A correction to the analytical solution of the mixed-mode bending (MMB) problem

This paper addresses the analytical solution of the mixed-mode bending (MMB) problem. The first published solutions used a load separation in pure mode I and mode II and were applied for a crack length less than the beam half-span, a <= L. In later publications, the same mode separation was used in deriving the analytical solution for crack lengths bigger than the beam half-span, a > L. In this paper it is shown that this mode separation is not valid when a > L and in some cases may lead to very erroneous results. The correct mode separation and the corresponding analytical solutions, when a > L, are presented. Results, of force vs. displacement and force vs. crack length graphs, obtained using the existing formulation and the corrected formulation are compared. A finite element solution, which does not use mode separation, is also presented

Fatigue behavior of laser-welded NiTi wires in small-strain cyclic bending

NiTi wires and their weldments are commonly used in micro-electro-mechanical systems (MEMS), and in such applications, cyclic loading are commonly encountered. In this paper, the bending-rotation fatigue (BRF) test was used to study the bending fatigue behavior of NiTi wire laser weldment in the small-strain regime. The fracture mechanism, which includes crack initiation, crack growth and propagation of the weldment in the BRF test, was investigated with the aid of SEM fractography and discussed in terms of the microstructure. It was found that crack initiation was primarily surface-condition dependent. The cracks were found to initiate at the surface defects at the weld zone (WZ) surface, and the crack propagation was assisted by the gas inclusions in the WZ. The weldment was finally fractured in a ductile manner. The fatigue life was found to decrease with increasing surface strain and also with increasing bending frequency (controlled by the rotational speed in the BRF test). In comparison, the fatigue life of the unwelded NiTi wires was higher than their welded counterparts at all strain levels and bending frequencies. The decrease in fatigue resistance of the weldment could be attributed to the surface and microstructural defects introduced during laser welding.

Polarisation analysis of VUV synchrotron radiation emitted from a bending magnet source in the energy range 20-50 eV: A comparison between measurements and theoretical predictions

The results of a study to characterise the polarisation properties of the photon beam emerging from beamline 5D, mounted on a bending magnet source at the Synchrotron Radiation Source, Daresbury Laboratory, are presented. The expectation values for the Stokes parameters corresponding to the light transmitted by the beamline have been calculated by combining ray-tracing and optical methods. The polarisation of the light at the source is modified both by the beamline geometry and by the reflections at the optical components. Although it is often assumed that the polarising properties of grazing incidence optics are negligible, this assumption leads to rather inaccurate results in the VUV region. A study of the reflectivity shows that even at incidence angles (theta(i) = 80-85degrees) which are far from the Brewster angle (theta(B) similar to 45degrees for VUV and soft X-ray radiation) the residual changes in the amplitudes of the reflected light can result in non-negligible polarisation effects. Furthermore, reflection at grazing incidence gives rise to a substantial change in the phase, and this has the effect of rotating the elliptically polarised state. Theoretical Stokes parameters have been compared with full polarisation measurements obtained using a reflection polarimeter in the energy range 20-40 eV. (C) 2003 Elsevier B.V. All rights reserved.

Strengthening an in-service reinforcement concrete bridge with prestressed CFRP bar

Carbon fiber reinforced polymer (CFRP) bars were prestressed for the structural strengthening of 8 T-shaped reinforced concrete (RC) beams of a 21-year-old bridge in China. The ultimate bearing capacity of the existing bridge after retrofit was discussed on the basis of concrete structures theory. The flexural strengths of RC beams strengthened with CFRP bars were controlled by the failure of concrete in compression and a prestressing method was applied in the retrofit. The field construction processes of strengthening with CFRP bars—including grouting cracks, cutting groove, grouting epoxy and embedding CFRP bars, surface treating, banding with the U-type CFRP sheets, releasing external prestressed steel tendons—were introduced in detail. In order to evaluate the effectiveness of this strengthening method, field tests using vehicles as live load were applied before and after the retrofit. The test results of deflection and concrete strain of the T-shaped beams with and without strengthening show that the capacity of the repaired bridge, including the bending strength and stiffness, is enhanced. The measurements of crack width also indicate that this strengthening method can enhance the durability of bridges. Therefore, the proposed strengthening technology is feasible and effective.

Bending It Like Beckham: How to Visually Fool the Goalkeeper

Background: As bending free-kicks becomes the norm in modern day soccer, implications for goalkeepers have largely been ignored. Although it has been reported that poor sensitivity to visual acceleration makes it harder for expert goalkeepers to perceptually judge where the curved free-kicks will cross the goal line, it is unknown how this affects the goalkeeper's actual movements.

Methodology/Principal Findings: Here, an in-depth analysis of goalkeepers' hand movements in immersive, interactive virtual reality shows that they do not fully account for spin-induced lateral ball acceleration. Hand movements were found to be biased in the direction of initial ball heading, and for curved free-kicks this resulted in biases in a direction opposite to those necessary to save the free-kick. These movement errors result in less time to cover a now greater distance to stop the ball entering the goal. These and other details of the interceptive behaviour are explained using a simple mathematical model which shows how the goalkeeper controls his movements online with respect to the ball's current heading direction. Furthermore our results and model suggest how visual landmarks, such as the goalposts in this instance, may constrain the extent of the movement biases.

Conclusions: While it has previously been shown that humans can internalize the effects of gravitational acceleration, these results show that it is much more difficult for goalkeepers to account for spin-induced visual acceleration, which varies from situation to situation. The limited sensitivity of the human visual system for detecting acceleration, suggests that curved free-kicks are an important goal-scoring opportunity in the game of soccer.

Crack detection of steel girders using Brillouin optical time domain analysis

This article presents the results from an experimental program designed to evaluate the performance of a system consisting of a readout unit and a ribbon type Fiber Optic Sensor (FOS) based on Brillouin Optical Time Domain Analysis (BOTDA). The system is intended for the detection of cracks as well as the monitoring of long-term performance for steel bridge girders. The program consisted of introducing a crack at the center of a 3-m-long steel beam and monitoring its progression using static loading tests performed at ambient and sub-zero temperatures. For sensor lengths similar to those used in the field, the resonant frequency shifts per unit increase in crack width were found to decrease from 114 MHz/mm at ambient temperature (~25C) to 65 MHz/mm at -10C. Results also revealed nonlinearity and variability, which can be attributed to an incompatibility between the settings of the laser pump in the readout unit and the sensor length. Significant losses were detected along the bonded segments of the sensor and were attributed to the presence of ripples along the sensor. These undulations worsen with a reduction in temperature and are induced by the bonding procedure as well as the slack provided in the plastic sleeves containing the splices.