Torsion and Section Analysis

The net torsion moment in a cross section consists of two components.

1. Integrated twisting moment across the cross section
2. Eccentricity of the applied shear to the cross section centroid.

The first component, twisting moment, is associated with the torsional stiffness of the beam and slab elements. It can be essentially eliminated by changing the behavior of the slab and beams to “No-Torsion” (see below). “No-Torsion” behavior factors the element torsional stiffness by 0.001. This results in a very low torsional stiffness, which results in very small twisting moments.

The second component is a function of the loading, shear stress distribution across the section, and the cross section geometry. The simple example below illustrates this component of torsion.

A section cut through a single bay building supported by columns is shown below. A typical design approach is to choose a design section that extends from the slab edge to mid-bay between the column lines.

Ignoring twisting stresses, the shear stress distribution across the section would be similar to what is shown in the graphic below. Because the shear force is ultimately directed into the columns, the resultant shear location is at the column location and not at the centroid of the section. For the section to be in equilibrium there must be a net shear force and a torsion moment at the cross section centroid.

Note that when designing slabs using the equivalent frame approach that variation in the shear stress is ignored and the net shear is assumed to coincide the section centroid. This is equivalent to designing the cross section for a uniform shear stress with the same magnitude resultant. However, it should be clear that a uniform stress distribution does not satisfy equilibrium.

Design strips that include a perimeter beam offset from the column grid line is another common condition that results in torsion due to eccentricity of the resultant shear.

In cases where the torsion due to eccentricity of shear is high, one approach to minimize the torsion is to divide the design strip into narrower full-width strips. This would capture the torsion by designing the narrower strips for a higher resultant shear force rather than a lower resultant shear and torsion at the centroid of a wider section. When using this approach, it is important to always select the “Consider Net Axial Force in Strength Design” option for the span segments and design sections. When narrow strips are used, there may be significant net axial resultants that are associated with flexural equilibrium. Ignoring those axial forces could be very unconservative.

Torsion and Section Design

RAM Concept can consider the net torsion design force on a cross section in four different ways. These four approaches are associated with the Beam, As Shear, As Bending, Wood-Armer, and None options shown below.

A brief discussion of each method follows:

1. Beam. Considers torsion by designing with code beam torsion equations. This method assumes torsion is resisted with a circular shear flow.
2. As Shear. Assumes that torsion is carried entirely by varying shear across the length of the shear core of the cross section. The design shear force is calculated as Vd = V +/- 6*T/L, where V = Shear, T = Torsion, and L = Shear Core Length. This method is appropriate for situations where the torsion is primarily by eccentricity of the resultant shear. “As Shear” assumes torsion is resisted with a vertical shear couple.
3. As Bending. Considers torsion by adding the torsion of the bending moment. The design moment is calculated as Md = M +/- T, where M = Moment and T = Torsion. “As Bending” assumes torsion is resisted with a horizontal shear couple, It is based on the assumption that reinforcement is provided in a perpendicular design strip and that the reinforcement in the two orthogonal design strips work together to resist torsion. This method is not recommended for strips containing beams.
4. Wood-Armer. See Section 53.1.21 in the RAM Concept Manual for more information. The design moment is calculated as Md = M +/- AT, where AT = Absolute Twist. The basis of this method is similar to “As Bending.” This method is not recommended for strips containing beams.
5. None. Torsion is completely ignored in the design even if there is a net torsion from the analysis.
   

See Also

ACI 447R-18 https://www.concrete.org/store/productdetail.aspx?ItemID=44718&Language=English&Units=US_AND_METRIC