This paper describes the implementation of a 3-dimensional concrete constitutive model for fiber-based analysis of reinforced concrete members subjected to combined loadings including torsion. The proposed model is formulated to address the interaction between the axial force, bidirectional shear, biaxial bending, and torsion. The shear mechanism along the beam is modeled using a Timoshenko beam approach with three dimensional (3-D) frame elements with arbitrary cross-section geometry. The model considers the 3D equilibrium, compatibility, and constitutive laws of materials at the section and structural level. The concrete constitutive law follows the Softened Membrane Model (SMM) with a tangent-stiffness formulation. The emphasis of the paper is on evaluation of the effect of the different stress states on the global and local behavior of the member. The ability of the model to assess the ultimate strength, stiffness, energy dissipation, failure modes under 3-dimensional loading is evaluated by correlation of analytical results with experimental tests of RC specimens.

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Analysis of Reinforced Concrete Columns Subjected to Combined Axial, Flexure, Shear, and Torsional Loads

A set of generalized strength equations based on the skewbending model has been developed to predict the torsional strength and failure mode of reinforced concrete beams with or without a small transverse opening A torsion‐bending‐shear interaction surface is generated using the proposed strength equations Twenty‐four rectangular reinforced‐concrete beams containing a transverse opening of constant dimensions were grouped into four different series and were tested under various combinations of torsion, bending, and shear The parameters were the ratio between top and bottom longitudinal reinforcement, the torsion‐moment ratio, and the moment‐shear ratio Close agreement is observed between the theoretical predictions and the test results of the writers and of other investigators

Beams with Small Rectangular Opening Under Torsion, Bending, and Shear

Fourteen prestressed high-strength concrete beams were tested to study their torsional behavior. The major variables were the concrete compressive strength, the aspect ratio of the beam cross section, the prestressing level, and the amount of torsional reinforcement. Keeping the area constant, three different cross-sectional dimensions, 240 × 240 mm, 170 × 340 mm, and 140 × 420 mm, were used to give aspect ratios of 1, 2, and 3, respectively. The concrete compressive strengths were 70 and 90 MPa (10,000 and 13,000 psi), and the beams were subjected to two levels of prestressing, corresponding to 0.05 f ′c and 0.10 f ′c. Test results showed that the torque-twist relations for the tested beams were approximately linear up to cracking, and thereafter they were nonlinear. The aspect ratio and the concrete compressive strength influence both the torsional strength and the torsional stiffnesses at all stages of loading. Several theoretical methods available in the literature and developed for normal-strength co...

Prestressed High-Strength Concrete Beams Under Torsion

Many structural elements are subjected to the effects of combined torsional and flexural movements. This paper presents an extension of an existing simplified method for combined stress-resultants model. The extension is used for the design and analysis of reinforced and partially- and fully-prestressed concrete beams subjected to combined torsional and bending moments. The interaction between torsion and flexure is achieved by superposing the steel required for the two moments. The observed ultimate loads of 111 beams are compared with the calculations of the proposed model. This includes comparing interaction diagrams and the effects of concrete strength, stirrups spacing, and T-beam flange width on the ultimate capacity. Very good agreement was obtained. The calculations by the American Concrete Institute code equations are also evaluated and shown to give satisfactory and, in some cases, overly conservative, results. Design and analysis examples are used to demonstrate the simplicity of the proposed model.

Combined Torsion and Bending in Reinforced and Prestressed Concrete Beams Using Simplified Method for Combined Stress-Resultants

Tre he current ACI Code (ACI 318-83)' includes provisions for the design of reinforced concrete members subjected to torsion but does not contain similar provisions for prestressed concrete members. Investigations relevant to the prestressed case include those by Ewida,2 and Ewida and McMullen, 3 wherein the skew bending theory first proposed by Lessig 4 was extended and mathematical models for predicting the behavior of reinforced and prestressed concrete beams under combined loading were developed. In another investigation, Collins and Mitchell-' proposed design recommendations for prestressed and nonprestressed concrete beams in shear and torsion using the truss model first suggested by Rausch.e More recently, Hsu and Mo 7 used a stress-strain curve for softened concrete

Prestressed Concrete Tests Compared With Torsion Theories

The results of tests on 18 rectangular reinforced concrete beams subjected to combined bending torsion and shear are reported. The principal variables were the ratio of twisting to bending moment, the transverse shear force, and the reinforcement configuration. The beams failed by one of three different modes which were characterized by the formation of a hinge adjacent to one face of the beam and yielding of the reinforcement adjacent to the face opposite to the hinge. In beams subjected to a constant twisting moment and a varying bending moment, failures with the hinge located adjacent to the bottom face occurred in the region subjected to the lowest bending moment and failures with the hinge located adjacent to the top face occurred in the region of highest bending moment. Idealized failure surfaces are defined and expressions for the strength of these beams are derived using an equilibrium approach. The results are presented both in tabular form and in interaction diagrams. Good correlation is obtained between the predicted and observed mode of failure and strength.

Concrete Beams in Bending, Torsion and Shear

Analyses are presented for determining the collapse load of a beam curved in a circular arc and subtending a central angle less than 180° The analyses are for the case of two concentrated loads placed at any point on the beam and are an extension of existing analyses that have been developed for single concentrated loads or distributed loads The modes of failure considered are valid for beams with constant plastic moment and torque capacities at any section of the beam In the case of reinforced concrete, the analyses are thus restricted to prismatic beams having constant reinforcement Tests were conducted on four curved reinforced concrete beams and it was found that the plastic theory gave a satisfactory prediction of the mode of failure, ie, location and type of plastic hinges The predicted value of the ultimate load was conservative for modes of failure containing pure bending and combined bending-torsion hinges, and slightly higher for modes of failure containing free hinges

Collapse of Curved Reinforced Concrete Beams

The behaviour of reinforced concrete members subjected to combined torsion and shear is studied in this investigation. An analysis is developed for predicting the deformations at all levels of load and for predicting the strength of the members under combined torsion and shear. Twelve specimens were tested in the experimental portion and the test results are presented and compared with the theoretical predictions.

Concrete Members Under Combined Torsion and Shear

An analysis is presented for predicting the strength of reinforced concrete beams that are subjected to torsion and have openings cast in them in order to provide for the passage of service ducts. The equations proposed are based on addition of stresses due to torsion and flexure in the longitudinal reinforcement and the addition of stresses due to torsion and transverse shear in the stirrups. Test results of 14 beams with openings are also presented. Correlation between the test results and the strength predicted by the analysis indicates that the equations conservatively but adequately predict the strength of the beams.

Torsion in Concrete Beams Containing an Opening

The principal structural actions in beams curved in plan are bending, torsion, and shear. Available methods of plastic analysis are based on the simplifying assumption that the effect of shear on the yield criterion is negligible. Clearly this is not a reasonable assumption in the case of reinforced concrete beams, and to account for the effect of shear, two three-dimensional bending-torsion-shear surfaces are proposed. The analysis of curved beams using the interaction surfaces is then described and the effect of shear on the modes of failure and the ultimate loads is demonstrated. As expected, the effect is significant and new modes of failure are found. Implications of the theory in the design of reinforced concrete beams are briefly described.

Effect of shear on collapse of curved beams

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