The post-cracking behaviour of structures subjected to torsion can be well predicted by Hsu's softened truss model. The softened truss model is applicable to structures having symmetry in their material properties on all four sides. Wrapping on three faces is a common phenomenon when the top face is provided with a flange or slab. Such a wrapping on three faces of a beam is referred to as a "U" wrap. "U" wraps are better wrapping strategies for distressed structures, as their top face is not accessible for many structures. The material property of an unwrapped face differs from the rest of wrapped faces. For the effective use of wrapping, the unwrapped face needs to be provided with a material having a higher resistance to tension and shear. For this, high-strength concrete in the core is a better option. Here, an attempt is made to predict the torsional capacity of "U" wrapped high-strength concrete beams having an asymmetry in the material using a softened truss model with suitable modifications of the material properties. Efficient algorithms are proposed for the solution of simultaneous equations. The predictions are found to be in good agreement with the experimental test results.
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