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EPFS - Elastic-plastic stress fields

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 regroups all published test results that were used to assess the performance of the numerical simulation using the jconc nonlinear Finite Element program that implements the Elastic-Plastic Stress Field (EPFS) approach.

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 fc of reinforcement ratio ρ. By clicking on the title of the publication, you will see a picture of the general geometry of the specimens and by clicking on the actual specimen name, the input file that was used for the calculation.

If you are interested in running the calculations yourself, you can copy this data, start the jconc applet and paste the data into the Model -> Input... input box (discarding what is already in the box) and press the Generate from input button. Access to the applet is free, but we require that you register to the web site, which is also free and will take you only a minute.

The calculation can take quite some time, so be ready to wait up to several hours. If you want to have first a general idea of the look of the structure, feel free to change on the second line steps,100* the number of iterations (here 100, in red) to a lower value, for instance 20. Of course, the calculation will not converge to a totally accurate solution, but it will take less time! Once the applet appears, the solution is done. Select Results -> Deform to see the deflected shape of the structure and Results -> Relative stresses to see the stresses acting in the element.

If you experience problems running our Java applets, make sure you read our pages on that subject. Not all browsers can run Java applets nowadays, alas! You are currently using Mozilla on mozilla/5.0 applewebkit/537.36 (khtml, like gecko; compatible; claudebot/1.0; +claudebot@anthropic.com).

Reinforced Concrete Members
Reference Spec. n° Spec. name fc
[MPa]
ρ
[%]
ρw
[%]
P/A
[MPa]
Failure mode Failure Subtype Qtest
[kN]
QEPSF
[kN]
Qtest/QEPSF 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
2
LT2
34
0.4
0.25
2.7
F
CR
863
860
1


EPSF Mesh Sensitivity - FE Mesh Size
Model Spec. n° Spec. name fc[MPa] ρ[%] ρw[%] P/A[MPa] Failure mode QEPSF
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
fc Concrete Compressive Strength
Plastic Concrete Compressive Strength (fcp) was introduced in the models according to following equation:
fcp=fc if fc≤30 MPa
fcp=fc(30/fc)1/3 if fc>30 MPa
ρ Longitudinal Reinforcement Ratio (ρ=As/(b d), where b refers to the width of the member and d to its effective depth)
ρw Transverse Reinforcement Ratio
P Prestressing Force
A Concrete gross cross section Area
Qtest Measured Ultimate Load
QEPSF 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