Equilibrium equations for plane slender bars undergoing large shear deformations

Summary Equilibrium equations for plane slender bars are derived using the principles of Continuum Solid Mechanics. Large shear deformations are accounted for. The equations are derived in an explicit form, yielding upon introduction of a constitutive law (not given here) a system of differential equations to be integrated on the undeformed length. Within certain limitations, the equations, derived in an exact form, incorporate expressions for finite strain. The stress distribution along a deformed section is studied.

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Gleichgewichtsbedingungen ebener schlanker Stäbe bei großen Schubverformungen

Zusammenfassung Gleichgewichtsbedingungen ebener schlanker Stäbe werden unter Verwendung der Sätze der Kontinuumstechnik hergeleitet. Große Schubverformungen werden berücksichtigt. Die Gleichungen werden in expliziter Form angegeben, sie führen mit einem hier nicht angegebenen Werkstoffgesetz auf ein System von Differentialgleichungen. Mit gewissen Einschränkungen schließen diese in exakter Form angegebenen Gleichungen die für endliche Verformungen ein. Die Spannungsverteilung in einem verformten Abschnitt wird untersucht.

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Notation position vector of material point in undeformed state - position vector of material point in deformed state - displacement vector of material point - u displacement component inx-direction - w displacement component inz-direction - covariant base vector in deformed state (i=1,2) - G _ij metric tensor in deformed state - g _ij metric tensor in undeformed state - slope of geometrical axis (elastic line) - shear deformation angle - rotation of plane section of bar - K curvature of geometrical axis - curvature of geometrical axis due to bending only - unit tangent vector to geometrical axis - unit normal vector to geometrical axis - _(ij) Lagrangian strain tensor - ^ij stress tensor - ^(ij) physical stress tensor - N normal force (parallel to geometrical axis) acting on plane section - S shear force (parallel to deformed section) acting on plane section - M bending moment - H horizontal external force acting on plane section - V vertical external force acting on plane section - vector of conservative body forces uniformly distributed along geometrical axis - f _x component of inx-direction - f _z component of inz-direction - unit normal vector to plane section - F _i force component on distorted plane section - F _(i) physical force component on distorted plane section - F _ij component ofF ⁱ inj-direction - inclination angle ofF ¹¹ toF ¹ (see Fig. 8) With 8 Figures     

Effects of design flow and treatment level on construction and operation costs of municipal wastewater treatment plants and their implications on policy making

Construction costs of 55 municipal wastewater treatment plants in Israel (secondary, advanced secondary, and advanced treatment) were analysed in order to derive cost functions expressing the effects of design flow and treatment level on construction costs. Three equations were derived (statistically significant, p<0.01), one for each treatment level. These indicate that economy of scale may become weaker as treatment level rises. Analysis of the distribution of construction costs revealed negative correlation (p<0.05) between the proportional cost of civil engineering and design flow, positive correlation (p<0.05) between the proportional cost of elecromechanical equipment and design flow, and no correlation between the proportional cost of electricity and control and design flow. Operation costs were found to be 20–70% more sensitive than construction costs to treatment level. The share of operation costs as part of the total annual costs was found to increase both with design flow and treatment level, whereas the share of construction costs concurrently decreased. The implication of the findings on policy, and consequently on treatment plants performance is discussed in the last part of the paper.     

Direct assessment of the tensile strength of the web in prestressed precast hollow-core slabs

The tensile strength of the web concrete in prestressed, precast, hollow-core slabs is investigated by direct measurements on specimens separated from the slabs as cast on the production line. The strength thus obtained tends to be relatively low but consistent and an excellent basis for estimating the shear strength of the slabs.

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Resume On examine la résistance en traction de l'ame de dalles alvéolaires en béton précontraint manufacturé par mesures directes sur des échantillons prélevés sur des poutres lors du moulage à la production. La résistance ainsi obtenue tend à être relativement faible, mais néanmoins elle concorde, et offre une excellente base pour estimer la résistance au cisaillement des dalles.

     

A computer program for the geometrically nonlinear analysis of plane slender bars and frames

A computer program, developed for the analysis of the geometrically nonlinear behavior of plane frames, is described. The mathematical solution employs the Newton Raphson iterative procedure for simultaneous nonlinear algebraic equations, derived from a discrete (finite difference) solution of a complete set of nonlinear equilibrium equations for the in-plane finite deflections of bars. Multiple-unknown problems are treated.     

A Zebrafish Model for a Rare Genetic Disease Reveals a Conserved Role for FBXL3 in the Circadian Clock System

The circadian clock, which drives a wide range of bodily rhythms in synchrony with the day–night cycle, is based on a molecular oscillator that ticks with a period of approximately 24 h. Timed proteasomal degradation of clock components is central to the fine-tuning of the oscillator’s period. FBXL3 is a protein that functions as a substrate-recognition factor in the E3 ubiquitin ligase complex, and was originally shown in mice to mediate degradation of CRY proteins and thus contribute to the mammalian circadian clock mechanism. By exome sequencing, we have identified a FBXL3 mutation in patients with syndromic developmental delay accompanied by morphological abnormalities and intellectual disability, albeit with a normal sleep pattern. We have investigated the function of FBXL3 in the zebrafish, an excellent model to study both vertebrate development and circadian clock function and, like humans, a diurnal species. Loss of fbxl3a function in zebrafish led to disruption of circadian rhythms of promoter activity and mRNA expression as well as locomotor activity and sleep–wake cycles. However, unlike humans, no morphological effects were evident. These findings point to an evolutionary conserved role for FBXL3 in the circadian clock system across vertebrates and to the acquisition of developmental roles in humans.     

Ductility requirements for redistribution of moments in reinforced concrete elements and a possible size effect

The possible demand for ductility, allowing for the redistribution of moments in linear reinforced concrete elements is examined, based on the results of two series of experiments aimed at verifying the actual stress/strain state in the reinforcing bars, with the elements designed to carry loads under the assumption of a broad spectrum of redistribution of moments. The tests included a series of beam tests and slab test with respective slenderness ratios (γ) of 11.73 and 21.12; thus one important aspect ofthe size effect was investigated. The final results tend to support the assumption that the high ductility class steel suggested in the Eurocode 2 is suitable for elements under static loading     

The shear strength of extruded hollow-core slabs

The shear strength of extruded prestressed precast hollow-core slabs, investigated experimentally and analytically, is reported. Ten slab specimens have been tested, all failing in the shear mode (six in shear tension mode). The analysis explores ways of employing existing procedures for predicting the shear capacity. It is concluded that modification of the FIP recommendations would lead to a better approximation of the test results.

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Resume On rend compte de la résistance au cisaillement de dalles alvéolaires extrudées étudiées expérimentalement et analytiquement. Dix échantillons de dalles ont été essayés, tous à rupture par cisaillement (six par cisaillement en traction). On envisage comment utiliser les modes opératoires existants pour prédire la tenue au cisaillement. On conclut qu'une modification des recommendations FIP permettrait une meilleure approximation des résultats d'essai.

     

New schemes for creating large optical Schrödinger cat states using strong laser fields

Recently, using conditioning approaches on the high-harmonic generation process induced by intense laser-atom interactions, we have developed a new method for the generation of optical Schrödinger cat states (Lewenstein et al. in Nat Phys, 17 1104–1108, 2021. https://doi/10.1038/s41567-021-01317-w). These quantum optical states have been proven to be very manageable as, by modifying the conditions under which harmonics are generated, one can interplay between kitten and genuine cat states. Here, we demonstrate that this method can also be used for the development of new schemes towards the creation of optical Schrödinger cat states, consisting of the superposition of three distinct coherent states. Apart from the interest these kind of states have on their own, we additionally propose a scheme for using them towards the generation of large cat states involving the sum of two different coherent states. The quantum properties of the obtained superpositions aim to significantly increase the applicability of optical Schrödinger cat states for quantum technology and quantum information processing.