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The torsional strength of reinforced concrete (RC) members is typically calculated through the thin-walled tube, space truss analogy. The governing equations are simple equilibrium conditions satisfied by closed stirrups, longitudinal reinforcement and spiral concrete diagonals at a variable angle. In building codes, like EC2 and ACI 318, the contribution of longitudinal reinforcement is averaged among the walls, considering the total amount of longitudinal re-bars of the overall cross section. However, longitudinal re-bars may be non-uniformly distributed along the walls. This is particular evident in beams with large aspect ratios and re-bars mainly located at the corners, or in beams with unsymmetrical bending-type longitudinal reinforcement arrangement. This paper presents a plasticity-based variable-angle space truss model accounting for non-uniform distribution of longitudinal reinforcement along the walls. The model, which is based on equilibrium conditions and the lower-bound theorem of plasticity, is first elaborated for a polygonal cross-section with an arbitrary number of walls incorporating arbitrary longitudinal reinforcement ratios and corresponding variable-angle concrete strut inclinations, and then particularized to the more common case of rectangular section with two representative longitudinal reinforcement ratios and two corresponding variable-angle strut inclinations. For practical design purposes, the results of this model are illustrated through normalized torsional strength curves in terms of non-dimensional reinforcement indexes. The model is validated by comparison with more than 200 experimental results of RC members under pure torsion collected from the literature, and very good agreement is found. The predictions of the model are also compared with those of some codes of practice and better results are obtained especially for beams with markedly non-uniform longitudinal reinforcement arrangement.

The evaluation of the structural safety of existing buildings is a worrying problem in many countries that have been recently shocked by unexpected, "spontaneous'" structural failures. Although several studies have tried to investigate the inherent structural deficiencies associated to such collapses, a uniform approach for the evaluation of a building's static vulnerability under gravity loads, accounting both for potential failures in vertical and horizontal elements, does not exist yet. This paper takes up this challenge, investigating the dependence of the different failure mechanisms of the main structural elements, in a Gravity Load Designed (GLD) Reinforced Concrete (R.C.) non-sway frame, on a number of design and material factors. In particular, applying basic principles of plasticity theory to the slabs, the beams and the columns of the structural system for different failure mechanisms, the collapse multipliers for the main structural elements are established. The proposed simplified formulations highlight the dependence of each failure condition on proper design parameters and mechanical properties; moreover they allow the explicit evaluation of the effect of some design errors or execution defects.

This paper presents a simple rational method for the design, capacity calculation and identification of mode of failure of membrane elements subjected to combined in-plane shearing and normal stresses. The non-iterative method named SMCS (simple model for combined stress-resultants) is based on a simplification of the results of the modified compression field theory (MCFT). The simplification leads to equations similar in format to the Plasticity Theory equations except that the contribution of reinforcement larger than the “balanced” reinforcement is neglected, and the maximum attainable shearing stress is limited to a crushing strength that is based on experimental data from normal and high strength concrete (100 MPa) membranes. A comparison with test results from 84 reinforced concrete membrane elements subjected to in-plane shearing and normal stresses gives an average of the experimental to calculated shearing strength of 1.03 and a coefficient of variation of 11.3%. For the original iterative MCFT, these values are 0.99 and 11.1% respectively. The results of the proposed method are also compared with those of the ACI code, the Simplified MCFT and the Plasticity Theory, and favorable results are obtained. The proposed SMCS was also capable of calculating the correct mode of failure in 45 out of 49 panels where the mode of failure was available. The simplicity of the model is illustrated using a design and a capacity calculation example.