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Title:Experimental and analytical investigation of large deflections of curved beams
Author(s):McWhorter, J.C., III; Sidebottom, O.M.; Wetenkamp, H.R.
Curved Beams
Abstract:An experimental and analytical investigation of the large deflections of curved beams was conducted with the purpose of determining the load-deflection behavior of curved beams made of ductile metals under loads which produced finite strains. In the analytical portion of this investigation, a procedure for calculating the large deflections of plane curved beams with solid symmetrical cross-sections was outlined. The procedure was based on the division of the curved beam into a number of pie shaped segments each of which was assumed to have circular arcs for its inner and outer boundaries, to have constant cross-section, and to be subjected to a constant bending moment and axial force. The deformations of the pie shaped segments were calculated by an iterative procedure which matched the internal moment and axial force to the applied moment and force on the segment. The engineering stress-strain diagram of the beam material was used in a piecewise linear form in calculating the internal forces and moments. The deformed shapes of the segments were calculated from the deformations and were reassembled to give the deformed shape of the curved beam. The deflection between any two points on the curved beam was then calculated by the distance formula. The load-deflection curves for 7 types of mild steel curved beams and for 30 types of crane hooks were determined experimentally with each curved beam being loaded until its original shape was severely distorted. Tension and compression specimens machined from the mild steel plate used in machining the mild steel curved beams and from the shanks and tips of the crane hooks were tested to provide engineering stress-strain diagrams for the analytical calculations. A comparison was made between the experimental load-deflection curves and the load-deflection curves calculated analytically for each of the 7 types of mild steel curved beams and 10 types of crane hooks. It was found that the analytical solution predicted the load at a given deflection within about five percent for the mild steel curved beams and within about ten percent for the crane hooks.
Issue Date:1969-10
Publisher:Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report:TAM R 327
Genre:Technical Report
Rights Information:Copyright 1969 Board of Trustees of the University of Illinois
Date Available in IDEALS:2021-11-04

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  • Technical Reports - Theoretical and Applied Mechanics (TAM)
    TAM technical reports include manuscripts intended for publication, theses judged to have general interest, notes prepared for short courses, symposia compiled from outstanding undergraduate projects, and reports prepared for research-sponsoring agencies.

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