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Limit State Design in Torsion: Equilibrium Torsion and Compatibility Torsion

Introduction

In reinforced concrete structures, torsion often occurs in combination with flexure shear. While pure torsion, as seen in metal shafts, is rare in reinforced concrete, the interaction of torsion with bending moments and flexural shear in concrete beams is complex. To simplify design, codes provide streamlined procedures, blending theory and experimentation. This chapter explores the general behavior of reinforced concrete beams under torsion and elucidates the concepts of equilibrium torsion and compatibility torsion.

Equilibrium Torsion and Compatibility Torsion

Torsion can manifest in various ways during load transfer in structural systems. In reinforced concrete design, two terms, namely "equilibrium torsion" and "compatibility torsion," describe different torsion-inducing situations. Equilibrium torsion arises from eccentric loading, relying solely on equilibrium conditions to determine twisting moments. Compatibility torsion, on the other hand, is induced by an angle of twist, and the resulting twisting moment depends on the torsional stiffness of the member.

In certain situations, both equilibrium and compatibility torsion may coexist, such as in circular beams supported on multiple columns.

Equilibrium Torsion

Equilibrium torsion involves twisting moments developed in a structural member to maintain static equilibrium with external loads. This torsion is independent of the torsional stiffness of the member. The magnitude of the twisting moment is determined by statics alone, and the member must be designed to resist this full torsion. Common scenarios for equilibrium torsion include beams supporting lateral overhanging projections or beams with curved plans subjected to gravity loads.

Ends of the member must be suitably restrained to effectively resist induced torsion.

Compatibility Torsion

Compatibility torsion is induced by rotations applied at one or more points along the length of the member. The twisting moments induced are directly dependent on the torsional stiffness of the member. Analysis involves compatibility conditions due to rotational deformations. Torsional stiffness is significantly reduced by torsional cracking, allowing designers to simplify structural analysis by neglecting torsional stiffness. However, to control cracking and enhance ductility, minimum torsional reinforcement is recommended.

Estimation of Torsional Stiffness

Torsional stiffness in reinforced concrete members is influenced by the amount of torsional reinforcement. In the linear elastic phase, torsional stiffness is similar to that of the plain concrete section. However, once torsional cracking occurs, there is a drastic reduction in stiffness, emphasizing the importance of proper torsional reinforcement.

In conclusion, understanding equilibrium and compatibility torsion is crucial for designing safe and resilient reinforced concrete structures. Equilibrium torsion relies on static equilibrium conditions, while compatibility torsion considers deformations induced by twists, requiring an accurate estimation of torsional stiffness. Striking a balance between these torsional considerations ensures the integrity and durability of reinforced concrete members under various loading conditions.