Code References:
ACI 318-14, PCI Handbook 8th Edition
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For horizontal simply supported members, 9.4.4.3 has defined the critical section for torsion to be a distance d from the face of the support for non-prestressed members and h/2 for prestressed members. If a concentrated load is present between the critical section and the face of the support, then the face of support should become the critical section. The user must make an affirmative response to move the critical section away from the support face. The critical section for non-simply supported members is the face of support (9.4.4.2).Only
Calculation Methods:
Three calculation methods are available in the analysis: ACI 318, Zia/Hsu, and slender spandrel. In all methods, note that only the non-composite section is used for the torsion resistance.True
Calculation Methods:
The ACI 318 method requires the use of closed stirrups, and generally requires more reinforcement than other methods, especially the longitudinal steel. Does This method does not take prestressing into account, which is probably why this method requires more there is a higher longitudinal steel requirement. May not need There does not appear to be any requirement to check the end region in this method, as there is no language that appears to require this, but probably should anyway for good practice. Could not find nor is there any language that deals with checking ledge hanger steel (if any) against combined steel, but it is probably good engineering practice to do sotorsion and shear steel.
The calculations steps for the ACI 318 method can be summarized as follows:
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The slender spandrel method is allowed under 9.5.4.7 when the aspect ratio (need to define. Not sure what the definition is. Stem Height / Stem Width?defined as the ratio of the height / width of the section resisting torsion) of the beam is greater than 4.5. This procedure recognizes that the member is acting as a plate near the ends, and not in torsion. Closed Closed stirrups are not required in this method.(This is my understanding)
The calculation steps for the slender spandrel method can be summarized as follows:
Calculate the factored loading at a section
Divide the length of the beam into the following regions:
End region (face of bearing to H)
Transition region (H to 2*H)
Flexure region (remainder of beam)
Check the maximum allowable torsion in the end region
Calculate the required longitudinal reinforcement for flexural resistance
Calculate the required transverse reinforcement for one-way shear
Calculate the required vertical reinforcement required to resist plate bending in the end and transition regions
Check the required vertical reinforcement on the inner web face (ledge or corbel) against the required hanger steel and provide the larger of the two
Verify that the amount of reinforcement crossing a plane along a 45 degree line drawn from the lower tieback at the support and the top of the member is sufficient
Provide sufficient reinforcement on the outer web face (basically Av/2)
Calculate the required longitudinal web reinforcement for the end and transition regions to satisfy plate bending. There is no need to consider plate being in the flexure region.
May want to at least calculate a threshold torsion for the flexure region based on Zia-Hsu (and flag it?)
Combined Shear and Torsion Reinforcement:
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Calculation of Area of Steel based on Stirrup Input, At,prov:
For the calculation of At,prov at each section, the following steps are performed:
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Start with closest stirrup, that is your base area of steel
Scan to left, divide that distance by 2 (S1/2)
Scan to right, divide that distance by 2 (S2/2)
Ar,prov = base area / (S1/2 + S2/2)
S1 and S2 are limited by end of member and Smax (0.x*h or 0.x*d, depending on what ACI 318 has for dv limits)
If a stirrup does not have another stirrup (or the end of the member) within Smax on one or both sides, then the At,prov for that entire stirrup ‘region’ (S1/2+S2/2) is equal to zero
Exceptions and notes:
Torsion resistance element(s) and stiffnesses. The supporting element should be the stiffest element (as measured by the torsional inertia), and one that also contains closed stirrups. When multiple elements have roughly the same torsional stiffness (inertia) and contain closed stirrups, the torsion is probably distributed based on the relative stiffnesses.
The slender spandrel method is not a torsional analysis per se, it is simply a recognition that the stem of a ‘slender spandrel’ will fail in plate bending before the spandrel fails in torsion.(This is my understanding but I do not believe is explicitly said)
References:
ACI Committee 318, Building Code Requirements for Structural Concrete (ACI 318-14), American Concrete Institute, Detroit, 2014.
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