Deflection (engineering)

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

Euler-Bernoulli beams with multiple singularities in the flexural stiffness

Abstract: Euler–Bernoulli beams under static loads in presence of discontinuities in the curvature and in the slope functions are the object of this study. Both types of discontinuities are modelled as singularities, superimposed to a uniform flexural stiffness, by making use of distributions such as unit step and Dirac's delta functions. A non-trivial generalisation to multiple different singularities of an integration procedure recently proposed by the authors for a single singularity is presented in this paper. The proposed integration procedure leads to closed form solutions, dependent on boundary conditions only, which do not require enforcement of continuity conditions along the beam span. It is however shown how, from the solution of the clamped-clamped beam, by considering suitable singularities at boundaries in the flexural stiffness model, responses concerning several boundary conditions can be recovered. Furthermore, solutions in terms of deflection of the beam are obtained for imposed displacements at boundaries providing the so called shape functions. The above mentioned shape functions can be adopted to insert beams with singularities as frame elements in a finite element discretisation of a frame structure. Explicit expressions of the element stiffness matrix are provided for beam elements with multiple singularities and the reduction of degrees of freedom with respect to classical finite element procedures is shown. Extension of the proposed procedure to beams with axial displacement and vertical deflection discontinuities is also presented.

Flexural behaviour of concrete beams reinforced with gfrp bars

Abstract: This study presents the results of the comparison made between the predicted and the measured load-deflection relationships for 12 concrete beams reinforced either by steel or glass fibre reinforced plastic (GFRP) bars. The numerical part of the study was carried out using: (i) the computer model which accounts for the actual properties of the composite constituents developed as part of this study, (ii) the ACI load-deflection model, and (iii) the modified load-deflection model available in the literature for beams reinforced by FRP bars. The last two models were implemented on a spreadsheet. The deflection limit and the ultimate strength of concrete were the control parameters in design of the test beams. The computer model provides an accurate prediction of the measured service and full load-deflection curves. The errors in prediction of service load deflection and ultimate flexural strength are less than 10% and 1%, respectively. In the case of GFRP reinforced beams, the service load deflection predicted by the ACI model is in error by 70%, while that predicted by the modified model is in error by less than 15%.

Prestressed concrete analysis and design

Abstract: Contents: Principle and Methods of Prestressing. Prestressing Materials: Steel and Concrete. The Philosophy of Design. Flexure: Working Stress Analysis and Design. Flexure: Ultimate Strength Analysis and Design. Design for Shear and Torsion. Deflection Computation and Control. Prestress Losses. Analysis and Design of Composite Beams. Cotinuous Beams and Indeterminate Structures. Prestressed Concrete Slabs. Analysis and Design of Tension Members. Analysis and Design of Compression Members. Bridges.