Continuous Chords Research Articles

Size dependence in chord characteristics from simulated and observed continental shallow cumulus

Abstract. In this study we compare long-term Doppler and Raman lidar observations against a full month of large eddy simulations of continental shallow cumulus clouds. The goal is to evaluate if the simulations can reproduce the mean observed vertical velocity and moisture structure of cumulus clouds and their associated subcloud circulations, as well as to establish if these properties depend on the size of the cloud. We propose methods to compare continuous chords of cloud detected from Doppler and Raman lidars with equivalent chords derived from 1D and 3D model output. While the individual chords are highly variable, composites of thousands of observed and millions of simulated chords contain a clear signal. We find that the simulations underestimate cloud size and fraction but successfully reproduce the observed structure of vertical velocity and moisture perturbations. There is a clear scaling of vertical velocity and moisture anomalies below the chords with chord size, but the moisture anomalies are only 1 %–2 % higher than the horizontal mean values. The differences between the observations and simulations are smaller than the difference in sampling the modeled chords in time or space. The shape of the vertical velocity and moisture anomalies from cloud chords sampled spatially from 3D model snapshots is almost perfectly symmetric. In contrast, the chords sampled temporally from the lidar observations and 1D model output have a marked asymmetry, with stronger updrafts and higher moisture anomalies occurring earlier on.

Analysis of rectangular hollow section trusses

A database of 26 previous full-scale experiments on rectangular hollow section (RHS) trusses is supplemented by nine tests on a 10-metre-span, simply supported, RHS Warren truss, reported herein. Measured axial forces, bending moments and truss deflections are compared to four 2D, elastic, frame-analysis models consisting of: (i) all joints pinned and concentric; (ii) all joints rigid and concentric; (iii) pin-ended webs connected eccentrically to continuous chords; and (iv) rigid-ended webs connected eccentrically to continuous chords. On average, all four models predict sufficiently accurate axial force distributions and deflections under elastic loading. However, all four models under-predict bending moment magnitudes. Implications for RHS truss analysis according to the “detailed method” of CSA S16-14 are discussed, and recommendations for modelling are made.

Metal structural roofing with a flat truss with continuous chords as an enlarged assembly unit

When building a new block of a health and recreation center, designer metal structures were used in the roofing coverage. The over covered three storey building consists of two blocks. It has a variable height and a mixed framework. Both building blocks were over covered with structural lattice roofing of similar design. When designing spatial structural roofing, the authors proposed a new design concept. The novelty of the design lies in the fact that a modified flat truss is used as the basic assembly unit of a spatial structure. To develop a spatial structure design the roof-girder trusses with continuous chords from rolled I-beams and a lattice from roll-welded sections with non gusset joists were used. They are well-known and work well in practice. When designing structural roofing, previously known trusses of the mentioned design were slightly modified. In particular, trusses with parallel chords were given greater camber (2.5% instead of 1.5%), the design of a supporting truss joist was changed and fixing elements for chord and lattice members joining trusses into a spatial structure were added to truss joists.

Geometry and the quest for theoretical generality

This paper reconsiders scale-theoretical ideas from the standpoint of voice leading. I begin by showing that Clough and Douthett's definition of ‘maximal evenness’ makes covert reference to voice-leading distances, albeit disguised by the form of their equations. I then argue that theirs is a special case of the broader problem of quantizing continuous chords to a scale, deriving some new results in this more general setting – including an analogue of the ‘cardinality equals variety’ property. In the second part of the paper, I show how Clough and Douthett's ‘J-function’ began as a device for generating maximally even collections, only later evolving into a tool for studying the voice leadings between them. Particularly important here are Julian Hook's ‘signature transformations’, which I generalize to a wider range of collections. I conclude with a few remarks about history and methodology in music theory.

Large Deformation of Inelastic Large Space Frame. II: Application

Material and geometric nonlinear analysis of the tested models for a large space frame is presented based on the 1D finite-element method. The analytical results have been confirmed to agree sufficiently with the experimental results up to a large deformed state. Members-coupled buckling of continuous chords and complicated collapsed states were simulated well. The analytical results of the partial models have shown that coupled buckling between several continuous chords appears to be asymmetric because of the difference in axial forces allowed by adjacent members. Except for whole bucklinglike phenomena, it is possible to analyze a large and complicated space frame with elastoplastic coupled buckling up to a large deformed state.

Experimental Study of Composite Space Trusses with Continuous Chords

The last decade saw the emergence of a new type of space truss built with continuous chord members. Earlier studies on these trusses confirmed that besides the cost savings resulting from their simple jointing methods, their behaviour is sound and ductile. The present study investigates the possibility of using either a concrete slab or top timber boards acting compositely with the top chord, to improve the behaviour of these trusses. New techniques are developed to allow the easy and inexpensive attachment of both types of top continuum. With these techniques, a high level of shear interaction can be developed, leading to significant improvements in behaviour. The paper also introduces an analytical study based on the finite element method for the analysis of space trusses with continuous chords, both in the composite and non-composite states.

Design of space truss structures

Space truss design usually involves two main assumptions: that truss members are pin-ended, and compression members possess brittle post-buckling characteristics. The validity of these assumptions in the design of a new group of space trusses with continuous chords and eccentric joints is questionable. With chord member continuity and the consequent improvement in compression member behaviour, current design practice might be too conservative. In this paper, it is shown that substantial improvements in overall truss strength have resulted when the true member end conditions are considered, thus indicating potential savings in truss weight with considerable magnitudes.

The Angirraq: Low Cost Prefabrication in Arctic Houses

Production models of the Angirraq hut, developed for the Department of Northern Affairs and National Resources, Ottawa, can be built for $4.00/sq ft, complete except for services. Basic stressed skin panels (fir plywood) with full thick glass fiber insulation packed in the closed panels and cedar plywood exterior are combined with open-joints to form an assembly, tied with shear dowels and continuous chords, to form a rigid box. Construction details and results of tests on panel bowing, condensation, heating, and effect of wind-blown rain and snow on joints, are discussed.