Journal of Engineering Mechanics

This paper presents a simplified approximate analysis of the overall collapse of the towers of World Trade Center in New York on September 11, 2001. The analysis shows that if prolonged heating caused the majority of columns of a single floor to lose their load carrying capacity, the whole tower was doomed.

A technique to localize damage in structures that can be treated as linear in the pre- and postdamage states is presented. Central to the approach is the computation of a set of vectors, designated as damage locating vectors (DLVs) that have the property of inducing stress fields whose magnitude is zero in the damaged elements (small in the presence of truncations and approximations). The DLVs are associated with sensor coordinates and are computed systematically as the null space of the change in measured flexibility. The localization approach based on the use of DLVs is not structure type dependent and can be applied to single or multiple element damage scenarios. Knowledge about the system is restricted to that needed for a static analysis in the undamaged state, namely, the undamaged topology and, if the structure is indeterminate, the relative stiffness characteristics. Numerical simulations carried out with realistic levels of noise and modeling error illustrate the robustness of the technique.

Traditionally, wind analysis procedures based on the “gust loading factor” approach and experimental techniques involving the high frequency base balance and the “stick-type” aeroelastic model test have assumed ideal structural mode shapes, i.e., linear lateral modes and uniform torsional modes. The influence of nonideal mode shapes manifests itself through modifications in the generalized wind load, the structural displacement, the equivalent static wind load (ESWL), and the attendant influence function. This has led to the introduction of several correction procedures, each focusing on an individual feature of the overall response analysis framework. This paper presents a systematic development of correction procedures in terms of correction factors (CFs) to account for nonideal mode shapes in the formulation of generalized load, analysis of structural response, and the derivation of the ESWL. A parameter study is conducted to examine the significance of CFs in estimating various load effects. It is observed that the influence of a nonideal mode shape is actually negligible for the displacement response and the base bending moment, but not so for other load effects, e.g., the base shear and the generalized wind load. Although the existing procedures are effective in correcting the intended response component, they should not be used indiscriminately for other load effects. This paper also presents a correction procedure for the influence of mode shapes on the ESWLs, a loading format that is very attractive for implementation in codes and standards and design practice as well as for the correct interpretation of wind tunnel measurements.

The inelastic behavior of concrete for highly nonproportional loading paths with rotating principal stress axes is studied. Test cylinders are first loaded in compression under uniaxial stress and then torsion is applied at constant axial displacement. Proportional compressive-torsional loading tests are also carried out for comparison. The tests demonstrate that the response of concrete for load increments parallel in the stress space to the current yield surface is highly inelastic (i.e., much softer than elastic) in the peak load range and especially in the postpeak range. The classical tensorial models of plasticity type incorrectly predict for such load increments the elastic stiffness. The experiments are simulated by three-dimensional finite element analysis using the microplane model M4, in which the stress-strain relations are characterized not by tensors but by vectors of stress and strain on planes of various orientations in the material. It is shown that the observed vertex effect is correctly predicted by this model, with no adjustment of its material parameters previously calibrated by other test results. The experiments are also simulated by a state-of-the-art fracture-plastic model of tensorial type and it is found that the vertex effect cannot be reproduced at all, although an adjustment of one material parameter suffices to obtain a realistic postpeak slope and achieve a realistic overall response. What makes the microplane model capable of capturing the vertex effect is the existence of more than 60 simultaneous yield surfaces. Capturing the vertex effect is important for highly nonproportional loading with rotating principal stress axes, which is typical of impact and penetration of missiles, shock, blasts, and earthquake.

Although soils are known to exhibit nonlinear behavior even at small strains, evaluations of the response of sedimentary basins to strong seismic motions are almost always based on linear, elastic solutions incorporating frequency-independent damping. The principal reasons for this relate to the robustness of the linear algorithm and the ease with which the required parameters can be determined experimentally in engineering practice. Most often, but not always, attempts are made in these analyses to compensate for the inelastic behavior by adjusting the material parameters for the representative levels of strain by means of an iterative method. However, both the standard iterative method and the direct linear solution without iterations suffer from two important shortcomings. First, they do not account for the effect of high confining pressures on inelastic behavior. However, it is known from experiments with sands subjected to cyclic shearing strains under confining pressures of up to 5 Mpa, that in highly confined samples, the material remains nearly elastic for a larger range of strains than do those samples subjected to a lesser pressure. Second, the amplification analyses disregard the fact that small-amplitude, high-frequency components of deformation involve hysteresis loops with little modulus degradation or damping (i.e., nearly elastic secondary loops). Thus, motions computed at the surface of the basin with the standard method usually exhibit unrealistically low amplitudes at high frequencies. This article presents the results obtained with a series of “true” nonlinear numerical analyses with inelastic (Masing-type) soils and layered profiles subjected to broadband earthquake motions, taking into account the effect of the confining pressure. These show that it is possible to simulate closely the actual inelastic behavior of rate-independent soils by means of linear analyses in which the soil moduli and damping change with frequency. It is emphasized that the variation in the linear model of the material parameters with frequency arises solely because the strains have broad frequency content, and not because the materials exhibit any rate dependence when tested cyclically. The proposed new model is successfully applied to a 1-km-deep model for the Mississippi embayment near Memphis, Tenn. The seismograms computed at the surface not only satisfy causality (which cannot be taken for granted when using frequency-dependent parameters), but their spectra contain the full band of frequencies expected.

A time-domain numerical method is developed to analyze the hydroelastic responses of flexible floating structures to waves; in which, the boundary element method is applied to evaluate the fluid motion and the finite-element method to analyze the elastic deformation of structure. The dynamic wave-structure interaction is simulated by prescribing the conditions on a wave generation boundary for each time step and by satisfying the continuity of the pressure and displacement on the fluid-structure interface. A time-domain solution is obtained in a predictor-corrector scheme and through a time-stepping computation. The effect of space and time discretizations on the convergence and stability of solution for regular, random and solitary waves is discussed by comparing among numerical solutions. The validity of the present method is verified by comparing it with the experimental results for the three kinds of waves mentioned. Further, the fission of a solitary wave under a flexible floating structure is observed both in numerical analysis and experiments.

An improved regular lattice network model is developed and validated for fracture of concrete structures. The improvements pertain to the inclusion of the tension softening response of the matrix phase, and of the modelling of structural response by incrementing the deformation rather than the load. A further development is the use of a regular square rather than a triangular lattice network to speed up the computations. These improvements eliminate the need for the introduction of arbitrary scaling parameters in the beam element failure criteria. Validation checks on notched three-point bend concrete specimens confirm the predictive capabilities of the improved lattice model with regard to both the load-deformation behavior and the energy dissipation mechanisms.

A procedure is presented for the probabilistic analysis of the seismic soil-structure interaction problem. The procedure accounts for uncertainty in both the free-field input motion as well as in local site conditions, and structural parameters. Uncertain parameters are modeled using a probabilistic framework as stochastic processes. The site amplification effects are accounted for via a randomized relationship between the soil shear modulus and damping on the one hand, and the shear strain of the subgrade on the other hand, as well as by modeling the shear modulus at low strain level as randomly fluctuating with depth. The various random processes are represented by their respective Karhunen-Loève expansions, and the solution processes, consisting of the accelerations and generalized forces in the structure, are represented by their coordinates with respect to the polynomial chaos basis. These coordinates are then evaluated by a combination of weighted residuals and stratified sampling schemes. The expansion can be used to carry out very efficiently, extensive Monte Carlo simulations. The procedure is applied to the seismic analysis of a nuclear reactor facility.

The second order differential equation of interface shear is formulated for fiber-reinforced polymer-strengthened beams using beam theory with a shear deformable adhesive layer. The solution of the boundary value problem is obtained in closed form and is used to derive deflection expressions for different loading conditions. The solution is also extended to analyze partially plated beams. The results converge to the extreme cases of very poorly and perfectly bonded plates and they help identify values of the adhesive shear modulus for effective stiffening. Furthermore, the solution of partially plated beams aids in defining anchorage lengths needed to develop the full or the highest possible composite action at midspan.

Characteristics of a pressure-impulse diagram for blast loads are studied based on a dimensional analysis and a single-degree-of-freedom model. Structural behavior is dominated by the fundamental elastic response mode and the structural damage is controlled by the maximum structural deflection. The blast loading is simplified into a descending pressure pulse. A characteristic curve in nondimensional loading parameter space is used to define an isodamage critical diagram, pressure-impulse diagram, to distinguish damaged and undamaged ranges in the loading parameter space. Three damage regimes on a pressure-impulse diagram, i.e., (I) impulse-controlled damage, (II) peak load and impulse-controlled damage, and (III) peak load-controlled damage, exist respectively for impulsive, dynamic and quasistatic structural response regimes determined by the ratio between loading time and the response period of a structure. It is observed that there is a noticeable loading shape influence on the pressure-impulse diagram in Regime-II when both peak load and impulse are important for dynamic structural response. A unique effective pressure-impulse diagram is proposed to eliminate the pulse loading shape effect on a pressure-impulse diagram.

Postbuckling analysis is presented for shear deformable cross-ply laminated composite rectangular plates subjected to the combination of in-plane edge compressive mechanical loading and thermal loads due to a linearly varying temperature across the thickness. The formulation is based on the first-order shear deformation theory and von-Karman-type nonlinearity. The analysis uses a quadratic extrapolation technique for linearization and Chebyshev polynomials for spatial discretization. An incremental iterative approach is employed to estimate the critical load. The boundary conditions consisting of clamped, simply supported, free edge, and their combinations are considered. The effects of the thinness ratio, aspect ratio, lamination scheme, the number of layers, and the modulus ratio on the critical load/limit load and postbuckling behavior are studied.

Slip-on buckle arrestors for offshore pipelines offer important advantages over other arrestor designs as they do not require welding. An additional advantage offered by the related concept of the two-part clamp-on arrestor is that it can be installed onto a continuous pipe. It has long been known that such devices often cannot reach higher arresting efficiencies. As a result, the use of slip-on arrestors in deepwater applications has been limited. The somewhat deficient performance is due to the fact that a propagating buckle can penetrate such devices via a folded-up U mode at pressures that are lower than the collapse pressure of the pipe. This can take place even for very rigid rings. A methodology for generating bounds on the maximum arresting efficiency that can be expected from slip-on arrestors is developed. An upper bound of their efficiency is related to the pressure at which a propagating buckle starts to penetrate a long and stiff circumferential confinement. A lower bound is established by relating the crossover pressure to the lowest pressure at which the buckle will propagate through the confinement. The parametric dependence of both of these pressures was established experimentally. The method developed yields the range of pipe $D/t’s$ where degradation in arresting efficiency can be expected and predicts its extent. The arresting efficiency degradation was shown to depend on the yield stress of the pipe. Pipe of higher yield stress exhibits smaller degradation in arresting efficiency.

General interaction relations for pipe sections subjected to combinations of normal forces, internal or external pressure, twisting moments, biaxial bending moments, and biaxial shearing forces are developed. The derivations are based on the fully plastic capacity of the pipe as determined by the maximum distortional energy density yield criterion. Close form interaction relations are obtained for general load combinations and an accurate approximation is proposed. Previously established interaction relations for bending moments, axial forces and internal pressure are recovered as a special case of the general solution. The developments are expressed as universal nondimensional relationships suitable for limit states design. Consideration is given to the limits of applicability of the interaction relations and a systematic design procedure is proposed based on the interaction relations obtained and their limits of applicability. The relations are applicable in the design of elevated pipes, submerged pipes, supports of offshore platforms, and tubular structural steel members.

A Latin hypercube sampling method, including a reduction of spurious correlation in input data, is suggested for stochastic finite element analysis. This sampling procedure strongly improves the representation of stochastic design parameters compared to a standard Monte Carlo sampling. As the correlation control requires the number of realizations to be larger than the number of stochastic variables in the problem, a principal component analysis is employed to reduce the number of stochastic variables. In many cases, this considerably relaxes the restriction on the number of realizations. The method presented offers the same general applicability as the standard Monte Carlo sampling method but is superior in computational efficiency.

A thermodynamically consistent constitutive model for brittle solids is presented. It is shown that damage functions, if not appropriately formulated, could lead to internal contradiction manifested in stress reversals. A solution strategy to circumvent this problem along with examples is provided.