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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.


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TL;DR: In this article, an analytical model for load-displacement curves of concrete beams is presented, where the fracture is modeled by a fictitious crack in an elastic layer around the midsection of the beam.
Abstract: An analytical model for load-displacement curves of concrete beams is presented. The load-displacement curve is obtained by combining two simple models. The fracture is modeled by a fictitious crack in an elastic layer around the midsection of the beam. Outside the elastic layer the deformations are modeled by beam theory. The state of stress in the elastic layer is assumed to depend bilinearly on local elongation corresponding to a linear softening relation for the fictitious crack. Results from the analytical model are compared with results from a more detailed model based on numerical methods for different beam sizes. The analytical model is shown to be in agreement with the numerical results if the thickness of the elastic layer is taken as half the beam depth. It is shown that the point on the load-displacement curve where the fictitious crack starts to develop and the point where the real crack starts to grow correspond to the same bending moment. Closed-form solutions for the maximum size of the fracture zone and the minimum slope on the load-displacement curve are given.

114 citations

Journal ArticleDOI
TL;DR: In this paper, a detailed analysis of the second-order diffraction problem of a uniform vertical circular cylinder in regular waves is presented, which can be used for calculating other quantities such as the hydrodynamic pressure at any point, the sectional force and bending moment in the cylinder or the free-surface elevation due to the secondorder effects.
Abstract: The main difficulty in second-order diffraction analysis stems from the contribution of the second-order potential, which obeys an inhomogeneous free-surface boundary condition. In some applications it is sufficient to know the second-order hydrodynamic force, which can be calculated without explicitly evaluating this second-order potential. This technique cannot however be used for calculating other quantities such as the hydrodynamic pressure at any point, the sectional force and bending moment in the cylinder or the free-surface elevation due to the second-order effects. This paper provides a detailed analysis of the second-order diffraction problem of a uniform vertical circular cylinder in regular waves. This furnishes results not only on the cylinder surface, but also on the free surface, and in principle in the fluid domain surrounding the body. The analysis may help to throw some light on the physical interpretation of the second-order theory and its mathematical description. Moreover, this information is intended to complement the development of general numerical methods for arbitrary bodies.

113 citations

Journal ArticleDOI
TL;DR: In this article, a theoretical interfacial stress analysis is presented for simply supported beams and slabs bonded with a thin FRP composite or steel plate and subjected to a uniformly distributed load in combination with a uniform bending moment.
Abstract: A new popular method for retrofitting reinforced concrete beams and slabs is to bond fiber-reinforced plastic (FRP) plates to the soffit. An important failure mode for such strengthened members is the debonding of the FRP plate from the member due to high interfacial stresses near the plate ends. Accurate predictions of the interfacial stresses are a prerequisite for designing against debonding failures. In this paper, a theoretical interfacial stress analysis is presented for simply supported beams and slabs bonded with a thin FRP composite or steel plate and subjected to a uniformly distributed load in combination with a uniform bending moment. The analysis leads to an exact closed-form solution, in which a plane stress model is used for beams and a plane strain model is used for slabs. The salient features of the new analysis include the consideration of nonuniform stress distributions in and the satisfaction of the stress boundary conditions at the ends of the adhesive layer. Numerical results from the present analysis are presented both to demonstrate the advantages of the present solution over existing ones and to illustrate the main characteristics of interfacial stress distributions in beams and slabs.

113 citations

Journal ArticleDOI
TL;DR: In this paper, an analytic model is developed to investigate the wave propagation and sound transmission characteristics of an infinite sandwich structure reinforced by two sets of orthogonal rib-stiffeners when subjected to convective fluid-loaded pressure.
Abstract: An analytic model is developed to investigate the wave propagation and sound transmission characteristics of an infinite sandwich structure reinforced by two sets of orthogonal rib-stiffeners when subjected to convective fluid-loaded pressure. The rib-stiffeners are assumed to be identical and uniformly spaced, which can exert not only tensional forces and bending moments but also torsional moments on the facesheets. Inertial terms of the tensional forces, bending moments and torsional moments are introduced to account for inertial effects arising from the mass of the rib-stiffeners. With the surrounding acoustic fluids restricted by the acoustic wave equation, fluid–structure coupling is considered by imposing velocity continuity condition at fluid–panel interfaces. By applying the Bloch theorem for periodic structures, the structural and acoustic responses are expressed in a superposition form of space harmonics for a given wavenumber. The application of the virtual work principle for one periodic element yields two infinite sets of simultaneous algebraic coupled equations, which are numerically solved by truncating them in a finite range insofar as the solution converges. The validity and feasibility of the analytic model is qualified by comparing model predictions with existing results, in which the necessity and advantage of the exact modeling of rib-stiffener motions are also demonstrated. Specifically, the influences of inertial effects arising from rib-stiffener mass, the periodicity spacing of rib-stiffeners, and the airborne as well as structure-borne paths on the transmission of sound across the sandwich structure are quantified and conclusions of significant practical implications are drawn.

113 citations

Journal ArticleDOI
TL;DR: In this article, the bending moment envelope above the base of the wall is shown to be greatly reduced by providing multiple rocking sections, while the peak displacements do not increase in magnitude or in variability.
Abstract: Base-rocking systems have been proposed as a way to limit the seismic forces experienced by a structure without accepting structural damage. However, structural forces can increase significantly, even when the base moment is limited, because of higher mode effects. This article suggests that these effects may be substantially reduced by designing to allow rocking to occur at multiple locations over the height of a base-rocking system. This is confirmed by a statistical study of the response of 24 systems of varying height and joint configuration to two suites of 20 earthquakes, as well as by a case study of the response of five 12-story systems designed using a displacement-based procedure. The bending moment envelope above the base of the wall is shown to be greatly reduced by providing multiple rocking sections, while the peak displacements do not increase in magnitude or in variability.

112 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023489
2022961
2021623
2020584
2019660
2018613