Gamow-Teller (GT) strength distributions were studied in the (p, n ) reaction at 136 MeV on the self-conjugate s-d shell nuclei Ne, Mg, and "Si. The measurements were performed in two separate experiments with the beam-swinger neutron time-of-flight facility at the Indiana University Cyclotron Facility. The flight paths were 91 and 131 m, respectively, for the two experiments. The neutrons were detected in large-volume plastic-scintillation detectors. The overall time resolutions were about 825 ps; this provided energy resolutions from 300 to 400 keV. GT strength was identified as El=0 contributions in transitions to discrete final states and also in the background and continuum. The 0', bi=0 cross sections were converted to B(GT) units using a "universal" conversion formula calibrated to (p, n ) reactions on other even-even s-d shell nuclei. The resulting B(GT) distributions were compared with full s-d shell-model predictions. The distribution for Mg is described well, but the distributions for Ne and Si are described poorly. The total B(GT) strength observed in discrete states (up to 12 MeV of excitation) for each reaction is 65+10 /o of that predicted. If one considers B(GT) strength observed in the continuum above a calculated quasi-free-scattering background, the strength increases to 70 -100% of that predicted.If one considers B(GT) strength in an analysis of the full continuum (up to -20 MeV), the entire amount predicted may be observed. These results are consistent with that observed in other light nuclei.
The accurate measurement of the hanger tensile forces of suspension bridges is crucial for construction control and bridge maintenance. However, the commonly used vibration frequency method is not applicable to the short-hanger force assessment. The configuration of the main cable of a suspension bridge is closely related to hanger forces so that the main cable configuration can reflect the hanger forces. Based on the multi-segment catenary theory, this study proposed an analytical algorithm for the reverse assessment of hanger forces based on the measured configuration data of the main cable. First, the relationship between the hanger force and two critical parameters, that is, the horizontal force of the main cable and the catenary parameter, is established, in which the influence of the saddle arc on the main cable configuration is considered. Then, the horizontal force of the main cable is used as the breakthrough point, and a geometric condition (measuring the coordinates of a non-hanging point on the main cable) or a mechanical condition (measuring the tension of a long hanger by the vibration frequency method) is added. Using the nonlinear generalized reduced gradient method, the nonlinear equations are solved, and all hanger forces are identified. The proposed method feasibility and effectiveness are proved using a suspension bridge with a main span of 730 m as an example. The results show that the algorithm of adding a mechanical condition is lower in sensitivity, less affected by the accuracy of the additional condition, higher in precision, and easier to control, comparing to that of adding a geometric condition. Meanwhile, the horizontal force of the main cable and each hanger force exhibit a nearly perfect linear correlation.
Construction of suspension bridges and their structural analysis are challenged by the presence of elements (chains or main cables) capable of large deflections leading to a geometric nonlinearity. For an accurate prediction of the main cable geometry of a suspension bridge, an innovative iterative method is proposed in this article. In the iteration process, hanger tensions and the cable shape are, in turns, used as inputs. The cable shape is analytically predicted with an account of the pylon saddle arc effect, while finite element method is employed to calculate hanger tensions with an account of the combined effects of the cable-hanger-stiffening girder. The cable static equilibrium state is expressed by three coupled nonlinear governing equations, which are solved by their transformation into a form corresponding to the unconstrained optimization problem. The numerical test results for the hanger tensions in an existing suspension bridge were obtained by the proposed iterative method and two conventional ones, namely, the weight distribution and continuous multiple-rigid-support beam methods. The latter two reference methods produced the respective deviations of 10% and 5% for the side hangers, respectively, which resulted in significant errors in the elevations of the suspension points. To obtain more accurate hanger tensile forces, especially for the side hangers, as well as the cable shape, the iterative method proposed in this article is recommended.
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