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EPFS - Elastic-plastic stress fields

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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 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 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

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
2 LT2 34 0.4 0.25 2.7 F CR 863 860 1

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