Cold-formed steel sections with web openings subjected to web crippling under two-flange loading conditions — Part II : Parametric study and proposed design equations

A parametric study of cold-formed steel sections with web openings subjected to web crippling was undertaken using finite element analysis, to investigate the effects of web holes and cross-section sizes on the web crippling strengths of channel sections subjected to web crippling under both interior-two-flange (ITF) and end-two-flange (ETF) loading conditions. In both loading conditions, the hole was centred beneath the bearing plate. It was demonstrated that the main factors influencing the web crippling strength are the ratio of the hole depth to the flat depth of the web, and the ratio of the length of bearing plates to the flat depth of the web. In this paper, design recommendations in the form of web crippling strength reduction factors are proposed, that are conservative to both the experimental and finite element results

Numerical study of web crippling strength in cold-formed austenitic stainless steel lipped channels with web openings subjected to interior-two-flange loading

In cold-formed stainless steel lipped channel-sections, use of web openings for service purposes are becoming increasingly popular. Web openings, however, result in the sections becoming more susceptible to web crippling. This paper presents a finite element investigation into the web crippling strength of cold-formed austenitic stainless steel lipped channel-sections with circular web openings under the interior-two-flange (ITF) loading condition. The cases of web openings located centred and offset to the bearing plates are considered in this study. In order to take into account the influence of the circular web openings, a parametric study involving 740 non-linear elasto-plastic finite element analyses was performed, covering austenitic EN1.4404 stainless steel grade. From the results of the parametric study, the effect of the size of the web opening, length of bearing plate and location of the web opening is investigated. Strength reduction factor equations are then proposed, that can be used to take into account such web openings in design

Effects of edge-stiffened circular holes on the web crippling strength of cold-formed steel channel sections under one-flange loading conditions

Cold-formed steel sections are often used as wall studs or floor joists and such sections often include web holes for ease of installation of services. The holes are normally punched or bored and are unstiffened; when the holes are near to points of concentrated load, web crippling can be the critical design consideration. Recently, a new generation of cold-formed steel channel sections with edge-stiffened circular holes has been developed, for which web crippling may not be so critical. In this paper, a combination of experimental investigation and non-linear elasto-plastic finite element analyses are used to investigate the effect of such edge-stiffened holes under the interior-one-flange (IOF) and end-one-flange (EOF) loading conditions; for comparison, sections without holes and with unstiffened holes are also considered. A total of 90 results comprising 36 tests and 54 finite element analysis results are presented. Owing to manufacturing constraints, in the test programme, the edge-stiffener length was fixed at 13 mm. Good agreement between the experimental and finite element results was obtained. For the case of the unstiffened hole, it is shown that the web crippling strength is reduced by up to 12% and 28% for the IOF and EOF loading conditions, respectively. However, with the edge-stiffened circular hole, the web crippling strength is only reduced by 3% for the IOF loading condition and there is no reduction in strength for the EOF loading condition. The finite element model was used for the purposes of a parametric study on the effects of different hole sizes, edge-stiffener length and distances of the web holes to the near edge of the bearing plate. The results indicate that with a suitable edge-stiffener length, the web crippling strength of cold-formed steel channel section with holes can be as high as the one without holes

Gravity-induced Wannier-Stark ladder in an optical lattice

We discuss the dynamics of ultracold atoms in an optical potential accelerated by gravity. The positions and widths of the Wannier-Stark ladder of resonances are obtained as metastable states. The metastable Wannier-Bloch states oscillate in a single band with the Bloch period. The width of the resonance gives the rate transition to the continuum.Comment: 5 pages + 8 eps figures, submitted to Phys. Rev.

Web crippling strength of cold-formed stainless steel lipped channels with web perforations under end-two-flange loading

This paper presents a finite element investigation into the web crippling strength of cold-formed stainless steel lipped channels with circular web perforations under end-two-flange (ETF) loading. The cases of web openings located both centred and offset to the load bearing plates, are considered. In order to take into account the influence of the circular web openings, a parametric study involving 2,190 finite element analyses was performed, covering duplex EN1.4462, austenitic EN1.4404 and ferretic EN1.4003 stainless steel grades; from the results of the parametric study, strength reduction factor equations are determined. The strength reduction factor equations are first compared to equations recently proposed for cold-formed carbon steel lipped channels. It is demonstrated that the strength reduction factor equations proposed for cold-formed carbon steel are conservative for the stainless steel grades by up to 10%. New coefficients for web crippling strength reduction factor equations are then proposed that can be applied to all three stainless steel grades

Effect of web holes on web crippling strength of cold-formed steel channel sections under end-one-flange loading condition - Part I: Tests and finite element analysis

Web openings could be used in cold-formed steel beam members, such as wall studs or floor joints, to facilitate ease of services in buildings. In this paper and its companion paper, a combination of tests and non-linear finite element analyses is used to investigate the effect of such holes on web crippling under end-one-flange (EOF) loading condition. The present paper includes a testing programme on web crippling of channel section and material tensile coupons, followed by a numerical study, where the models are firstly validated against the performed experiments. The results of 74 web crippling tests are presented, with 22 tests conducted on channel sections without web openings and 52 tests conducted on channel sections with web openings. In the case of the tests with web openings, the hole was either located centred above the bearing plates or having a horizontal clear distance to the near edge of the bearing plates. A non-linear finite element model is described, and the results compared against the laboratory test results; a good agreement between the tests and finite element analyses was obtained in term of both strength and failure modes

Some general properties of the renormalized stress-energy tensor for static quantum states on (n+1)-dimensional spherically symmetric black holes

We study the renormalized stress-energy tensor (RSET) for static quantum states on (n+1)-dimensional, static, spherically symmetric black holes. By solving the conservation equations, we are able to write the stress-energy tensor in terms of a single unknown function of the radial co-ordinate, plus two arbitrary constants. Conditions for the stress-energy tensor to be regular at event horizons (including the extremal and ``ultra-extremal'' cases) are then derived using generalized Kruskal-like co-ordinates. These results should be useful for future calculations of the RSET for static quantum states on spherically symmetric black hole geometries in any number of space-time dimensions.Comment: 9 pages, no figures, RevTeX4, references added, accepted for publication in General Relativity and Gravitatio

The composition of the protosolar disk and the formation conditions for comets

Conditions in the protosolar nebula have left their mark in the composition of cometary volatiles, thought to be some of the most pristine material in the solar system. Cometary compositions represent the end point of processing that began in the parent molecular cloud core and continued through the collapse of that core to form the protosun and the solar nebula, and finally during the evolution of the solar nebula itself as the cometary bodies were accreting. Disentangling the effects of the various epochs on the final composition of a comet is complicated. But comets are not the only source of information about the solar nebula. Protostellar disks around young stars similar to the protosun provide a way of investigating the evolution of disks similar to the solar nebula while they are in the process of evolving to form their own solar systems. In this way we can learn about the physical and chemical conditions under which comets formed, and about the types of dynamical processing that shaped the solar system we see today. This paper summarizes some recent contributions to our understanding of both cometary volatiles and the composition, structure and evolution of protostellar disks.Comment: To appear in Space Science Reviews. The final publication is available at Springer via http://dx.doi.org/10.1007/s11214-015-0167-

Search for direct production of charginos and neutralinos in events with three leptons and missing transverse momentum in √s = 7 TeV pp collisions with the ATLAS detector

A search for the direct production of charginos and neutralinos in final states with three electrons or muons and missing transverse momentum is presented. The analysis is based on 4.7 fb−1 of proton–proton collision data delivered by the Large Hadron Collider and recorded with the ATLAS detector. Observations are consistent with Standard Model expectations in three signal regions that are either depleted or enriched in Z-boson decays. Upper limits at 95% confidence level are set in R-parity conserving phenomenological minimal supersymmetric models and in simplified models, significantly extending previous results