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)
	B110.3	P	0.160	0.275	-	0.120	0.235	5.15	7.72	15.44	8.73	105.1	629.0	655.0
Koutchoukali, Belarbi (2001)	B5UR1	P	0.203	0.305	-	0.165	0.267	2.53	2.53	5.16	6.56	39.6	386.0	373.0
	B7UR1	P	0.203	0.305	-	0.165	0.267	2.53	2.53	5.16	6.56	64.6	386.0	399.0
	B9UR1	P	0.203	0.305	-	0.165	0.267	2.53	2.53	5.16	6.56	75.0	386.0	373.0
	B12UR1	P	0.203	0.305	-	0.165	0.267	2.53	2.53	5.16	6.56	80.6	386.0	399.0
	B12UR2	P	0.203	0.305	-	0.165	0.267	2.53	2.53	5.16	6.95	76.2	386.0	386.0
	B12UR3	P	0.203	0.305	-	0.165	0.267	2.53	3.25	6.58	7.46	72.9	379.5	386.0
	B12UR4	P	0.203	0.305	-	0.165	0.267	2.53	3.80	7.74	7.88	75.9	373.0	386.0
	B12UR5	P	0.203	0.305	-	0.165	0.267	3.97	3.97	8.00	10.13	76.7	380.0	386.0
	B14UR1	P	0.203	0.305	-	0.165	0.267	2.53	2.53	5.16	6.56	93.9	386.0	386.0
Fang, Shiau (2004)	H-06-06	P	0.350	0.500	-	0.300	0.450	3.97	9.93	11.92	7.13	78.5	440.0	440.0
	H-06-12	P	0.350	0.500	-	0.300	0.450	5.07	12.67	20.65	7.10	78.5	410.0	440.0
	H-07-10	P	0.350	0.500	-	0.300	0.450	5.73	14.33	17.03	7.89	68.4	500.0	420.0
	H-07-16	P	0.350	0.500	-	0.300	0.450	8.60	22.92	28.39	7.89	68.4	500.0	420.0
	H-12-12	P	0.350	0.500	-	0.300	0.450	5.07	12.67	20.65	14.19	78.5	410.0	440.0
	H-12-16	P	0.350	0.500	-	0.300	0.450	8.60	18.62	28.39	14.19	78.5	520.0	440.0
	H-14-10	P	0.350	0.500	-	0.300	0.450	5.73	14.33	17.03	16.13	68.4	500.0	360.0
	H-20-20	P	0.350	0.500	-	0.300	0.450	8.60	22.92	34.06	23.46	78.5	560.0	440.0
	N-06-06	P	0.350	0.500	-	0.300	0.450	3.97	9.93	12.00	7.10	35.5	440.0	440.0
	N-06-12	P	0.350	0.500	-	0.300	0.450	5.07	12.67	20.65	7.10	35.5	410.0	440.0
	N-07-10	P	0.350	0.500	-	0.300	0.450	5.73	14.33	17.03	7.89	33.5	500.0	420.0
	N-07-16	P	0.350	0.500	-	0.300	0.450	8.60	20.06	28.39	7.89	33.5	500.0	420.0
	N-12-12	P	0.350	0.500	-	0.300	0.450	5.07	12.67	20.65	14.19	35.5	410.0	440.0
	N-12-16	P	0.350	0.500	-	0.300	0.450	8.60	20.06	28.39	14.19	35.5	520.0	440.0
	N-14-10	P	0.350	0.500	-	0.300	0.450	5.73	14.33	17.03	16.13	33.5	500.0	360.0
	N-20-20	P	0.350	0.500	-	0.300	0.450	8.60	22.92	34.06	23.46	35.5	560.0	440.0
Chiu et al. (2007)	HAS-51-50	P	0.420	0.420	-	0.370	0.370	3.80	3.25	9.03	5.94	76.0	396.0	385.0
	NAS-61-35	P	0.420	0.420	-	0.370	0.370	4.68	4.69	10.80	4.19	48.0	394.0	385.0
	HAS-90-50	P	0.420	0.420	-	0.370	0.370	5.96	5.96	15.89	5.94	78.0	400.0	385.0
	NBS-43-44	P	0.350	0.500	-	0.300	0.450	2.53	3.80	7.60	5.09	35.0	400.0	385.0
	HBS-74-17	P	0.350	0.500	-	0.300	0.450	5.73	6.44	12.89	2.02	67.0	505.0	600.0
	HBS-82-13	P	0.350	0.500	-	0.300	0.450	5.73	7.16	14.31	1.49	67.0	493.0	600.0
	NBS-82-13	P	0.350	0.500	-	0.300	0.450	5.73	7.16	14.31	1.49	35.0	493.0	600.0
	HBS-60-61	P	0.350	0.500	-	0.300	0.450	3.97	5.24	10.48	7.13	67.0	402.0	385.0
	HCS-52-50	P	0.250	0.700	-	0.200	0.650	2.53	4.51	9.03	5.09	76.0	396.0	385.0
	HCS-91-50	P	0.250	0.700	-	0.200	0.650	3.97	7.94	15.89	5.09	78.0	400.0	385.0
Lee and Kim (2010)	T1-1	P	0.300	0.350	-	0.260	0.310	2.53	2.53	5.07	5.48	43.2	410.0	370.0
	T1-2	P	0.300	0.350	-	0.260	0.310	2.53	3.80	7.60	8.39	44.0	410.0	370.0
	T1-3	P	0.300	0.350	-	0.260	0.310	2.53	5.07	10.14	10.97	41.7	410.0	370.0
	T1-4	P	0.300	0.350	-	0.260	0.310	3.97	5.96	11.92	16.89	42.6	510.0	355.0
	T2-2	P	0.300	0.350	-	0.260	0.310	3.97	5.96	7.94	5.48	41.7	510.0	370.0
** P—Plain section; H—Hollow section.