Torsion-Bending-Shear Interaction for Concrete Beams

by Lennart Elfren, Assoc. Prof. of Struct. Engrg.; Univ. of Luleå, Luleå, Sweden,
Inge Karlsson, Proj. Engr.; Cementa AB, Malmö, Sweden,
Anders Losberg, Prof. and Head; Div. of Concrete Structures, Chalmers Univ. of Tech., Göteborg, Sweden,

Serial Information: Journal of the Structural Division, 1974, Vol. 100, Issue 8, Pg. 1657-1676

Document Type: Journal Paper


A rational, simple method is presented for analysis of the torsion-bending-shear interaction at failure for reinforced concrete beams. Equilibrium equations are studied for observed failure mechanisms. Three mechanisms can occur depending on where the concrete compression zone is formed: in the top (mode t), in the bottom (mode b), or in one vertical side (mode s). In modes t and b, the torsion-bending and the shear-bending interaction are governed by second-degree parabolas, whereas the torsion-shear interaction is governed by an ellipse. In mode s, the interaction surface is a cylinder with an elliptic base in the torsion-shear plane. The interaction in this mode is not influenced by the value of the bending moment, M. Approximations regarding the lengths of the moment lever arms and regarding the shear-carrying capacity are examined. Some test results are presented to demonstrate the accuracy of the method. The main feature of the method is that the vertical shear forces are considered in a simple but rational way.

Subject Headings: Concrete beams | Failure analysis | Torsion | Reinforced concrete | Moment (mechanics) | Shear forces | Material failures | Structural failures

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