Compact Sections Research Articles

Borel sets with σ-compact sections for nonseparable spaces

We prove that every (extended) Borel subset $E$ of $X\times Y$, where $X$ is complete metric and $Y$ is Polish, can be covered by countably many extended Borel sets with compact sections if the sections $E_x=\{y\in Y:(x,y)\in E\}$, $x\in X$, are $\sigma$-

Robust Positively Invariant Cylinders in Constrained Variable Structure Control

This paper proposes the use of cylinders as primary invariant sets to be used in certain state-constrained control designs. Following the idea originally introduced by O'Dell, the primary invariant set is intersected with the state constraints to yield sets which retain the invariance under some conditions. Although several results presented here apply to fairly general nonlinear systems and primary invariant sets of any shape, the focus is on constrained sliding-mode control (SMC) using infinite cylinders as the primary invariant set. Their use is motivated by a coordinate transformation where the sliding motion is decoupled from the overall convergence to the origin. Robust positive invariance conditions are given for cylinders having convex and compact cross sections. For the case of cylinders with ellipsoidal cross sections, the invariance condition is given in the form of a linear matrix inequality. Further, a decision procedure to qualify each state constraint is given as a tool for the selection of the switching gain. A numerical example for a third-order plant illustrates the method.

TU‐D‐BRA‐02: Compact Laser Acceleration of Paticles for Oncological Applications

The proton beam therapy of cancer has been practiced to yield good therapeutic results. However, it remains a costly treatment, primarily because of its huge accelerator facility needed to drive proton beams. The introduction of laser acceleration promises to greatly reduce the size and possible cost to accelerate and provide a medically needed system for therapy. Not only its compact acceleration section, but also its compactness of necessary radiation shield and beam handling section (a portion similar to the gantry) contribute to the compactness of the overall therapy machine size. A series of innovations such as the adiabatic acceleration, double‐layer target, the optimized target thickness, etc. constitutes to provide a new paradigm of laser‐driven compact therapy. We envision that the verification of dosage with the self‐auto‐activation by PET combined with pencil‐beam scanning characteristics amounts to a new feedback therapy of cancer.

A linear curved-beam model for the analysis of galloping in suspended cables

A linear model of curved, prestressed, no-shear, elastic beam, loaded by wind forces, is formulated. The beam is assumed to be planar in its reference configuration, under its own weight and static wind forces. The incremental equilibrium equations around the prestressed state are derived, in which shear forces are condensed. By using a linear elastic constitutive law and accounting for damping and inertial effects, the complete equations of motion are obtained. They are then greatly simplified by estimating the order of magnitude of all their terms, under the hypotheses of small sag-to-span ratio, order-1 aspect ratio of the (compact) section, characteristic section radius much smaller than length (slender cable), small transversal-to-longitudinal and transversal-to-torsional wave velocity ratios. A system of two integrodifferential equations is drawn in the two transversal displacements only. A simplified model of aerodynamic forces is then developed according to a quasisteady formulation. The nonlinear, nontrivial equilibrium path of the cable subjected to increasing static wind forces is successively evaluated, and the influence of the angle of twist on the equilibrium is discussed. Then stability is studied by discretizing the equations of motion via a Galerkin approach and analyzing the small oscillations around the nontrivial equilibrium. Finally, the role of the angle of twist on the dynamic stability of the cable is discussed for some sample cables.

Framed Steel Plate Wall Behavior under Cyclic Lateral Loading

An experimental study was performed to investigate the cyclic behavior of framed steel walls with thin infill plates. Five specimens with a single bay and three stories were tested. Test parameters for the specimens were the plate thickness and the strength and compactness of the column. The test results showed that unlike conventional reinforced concrete walls and braced frames, well-designed steel plate walls exhibited large ductility and energy dissipation capacity as well as high strength. The steel plate walls with relatively thin plates showed shear-dominated behavior by the moment–frame action. On the other hand, steel plate walls with thick plates showed flexure-dominated behavior by the cantilever action. The shear-dominated walls showed better ductility. To achieve large ductility, the boundary columns must resist the combined axial force and transverse force developed by the tension–field action of the infill plates. Also, the columns must have compact sections to prevent their early local buckling.

EFFECT OF CONCRETE CRUSHING ON FLEXURAL STRENGTH OF STEEL-CONCRETE COMPOSITE GIRDERS

The ultimate flexural strength of composite steel girders with compact sections is examined through experimental investigation and elasto-plastic finite displacement analyses to develop a reduction factor of the ultimate flexural strength. A two-point loading test of a composite girder was carried out to verify the numerical modeling by comparing the experimental and numerical results. Then, a parametric study was performed using finite element analyses to investigate the effect of concrete crushing on the flexural strength of composite girders constructed using SM570 grade steel. Observations made by comparison of the ultimate flexural strength obtained from the experimental and numerical results with that according to the AASHTO and Eurocode show that the existing reduction factor equations are conservative and can be relaxed when the strength is controlled by crushing of concrete slab. A new reduction factor for the ultimate flexural strength for composite I-girders under positive bending is proposed.

Compact kernel sections of long-wave–short-wave resonance equations on infinite lattices

In the present paper, we consider the nonautonomous long-wave–short-wave resonance equations on infinite lattices. We first prove the existence of compact kernel sections for the associated process. Then we give an upper bound of the Kolmogorov ε -entropy and verify the upper semicontinuity of these kernel sections.

There are significantly more nonegative polynomials than sums of squares

We study the quantitative relationship between the cones of nonnegative polynomials, cones of sums of squares and cones of sums of even powers of linear forms. We derive bounds on the volumes (raised to the power reciprocal to the ambient dimension) of compact sections of the three cones. We show that the bounds are asymptotically exact if the degree is fixed and number of variables tends to infinity. When the degree is larger than two, it follows that there are significantly more nonnegative polynomials than sums of squares and there are significantly more sums of squares than sums of even powers of linear forms. Moreover, we quantify the exact discrepancy between the cones; from our bounds it follows that the discrepancy grows as the number of variables increases.

Compact kernel sections for nonautonomous Klein–Gordon–Schrödinger equations on infinite lattices

In this paper, we study the nonautonomous Klein–Gordon–Schrödinger equations on infinite lattices. We first prove the existence of compact kernel sections for the corresponding process and then obtain an upper bound of the Kolmogorov ε-entropy for these kernel sections. Finally, we establish the upper semicontinuity of the kernel sections.

Nonlinear analysis of concrete-filled steel SHS and RHS columns

This paper presents an accurate nonlinear finite element model for the behaviour and design of axially loaded concrete-filled square hollow section (SHS) and rectangular hollow section (RHS) steel tube columns. The nonlinear material models for confined concrete and steel tubes were carefully modeled in the finite element analysis. The column strengths and load-axial shortening curves were evaluated. The results obtained from the finite element analysis were verified against experimental results. An extensive parametric study was conducted to investigate the effects of different concrete strengths and cross-section geometries on the strength and behaviour of concrete-filled SHS and RHS steel tube columns. The study was conducted over a wide range of concrete cube strengths ranged from 30 to 110 MPa. The overall depth of the steel tube-to-plate thickness ratio ranged from 10 to 40 covering compact SHS and RHS steel tube sections. The column strengths predicted from the finite element analysis were compared with the design strengths calculated using the American, Australian and European specifications. Based on the results obtained from the parametric study, it is found that the design strengths calculated using the American Specifications and Australian Standards are conservative, while the design strengths calculated using the European Code are accurate, except for the concrete-filled RHS compact steel tube columns having the overall depth of the steel tube-to-plate thickness ratio of 40.

Phase-hologram-based compact RCS test range at 310 GHz for scale models

A compact radar cross section (RCS) test range based on a phase hologram has been developed for scale-model measurements. The phase hologram converts the feed-horn radiation to a plane wave needed for RCS determination. The measurements are performed at 310 GHz using continuous-wave operation. A monostatic configuration is realized using a dielectric slab as a directional coupler. The main advantage of a scale-model RCS range is that the dimensions of radar targets are scaled down in proportion to the wavelength. Therefore, RCS data of originally large objects can be measured indoors in a controlled environment. Test objects such as metal cylinders and simplified targets have been measured. The feasibility of the phase-hologram RCS range has been verified. The operation and measurement results of the monostatic measurement range are reported here. A comparison with simulated results is also included

Structural Design and Optimisation of the Beijing National Olympic Swimming Centre

The design of the Beijing National Olympic Swimming Centre involved finding a strength design solution for the 22,000 beam wall and roof structure whilst minimising the structural steel weight. Both global and local optimisation techniques were employed in determining this strength design solution. Each member cross section represents a design variable, while the strength utilisations for each member for a given load combination and strength check equation represent a design constraint. Due to the large number of design constraints and variables, gradient methods of optimisation were not feasible for optimisation of this structure. A method of constraint satisfaction optimisation using discrete variables was developed and employed for the global structure design, resulting in significant steel tonnage reduction. The automated procedure is presented in this paper. The discrete variable choices for member cross sections were determined by using simulated annealing optimisation techniques to maximise strength of cross sections per kg of steel. Three groups of discrete variables were generated for the three different parts of the building using this method (surface member, edge member, internal member). The global constraint satisfaction optimisation procedures then used these optimised cross section groups Investigation of the use of stiffened cross sections instead of compact cross sections was also considered in the design process as a method of reducing steel tonnage. The effectiveness of stiffened cross sections loaded plastically in seismic regions is discussed.

DEVELOPMENT OF WEB SLENDERNESS LIMITS FOR COMPOSITE I-GIRDERS ACCOUNTING FOR INITIAL BENDING MOMENT

The positive bending momen tcapacity of composite steel girders is examined through parametric study employing elasto-plastic finite displacement analyses. The effects of initial bending moment on the bending moment capacity and on the web slenderness limit for section classification are investigated. Observations made during the numerical study indicate that the noncompact web slenderness limits in conventional design standards, which are based on tests of steel I-sections, are conservative for composite sections. Many sections, which are classified as slender by current specifications, demonstrate suffficient flexural capacity as noncompact. The conventional web slenderness limits for noncompact sections, independent of initial bending moment seems inappropriate for composite I-girders. The initial bending moment has considerable effect on the noncompact web slenderness limits. The web slenderness limits for compact and noncompact sections are proposed on the basis of the parametric study.

Study of the History of Christianity in U.S.-China Relations: A New Departure?

AbstractForty years ago, in late December 1968, John K. Fairbank, the longtime dean of American China scholars, gave a memorable presidential address to the annual meeting of the American Historical Association (AHA) in New York City. In it, he urged his fellow historians to take up a task expressed in the title of his address, “Assignment for the 1970s: The Study of American–East Asian Relations.” Although he spoke amid academic upheaval over the Vietnam War, his address made it clear that he was mainly referring to China and Sino-American relations. He described China as .a uniquely large and compact section of mankind…too big and too different to be assimilated into our…culture.. He also argued that .China is too weak to conquer the world but too large to be digested by it.

Behaviour of normal and high strength concrete-filled compact steel tube circular stub columns

This paper presents the behaviour and design of axially loaded concrete-filled steel tube circular stub columns. The study was conducted over a wide range of concrete cube strengths ranging from 30 to 110 MPa. The external diameter of the steel tube-to-plate thickness ( D / t ) ratio ranged from 15 to 80 covering compact steel tube sections. An accurate finite element model was developed to carry out the analysis. Accurate nonlinear material models for confined concrete and steel tubes were used. The column strengths and load–axial shortening curves were evaluated. The results obtained from the finite element analysis were verified against experimental results. An extensive parametric study was conducted to investigate the effects of different concrete strengths and cross-section geometries on the strength and behaviour of concrete-filled compact steel tube circular stub columns. The column strengths predicted from the finite element analysis were compared with the design strengths calculated using the American, Australian and European specifications. Based on the results of the parametric study, it is found that the design strengths given by the American Specifications and Australian Standards are conservative, while those of the European Code are generally unconservative. Reliability analysis was performed to evaluate the current composite column design rules.

Experimental investigation of concrete-filled cold-formed high strength stainless steel tube columns

This paper presents an experimental investigation of concrete-filled cold-formed high strength stainless steel tube columns. The high strength stainless steel tubes had a yield stress and tensile strength up to 536 and 961 MPa, respectively. The behaviour of the columns was investigated using different concrete cylinder strengths varied from 40 to 80 MPa. A series of tests was performed to investigate the effects of the shape of the stainless steel tube, plate thickness and concrete strength on the behaviour and strength of concrete-filled high strength stainless steel tube columns. The high strength stainless steel tubes were cold-rolled into square and rectangular hollow sections. The depth-to-plate thickness ratio of the tube sections varied from 25.7 for compact sections to 55.8 for relatively slender sections. The columns had different lengths so the length-to-depth ratio generally remained at a constant value of 3. The concrete-filled high strength stainless steel tube specimens were subjected to uniform axial compression. The column strengths, load–axial strain relationships and failure modes of the columns were presented. The test strengths were compared with the design strengths calculated using the American specifications and Australian/New Zealand standards that consider the effect of local buckling using an effective width concept in the calculation of the stainless steel tube column strengths. Based on the test results, design recommendations were proposed for concrete-filled high strength stainless steel tube columns.

Strings at the bottom of the deformed conifold

We present solutions of the equations of motion of macroscopic F and D strings extending along the non compact 4D sections of the conifold geometry and winding around the internal directions. The effect of the Goldstone modes associated with the position of the strings on the internal manifold can be seen as a current on the string that prevents it from collapsing and allows the possibility of static 4D loops. Its relevance in recent models of brane inflation is discussed.

Meeting the winds of change: New wind tower structures for the future

A new kind of modular wind tower structure for use in multi-megawatt wind turbines has been developed in the USA which provides an alternative solution to conventional large wind turbine tower structures. The benefits of the modular system mean that it can be transported in compact sections using up much less space. Peder Hansen from Valmont, USA reports.

Experimental study of prestressed steel–concrete composite beams with external tendons for negative moments

Four groups of prestressed steel–concrete composite beams with external tendons in negative moment regions were tested, and the cracking behaviours and the ultimate negative moment resistances of the composite beams were investigated experimentally. It is found that in hogging moment regions, on adding prestressing to the composite beams with external tendons, the cracking resistance of the beams can be effectively increased; however, the incremental internal tendon forces of the prestressed composite beams are rather small, and therefore can be neglected in the evaluation of the negative moment resistance of the beams. In hogging moment regions, the ultimate resistance of a composite beam prestressed with external tendons is governed by either distortional lateral buckling or local buckling, or an interactive mode composed of the two bucklings. For a beam with a compact section, the negative bending moment can reach the plastic moment when the steel section is fully plastic, and for a non-compact section, the negative bending moment is limited to the yield moment at which the compression steel flange initiates yield. The method for evaluating the buckling resistance of the composite beams is discussed, and a tentative design method based on BS5400: Part 3 is proposed to assess the buckling resistances of the prestressed composite beams.

Physical properties of soils under intensive agricultural management

Pedologic alterations after long-term sugar cane (Saccharum officinarum) cropping cycles under traditional soil management systems were studied on a farm in Bariri, SP, Brazil. A toposequence was established to evaluate the effects of the soil position in the relief in changing soil physical attributes. Morphological field descriptions and laboratory analyses were carried out on vertical profiles of the upper, middle and lower thirds of a Typic Haplorthox slope. Soil bulk density and macroporosity changed along the toposequence reflecting on soil hydrodynamics, especially in the lower slope parts. At sites with high clay levels, empty spaces were filled forming block shaped structures together with the micro-aggregate structure. The intensive cultivation induced the greatest soil structure alterations, even at the deepest layers. The study pointed out the importance of performing detailed morphological observations in vertical profiles, due to the great variation on pedological attributes over short distances. Compacted soil sections were observed side-by-side with desaggregated mottles in the same soil profile. This fact evidenced that both vertical (in each profile) and horizontal gradients (along a toposequence) need to be considered in studies of time sequence variation of pedological parameters.