Lateral Pedestrian Excitation of Footbridges

The phenomenon of synchronized lateral pedestrian excitation of footbridges has been highlighted in recent years by the widely publicized problems encountered with the London Millennium Footbridge. On opening day, during which a large number of pedestrians crossed the bridge, it exhibited alarming and unstable amplitudes of lateral vibration, which resulted in an 18 months closure and a 7 million dollar retrofit. Subsequent investigations revealed that the dynamic characteristics of the bridge did not differ significantly from those of other footbridges of similar span, and that the phenomenon of synchronized lateral excitation had recently been exhibited by several other bridges. An analysis of lateral pedestrian excitation of bridges, based on the governing differential equations of motion, is presented. Analytical models of lateral pedestrian loading are developed which can be used to assess both the subcritical response and the critical number of pedestrians likely to induce synchronized excitation. Theoretical predictions of synchronization are compared, and show close correlation, with the results of full-scale tests on the Millennium Footbridge.     

Combined Experimental-Operational Modal Testing of Footbridges

In combined vibration testing, an artificial, measured force is used in operational conditions. This requires the identification of a system model that takes both the measured and the operational excitation into account. Advantages with respect to the classical operational modal analysis approach are the possibility of obtaining mass-normalized mode shapes and the increase of the excitation level and its frequency content. An advantage with respect to the classical experimental modal analysis approach, where the ambient excitation is not modeled, but considered as disturbing noise, is the possibility of using excitation levels that are of the same amplitude, or even smaller, than the ambient excitation levels. In this paper, combined modal testing of footbridges is explored using two case studies: a steel arch footbridge with spans of 75.2 m and 30.3 m and a concrete stress-ribbon footbridge with spans of 30 m and 28 m. The comparison of the modal parameters (eigenfrequencies, damping ratios, mode shapes, and modal scaling factors) obtained from a combined vibration test with the ones obtained from other modal tests and from a finite-element model, demonstrates the feasibility of using small and practical excitation devices for the modal testing of footbridges.     

Lateral and Upward Soil-Pipeline Interactions in Sand for Deep Embedment Conditions

The soil–pipeline interactions in sand under lateral and upward movements are investigated with particular attention to the peak forces exerted on the pipe. The analytical solutions for estimating the peak forces are summarized and it is shown that, for deep embedment condition, there is large uncertainty in the true values since the bounds established by the analytical solutions are large. In order to find the solution for the peak force and to investigate its transition from shallow to deep failure mechanism, finite element analyses of lateral and upward pipe movements are performed for different embedment conditions. Two different soil models (Mohr–Coulomb and Nor–Sand models) are used for the simulations. The accuracy of the analysis is first examined by simulating experimental tank tests. The analysis is further extended to deeper embedment ratios of as large as 100. The obtained finite element results are used to construct a design chart for deep embedded pipelines.     

Swaying of Pedestrian Bridges

The paper considers nonlinear (autoparametric) resonance in footbridges as a reason for excessive lateral vibrations induced by walking pedestrians. To describe the above-mentioned phenomenon, a physical model (an elastic pendulum) is proposed. Under the special frequency conditions (the ratio between frequencies of vertical and lateral beam modes is about 2, or 2:1), nonlinear resonance becomes possible if a vertically excited mode is near a primary resonance and a load parameter (a static displacement caused by pedestrians) is equal or more than its critical value. When the increasing load parameter passes through the critical value, a jump phenomenon is observed for the lateral mode and the vertical mode is saturated. Swaying of pedestrian bridges can be treated as a two-step process. The first step (achievement of the jump phenomenon), described in the paper, is the condition for the beginning of the second step—the process of interaction between applied forces and the lateral mode of vibration.     

Approximate Boundaries for Finite-Element Models of Static Soil–Foundation Interaction Problems

In this paper, we examine the use of boundary springs as approximate external boundary conditions for the typical soil islands encountered in finite-element (FE) models of soil–foundation interaction problems. We present a set of simple uniformly distributed boundary springs and a set of variable boundary springs that account for the lateral distribution of contact forces between the foundation and the soil. We evaluate the accuracy of the approach for shallow foundations resting on soil islands of different dimensions. It is shown that significantly smaller errors can be achieved with these boundary springs than those obtained when fixed-fixed or fixed-free external boundary conditions are used. We present an iterative approach to determine the boundary springs for cases in which extremely small soil islands are required. Although the approach suggested to determine the boundary springs is best suited to shallow foundations, good results are also obtained for pile foundations. The approach presented applies to a uniform elastic half-space, but extensions to layered media are possible.     

Vibration Studies of a Cantilevered Structure Subjected to Human Activities Using a Remote Monitoring System

Long cantilevered balconies used as seating areas in auditoriums, theaters, churches, and stadiums are often susceptible to excessive vibrations because of crowd movements. Measurement and analysis of the responses of such structures when subjected to human movements can provide a reasonable estimate of their dynamic properties. However, it is generally very difficult to artificially excite such massive structures with a measured input force at the same level as that exerted by a crowd. In addition, it is not yet well understood how human occupants’ presence may change the dynamic properties of these structures. This paper presents details of a remote vibration monitoring system (RVMS) installed on a large cantilevered balcony structure to collect the vibration records generated by rhythmic crowd activities. The results of the studies conducted indicate that the presence of human occupants resulted in a consistent reduction in the natural frequencies of the structure and an increase in the damping ratios for higher modes. Conclusions were also drawn regarding the applicability of the damping ratios recommended by a number of standards and design guides for the structure used in this study.     

3D FE Analyses of Buried Pipeline with Elbows Subjected to Lateral Loading

This study investigates the interaction between soil and pipeline in sand subjected to lateral ground displacements with emphasis on the peak force exerted to a bended elbow-pipe. A series of three-dimensional (3D) finite-element (FE) analyses were performed in both opening and closing modes of the elbow section for different initial pipe bending angles. To model the mechanical behavior of sands, two soil models were adopted: Mohr-Coulomb and Nor-Sand soil model. Investigations also included the effects of pipe embedment depth and soil density. Results show that the opening mode exhibits higher ultimate forces and greater localized deformations than the closing mode. Nondimensional charts that account for pipeline location, bending angle, and soil density are developed. Soil-spring pipeline analyses of an elbow-pipe were performed using modified F-δ soil-spring models based on the 3D FE results and were compared to the findings of conventional spring model analyses using the standard two-dimensional soil-spring model. Results show that the pipe strain does not change in the closing mode case. However, in the opening mode case, the pipe strain computed by the modified analysis is larger than that by the conventional analysis and the difference is more pronounced when the pipe stiffness is stiffer.     

Transient Response of Supported Beams to Moving Forces with Sinusoidal Time Variation

Moving forces are a common loading pattern for flexible beams, found in many applications in both civil and mechanical engineering. These forces give rise to a transient response, the nature of which depends on the time variation of the amplitude of the force and its position along the beam. In addition to the possibility of numerical evaluation, closed form solutions of the beam response are beneficial for their simplicity of use, and because they allow an understanding of the system behavior. On the other hand, these prove to be rather complicated in most cases, and only a limited number of cases are available in the literature. This paper studies the simple but common case of a supported beam loaded by a force with sinusoidal time variation moving at a constant speed. Simple equations are presented for the approximated responses at and away from resonance, and their accuracy is discussed. Transient frequency response functions are also shown. Finally, as an example, the results are applied to an evaluation of the response of a beam footbridge to the action of a walker, and compared to code specifications.     

Stress radiographical measurement of the anteroposterior, medial and lateral stability of the knee joint

A hydraulically operated machine for applying well-defined forces to the knee joint is described. The measurement of anteroposterior as well as lateral and medial stability in the knee joint is based upon roentgenograms exposed while the forces are being exerted on the patient. The advantage of the radiological measuring method over methods using external measurements is the elimination of inaccuracies due to displacements of the soft tissues of the limb. The accuracy was evaluated by test/retest examination of 50 healthy subjects. The radiographs were measured at random after cessation of examinations in the gonylaxometer. The accuracy is +/- 1.2 nm for medial/lateral, +/- 2.4 nm for drawer sign. Diagnostically the difference between the two knees must exceed 2.0 nm (collateral instability) or 3.1 nm (drawer) to exceed standard values. The standard values for the different ligament laxities are given. The applied force to be used for evaluation of medial/lateral stability is recommended to be 9 kg, and for anteroposterior stability between 20 and 30 kg.     

Performance Simulation of Nuclear Containments for Security

Under blast loading, nuclear containment structures are subjected to cyclic flexural, axial, and shear forces. Less attention has been paid to modeling the cyclic behavior of reinforced concrete elements in which shear deformations are significant, such as in nuclear containments. Research has demonstrated that the strength of concrete in the principal compression direction is softened by tension in the lateral direction. This interaction has been considered for monotonic loading for many years. To consider this interaction for cyclic loading, the material laws recently derived by Mansour et al. in 2001 for the cyclic softened membrane model (CSMM) can be used. Both fire and explosion effects resulting from blast loading can also be incorporated into the constitutive models of concrete and reinforcing bars. This paper presents a method to implement the CSMM model, so that it can be used to simulate the performance of nuclear containments for security by the design communities.     

Prediction of Flow in Centrifugal Blower Using Quasi-Steady Rotor–Stator Models

A computational fluid dynamics (CFD)-based computational tool, named STREAM, is used to analyze fluid flow in a centrifugal blower. The unsteady interaction of the flow in the rotating impeller (rotor) and the stationary volute (stator) is modeled via quasi-steady rotor–stator models. Two such models are developed: one based on a local exchange of information and the other based on a circumferential averaging procedure at the rotor–stator interface. Due care is exercised to ensure that inadequate grid resolution and numerical dissipation do not smear out the small pressure rise typical of the blower considered here. Computed results based on the proposed models with multiblock structured grids are presented; global quantities such as static pressure rise, horsepower, and static efficiency, available from test data for different mass flow rates, are used to evaluate the trends predicted by the CFD results. Overall, the predictions by the proposed models are satisfactory.     

Was Anna O.''s black snake hallucination a sleep paralysis nightmare? Dreams, memories, and trauma

Complex combinations of linear forces, moments, and couples are developed by the arch wire during orthodontic treatment. For instance, application of torque to a canine during distal driving may create force interactions if the tooth tips distally toward the extraction site. This investigation studied the effect of second-order couples and bracket angulations on the application of torque to a single tooth. By using a test apparatus to simulate application of torque to a single tooth, 0.016 x 0.022 inch stainless steel wires were tested in longitudinal torsion simultaneous to fixed amounts of second-order couples or fixed degrees of second-order bracket angulation. Application of a second-order couple through a bracket to a longitudinally twisted arch wire produces a third-order couple, since the bracket slot walls exert forces on the wire, tending to detwist it. This third-order couple will usually be small as the distance between the two couple members is short. Nevertheless, it may have a restraining effect on the third-order wire-bracket interaction. The results show that application of second-order couples or bracket angulations lead to an increase in exerted torque for angles of twist below 22 degrees. Because of torsional play, a wire twisted 18 degrees in a 0.018-inch bracket slot did not exert any torque unless it was subjected to a second-order couple. Thus, in an in vivo situation where forces interact, the actual torsional play may be substantially less than predicted from theoretical models only regarding third-order mechanics. The restraining effect of second-order couples tapered when the torque created by longitudinal twisting became much larger than the torque exerted by the second-order couple. Second-order couples of biologically acceptable magnitudes had little effect on the level of torque after the third-order clearance had been eliminated.     

Deformation and Cracking of Seepage Barriers in Dams due to Changes in the Pore Pressure Regime

A procedure is presented for analyzing postconstruction deformation of seepage barriers due to changes in the pore pressure regime after seepage barrier construction. The procedure uses the changes in pore pressures calculated by finite-element seepage analyses to calculate changes in buoyancy and seepage forces that occur as a result of seepage barrier construction. When the buoyancy and seepage forces are applied to a finite-element soil-structure interaction model, the result is an effective-stress analysis that rigorously models seepage effects. This paper discusses application of the procedure to five dams to calculate postconstruction deformation and stresses in seepage barriers. The results of the analyses indicate that deformation due to pore pressure regime changes is a likely mechanism causing cracking in rigid seepage barriers.     

Analysis of left ventricular wall motion based on volumetric deformable models and MRI-SPAMM

We present a new approach for the analysis of the left ventricular shape and motion based on the development of a new class of volumetric deformable models. We estimate the deformation and complex motion of the left ventricle (LV) in terms of a few parameters that are functions and whose values vary locally across the LV. These parameters capture the radial and longitudinal contraction, the axial twisting, and the long-axis deformation. Using Lagrangian dynamics and finite-element theory, we convert these volumetric primitives into dynamic models that deform due to forces exerted by the datapoints. We present experiments where we used magnetic tagging (MRI-SPAMM) to acquire datapoints from the LV during systole. By applying our method to MRI-SPAMM datapoints, we were able to characterize the 3-D shape and motion of the LV both locally and globally, in a clinically useful way. In addition, based on the model parameters we were able to extract quantitative differences between normal and abnormal hearts and visualize them in a way that is useful to physicians.     

Modal Testing, Finite-Element Model Updating, and Dynamic Analysis of an Arch Type Steel Footbridge

This paper describes an arch type steel footbridge, its analytical modeling, modal testing, finite-element model updating, and dynamic analysis. A modern steel footbridge which has an arch type structural system and is located on the Karadeniz coast road in Trabzon, Turkey is selected as an application. An analytical modal analysis is performed on the developed three-dimensional finite-element model of footbridge to provide analytical frequencies and mode shapes. Field ambient vibration tests on the footbridge deck under natural excitation such as human walking and traffic loads are conducted. The output-only modal parameter identification is carried out by using peak picking of the average normalized power spectral densities in the frequency domain and stochastic subspace identification in the time domain, and dynamic characteristics such as natural frequencies, mode shapes, and damping ratios are determined. The finite-element model of the footbridge is updated to minimize the differences between analytically and experimentally estimated modal properties by changing some uncertain modeling parameters such as material properties. Dynamic analyses of the footbridge before and after finite-element model updating are performed using the 1992 Erzincan earthquake record. At the end of the study, maximum differences in the natural frequencies are reduced from 22 to only 5% and good agreement is found between analytical and experimental dynamic characteristics such as natural frequencies and mode shapes by model updating. Also, maximum displacements and principal stresses before and after model updating are compared with each other.     

Structural Response of 34‐m Darrieus Rotor to Turbulent Winds

The results of a mathematical investigation of the dynamic response of the Sandia/Department of Energy/U.S. Department of Agriculture 34‐m‐diameter Darrieus rotor wind turbine erected at Bushland, Tex., are presented. The formulation used a double multiple stream‐tube aerodynamic model combined with a turbulent airflow and included the effects of (linear) aeroelastic forces. The structural analysis was carried out using previously established procedures with the computer program MSC/NASTRAN. A number of alternative expressions for the spectrum of turbulent wind were used. The modal loading represented by each did not differ significantly; a more significant difference was caused by imposing full lateral coherence of the turbulent flow. Spectra of the predicted stresses at various locations show that without aeroelastic forces, very severe resonance is likely to occur at certain natural frequencies. Inclusion of aeroelastic effects greatly attenuates this stochastic response, especially in modes involving in‐plane blade bending. Comparison is made with preliminary field data collected at medium‐low wind speeds (11.3 m/s) from critical locations on the blade. This comparison shows generally good agreement between measured stress spectra and model predictions based on 10% turbulence intensity and including aeroelastic forces.     

Seismic Response of Isolated Bridges

The seismic response of bridges seismically isolated by lead-rubber bearings (L-RB) to bidirectional earthquake excitation (i.e., two horizontal components) is presented in this paper. The force-deformation behavior of L-RB is considered as bilinear, and the interaction between the restoring forces in two orthogonal horizontal directions is duly considered in the response analysis. The specific purpose of the study is to assess the effects of seismic isolation on the peak response of the bridges, and to investigate the effects of the bidirectional interaction of restoring forces of isolation bearings. The seismic response of the lumped mass model of continuous span isolated bridges is obtained by solving the governing equations of motion in the incremental form using an iterative step-by-step method. To study the effectiveness of L-RB, the seismic response of isolated bridges is compared with the response of corresponding nonisolated bridges (i.e., bridges without isolation devices). A comparison of the response of the isolated bridges obtained by considering and ignoring the bidirectional interaction of bearing forces is made under important parametric variation. The important parameters included are the flexibility of the bridge piers and the stiffness and yield strength of the L-RB. The results show that the bidirectional interaction of the restoring forces of the L-RB has considerable effects on the seismic response of the isolated bridges. If these interaction effects are ignored, then the peak bearing displacements are underestimated, which can be crucial from the design point of view.     

Dynamic Response of Suspension Bridge to High Wind and Running Train

A framework is presented for predicting the dynamic response of long suspension bridges to high winds and running trains. A three-dimensional finite-element model is used to represent a suspension bridge. Wind forces acting on the bridge, including both buffeting and self-excited forces, are generated in the time domain using a fast spectral representation method and measured aerodynamic coefficients and flutter derivatives. Each 4-axle vehicle in a train is modeled by a 27-degrees-of-freedom dynamic system. The dynamic interaction between the bridge and train is realized through the contact forces between the wheels and track. By applying a mode superposition technique to the bridge only and taking the measured track irregularities as known quantities, the number of degrees of freedom of the bridge-train system is significantly reduced and the coupled equations of motion are efficiently solved. The proposed formulation is then applied to a real wind-excited long suspension bridge carrying a railway inside the bridge deck of a closed cross section. The results show that the formulation presented in this paper can predict the dynamic response of the coupled bridge-train systems under fluctuating winds. The extent of interaction between the bridge and train depends on wind speed and train speed.     

Judgments about forces in described interactions between objects.

In 4 experiments, participants made judgments about forces exerted and resistances put up by objects involved in described interactions. Two competing hypotheses were tested: (1) that judgments are derived from the same knowledge base that is thought to be the source of perceptual impressions of forces that occur with visual stimuli, and (2) that judgments are generated using simple models or heuristics for deriving force judgments from kinematic information. The results show some similarities with perceptual impression research, particularly that an active object is judged to exert more force on an inactive object than the latter exerts on the former. However, most of the available kinematic information had little or no effect on judgment, supporting the hypothesis that force judgments are generated according to simple rules. Presentation of information about damage to the objects resulted in use of all available kinds of information; this could reflect greater imageability of damage information than kinematic information. (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

Effect of lateral forces on the movement of myosin-coated beads on actin cables studied using a centrifuge microscope

We developed an in vitro motility assay system, in which myosin-coated polystyrene beads were made to slide on actin filament arrays (actin cables) in giant algal cells and subjected to centrifugal forces, which were parallel to the direction of bead movement to serve as external loads on actin-myosin sliding (Oiwa et al. (1990) Proc Natl Acad Sci USA 87: 7893-7897), and succeeded in determining the steady-state force-velocity relation of ATP-dependent actin-myosin sliding. To give further information about the properties of actin-myosin sliding, we have applied centrifugal forces, in parallel with the plane of actin-myosin sliding but at right angles with the direction of bead movement, and have found that such "lateral" centrifugal forces reduced the velocity of bead movement. In addition, we have also found that the velocity of bead movement is reduced more markedly with lateral forces applied from the left side of the bead ("left" lateral forces) than those applied from the right side of the bead ("right" lateral forces). These results are discussed in connection with the direction of sliding force generated by the myosin heads on the bead which interact with the right-handed double helix of actin monomers constituting actin filaments.