Modal Combinations Research Articles

Effect of Dynamic Analysis and Modal Combinations on Structural Design of Irregular High Rise Steel Buildings

Effect of Dynamic Analysis and Modal Combinations on Structural Design of Irregular High Rise Steel Buildings

Assessing Energy, Environmental, and Economic Tradeoffs in Intermodal Freight Transportation

This paper presents an energy and environmental network analysis model to explore tradeoffs associated with freight transport. The geospatial model uses an intermodal network built by the authors to connect various modes (rail, road, water) via intermodal terminals. Routes along the network are characterized not only by temporal and distance attributes, but also by cost, energy, and emissions attributes (including emissions of carbon dioxide, particulate matter, sulfur oxides, volatile organic compounds, and oxides of nitrogen). Decision-makers can use the model to explore tradeoffs among alternative route selection across different modal combinations, and to identify optimal routes for objectives that feature energy and environmental parameters (e.g., minimize carbon dioxide emissions). The model is demonstrated with three case studies of freight transport along the U.S. eastern seaboard.

Service Orientation, Bus–Rail Service Integration, and Transit Performance

Service orientation is one of the most important decisions that a transit manager makes. A manager can concentrate service on the central business district (CBD) or disperse service to connect multiple destinations. Conventional wisdom suggests that transit managers should focus on serving the CBD, because that—such wisdom suggests—is where riders wish to travel. In some places, the service orientation decision is complicated by the need to define the specific role to be played by rail service. Some managers may view rail transit as part of an integrated network structure. Other managers may view it simply as the functional equivalent of a high-capacity bus route. This research examines the relationship between service orientation, bus–rail service integration, and transit performance in U.S. metropolitan areas with between 1 million and 5 million people. Metropolitan areas that have integrated their rail transit into a decentralized network structure are found to enjoy higher riding habit, higher service productivity, and better cost-effectiveness than metropolitan areas with other network structures or modal combinations. These findings suggest the need for transit managers to carefully consider the relationship between service orientation and bus–rail integration to better serve their customers and improve overall transit performance.

Adaptive Modal Combination Procedure for Nonlinear Static Analysis of Building Structures

A new pushover analysis procedure derived through adaptive modal combinations (AMC) is proposed for evaluating the seismic performance of building structures. The methodology offers a direct multimode technique to estimate seismic demands and attempts to integrate concepts built into the capacity spectrum method recommended in ATC-40 (1996), the adaptive method originally proposed by Gupta and Kunnath (2000) and the modal pushover analysis advocated by Chopra and Goel (2002). The AMC procedure accounts for higher mode effects by combining the response of individual modal pushover analyses and incorporates the effects of varying dynamic characteristics during the inelastic response via its adaptive feature. The applied lateral forces used in the progressive pushover analysis are based on instantaneous inertia force distributions across the height of the building for each mode. A novel feature of the procedure is that the target displacement is estimated and updated dynamically during the analysis by incorporating energy-based modal capacity curves in conjunction with constant-ductility capacity spectra. Hence it eliminates the need to approximate the target displacement prior to commencing the pushover analysis. The methodology is applied to two existing steel moment-frame buildings and it is demonstrated that the AMC procedure can reasonably estimate critical demand parameters such as roof displacement and interstory drift for both far-fault and near-fault records, and consequently provides a reliable tool for performance assessment of building structures.

Simplified buckling analysis of skeletal structures

A simplified approach is proposed for buckling analysis of skeletal structures, which employs a ‘rotational spring analogy’ for the formulation of the geometric stiffness matrix. The benefit of this analogy is that it offers an intuitive framework, which is based on the common notions of linear structural analysis. Assuming that the structural deflections prior to buckling are negligible, a linear eigenvalue problem, utilising the geometric and material stiffness matrices, can be easily formulated and solved for the critical buckling loads. This can be further simplified using an assumed mode, where the rotational spring analogy is shown to provide considerable computational benefits and significant insight into the buckling of various forms of skeletal structure. In this context, the use of different assumed modes can be conceived as a process of probing the structure to establish the most likely mode for buckling and the corresponding critical load. It is also shown that the approximation inherent in the assumed mode approach together with the discrete form of the rotational spring analogy can be significantly improved through modal combinations and increasing the number of elements, respectively, where convergence to the exact buckling solution is demonstrated. Several illustrative examples are provided in this paper, which highlight the simplicity of the proposed approach, its application using a linear structural analysis tool and its ability to shed significant light on important issues in buckling analysis of skeletal structures.

Identification of Modal Combinations for Nonlinear Static Analysis of Building Structures

Abstract: An essential requisite in performance‐based seismic design is the estimation of inelastic deformation demands in structural members. An increasingly popular analytical method to establish these demand values is a “pushover” analysis in which a model of the building structure is subjected to an invariant distribution of lateral forces. Although such an approach takes into consideration the redistribution of forces following yielding of sections, it does not incorporate the effects of varying dynamic characteristics during the inelastic response. Simple modal combination schemes are investigated in this article to indirectly account for higher mode effects. Because the modes that contribute to deformations may be different from the modes that contribute to forces, it is necessary to identify unique modal combinations that provide reliable estimates of both force and deformation demands. The proposed procedure is applied to typical moment frame buildings to assess the effectiveness of the methodology. It is shown that the envelope of demands obtained from a series of nonlinear static analysis using the proposed modal‐combination‐based lateral load patterns results in better estimation of inter‐story drift, a critical parameter in seismic evaluation and design.

The evolutionary history of shell geometry in Paleozoic ammonoids

Abstract Tracking the geometry of all 597 ammonoid genera from the Lower Devonian into the Lower Triassic, a 145-Myr period that spans three mass extinctions, shows that Paleozoic ammonoid shell geometries were strongly biased for a few combinations of whorl expansion (W), whorl overlap (D), and whorl shape (S). Just three modal combinations accommodated approximately 432 genera (72% of total) and just one combination accommodated 239 genera (40%). All three primary modal forms have similar low expansion rates (W ≈ 1.75) and differ only in coiling tightness (D). These geometries resulted in long body chambers (≈400°) with Nautilus-like static in-life aperture orientations (≈30°) for the great majority (>80%) of Paleozoic ammonoids. The ancestral clade Agoniatitida included a unique spectrum of openly coiled geometries that went extinct at the Frasnian/Famennian boundary (and were not seen again until the Triassic). The Devonian/Mississippian extinction terminated the brief, explosive radiation of the Clym...

Polarization in millimeter-wavelength collective Thomson scattering on FTU tokamak

We investigate performance degradation caused in mm-wave collective Thomson scattering on the high-field tokamak FTU by the joint effects of refraction and polarization. It is shown that optimized performances can be recovered, in different parts of the FTU density range, by selecting the most suitable of the four modal combinations potentially contributing to the scattered signal. This can be achieved by matching the limiting polarization of the selected mode at both the transmitting and the receiving side. A full polarization-control capability is required at this purpose.

Simultaneous determination of fibre parameters by an improved four-photon mixing technique

We demonstrate the possibility of determining simultaneously the parameters of optical fibres using a stimulated four-wave mixing method without the requirement of considering the particular refractive index profile. The most suitable modal combinations that minimize the error in neglecting the refractive index profile are found and their dependence on the value of the V parameter. Experimental results that verify the accuracy of the proposed method are also given.

System reliability developments in structural engineering

Two major limitations occur in present structural design code developments utilizing reliability theory. The notional system reliabilities may differ significantly from calibrated component reliabilities. Secondly, actual failures are often due to gross errors not reflected in most present code formats. A review is presented of system reliability methods and further new concepts are developed. The incremental load approach for identifying and expressing collapse modes is expanded by employing a strategy to identify and enumerate the significant structural collapse modes. It further isolates the importance of critical components in the system performance. Ductile and brittle component behavior and strength correlation is reflected in the system model and illustrated in several examples. Modal combinations for the system reliability are also reviewed. From these developments a system factor can be addended to component safety cheking equations. Values may be derived from system behavior by substituting in a damage model which accounts for the response range from component failure to collapse. Other strategies are discussed which emphasize quality assurance during design and in-service inspection for components whose behavior is critical to the system reliability.

Reply to comments by Albert J. Hatch

Shape changing effects of spatial variations of electromagnetic fields in the vicinity of small plasma spheres can be avoided by modal combinations giving uniform pressure over the plasma sphere. Practically, it is necessary to design configurations for which the actual modes are sufficiently good approximations to spherical cavity modes. Misprints in Table II and in Eq. (24) are corrected.

Modal operators and functional completeness, II

In the Kripke semantics for propositional modal logic, a frame W = (W, ≺) represents a set of “possible worlds” and a relation of “accessibility” between possible worlds. With respect to a fixed frame W, a proposition is represented by a subset of W (regarded as the set of worlds in which the proposition is true), and an n-ary connective (i.e. a way of forming a new proposition from an ordered n-tuple of given propositions) is represented by a function fw: (P(W))n → P(W). Finally a state of affairs (i.e. a consistent specification whether or not each proposition obtains) is represented by an ultrafilter over W. {To avoid possible confusion, the reader should forget that some people prefer the term “states of affairs” for our “possible worlds”.}In a broader sense, an n-ary connective is represented by an n-ary operatorf = {fw∣ W ∈ Fr}, where Fr is the class of all frames and each fw: (P(W))n → P(W). A connective is modal if it corresponds to a formula of propositional modal logic. A connective C is coherent if whether C(P1,…, Pn) is true in a possible world depends only upon which modal combinations of P1,…,Pn are true in that world. (A modal combination of P1,…,Pn is the result of applying a modal connective to P1,…, Pn.) A connective C is strongly coherent if whether C(P1, …, Pn) obtains in a state of affairs depends only upon which modal combinations of P1,…, Pn obtain in that state of affairs.

The motion and damping of buildings relative to seismic response spectra

abstract The response spectrum is very useful in dynamic analysis even though its use for multimass systems involves approximations as to modal combinations. It is especially useful in predicting effects of possible real earthquakes or of proposed nuclear detonations because it may be postulated or predicted much more readily than a complete time history of ground motion. The relationships of multimass system response—in terms of displacement, velocity, acceleration, force, shear, and moment—to elastic spectral response are given, together with examples taken from the AEC nuclear testing program in Nevada. The effects of relative building stiffnesses and stiffness taper on mode shape and thus on response are shown, as are the base shears relative to spectral response for several idealized fundamental mode shapes. A Spectral Response Reconciliation procedure is presented and demonstrated by which procedure spectral response is reconciled with measured real building motion to obtain damping or other data under actual response to ground motion of any intensity. Damping values of highrise buildings are determined by this procedure. Comparisons are made between 5 per cent damped response spectral values at the fundamental mode period of buildings and measured building motion.

Response of higherise buildings to ground motion from underground nuclear detonations

abstractTypical data obtained thus far in the AEC nuclear test program on the response of highrise Las Vegas buildings to ground motion from distant nuclear events including Boxcar and Benham are presented, together with measured building response to distant earthquakes and to wind gusts. Major variations in response spectra are shown over the city for a specific event, from period band to period band at the same location for different events, and statistical parameters are shown for the randomness of spectral response. The peak response of tall buildings is shown for the top levels in translation and in orbital motion, and in the vertical plane with simultaneous multi-level measurements. The variation of peak modal response is shown with elapsed time, modal combinations are noted, and an example of time-history computed response is compared to measured response. It is shown that highrise Las Vegas buildings respond to ground motion with considerable amplification, that the fundamental modes tend to dominate the peak responses although there are exceptions, that there can be significant modification of loading conditions because of simultaneous motion in the two horizontal axes even though a building is symmetric, and that some building periods vary with amplitude and history of non-damaging prior response while others do not. In general there are indications that code earthquake design criteria are by no means conservative.