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.

Nonlocal strain gradient exact solutions for functionally graded inflected nano-beams

Abstract: The size-dependent bending behavior of nano-beams is investigated by the modified nonlocal strain gradient elasticity theory. According to this model, the bending moment is expressed by integral convolutions of elastic flexural curvature and of its derivative with the special bi-exponential averaging kernel. It has been recently proven that such a relation is equivalent to a differential equation, involving bending moment and flexural curvature fields, equipped with natural higher-order boundary conditions of constitutive type. The associated elastostatic problem of a Bernoulli-Euler functionally graded nanobeam is formulated and solved for simple statical schemes of technical interest. An effective analytical approach is presented and exploited to establish exact expressions of nonlocal strain gradient transverse displacements of doubly clamped, cantilever, clamped-simply supported and simply supported nano-beams, detecting thus also new benchmarks for numerical analyses. Comparisons with results of literature, corresponding to selected higher-order boundary conditions are provided and discussed. The considered nonlocal strain gradient model can be advantageously adopted to characterize scale phenomena in nano-engineering problems.

Axial-flexural interaction in square RC columns confined by intermittent CFRP wraps

Abstract: External reinforcing of concrete elements by CFRP composites is a well-accepted method adopted for strengthening all structural load-bearing members including reinforced concrete (RC) columns. Previous studies have been mostly focused on strengthening RC columns for pure axial-loads, while most RC columns practically function as beam-columns; that is, they are subjected to both axial loads and bending moments simultaneously. It is the objective of the current study to carry out an experimental assessment of the load bearing capacity and ductility of columns externally strengthened with intermittent CFRP wraps when subjected to simultaneous axial loading and bending moment. The assessment is accomplished by comparing intermittently wrapped columns with unconfined ones in terms of their strength and ductility. For this purpose, 10 square RC columns, 133 × 133 mm across and 500 mm in height, were subjected to zero, 30, 60, 90, and 120 mm loading eccentricities. The results of the study showed that, compared to unconfined RC columns, intermittent wrapping of square RC columns with CFRP improved their performance through enhanced load carrying capacity and ductility under eccentric loading. Finally, the P–M (axial loading-bending moment) interaction diagrams were drawn for the strengthened columns. Comparison of the experimental results with those obtained from the expressions suggested in different codes such as ACI 440.2R and fib bulletin 14 showed the conservative estimates of these codes in comparison to experimental measurements.

Behaviour of flush end-plate beam-to-column joints under bending and axial force

Abstract: Steel beam-to-column joints are often subjected to a combination of bending and axial forces. The level of axial forces in the joint may be significant, typical of pitched-roof portal frames, sway frames or frames with incomplete floors. Current specifications for steel joints do not take into account the presence of axial forces (tension and/or compression) in the joints. A single empirical limitation of 10% of the beam`s plastic axial capacity is the only enforced provision in Annex J of Eurocode 3. The objective of the present paper is to describe some experimental and numerical work carried out at the University of Coimbra to try to extend the philosophy of the component method to deal with the combined action bending moment and axial force.

Bending Stiffness In A Simulation Of Undersea Cable Deployment

Abstract: Bending stiffness is introduced in a three-dimensional model for submerged cable dynamics to eliminate singular behavior when cable tension becomes zero. The equations of motion are written in a local tangential-normal reference frame, and are simplified by neglecting the torsional rigidity of the cable. A centered-centered finite difference algorithm is used for the numerical simulation. The addition of bending stiffness eliminates the singularity for zero tension. However, because the bending stiffness is small, sharp gradients in the shear forces and bending moments occur at the boundaries. In this paper two sets of results are presented: configuration of an anchoring system during a steady tow, and the tension and geometry of a cable immediately following touchdown on the seafloor. The first result illustrates the discretization error caused by the sharp gradients in the curvatures and shear forces. The second result provides evidence that the bending stiffness does prevent singular behavior for negative or zero tension. It also illustrates that the contact of the cable with the seafloor only affects the cable geometry close to the seafloor.