EPSF - Elasto-Plastic Stress Fields examples

This page was created as part of the PhD dissertation of Filip Niketic on the behaviour of reinforced and prestressed concrete elements. Numerical analyses were run and compared with actual test results, obtained at EPFL but also world wide.

The table below gives for each test series the reference of the publication that the data was obtained from and the main parameters, surch as concrete strength f_c of reinforcement ratio ρ. By clicking on the title of the publication, you will see a picture of the general geometry of the series of specimens and have access to the input file that was used for the calculation or each specimen. Access to these pages and to the applet is free, but we ask you to register to the web site, if you have done it yet and to login. Registration is free and will take you only a minute.

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If you use a suitable browser, you have the possibility to directly run a simulation, either a simplified linear elastic calculation or more involved nonlinear calculations, by specifying the number of iterations you would like to run. Depending on your computer configuration, some files may not run at all, ending with a Java error message. Otherwise,be prepared to wait for at least a couple seconds before the applet appears, which signals that the calculation is finished, and beware that for some specimens the running time can be extremely long (several hours). It is always advisable to first run a linear elastic calculation to have an idea of the time that will be required.
Calculations made with a lower number of iterations will not converge to a totally accurate solution, but they will take less time! Once the applet appears, the solution is done. Select Results -> Deformed to see the deflected shape of the structure and Results -> Relative stresses to see the stresses acting in the element.

Reinforced Concrete Members
n°	Reference	Spec. n°	Spec. name	f_c [MPa]	ρ [%]	ρ_w [%]	P/A [MPa]	Failure mode	Failure Subtype	Q_test [kN]	Q_EPSF [kN]	Q_test/Q_EPSF	Average	COV
1	Vecchio F.J., Shim W., Experimental and Analytical Investigation of Classic Concrete Beam Tests, Journal of Structural Engineering , Vol. 130, No. 3, March 2004., pp. 460-469	1	A1	22.6	1.94	0.1	0	V	CR	459	450	1.02	1.03	0.05
		2	A2	25.9	2.44	0.1	0	V	CR	439	452	0.97
		3	A3	43.5	2.94	0.1	0	F	CR	420	426	0.99
		4	B1	22.6	2.58	0.15	0	V	CR	434	416	1.04
		5	B2	25.9	2.58	0.15	0	V	CR	365	331	1.1
		6	B3	43.5	3.25	0.15	0	F	CR	342	344	0.99
		7	C1	22.6	2.45	0.2	0	V	CR	282	247	1.14
		8	C2	25.9	3.89	0.2	0	V	CR	290	290	1
		9	C3	43.5	3.89	0.2	0	F	CR	265	260	1.02
2	Yoon Y.S., Cooc W.D., Mitchell D., Minimum Shear Reinforcement in Normal, Medium and High-Strength Concrete Beams, ACI, Vol. 93, No. 5, Sept.-Oct. 1996., pp. 576-584	1	N1_N	36	2.8	0.08	0	V	DT	914	840	1.09	0.95	0.07
		2	N2_S	36	2.8	0.08	0	V	DT	726	800	0.91
		3	N2_N	36	2.8	0.12	0	V	CR	966	1030	0.94
		4	M1_N	67	2.8	0.08	0	V	DT	810	962	0.84
		5	M2_S	67	2.8	0.12	0	V	CR	1104	1120	0.99
		6	M2_N	67	2.8	0.16	0	V	CR	1378	1370	1.01
		7	H1_N	87	2.8	0.08	0	V	DT	966	1012	0.95
		8	H2_S	87	2.8	0.14	0	V	DT	1196	1302	0.92
		9	H2_N	87	2.8	0.24	0	V	CR	1442	1656	0.87
3	Sagaseta J., Vollum R.L., Influence of beam crosssection, loading arrangement and aggregate type on shear strength, Magazine of Concrete Research, Vol.63, Issue 2, 2011., pp. 139-155	1	BG1	31.7	3.32	0.5	0	V	CR	950	990	0.96	1.03	0.09
		2	BG2	31.7	3.32	0.83	0	V	CR	1074	1250	0.86
		3	BL1	53.11	3.32	0.5	0	V	SY	1169	1126	1.04
		4	BL2	53.11	3.32	0.83	0	V	SP	1594	1476	1.08
		5	CB1	49.35	2.8	0.36	0	V	SY	1029	1020	1.01
		6	CB2	49.35	2.8	0.53	0	V	SY	1429	1257	1.14
		7	DB1	49.35	2.8	0.36	0	V	SY	597	540	1.11
4	Mansur M.A., Lee Y.F., Tan K.H., Lee S.L., Test on Continuous Beams with Openings, Journal of Structural Engineering , Vol. 117, No. 6, June 1991., pp. 1593-1606	1	B1	38.4	1.54	0.28	0	F	SP	135	127	1.06	0.99	0.06
		2	B2	40.5	1.54	0.28	0	F	SP	155	145	1.07
		3	B3	43.8	1.54	0.28	0	F	SP	140	144	0.97
		4	C1	43.8	1.54	1.01	0	F	SP	260	261	1
		5	C2	38.4	1.54	1.01	0	F	SP	230	244	0.94
		6	C3	40.5	1.54	1.01	0	F	SP	230	232	0.99
		7	C4	28.8	1.54	1.01	0	F	SP	240	253	0.95
		8	C5	28.8	1.54	1.01	0	F	SP	180	200	0.9
5	Hong S.G., Kim D.J., Kim S.Y., Hong N.K., Shear Strength of Reinforced Concrete Deep Beams with End Anchorage Failure, ACI, Vol. 99, No. 1, Jan.-Feb. 2002., pp. 12-22	1	SS_1	23.5	1.66	0.42	0	V	DT	662.28	610	1.09	1.06	0.05
		2	SS_2	23.5	1.66	0.42	0	V	DT	610.34	538	1.13
		3	SS_3	23.5	1.66	0.42	0	L	A	560.66	507	1.11
		4	SS_4	23.5	1.66	0.42	0	L	A	479.22	494	0.97
		5	LBS_2	23.5	1.66	0.42	0	L	A	579.96	576	1.01
		6	VSR_1	23.5	1.66	0.52	0	L	A	593.29	566	1.05
		7	VSR_2	23.5	1.66	0.7	0	V	DT	658.07	608	1.08
6	Sorensen H.C., Test on 12 Reinforced Concrete T-beams (In English), Test Rapport No. R 60, Technical University of Denmark (Structural Research Labobatory), Lyngby, Denmark, 1974., 52 pp.	1	T23	34.2	1.06	0.34	0	V	DT	139	139	1	1.16	0.06
		2	T1a	22.9	1.06	0.59	0	F	CR	133	115	1.16
		3	T2a	24.6	1.06	0.41	0	F	CR	137	122	1.12
		4	T3a	24.6	1.06	0.49	0	V	AS	126	105	1.20
		5	T4a	25.2	1.06	0.34	0	V	AS	131	114	1.15
		6	T1b	23.1	1.06	0.44	0	V	CR	118	102	1.16
		7	T2b	24.9	1.06	0.3	0	V	DT	129	108	1.19
		8	T3b	24.6	1.06	0.29	0	V	DT	116	89	1.30
		9	T4b	24.7	1.06	0.2	0	V	DT	106	94	1.13
		10	T5	25.5	1.06	0.2	0	V	DT	110	95	1.16
7	Leonhardt F., Walter R., “Shear tests on slabgirders with different shear reinforcement“ (In German: “Schunversuche an Plattenbalken mit unterschiedlicher Schubbewehrung“), Deutscher Ausschuss für Stahlbeton, No. 156, Berlin, Germany, 1963, 62 pp.	1	TA1	15.2	0.84	1.29	0	V	CR	670	582	1.15	1.11	0.06
		2	TA2	15.2	0.84	0.86	0	V	SY	638	530	1.20
		3	TA3	15.1	0.84	0.59	0	V	SY	544	476	1.14
		4	TA4	15.1	0.84	0.34	0	V	SY	458	382	1.2
		5	TA13	17.9	0.84	1.29	0	F	CR	700	635	1.10
		6	TA14	17.9	0.84	0.86	0	V	SY	666	597	1.12
		7	TA15	17.1	0.84	0.59	0	V	SY	584	514	1.14
		8	TA9	24.8	0.84	1.29	0	F	Y	700	700	1.00
		9	TA10	24.8	0.84	0.86	0	F	Y	714	690	1.03
		10	TA11	24.4	0.84	0.59	0	V	SY	670	586	1.14
		11	TA12	24.4	0.84	0.34	0	V	SY	530	468	1.13
		12	TA5	15.1	0.84	1.3	0	L	SP	453	450	1.01
		13	TA17	20.3	0.84	1.3	0	V	CR	677	614	1.10
		14	TA18	26.8	0.84	1.3	0	F	Y	709	628	1.13
		15	TA6	15.1	0.84	0.59	0	V	SY	465	480	0.97
		16	TA16	17.1	0.84	0.59	0	V	SY	587	506	1.16
8	Kaufmann W., Marti P., “Tests on Reinforced Concrete Beams under Normal and Shear Force“ (In German : “Versuche an Stahlbetonträgern unter Normal-und Querkraft“), Institute of Structural Engineering, Eidgenössische Technische Hochschule Zürich (ETHZ), Zürich, Switzerland, 1996., pp. 141	1	VN1	53.9	4.23	0.34	0	V	SY	542	546	0.99	1.03	0.03
		2	VN2	52.6	4.23	0.34	0	V	SY	548	522	1.05
		3	VN3	60.2	4.23	0.34	0	V	SY	540	510	1.06
		4	VN4	61.9	4.23	0.34	0	V	SY	564	555	1.02
9	Nagrodzka-Godycka K., Piotrkowski P., Experimental Study of Dapped End Beams Subjected to Inclined Load, ACI, Vol. 109, No. 1, Jan.-Feb. 2012., pp. 11-20	1	WB_1_L	36.4	0.63	0.76	0	L	SY	130	126	1.03	0.98	0.07
		2	WB_1_P	36.4	0.63	0.76	0	L	SY	140	126	1.11
		3	WB_2_L	36.4	0.63	0.76	0	L	SP	180	188	0.96
		4	WB_2_P	36.4	0.63	0.76	0	L	SP	180	180	1
		5	WB_3_L	36.4	1.26	1.52	0	L	SY	206	206	1
		6	WB_3_P	36.4	1.26	1.52	0	L	SY	206	206	1
		7	WB_4_L	36.4	1.26	1.52	0	L	SP	270	272	0.99
		8	WB_4_P	36.4	1.26	1.52	0	L	SP	280	272	1.03
		9	WB_5_L	36.4	0.56	0.73	0	L	SY	172	180	0.96
		10	WB_5_P	36.4	0.84	0.98	0	L	SP	200	248	0.81
		11	WB_6_L	36.4	0.56	0.73	0	L	SP	238	256	0.93
		12	WB_6_P	36.4	0.84	0.98	0	L	SP	320	354	0.9
10	J. Mata-Falcón, «Serviceability and Ultimate Behaviour of Dapped-end Beams (In Spanish: Estudio del comportamiento en servicio y rotura de los apoyos a media madera)», PhD Thesis, Universitat Politècnica de València, Valencia, Spain, 2015.	1	DEB-1.1_T1	41.1	1.1	0.27	0	L	SY+SP	483.91	471	1.03	0.99	0.07

		2	DEB-1.2_T1	39.3	0.99	0.27	0	L	SY+SP	364.53	339	1.08

		3	DEB-1.2_T2	39.3	0.99	0.27	0	L	SY+SP	331.77	339	0.98

		4	DEB-1.3_T1	39.9	1.1	0.23	0	L	SY	302.78	338	0.9

		5	DEB-1.3_T2	39.9	1.1	0.23	0	L	SY	332.49	338	0.98

		6	DEB-1.4_T1	40.4	1.1	0.27	0	L	SY+SP	457.42	441.5	1.04

		7	DEB-1.4_T2	40.4	1.1	0.27	0	L	SY	426.07	441.5	0.97

		8	DEB-1.5_T1	40.8	0.99	0.27	0	L	SY	313.24	303	1.03

		9	DEB-1.6_T1	31.1	2.38	0.55	0	L	SY+SP	773.04	634	1.22

		10	DEB-1.6_T2	31.1	2.38	0.55	0	L	SY+SP	627.25	634	0.99

		11	DEB-1.7_T1	30	2.15	0.55	0	L	SY	485.99	506.5	0.96

		12	DEB-1.7_T2	30	2.15	0.55	0	L	SY	472.01	506.5	0.93

		13	DEB-1.8_T1	32.2	1.69	0.41	0	L	SY	488.13	575	0.85

		14	DEB-1.8_T2	32.2	1.69	0.41	0	L	SY	497.64	575	0.87

		15	DEB-1.9_T1	31.9	1.54	0.41	0	L	SY	354.37	421	0.84

		16	DEB-1.9_T2	31.9	1.54	0.41	0	L	SY	363.69	421	0.86

		17	DEB-2.1_T1	40.2	1.07	0.27	0	L	SY+SP	487.18	471	1.03

		18	DEB-2.1_T2	40.2	1.07	0.27	0	L	SY	498.96	471	1.06

		19	DEB-2.2_T1	33.3	2.29	0.54	0	L	SY+SP	804.55	792	1.02

		20	DEB-2.2_T2	33.3	2.29	0.54	0	L	SY	824.41	792	1.04

		21	DEB-2.3_T1	33.3	1.64	0.42	0	L	SY+SP	601.21	619	0.97

		22	DEB-2.4_T1	36.9	2.25	0.54	0	L	SY+SP	779.8	813.67	0.96

		23	DEB-2.4_T2	36.9	2.25	0.54	0	L	SY+SP	773.62	813.67	0.95

		24	DEB-2.5_T1	37.1	2.18	0.53	0	L	SY+SP	662.66	705.75	0.94

		25	DEB-2.5_T2	37.1	2.18	0.53	0	L	SY+SP	737.34	705.75	1.04

		26	DEB-2.6_T1	38.3	2.62	0.53	0	L	SY+SP	820.23	788	1.04

		27	DEB-3.1_T1	33.7	2.25	0.54	0	L	SY+SP	794.81	814	0.98

		28	DEB-3.1_T2	33.7	2.25	0.54	0	L	SY+SP	850.56	814	1.04

		29	DEB-3.2_T1	37.2	2.18	0.53	0	L	SY+SP	780.04	743.38	1.05

		30	DEB-3.2_T2	37.2	2.18	0.53	0	L	SY+SP	796.45	743.38	1.07

		31	DEB-3.3_T1	38.8	2.62	0.53	1.24	L	SY+SP	875.88	847	1.03

		32	DEB-3.3_T2	38.8	2.62	0.53	1.06	L	SY+SP	841.16	842	1

33	DEB-3.4_T1	34.55	2.38	0.55	0	L	SY+SP	653.99	669	0.98
34	DEB-3.4_T2	34.55	2.38	0.55	0	L	SY+SP	665.16	669	0.99
35	DEB-3.5_T1	33.05	2.29	0.54	0	L	SY	849.48	838.33	1.01
36	DEB-3.5_T2	33.05	2.29	0.54	0	L	SY	855.9	838.33	1.02
37	DEB-3.6_T1	36.7	1.69	0.41	0	L	SY	567.42	591	0.96
38	DEB-3.6_T2	36.7	1.69	0.41	0	L	SY+SP	553.15	591	0.94
39	DEB-3.7_T1	45.5	2.38	0.55	0	L	SY	831.8	796	1.04
40	DEB-3.7_T2	45.5	2.38	0.55	0	L	SY	820.83	796	1.03
41	DEB-3.8_T1	48.8	2.38	0.55	0	L	SY	908.35	882.22	1.03
42	DEB-3.8_T2	48.8	2.38	0.55	0	L	SY	903.95	882.22	1.02
43	DEB-3.9_T1	48.4	2.38	0.55	0	L	SY	886.22	928.75	0.95
44	DEB-3.9_T2	48.4	2.38	0.55	0	L	SY	924.96	928.75	1
45	DEB-3.10_T1	41.8	0	0.53	1.75	L	SY+SP	887.17	888	1
46	DEB-3.1_T2	41.8	0	0.53	1.39	L	SY+SP	925.58	886	1.04
47	DEB-3.11_T1	45.5	0	0.53	2.23	L	SY+SP	1028.08	1001	1.03
48	DEB-3.11_T2	45.5	0	0.53	2.29	L	SY+SP	988.36	1001	0.99
49	DEB-3.12_T1	48.4	0	0.53	3.41	L	SY+SP	1009.77	1089	0.93
50	DEB-3.12_T2	48.4	0	0.53	3.04	L	SY+SP	1033.2	1085	0.95
11	Chan, T., A Study of the Behavior of Reinforced Concrete Dapped-end Beams, Master Thesis, University of Washington, Seattle, USA, 1979, 167 p.	1	1A	33.62	1.71	0.47	0	L	-	144.12	136	1.06	1.02	0.05

		2	1B	30.52	2.33	0.47	0	L	-	190.96	184	1.04

		3	2A	33	1.88	0.44	0	L	-	178.37	182	0.98

		4	2B	30.86	2.33	0.44	0	L	-	169.48	184	0.92

		5	3A	37.03	1.88	0.47	0	L	-	215.83	194	1.11

		6	3B	30.28	2.33	0.47	0	L	-	176.59	181	0.98

		7	4A	30.28	1.88	0.43	0	L	-	188.74	187	1.01

		8	4B	29.38	2.33	0.43	0	L	-	176.95	169	1.05

12	Khan, T., A Study of the Behavior of Reinforced Concrete Dapped-end Beams, Master Thesis, University of Washington, Seattle, USA, 1981, 145 p.	1	1A	28.76	2.39	0.53	0	L	-	215.29	198	1.09	1.03	0.07

		2	1B	29.76	2.71	0.5	0	L	-	187.71	190	0.99

		3	2A	29.69	2.71	0.54	0	L	-	208.18	184	1.13

		4	2B	31.03	2.97	0.53	0	L	-	189.49	168	1.13

		5	3A	33.72	2.41	0.61	0	L	-	197.5	210.33	0.94

		6	3B	37.14	2.67	0.59	0	L	-	189.05	204.6	0.92

		7	4A	28.97	2.16	0.59	0	L	-	175.7	165.2	1.06

		8	5B1	33.66	2.43	0.6	0	L	-	163.69	152.4	1.07

		9	5B2	34.48	2.43	0.6	0	L	-	142.79	148	0.96

13	Cook, W.D., Studies of Disturbed Region Near Discontinuities, PhD Thesis, McGill University, Montreal, Québec, Canada, 1987, 153 p.	1	D-1	29.8	2.61	0.4	0	L	-	307	324	0.95	0.99	0.04

		2	D-3	36.3	2.51	0.47	0	L	-	372	381.67	0.97

		3	D-4	36.3	2.6	0.46	0	L	-	340	324	1.05

14	Zhu, R.R.H., Wanichakorn, W., Hsu, T.T.C., Vogel, J., Crack Width Prediction Using Compatibility-Aided Strut-and-Tie Model, ACI Structural Journal, Vol. 100, No. 4, July-Aug. 2003, pp. 413-421.	1	T2	41.75	0.52	0.25	0	L	-	562.7	544.4	1.03	1.06	0.07

		2	T3	33.55	0.64	0.36	0	L	-	538.23	513	1.05

		3	T4	41.46	0.52	0.25	0	L	-	571.6	618.33	0.92

		4	T5	38.96	0.52	0.36	0	L	-	920.78	789	1.17

		5	T6	43.33	0.52	0.36	0	L	-	467.06	445	1.05

		6	T7	47.08	0.61	0.44	0	L	-	1196.57	1061.8	1.13

15	R. Herzinger, “Stud reinforcement in dapped ends of concrete beams”, Thesis, University of Calgary, Calgary, Alberta, Canada, 2008.	1	DE-A-1.0_T1	38.1	2.31	0.42	0	L	-	216	204	1.06	0.99	0.06

		2	DE-A-1.0_T2	48.4	2.31	0.42	0	L	-	255	222	1.15

		3	DE-A-0.5_T1	38	2.31	0.45	0	L	-	231	231.02	1

		4	DE-B-1.0_T1	38.6	2.28	0.42	0	L	-	203	218.72	0.93

		5	DE-B-1.0_T2	40.4	2.28	0.42	0	L	-	226	218.72	1.03

		6	DE-B-0.5_T1	36.9	2.28	0.45	0	L	-	205	228.15	0.9

		7	DE-B-0.5_T2	36.9	2.28	0.45	0	L	-	222	228.15	0.97

		8	DE-C-1.0_T1	39.1	2.3	0.38	0	L	-	181	202.59	0.89

		9	DE-C-1.0_T2	41.6	2.3	0.38	0	L	-	212	202.59	1.05

		10	DE-C*-1.0_T1	42.2	2.3	0.49	0	L	-	260	275.4	0.94

		11	DE-C*u-1.0_T1	41.9	2.3	0.54	0	L	-	270	268.6	1.01

		12	DE-D-1.0_T1	38.8	2.23	0.4	0	L	-	220	222.15	0.99

		13	DE-Du-1.0_T1	36.8	2.23	0.4	0	L	-	213	224	0.95

		14	DE-Du-1.0_T2	37.4	2.23	0.4	0	L	-	222	224	0.99

		15	DE-D*-1.0_T1	39.9	2.21	0.41	0	L	-	214	222	0.96

		16	DE-D*-1.0_T2	40.5	2.21	0.41	0	L	-	203	222	0.91

		17	DE-Du*-1.0_T1	39.2	2.21	0.41	0	L	-	212	219.94	0.96

		18	DE-Du*-1.0_T2	40.3	2.21	0.41	0	L	-	227	219.94	1.03

16	Campana S., Muttoni A., “Testing frame corners of a polygonal section covered trench with opening moments“ (In French: “Essais d'ouverture d'angles de cadre d'une tranchée couverte à section polygonale“), Test Rapport No. 08.03-RE02, IBETON, EPFL, Lausanne, Switzerland, November, 2011., 184 pp.	1	SC26	41.9	0.71	0	0	L	DT	107.6	117.5	0.92	0.97	0.06
		2	SC27	41.6	0.71	0	0	L	DT	123.6	127.5	0.97
		3	SC31	41.7	0.71	0	0	L	DT	118.6	127.5	0.93
		4	SC34	41.4	0.72	0	0	L	DT	113.5	107.5	1.06
		5	SC35	42.1	0.72	0	0	L	CR	134	127.5	1.05
		6	SC38	31.3	0.7	0.17	0	L	DT	110.3	112.5	0.98
		7	SC39	31.1	0.71	0.19	0	L	DT	108.7	122.5	0.89
		8	SC40	30.9	0.7	0.19	0	L	DT	105.9	125	0.85
		9	SC41	30.9	0.7	0.22	0	L	CR	131.8	127.5	1.03
		10	SC42	31	0.71	0.22	0	L	CR	127.3	127.5	1
		11	SC43	31.1	0.7	0.26	0	L	CR	128.7	127.5	1.01
		12	SC44	30.9	0.7	0.19	0	L	DT	118.4	122.5	0.97
		13	SC45	30.8	0.7	0.22	0	L	CR	123.3	125	0.99
17	Placas A., "Shear Strength of Reinforced Concrete Beams", PhD thesis, Imperial College of Science and Technology, London, UK, November 1969, pp. 589	1	R10	29.6	0.97	0.21	0	V	CR	75.5	73	1.03	1.04	0.14

		2	R11	26.2	1.95	0.21	0	V	CR	90	83	1.08

		3	R12	34	4.17	0.21	0	V	CR	110	98	1.12

		4	R14	29	1.46	0.14	0	V	DT	90	67	1.34

		5	R17	13	1.46	0.21	0	V	CR	70	54	1.3

		6	R20	43	1.46	0.21	0	V	CR	90	92	0.98

		7	R22	29.5	1.46	0.21	0	V	CR	80	82	0.98

		8	R24	31	1.46	0.21	0	V	DT	92.5	84	1.1

		9	R25	31	4.17	0.21	0	V	DT	105	95	1.11

		10	T1	28	0.31	0.21	0	V	DT	110.5	95	1.16

		11	T3	27.5	0.36	0.21	0	V	DT	105	97	1.08

		12	T4	32.5	0.48	0.21	0	V	DT	110	114	0.96

		13	T7	27.4	0.75	0.21	0	V	DT	110	118	0.93

		14	T8	31	1.04	0.21	0	V	DT	125	130	0.96

		15	T10	28.1	0.36	0.14	0	V	DT	87	90	0.97

		16	T13	13	0.36	0.21	0	V	DT	90	64	1.41

		17	T15	33.2	1.04	0.21	0	V	SY	105	115	0.91

		18	T16	32.7	1.04	0.14	0	V	SY	90	117	0.77

		19	T19	30	1.04	0.21	0	V	CR	112.5	112	1

		20	T25	54	0.36	0.21	0	V	SY	115	125	0.92

		21	T31	31	0.36	0.21	0	V	SY	95	103	0.92

		22	T34	34	2.08	0.21	0	V	SY	112.5	117	0.96

		23	T35	34	0.59	0.21	0	V	SY	115	119	0.97

18	Bach F., Nielsen M.P., Braestrup M.W.,"Shear Tests on Reinforced Concrete T-beams Series V, U, X,B ans S", RapportNo. R 120,Structural Research Laboratory, Technical University of Denmark, pp. 89, 1980	1	V6002W	35.7	0.72	0.27	0	V	DT	245	233	1.05	1.14	0.12

		2	V6002E	35.7	0.72	0.27	0	V	DT	253	233	1.09

		3	V6004W	36.4	0.72	0.43	0	V	DT	306	292	1.05

		4	V6004E	36.4	0.72	0.43	0	V	DT	347	292	1.19

		5	U6002W	19.5	0.72	0.13	0	V	DT	194	144	1.35

		6	U6002E	19.5	0.72	0.13	0	V	DT	200	144	1.39

		7	U6004W	21.1	0.72	0.27	0	V	DT	224	193	1.16

		8	U6004E	21.1	0.72	0.27	0	V	DT	237	193	1.23

		9	X6009W	7.3	0.32	0.27	0	V	DT	133	145	0.92

		10	X6009E	7.3	0.32	0.27	0	V	DT	143	145	0.99

		11	B6009W	10.7	0.57	0.23	0	V	DT	286	237	1.21

		12	B6009E	10.7	0.57	0.23	0	V	DT	245	230	1.07

19	Leonhardt F., and Walther, R. “Deep beams” (in German, “Wandartige Träger”), Deutscher Ausschuss für Stahlbeton, Heft 178, Berlin, 1966, 159 pp.	1	WT4	28	0.4	0.16	0	F	SY	1526	1590	0.96	1.02	0.04

		2	WT7	30	0.4	2.51	0	F	SY	1119	1130	0.99

		3	IWT1	28	0.98	0.7108	0	L	CR	1152	1130	1.02

		4	IWT2	28	0.98	0.38	0	V	CR	1177	1114	1.06

20	Leonhardt, F., Walther, R., Dilger, W., Schubversuche an indirekt gelagerten, einfeldrigen und durchlaufenden Stahlbetonbalken, Deutscher Ausschuss für Stahlbeton, Heft 201, Berlin, 1968, 69 pp.	1	ETI1	30	1.32	0.16	0	V	SY	273	276	0.99	1.01	0.04

		2	ETI2	26	1.4	0.28	0	F	CR	257	250	1.03

		3	ETI3	25	1.4	0.76	0	F	CR	240	222	1.08

		4	ETI4	27	1.4	0.86	0	F	CR	245	250	0.98

		5	ETI5	28	1.42	0.27	0	V	SY	240	246	0.98

21	Baumann, T., Rüsch, H., Schubversuche mit indirekter Krafteinleitung, Versuche zum Studium der Verdübelungswirkung der Biegezugbewehrung eines Stahlbetonbalkens, TH München, Deutscher Ausschuss für Stahlbeton, Heft 210, Berlin 1970, pp. 1–41.	1	64/1	59.3	3.48	0.37	0	F	CR	101.5	102	1	1.06	0.06

		2	65/1A	50.5	3.48	0.37	0	L	SY	140	130	1.08

		3	65/1B	50.5	3.48	0.37	0	F	CR	104.4	104	1

		4	65/2A	56.3	3.48	0.37	0	F	CR	93	92	1.01

		5	65/2B	56.3	3.48	0.8	0	F	CR	103	96	1.07

		6	65/3A	48.2	3.48	0.37	0	F	CR	92	80	1.15

		7	65/3B	48.2	3.48	0.802	0	F	CR	112	98	1.14

Prestressed/Post-tensioned Concrete Members
22	Saqan E. I., Frosch R. J., Influence of flexural reinforcement on shear strength of prestressed concrete beams, ACI Structural Journal, Vol. 106, No. 1, Jan.-Feb.2009., pp. 60-68.	1	V-4-0	52.1	0	0	1.9	V	DT	488	408	1.2	1.23	0.10
		2	V-4-0.93	52.7	0	0	1.9	V	DT	668	600	1.11
		3	V-4-2.37	53.4	0	0	1.9	V	DT	734	734	1
		4	V-7-0	54.5	0	0	1.94	V	DT	740	552	1.34
		5	V-7-1.84	53.1	0	0	1.94	V	DT	968	708	1.37
		6	V-7-2.37	53.1	0	0	1.94	V	DT	856	726	1.18
		7	V-10-0	51.7	0	0	1.95	V	DT	812	584	1.39
		8	V-10-1.51	51.7	0	0	1.95	V	DT	880	702	1.25
		9	V-10-2.37	51.7	0	0	1.95	V	DT	880	738	1.19
23	Kaufman M.K., Ramirez J.A., Re-evaluation of the Ultimate Shear Behavior of High Strength Concrete Prestressed I-Beams, ACI Structural Journal, Vol. 85, No. 3, May-June 1988., pp. 295-303.	1	I-1	57.5	0	0.29	7.45	F	SY	1094	942	1.16	1.07	0.07
		2	I-2	57.5	0	0.24	7.45	V	CR	1288	1130	1.14
		3	I-3	57.7	0	0.33	7.66	V	CR	890	890	1.00
		4	I-4	57.7	0	0.24	7.76	V	CR	978	908	1.08
		5	II-1	62.7	0	0.33	7.94	V	SY	1246	1328	0.94
		6	II-2	62.7	0	0.33	7.79	F	SY	1788	1604	1.11
24	Kuchma, D., Kim, K. S., Nagle, T. J., Sun, S. und Hawkins, N. M., Shear Tests on High-Strength Prestressed Bulb-Tee Girders: Strengths and Key Observations, ACI Structural Journal, Vol. 105, No. 3, May-June 2008., pp. 358-367.	1	G1E	83.4	0	0.55	7.7	V	SY	4438	4228	1.05	1.09	0.07
		2	G1W	83.4	0	0.55	7.7	V	SY	5102	4954	1.03
		3	G2E	86.9	0	0.93	8.5	V	SY	5916	5100	1.16
		4	G2W	86.9	0	0.93	8.5	V	SY	6856	6014	1.14
		5	G3E	109.6	0	0.82	9.6	V	SY	6098	5594	1.09
		6	G3W	109.6	0	0.82	9.6	V	SY	6634	5870	1.13
		7	G4E	112.4	0	1.7	9.6	V	SY	7780	7554	1.03
		8	G4W	112.4	0	1.7	9.6	V	SY	7780	7780	1
		9	G5E	122.7	0	0.18	6.4	V	SY	3626	3454	1.05
		10	G5W	122.7	0	0.18	6.4	V	SY	2980	2638	1.13
		11	G6E	87.6	0	0.85	10.4	V	SY	5550	5138	1.08
		12	G6W	87.6	0	0.85	9.1	V	SY	4842	4484	1.08
		13	G7E	86.2	0	0.82	10.4	V	SY	5786	5076	1.14
		14	G7W	86.2	0	0.82	10.4	V	SY	6400	6336	1.01
		15	G8E	91.7	0	0.82	9.9	V	SY	5508	5738	0.96
		16	G9E	66.2	0	1.57	8.5	V	CR	5998	5504	1.09
		17	G9W	66.2	0	1.57	8.5	V	CR	5982	5808	1.03
		18	G10E	73.1	0	1.14	8.9	V	SY	6116	4932	1.24
		19	G10W	73.1	0	1.14	8.9	V	SY	7302	5618	1.3
25	Rupf, M. and Muttoni, A., “Shear Test on Post-tensioned Reinforced Concrete Beams with Insufficient Transverse Reinforcement“ (In German: “Schubversuche an vorgespannten Stahlbetonträgern mit ungenügender Schubbewehrung“), IBETON, EPFL, Test Rapport No. 09.02-01, Lausanne, Switzerland, 2012., 159 pp.	1	SR21	30.8	0	0.09	2.5	V	SY	1197	1110	1.08	1.06	0.05
		2	SR22	33.7	0	0.13	2.5	V	CR	1377	1290	1.07
		3	SR23	35.3	0	0.06	2.5	V	SY	1092	1065	1.03
		4	SR24	31.3	0	0.25	2.5	V	CR	1737	1680	1.03
		5	SR25	33.1	0	0.09	5	V	CR	1452	1410	1.03
		6	SR26	36.9	0	0.06	5	V	SY	1371	1335	1.03
		7	SR27	28.3	0	0.19	5	V	CR	1818	1740	1.04
		8	SR28	37.8	0	0.09	0	V	SY	666	660	1.01
		9	SR29	29.8	0	0.25	2.5	V	CR	1755	1680	1.04
		10	SR30	31.4	0	0.25	2.5	V	CR	1743	1620	1.08
		11	SR31	31.3	0	0.09	3	V	DT	927	795	1.17
		12	SR31B	31.3	0	0.09	3	V	DT	909	795	1.14
		13	SR32	35.2	0	0.09	0	V	DT	519	525	0.99
26	Fernandez Ruiz M., Muttoni A., Shear Strength of Thin-Webbed Post-Tensioned Beams, ACI Structural Journal, Vol. 105, No. 3, May.-June 2008., pp. 308-317.	1	SH1	53.4	0	0.63	4.2	V	CR	2980	3136	0.95	0.98	0.05
		2	SH2	52.3	0	0.63	4.2	V	CR	2520	2400	1.05
		3	SH3	55.8	0	0.63	4.2	V	CR	3060	3188	0.96
		4	SH4a	49.5	0	0.63	4.2	V	CR	2240	2434	0.92
		5	SH4b	60	0	0.63	4.2	V	CR	3340	3478	0.96
		6	SH5	47.2	0	0.63	4.2	V	CR	3320	3254	1.02
27	Moore, A. M., Shear Behaviour of Post-Tensioned Spliced Girders, PhD Thesis, The University of Texas at Austin, USA, 268 p., 2014.	1	Tx62-1S	73.1	1.51	0.93	11.8	V	CR	3056	3217	0.95	1	0.07

		2	Tx62-2S	82.7	1.51	0.93	12.3	V	CR	3332	3744	0.89

		3	Tx62-2N	82.7	1.51	0.93	12.3	V	CR	3630	3742	0.97

		4	Tx62-3	80.7	1.51	0.93	0	V	CR	4386	4024	1.09

		5	Tx62-4S	95.8	1.51	1.4	12.5	V	CR	3696	4062	0.91

		6	Tx62-4N	93.8	1.51	1.4	12.5	V	CR	3701	3738	0.99

		7	Tx62-5S	86.2	1.51	0.31	12.5	V	CR	3127	3191	0.98

		8	Tx62-5N	86.2	1.51	0.31	12.5	V	CR	3269	3302	0.99

		9	Tx62-6S	85.5	1.52	1.14	13	V	CR	4137	3831	1.08

		10	Tx62-6N	91	1.52	1.14	13	V	CR	4888	4887	1

		11	Tx62-7S	84.1	1.52	1.14	13	V	CR	5186	4630	1.12

28	De Wilder K., Lava P., Debruyne D., Wang Y., De Roeck G., Vandewalle L., "Stress Field Based Truss Model for Shear-Critical Prestressed Concrete Beams", Research Journal of The Institution of Structural Engineers, Vol. 3, August 2015., pp. 28-42	1	B101	77.5	2.08	0.27	19.3	V	DT	377.7	367	1.03	0.98	0.04

		2	B102	77.5	2.08	0.27	19.3	V	DT	321.6	309	1.04

		3	B104	88.9	2.08	0.27	9.6	V	DT	281.8	303	0.93

		4	B105	88.9	2.08	0.27	9.6	V	DT	251.2	255	0.98

		5	B107	89.3	0.97	0.27	10.7	F	CR	271.3	284	0.95

		6	B108	89.3	0.97	0.27	10.7	F	CR	213.8	221	0.97

29	Leonhardt, F., Koch, R., Rostásy, F. S., Schubversuche an Spannbetonträgern, Deutscher Ausschuss für Stahlbeton, Heft 227, Berlin, 1973, 179 pp.	1	ILT1	30.4	0.35	1.01	4.3	V	SY	1809.5	1690	1.07	1.05	0.03

		2	ILT2	30.4	0.35	0.7	4.3	V	SY	1564.5	1540	1.02

		3	IILT1	33.6	0.35	1.01	4.3	v	SY	1667	1552	1.07

30	Büeler, Ch. und Thoma, K., Indirekt gelagerter Spannbetonträger – Versuchsbericht, CC Konstruktiver Ingenieurbau, Hochschule Luzern – Technik & Architektur, Bericht, 2010, 61 pp.	1	LT1	34	0.17	0.25	2.7	F	CR	635	630	1.01	1.01	0.01
30		2	LT2	34	0.4	0.25	2.7	F	CR	863	860	1	1.01	0.01

EPSF Mesh Sensitivity - FE Mesh Size

n° Model Spec. n° Spec. name f_c[MPa] ρ[%] ρ_w[%] P/A[MPa] Failure mode Q_EPSF

Uniform Stress State

I Compression 1 M1 38 0.1 0.1 0 CR 11088

2 M2 38 0.1 0.1 0 CR 11088

3 M3 38 0.1 0.1 0 CR 11088

4 M4 38 0.1 0.1 0 CR 11088

II Tension 1 M1 38 0.1 0.1 0 SY 158

2 M2 38 0.1 0.1 0 SY 158

3 M3 38 0.1 0.1 0 SY 158

4 M4 38 0.1 0.1 0 SY 158

III Shear 1 M1 38 0.1 0.1 0 SY 129

2 M2 38 0.1 0.1 0 SY 129

3 M3 38 0.1 0.1 0 SY 129

4 M4 38 0.1 0.1 0 SY 129

Non-uniform Stress State

I TT-Cross Section Beam with 30 mm web thickness 1 M1 38 3.45 1.13 0 CR 368

2 M2 38 3.45 1.13 0 CR 373

3 M3 38 3.45 1.13 0 CR 386

4 M4 38 3.45 1.13 0 CR 400

II TT-Cross Section Beam with 50 mm web thickness 1 M1 38 3.34 0.68 0 CR 513

2 M2 38 3.34 0.68 0 CR 518

3 M3 38 3.34 0.68 0 CR 536

4 M4 38 3.34 0.68 0 CR 552

III TT-Cross Section Beam with 100 mm web thickness 1 M1 38 3.07 0.34 0 CR 740

2 M2 38 3.07 0.34 0 CR 754

3 M3 38 3.07 0.34 0 CR 764

4 M4 38 3.07 0.34 0 CR 776

IV TT-Cross Section Beam with 200 mm web thickness 1 M1 38 2.65 0.17 0 CR 1020

2 M2 38 2.65 0.17 0 CR 1022

3 M3 38 2.65 0.17 0 CR 1027

4 M4 38 2.65 0.17 0 CR 1039

EPSF Mesh Sensitivity - FE Mesh Shape

TT-Cross Section Beam with 100 mm web thickness 1 Mdef,ref 38 3.07 0.34 0 CR 813

2 Mdef,1 38 3.07 0.34 0 CR 820

3 Mdef,2 38 3.07 0.34 0 CR 807

4 Mdef,3 38 3.07 0.34 0 CR 801

5 Mdef,4 38 3.07 0.34 0 CR 798

EPSF Mesh Sensitivity - FE Mesh Orientation

TT-Cross Section Beam with 100 mm web thickness 1 Morient,1 38 3.07 0.34 0 CR 882

2 Morient,2 38 3.07 0.34 0 CR 818

3 Morient,2 38 3.07 0.34 0 CR 798

4 Morient,2 38 3.07 0.34 0 CR 778

5 Morient,2 38 3.07 0.34 0 CR 839

6 Morient,2 38 3.07 0.34 0 CR 757

7 Morient,3 38 3.07 0.34 0 CR 768

8 Morient,4 38 3.07 0.34 0 CR 764

Notation

f_c Concrete Compressive Strength
Plastic Concrete Compressive Strength (f_cp) was introduced in the models according to following equation:
f_cp=f_c if f_c≤30 MPa
f_cp=f_c(30/f_c)^1/3 if f_c>30 MPa

ρ Longitudinal Reinforcement Ratio (ρ=A_s/(b d), where b refers to the width of the member and d to its effective depth)

ρ_w Transverse Reinforcement Ratio

P Prestressing Force

A Concrete gross cross section Area

Q_test Measured Ultimate Load

Q_EPSF Calculated Ultimate Load

COV Coefficient of Variance

Faliure Modes
F Flexural Failure

V Shear Failure

L Local Failure

Failure Subtype

CR Concrete Crushing

SP Concrete Spalling

DT Diagonal Tension

SY Reinforcement Yealding

AS Arch Stability

A Reinforcement Anchorage

EPSF Mesh Sensitivity - FE Mesh Size
n°	Model	Spec. n°	Spec. name	f_c[MPa]	ρ[%]	ρ_w[%]	P/A[MPa]	Failure mode	Q_EPSF
Uniform Stress State
I	Compression	1	M1	38	0.1	0.1	0	CR	11088

		2	M2	38	0.1	0.1	0	CR	11088

		3	M3	38	0.1	0.1	0	CR	11088

		4	M4	38	0.1	0.1	0	CR	11088

II	Tension	1	M1	38	0.1	0.1	0	SY	158

		2	M2	38	0.1	0.1	0	SY	158

		3	M3	38	0.1	0.1	0	SY	158

		4	M4	38	0.1	0.1	0	SY	158

III	Shear	1	M1	38	0.1	0.1	0	SY	129

		2	M2	38	0.1	0.1	0	SY	129

		3	M3	38	0.1	0.1	0	SY	129

		4	M4	38	0.1	0.1	0	SY	129

Non-uniform Stress State
I	TT-Cross Section Beam with 30 mm web thickness	1	M1	38	3.45	1.13	0	CR	368

		2	M2	38	3.45	1.13	0	CR	373

		3	M3	38	3.45	1.13	0	CR	386

		4	M4	38	3.45	1.13	0	CR	400

II	TT-Cross Section Beam with 50 mm web thickness	1	M1	38	3.34	0.68	0	CR	513

		2	M2	38	3.34	0.68	0	CR	518

		3	M3	38	3.34	0.68	0	CR	536

		4	M4	38	3.34	0.68	0	CR	552

III	TT-Cross Section Beam with 100 mm web thickness	1	M1	38	3.07	0.34	0	CR	740

		2	M2	38	3.07	0.34	0	CR	754

		3	M3	38	3.07	0.34	0	CR	764

		4	M4	38	3.07	0.34	0	CR	776

IV	TT-Cross Section Beam with 200 mm web thickness	1	M1	38	2.65	0.17	0	CR	1020

		2	M2	38	2.65	0.17	0	CR	1022

		3	M3	38	2.65	0.17	0	CR	1027

		4	M4	38	2.65	0.17	0	CR	1039

EPSF Mesh Sensitivity - FE Mesh Shape
TT-Cross Section Beam with 100 mm web thickness		1	Mdef,ref	38	3.07	0.34	0	CR	813

		2	Mdef,1	38	3.07	0.34	0	CR	820

		3	Mdef,2	38	3.07	0.34	0	CR	807

		4	Mdef,3	38	3.07	0.34	0	CR	801

		5	Mdef,4	38	3.07	0.34	0	CR	798

EPSF Mesh Sensitivity - FE Mesh Orientation
TT-Cross Section Beam with 100 mm web thickness		1	Morient,1	38	3.07	0.34	0	CR	882

		2	Morient,2	38	3.07	0.34	0	CR	818

		3	Morient,2	38	3.07	0.34	0	CR	798

		4	Morient,2	38	3.07	0.34	0	CR	778

		5	Morient,2	38	3.07	0.34	0	CR	839

		6	Morient,2	38	3.07	0.34	0	CR	757

		7	Morient,3	38	3.07	0.34	0	CR	768

		8	Morient,4	38	3.07	0.34	0	CR	764

Notation
f_c	Concrete Compressive Strength Plastic Concrete Compressive Strength (f_cp) was introduced in the models according to following equation: f_cp=f_c if f_c≤30 MPa f_cp=f_c(30/f_c)^1/3 if f_c>30 MPa
ρ	Longitudinal Reinforcement Ratio (ρ=A_s/(b d), where b refers to the width of the member and d to its effective depth)
ρ_w	Transverse Reinforcement Ratio
P	Prestressing Force
A	Concrete gross cross section Area
Q_test	Measured Ultimate Load
Q_EPSF	Calculated Ultimate Load
COV	Coefficient of Variance

Faliure Modes
F	Flexural Failure
V	Shear Failure
L	Local Failure

Failure Subtype
CR	Concrete Crushing
SP	Concrete Spalling
DT	Diagonal Tension
SY	Reinforcement Yealding
AS	Arch Stability
A	Reinforcement Anchorage