Moment-Strain Relationships in Elastic-Plastic Bending of Beams
ARMY ARMAMENT RESEARCH AND DEVELOPMENT CENTER WATERVLIET NY LARGE CALIBER WEAPON SYSTEMS LAB
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Theoretical expressions for bending moment versus depth of elastic- plastic interface for both rectangular, tubular, and solid circular beams are developed. Theoretical expressions for strain as a function of geometry and depth of elastic-plastic interface for each type of cross section are derived. The possibility of a strain singularity occurring as the elastic-plastic interface approaches the neutral axis is pointed out. The assumption that planes remain plane is examined. Experimental data is presented which supports the assumption. The basis for determining residual or permanent strains and expressions for their calculation are given. Finally a brief section of strain- curvature relationships is presented.