Deflection (engineering)

About: Deflection (engineering) is a research topic. Over the lifetime, 30862 publications have been published within this topic receiving 298849 citations.

Thin Plates and Shells

Abstract: In the preceding chapter, several cases of thin elastic plates loaded in the plane of the plate were analyzed using plane stress or plane strain equations. The resulting deformations are confined to the plane of the plate in accordance with the plane strain assumption. If such a plate is loaded transverse to the plane, the plate bends and the deflection of the surface in the normal direction is predominant, similar to a gridwork of beams. Correspondingly a distributed transverse loading can be efficiently resisted by an initially curved thin surface structure such as a cylindrical or spherical tank. The initial curvature mobilizes in-plane or membrane resistance that can be far more efficient than the bending resistance provided by flat plates. Several classical problems for the bending of rectangular and circular plates and for the membrane behavior of thin shells of revolution are presented as an introduction to this extensive topic.

Strengthening Reinforced Concrete Beams Using Fiber Reinforced Polymer (FRP) Laminates

Abstract: The behavior of reinforced concrete beams strengthened with various types of fiber reinforced polymer (FRP) laminates is presented. The experimental program included strengthening and testing 24 simply supported rectangular cross section beams. Each beam was initially loaded above its cracking load. The cracked beams were strengthened with FRP laminates and then tested until complete failure. Five available strengthening systems of various types of carbon/glass fiber reinforced polymer (CFRP/GFRP) strengthening materials were used. These materials included two types of CFRP sheets, bi- and unidirectional GFRP sheets, and CFRP plates. The effects of strengthening on deflection, failure load and failure mode, strain, and beam ductility are discussed. In addition, the influence of different numbers of FRP layers, type of epoxy, and strengthening pattern on the behavior of beams was examined. The ratio of absorbed energy at failure to total energy, or energy ratio, was used as a measure of beam ductility. It is concluded that, in addition to the longitudinal layers, the fibers oriented in the vertical direction forming a U-shape around the beam cross section significantly reduce beam deflections and increase beam load carrying capacity. Furthermore, the presence of vertical and horizontal sheets, together with a proper epoxy, can lead to a doubling of the ultimate load carrying capacity of the beam. However, all the strengthened beams experienced brittle failure, mandating a higher factor of safety in design.

A Comprehensive Elliptic Integral Solution to the Large Deflection Problems of Thin Beams in Compliant Mechanisms

Abstract: The elliptic integral solution is often considered to be the most accurate method for analyzing large deflections of thin beams in compliant mechanisms. In this paper, a comprehensive solution based on the elliptic integrals is proposed for solving large deflection problems. By explicitly incorporating the number of inflection points and the sign of the end-moment load in the derivation, the comprehensive solution is capable of solving large deflections of thin beams with multiple inflection points and subject to any kinds of load cases. The comprehensive solution also extends the elliptic integral solutions to be suitable for any beam end angle. Deflected configurations of complex modes solved by the comprehensive solution are presented and discussed. The use of the comprehensive solution in analyzing compliant mechanisms is also demonstrated by examples.

Calculations of Properties of Magnetic Deflection Systems

Abstract: A convenient matrix method for calculating properties of magnetic deflection systems is presented. This method is applicable to particle beams of small spatial and angular extent, and small energy spread. Equations for quadrupole lenses and for deflecting magnets are given. Examples are given to show the procedure for calculating the parameters of magnet systems.

An experimental, analytical and numerical study of the static behavior of steel beams reinforced by pultruded CFRP strips

Abstract: The paper presents the results of an experimental and numerical programme to characterize the static behaviour of steel beams reinforcement by pultruded carbon fibre reinforced polymer (CFRP) strips. Traditional H shaped steel beams with different CFRP reinforcement geometries bonded to the tension flanges using different epoxy adhesives were tested under three points bending configuration. Beams were not naturally or artificially corroded or notched but they were in good conditions before testing. The mid-span deflection and the strain along the whole CFRP lamina were recorded as function of the applied loading. The main objective of the experimental programme was the evaluation of the force transfer mechanism, the increment of the beam load carrying capacity and the bending stiffness. It allowed also to validate different analytical and numerical models for the static analysis of reinforced beams. In particular, a finite element model validated against the experimental data is presented.