Elastic theory of torsion is the fundamental base on steel beam design in torsion. In this theory, the material behaves elastically, with pure torsion as the fundamental form.
Pure torsion, also known as St Venant torsion, occurs when a uniform bar subject to equal and opposite torques at each free to wrap end to resist the torque at each cross-section area. The total shear stress over the cross-section is equal to the torsional moment in the beam and the beam will twist about a longitudinal axis known as its shear centre. A close section is much more effective in pure torsion because of the shear stress direction along the cross-section is almost uniform, different from an open section which has opposite stress variation. Wrapping is generated due to non-uniform stress along the cross-section. Hence, except perfectly circular elements, wrapping will be experienced. For solid, hollow section, angle and Tee sections, wrapping is negligible. It is much more significant in double flange open section.
Warping torsion occurs when warping of the cross-sections is constrained, longitudinal stresses and additional shear stresses are developed and the torsion is partly resisted by those additional shear stresses. At any point in the span, the torsion is carried partly as St Venant torsion and party warping torsion (by the shear stresses caused by the restraint of warping). To determine the effect of the two types of torsion, a deflection shape is formulated that reflects the various stiffnesses.
Warping stresses can occur from either internal restraint associated with a non-uniform moment or to external restraint at the ends. Longitudinal warping stresses are greatest at the tip of the flange and the warping shear stress is greatest at the junction with the web. For I section, warping shear stress is small enough to be ignored.
A conservative assessment of warping effects in a flanged beam would be to ignore the St Vanent torsional stiffness and apply the torque as a couple of forces between the top and bottom flanges. For a long beam, this can be very conservative.
Torsional bending constant which has the dimensions of length is an indicator of how quickly the effect of the warping restraint dissipates. The larger the value means a larger warping moment. It is observed that within sections with a similar depth, heavier section rely more on pure torsion, likely due to the increase in cross-section area which leads to larger utility in shear stress.
Temporary stability should be accounted for when looking at the construction stage. The first thing to look at is the floor type. For in-situ composite slab, the beam is either restrained by fixed decking spanning transverse to the beam with in-plane stiffness, or by secondary beams that support longitudinal decking at 3 to 4m centres. When precast is used, provided that are of equal span to either side of the beam they may be assumed to provide restraint through a combination of restoring moment and friction for beam spans to 500/3 times the unit’s bearing width. This means spans up to 8m may typically be assured to be restrained.