Deflection (engineering)

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

Modeling of Flexural Beams Subjected to Arbitrary End Loads

Abstract: The analysis of compliant mechanisms is often complicated due to the geometric nonlinearities which become significant with large elastic deflections. Pseudo rigid body models (PRBM) may be used to accurately and efficiently model such large elastic deflections. Previously published models have only considered end forces with no end moment or end moment acting only in the same direction as the force. In this paper we present a model for a cantilever beam with end moment acting in the opposite direction as the end force, which may or may not cause an inflection point. Two pivot points are used, thereby increasing the model's accuracy when an inflection point exists. The Bernoulli-Euler beam equation is solved for large deflections with elliptic integrals, and the elliptic integral solutions are used to determine when an inflection point will exist. The beam tip deflections are then parameterized using a different parameterization from previous models, which renders the deflection paths easier to model with a single degree of freedom system. Optimization is used to find the pseudo rigid body model which best approximates the beam deflection and stiffness. This model, combined with those models developed for other loading conditions, may be used to efficiently analyze compliant mechansims subjected to any loading condition.

Behavior of full-scale reinforced concrete beams retrofitted for shear and flexural with FRP laminates

Abstract: Four full-scale reinforced concrete beams were replicated from an existing bridge. The original beams were substantially deficient in shear strength, particularly for projected increase of traffic loads. Of the four replicate beams, one served as a control and the remaining three were implemented with varying configurations of carbon fiber reinforced polymers (CFRP) and glass FRP (GFRP) composites to simulate the retrofit of the existing structure. CFRP unidirectional sheets were placed to increase flexural capacity and GFRP unidirectional sheets were utilized to mitigate shear failure. Four-point bending tests were conducted. Load, deflection and strain data were collected. Fiber optic gauges were utilized in high flexural and shear regions and conventional resistive gauges were placed in eighteen locations to provide behavioral understanding of the composite material strengthening. Fiber optic readings were compared to conventional gauges. Results from this study show that the use of fiber reinforced polymers (FRP) composites for structural strengthening provides significant static capacity increases approximately 150% when compared to unstrengthened sections. Load at first crack and post cracking stiffness of all beams was increased primarily due to flexural CFRP. Test results suggest that beams retrofit with both the designed GFRP and CFRP should well exceed the static demand of 658 kN m sustaining up to 868 kN m applied moment. The addition of GFRP alone for shear was sufficient to offset the lack of steel stirrups and allow conventional RC beam failure by yielding of the tension steel. This allowed ultimate deflections to be 200% higher than the pre-existing shear deficient beam. If bridge beams were retrofit with only the designed CFRP failure would still result from diagonal tension cracks, albeit at a 31% greater load. Beams retrofit with only the designed shear GFRP would fail in flexure at the mid-span at an equivalent 31% gain over the control specimen, failing mechanism in this case being yielding of the tension steel. Successful monitoring of strain using fiber optics was achieved. However, careful planning tempered by engineering judgement is necessary as the location and gauge length of the fiber optic gauge will determine the usefulness of the collected data.

Parametric Study of Beams with Externally Bonded FRP Reinforcement

Abstract: FRP reinforcement may be externally bonded to the soffit of existing flexural members in order to increase their strength and rigidity. A parametric analysis is conducted to investigate the effects of FRP reinforcement on serviceability, strength, and failure mechanisms of repaired RC beams. FRP reinforcement parameters considered in the analysis are: stiffness, bonded length, thickness, and the adhesive stiffness. The choice of the repair material parameters is important in the design phase in order to obtain the desired results of strengthening or stiffening without other unforeseen effects. In this paper, three typical RC beam cross sections are considered with height-to-width ratios of 0.5, 1, and 4. Two characteristic compressive strength levels (20 and 30 MPa), and two shear span-to-reinforcement depth ratios (4.5 and 7) are considered. All other parameters related to material and geometry of the beams are maintained constant. The results of the analysis are shown in terms of repaired-to-un-repaired strength and deflection ratios. They indicate that brittle failure mechanisms can develop at loads much lower than expected when considering only flexural performance controlled by concrete crushing and FRP tensile rupture. The analytical model used for the parametrization accounts for brittle failure mechanisms induced by debonding of the FRP reinforcement or shear-tension failure in concrete in the plane of the main longitudinal steel reinforcing bars. Even when considering the limitation of the RC member due to its un-modifiable shear resistance, it is shown that the application of FRP reinforcement can considerably increase load resistance capacity and limit deflection at service.