Bending moment

About: Bending moment is a research topic. Over the lifetime, 14577 publications have been published within this topic receiving 158834 citations. The topic is also known as: bending moment.

Web design under compressive edge loads

Abstract: The studies on crippling of rolled beams and plate girders' webs, subjected to patch or distributed edge loading, summarized in this report. Solutions are available for the elastic critical buckling loads of idealized web panels which show little or no correlation to crippling loads determined from tests. Semi-empirical formulae are available to predict the crippling load with an accuracy that is acceptable for practical purposes. Formulae to predict the crippling load are recommended. Semi-empirical formulae to predict loads above which membrane yielding of the web becomes pronounced are also available. The effects of coexistent global bending moment or shearing force were discussed. Reduction of P sub u due to coexistent global moment has been established by the way of a formula for a reduction factor. A conservative approach is recommended. The requirements to prevent crippling given in the AISC building specification, as well as the proposed AISC LRFD specification, have to be reexamined in the light of the information in this report. (Author)

Effect of load distribution and variable depth on shear resistance of slender beams without stirrups

Abstract: The shear resistance of elements without stirrups has mainly been investigated by test setups involving simply supported beams of constant thickness subjected to one- or two-point loading, and most of the formulas included in codes have been adjusted using this experimental background. It is a fact, however, that most design situations involve constant or triangular distributed loading (such as retaining walls or footings) on tapered members. Furthermore, there seems to be few shear tests involving cantilever structures subjected to distributed loading. These structures, which are common in everyday practice, fail in shear near the clamped end, where the shear forces and bending moments are maximum (contrary to simply supported beams of tests, where shear failures under distributed loading develop near the support region for large shear forces but limited bending moments). In this paper, a specific testing program undertaken at the Poly- technic University of Madrid (UPM), Madrid, Spain, in close collab- oration with Ecole Polytechnique Federale de Lausanne (EPFL), Lausanne, Switzerland, is presented. It was aimed at investigating the influence of load distribution and tapered beam geometrics on the shear strength. The experimental program consists of eight slender beams without stirrups. Four specimens had a constant depth, whereas the others had variable depths (maximum depth of 600 mm [23.6 in.]). Each specimen was tested twice: one side was tested first under point loading, and then (after repairing) the other side was tested under either uniform loading or triangular loading. The setup allowed direct comparisons between point and distributed loading. The experimental results showed a significant influence of the type of loading and of tapered geometries on the shear strength. On the basis of these results, and using the funda- mentals of the critical shear crack theory, a consistent physical explanation of the observed failure modes and differences in shear strength is provided. Also, comparisons to current design provisions (ACI 318-08 and EC2) are discussed.

On the strain energy release rate for a cracked plate subjected to out-of-plane bending moment

Abstract: For a through-the-thickness crack in an infinite plate subjected to out-of-plane uniform bending moment, the strain energy release rate is determined using the virtual crack extension and the variation of potential energy It is shown that the strain energy release rate for the Reissner's plate approaches the classical plate solution as the ratio of plate thickness to crack size becomes infinitesimally small By using this result, the limiting expression of the stress intensity factor can be explicitly obtained For general problems, the modified crack closure method is shown to be an efficient tool for evaluating the strain energy release rates from which the stress intensity factor can be calculated Both the classical plate element and the Mindlin plate element are investigated, and the applicability of the classical plate element is evaluated Because the stress-free conditions along the crack face lead to inter-penetration of the plate, a line contact model is assumed to investigate the closure effect using Reissner plate theory Closure at the compressive side is shown to reduce crack opening displacement and consequently the stress intensity factors When closure is considered, the strain energy rate based on the Reissner plate theory converges to the classical plate solution This is similar to the nonclosure case

Combined Torsion and Bending in Reinforced and Prestressed Concrete Beams

Abstract: This paper presents an evaluation of the Modified Compression Field Theory for combined bending and torsion. A recently developed theoretical model for combined shear, torsion, and other stress resultants based on this theory is modified to better capture the effects of the varying longitudinal strains in members subjected to bending. The calculated response and ultimate capacities are compared with experimental data obtained from 2 available comprehensive test programs that cover under- and over-reinforced hollow and solid prestressed and nonprestressed beams subjected to combined torsion and bending. The calculated deformations and ultimate capacities are shown to be in very good agreement with the experimental results.

An analysis of the forces and bending moments generated during the notched beam impact test

Abstract: An analysis is presented which predicts the hammer force and specimen bending moment-time responses during impact from the dynamics of the system and the fracture characteristics of the material. The theoretical predictions are compared to available experimental observations and good agreement is obtained for brittle materials.