Improved Equations for the Torsional Strength of Reinforced Concrete Beams for Codes of Practice Based on the Space Truss Analogy

. 2022 May 27;15(11):3827. doi: 10.3390/ma15113827

	CSA A23.3-14
Limit of the section wall thickness	Wall thickness of the hollow section: If $t \geq A_{o h} / p_{h}$ the section is considered as a plain section; If $t < A_{o h} / p_{h}$ the section is considered as an equivalent plains section.
Shear stresses and shear forces due to torsion	Not available
Safety condition	Condition: $T_{u} \leq T_{R}$ where $T_{R} = 2 A_{o} ϕ_{s} \frac{A_{t}}{s} f_{y t} \cos θ$ with $A_{o} = 0, 85 A_{o h}$ and $ϕ_{s} = 1$ (for the present study).
Maximum limit by the tension in concrete struts	Maximum limit to plain section: $T_{u} \leq 0.25 ϕ_{c} f_{c} 1.7 \frac{A_{o h}^{2}}{p_{h}}$ Maximum limit to hollow section: $T_{u} \leq 0.25 ϕ_{c} f_{c} 1.7 A_{o h} t$ where $ϕ_{c} = 1$ (for the present study).
*	$\cot^{2} θ = \frac{A_{l} f_{y l} s}{0.45 A_{t} f_{y t} p_{h}}$
* Angle between the concrete struts and the longitudinal axis of the beams.