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Practical calculation formulas for fundamental frequency of continuous beams(PDF)

长安大学学报(自然科学版)[ISSN:1006-6977/CN:61-1281/TN]

Issue:
2017年01期
Page:
50-57
Research Field:
桥梁与隧道工程
Publishing date:

Info

Title:
Practical calculation formulas for fundamental frequency of continuous beams
Author(s):
WANG Ling-bo JIANG Pei-wen MA Yin-ping
1. Key Laboratory of Old Bridge Detection and Reinforcement Technology of Ministry of Transport, Chang’an University, Xi’an 710064, Shaanxi, China; 2. Engineering Supervision Department, Basic Construction Project Quality Supervision Station of Shaanxi Provincial Transport Department, Xi’an 710075, Shaanxi, China
Keywords:
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PACS:
U448.215
DOI:
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Abstract:
Fundamental frequency is one of the most important parameters for continuous beams, which has important theoretical significance in several aspects, such as structural dynamic response, seismic design, impact factor and resonance analysis. Aiming at the obvious deviation between “General Code for Design of Highway Bridges and Culverts” (JTG D60—2015) and actual structure in fundamental frequency calculation, approximate fundamental frequency calculation for both normal cross-section and long-span variable cross-section continuous beams were studied. Approximate calculation formula of fundamental frequency for continuous beams was derived based on structural dynamic equations. Common range data of structural parameters were handled and uniformly recovered to be parameters sample. A series of simplification were carried out during the analysis, for example, the influences of structure details such as shear deformation, horizontal clapboard and tooth plate were ignored. A sample of more than 100 thousand continuous beams with uniform section and variable section was analyzed, of which structural parameters cover all common parameters of continuous beam. Then the fundamental frequency of the sample was batch computed after APDL program language’s secondary development based on ANSYS and competitive computation power of work station. Finally, the theoretical analysis was conducted to the form of approximate calculation formula of fundamental frequency of continuous beam. In addition, the optimal practical formulas with concise form and high calculation accuracy were obtained by nonlinear fitting all kinds of possible calculation formulas through 1stopt and MATLAB. The results show that the maximum deviation from finite element calculation result to presented formulas result is 2.1%, the average absolute deviation is 0.3%, and the determination coefficient R2 exceeds 0.999 9, which proves that the formulas coincide well with the facts. Through practical engineering verification, the practical formulas can estimate and calculate the fundamental frequency of continuous beams conveniently and precisely.

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Last Update: 2017-01-21