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

Ref.	Beam	**	$x$	$y$	$t$	$x_{1}$	$y_{1}$	$A_{l 1}$	$A_{l 2}$	$A_{l}$	$A_{t} / s$	$f_{c}$	$f_{y l}$	$f_{y t}$
Ref.	Beam	**	(m)	(m)	(m)	(m)	(m)	(cm²)	(cm²)	(cm²)	(cm²/m)	(MPa)	(MPa)	(MPa)
	T2-3	P	0.300	0.350	-	0.260	0.310	3.97	5.96	11.92	8.10	42.7	510.0	370.0
	T2-4	P	0.300	0.350	-	0.260	0.310	5.73	7.00	14.00	9.51	42.6	512.4	370.0
Peng, Wong (2011)	SW12-1	P	0.150	1.200	-	0.100	1.150	2.26	11.31	22.62	3.93	44.2	480.0	459.0
	SW10-1	P	0.150	1.000	-	0.100	0.950	2.26	9.05	18.10	3.93	29.5	499.0	459.0
	SW10-2	P	0.150	1.000	-	0.098	0.948	2.26	9.05	18.10	7.54	44.2	480.0	480.0
	SW10-3	P	0.150	1.000	-	0.098	0.948	2.26	9.05	18.10	11.31	29.5	499.0	499.0
	SW10-4	P	0.150	1.000	-	0.094	0.944	4.02	16.08	32.16	16.08	33.8	497.0	497.0
	SW8-1	P	0.150	0.800	-	0.102	0.752	1.57	7.07	14.14	4.02	29.5	459.0	433.0
	SW8-2	P	0.150	0.800	-	0.098	0.748	1.57	7.07	14.14	11.31	29.5	459.0	499.0
Joh et al. (2019)	RA-SD4-3.2-0.3-3.28	P	0.300	0.400	-	0.270	0.370	11.91	11.91	30.97	7.13	73.7	452.0	484.0
	RA-SD5-3.2-0.3-3.21	P	0.300	0.400	-	0.270	0.370	11.61	11.61	30.97	6.48	73.7	499.0	538.0
	RA-SD6-3.2-0.2-3.21	P	0.300	0.400	-	0.270	0.370	11.61	11.61	30.97	6.48	73.7	630.0	538.0
	RA-SD4-3.2-0.5-2.13	P	0.300	0.400	-	0.270	0.370	5.73	8.60	17.19	7.13	84.7	456.0	484.0
	RA-SD5-3.2-0.7-1.63	P	0.300	0.400	-	0.270	0.370	3.97	5.96	11.92	6.48	84.7	529.0	538.0
	RA-SD6-3.2-0.6-1.63	P	0.300	0.400	-	0.270	0.370	3.97	5.96	11.92	6.48	84.7	627.0	538.0
	RA-SD4-3.2-1.1-1.33	P	0.300	0.400	-	0.270	0.370	2.53	3.80	7.60	7.13	83.1	474.0	484.0
	RA-SD5-3.2-1.0-1.26	P	0.300	0.400	-	0.270	0.370	2.53	3.80	7.60	6.48	83.1	522.0	538.0
	RA-SD6-3.2-0.8-1.26	P	0.300	0.400	-	0.270	0.370	3.97	3.97	7.94	6.48	83.1	627.0	538.0
Ju et al. (2019)	MR30-0.77	P	0.350	0.500	-	0.300	0.450	2.53	3.80	7.60	3.96	29.3	489.8	467.5
	MT30-1.32	P	0.350	0.500	-	0.300	0.450	5.73	8.60	17.19	3.96	29.3	500.4	467.5
	MT40-1.32	P	0.350	0.500	-	0.300	0.450	5.73	8.60	17.19	3.96	40.3	500.4	467.5
	MT40-1.89	P	0.350	0.500	-	0.300	0.450	5.73	8.60	17.19	10.57	40.3	489.8	489.8
Ibrahim et al. (2020)	NSC-S1-C30	P	0.200	0.300	-	0.168	0.268	2.26	2.26	4.52	6.28	42.1	689.7	534.1
	NSC-S1-C45	P	0.200	0.300	-	0.138	0.238	2.26	2.26	4.52	6.28	39.4	689.7	534.1
	HSC-C30	P	0.200	0.300	-	0.168	0.268	2.26	2.26	4.52	6.28	60.8	689.7	534.1
	HSC-C45	P	0.200	0.300	-	0.138	0.238	2.26	2.26	4.52	6.28	60.8	689.7	534.1
Kim et al. (2020)	S08-3-65	P	0.400	0.600	-	0.310	0.510	5.24	7.77	18.08	10.97	35.4	313.3	334.9
	S08-4-90	P	0.400	0.600	-	0.310	0.510	2.85	5.23	13.30	7.92	35.4	474.6	485.8
	S08-5-122.5	P	0.400	0.600	-	0.310	0.510	3.80	3.96	10.45	5.82	35.4	569.6	595.9
	S10-3-52.5	P	0.400	0.600	-	0.310	0.510	5.24	9.93	22.39	13.58	35.4	320.5	334.0
	S10-4-72.5	P	0.400	0.600	-	0.310	0.510	5.07	5.78	16.63	9.83	35.4	467.6	485.1
	S10-5-100	P	0.400	0.600	-	0.310	0.510	3.80	5.23	12.98	7.13	35.4	567.6	595.2
	S06-3-90	P	0.400	0.600	-	0.310	0.510	2.85	5.23	13.30	7.92	35.4	319.4	334.3
	S10-5-90	P	0.400	0.600	-	0.310	0.510	3.96	5.78	14.41	7.92	35.4	569.6	594.8
	S08-3-72.5	P	0.400	0.600	-	0.310	0.510	5.07	5.78	16.63	9.83	35.4	308.8	334.8
	S12-5-72.5	P	0.400	0.600	-	0.310	0.510	5.24	7.77	18.05	9.83	35.4	565.1	595.2
Hsu (1968)	D3	H	0.254	0.381	0.064	0.216	0.343	*	*	11.36	10.16	28.4	341.4	333.1
Hsu (1968)	D4	H	0.254	0.381	0.064	0.216	0.343	30.97	30.97	15.48	14.01	30.6	330.3	333.1
[17,38]	T0	H	0.500	0.500	0.080	0.430	0.430	*	*	32.16	10.28	45.1	345.2	357.0
	T1	H	0.500	0.500	0.080	0.454	0.454	4.52	4.52	18.10	10.28	35.3	356.7	356.7
	T2	H	0.500	0.500	0.080	0.430	0.430	*	*	18.10	10.28	35.3	357.0	357.0
* No sufficient data; ** P—Plain section; H—Hollow section.