis of the fracture parameters obtained with the size effect law. Thus, the proposed model uses the peak tensile stress and the softening modulus, which vary depending on the size of the beam. To study the effect of the strength of high-performance concrete (HPC) on the concrete tensile stress-strain relationship, the experimental load-deflection plots of different-sized beams are compared with those obtained by using the proposed analytical model for eight different mixes made with locally available fly ash and slag. The model is also extended for lightly reinforced concrete beams, and the results are compared with those in the literature and are found to be in good agreement.

This paper evaluates the softened truss model and the softened strut-and-tie model for predicting shear strength of reinforced concrete squat walls. The prediction accuracy of analytical solutions is examined using the experimental data of 62 test shear walls available in the literature. It was found that the analytical solutions, which utilize the softening laws of cracked reinforced concrete under compression, can yield better estimations of shear strength. Further, the state of stresses in the web of a squat wall may be better assumed to be concentrated rather than uniformly distributed. The assumption of uniform distribution of stress of the softened truss model for squat walls causes some drawbacks. The upper bound solution of the softened truss model is found to generate unreasonably large horizontal clamping stresses, whereas the estimation of the lower bound solution is governed mainly by the yield of reinforcement, which is not the actual failure behavior of squat walls.

This paper presents a new model for analyzing a nonlinear soil–pile interaction subject to horizontal shaking of a vertical circular pile embedded in a soil layer of finite thickness. The pile rests on bedrock with either a pinned or a clamped support. The soil mass is assumed composing of a “semi-nonlinear” inner soil zone around the pile and a linear viscoelastic soil zone outside the inner zone. When the inner soil behaves linearly, the present solutions are identical to those obtained by Nogami and Novak in 1977. Numerical results show that soil resistance of less slender piles developed against the vibration is larger than that of more slender piles. Soil resistance depends more strongly on the size of the nonlinear inner zone when the pile is vibrating at a frequency higher than the natural frequency of the soil. Soil nonlinearity, in general, results in a smaller damping and stiffness of the soil–pile system, except at high frequency. At higher vibration frequency, the situation can be very complicated. The exact value of the dynamic stiffness of the soil–pile system depends on elastic shear wave speed, soil nonlinearity, vibration frequency, slenderness ratio of the pile, magnitude of vibration, and tip conditions of the pile. Generally speaking, the dynamic stiffness is smaller than the static stiffness. The normalized dynamic stiffness for pile with a pinned tip is, in general, larger than that with a clamped tip, while the reverse is true for the damping.

This paper investigates the fundamental behavior of long water waves propagating through branching channels of uniform depth and width. Numerical simulations based on the Boussinesq long wave model were carried out to investigate the effects of channel width $b$ , effective wavelength ${\lambda }_e$ , wave amplitude $\alpha$ , and angle $\theta$ between channel branches on wave transmission and reflection. Our results showed that the transmission and reflection of long waves through branching channels are dominantly governed by a single dimensionless parameter $b∕{\lambda }_e$ , whereas other parameters such as the angle between channel branches are less important. Detailed quantitative results for predicting long wave transmission and reflection in different branching channels based on the similarity parameter $b∕{\lambda }_e$ were determined. From these results, we have discovered some very interesting and distinct long wave behaviors in narrow and wide branching channels. To verify the numerical results, experiments were conducted in a right-angled branching channel, and the experimental results showed good agreement with the numerical predictions.