Dynamic Transverse Loading of Beams of a Material Exhibiting Linear Strain-Hardening
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Author(s):
Conroy, Margaret F.
Corporate Author(s): Brown University
Corporate Report Number: TR 82
Date of Publication: 1952-01
Pages: 27
DoD Task:
PB Number: PB108593
Identifier: AD0007083
Abstract:
An analysis was performed to determine the permanent deformation of beams subjected to transverse loading of such a magnitude that the plastic strains produced are large compared to the elastic strains. A satisfactory approximation to the solution of the problems can be obtained by the techniques used in elastic beam theory. The analysis is based on the assumptions (1) that the strain-hardening bending moment-curvature relationship is linear, and (2) that the rate of change of curvature of the beam is everywhere greater than or equal to zero, or everywhere less than or equal to zero, for the range of time considered. Elastic strains are ignored, and the beam is considered to be either rigid or plastic. Initial motion and stress problems are solved by the method of superposition. The free boundary problem for a cantilever beam is solved by an inverse method, whereby the form of the solution is assumed and the physical problem associated with this solution is then determined.
Corporate Author(s): Brown University
Corporate Report Number: TR 82
Date of Publication: 1952-01
Pages: 27
DoD Task:
PB Number: PB108593
Identifier: AD0007083
Abstract:
An analysis was performed to determine the permanent deformation of beams subjected to transverse loading of such a magnitude that the plastic strains produced are large compared to the elastic strains. A satisfactory approximation to the solution of the problems can be obtained by the techniques used in elastic beam theory. The analysis is based on the assumptions (1) that the strain-hardening bending moment-curvature relationship is linear, and (2) that the rate of change of curvature of the beam is everywhere greater than or equal to zero, or everywhere less than or equal to zero, for the range of time considered. Elastic strains are ignored, and the beam is considered to be either rigid or plastic. Initial motion and stress problems are solved by the method of superposition. The free boundary problem for a cantilever beam is solved by an inverse method, whereby the form of the solution is assumed and the physical problem associated with this solution is then determined.