Numerical and Geometrical Evaluation of Steel Plates with Transverse Hat-Stiffeners Under Bending
Abstract
1. Introduction
2. Materials and Methods
3. Results and Discussions
3.1. Computational Model Validation and Verification
3.2. Case Study
3.3. Comparison Between Plates Reinforced with Transverse or Longitudinal Hat-Stiffeners
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
hs (mm) | ts (mm) | (mm) | (mm) | RD (%) |
---|---|---|---|---|
400 | 6.35 | 1.1309 | 1.1310 | 0.005 |
375 | 6.35 | 1.1700 | 1.1700 | −0.003 |
350 | 6.35 | 1.2083 | 1.2084 | 0.007 |
325 | 6.35 | 1.2462 | 1.2461 | −0.004 |
300 | 6.35 | 1.2833 | 1.2834 | 0.006 |
275 | 6.35 | 1.3202 | 1.3202 | −0.003 |
250 | 6.35 | 1.3569 | 1.3569 | 0.003 |
225 | 6.35 | 1.3938 | 1.3939 | 0.007 |
200 | 6.35 | 1.4316 | 1.4316 | −0.003 |
175 | 6.35 | 1.4713 | 1.4713 | 0.003 |
150 | 6.35 | 1.5146 | 1.5146 | −0.002 |
125 | 6.35 | 1.5644 | 1.5645 | 0.004 |
100 | 6.35 | 1.6248 | 1.6248 | 0.002 |
75 | 6.35 | 1.6953 | 1.6954 | 0.005 |
50 | 6.35 | 1.7542 | 1.7542 | 0.002 |
25 | 6.35 | 1.7712 | 1.7712 | 0.002 |
400 | 8.00 | 0.5481 | 0.5481 | 0.000 |
375 | 8.00 | 0.5906 | 0.5907 | 0.014 |
350 | 8.00 | 0.6337 | 0.6337 | 0.000 |
325 | 8.00 | 0.6767 | 0.6768 | 0.012 |
300 | 8.00 | 0.7201 | 0.7201 | 0.000 |
275 | 8.00 | 0.7634 | 0.7635 | 0.010 |
250 | 8.00 | 0.8067 | 0.8067 | 0.000 |
225 | 8.00 | 0.8500 | 0.8501 | 0.009 |
200 | 8.00 | 0.8933 | 0.8934 | 0.009 |
175 | 8.00 | 0.9370 | 0.9370 | 0.000 |
150 | 8.00 | 0.9812 | 0.9813 | 0.008 |
125 | 8.00 | 1.0274 | 1.0274 | −0.001 |
100 | 8.00 | 1.0776 | 1.0777 | 0.006 |
75 | 8.00 | 1.1383 | 1.1383 | 0.000 |
50 | 8.00 | 1.2264 | 1.2265 | 0.007 |
25 | 8.00 | 1.4100 | 1.4100 | 0.001 |
400 | 9.53 | 0.2203 | 0.2203 | 0.000 |
375 | 9.53 | 0.2537 | 0.2538 | 0.024 |
350 | 9.53 | 0.2887 | 0.2887 | 0.000 |
325 | 9.53 | 0.3248 | 0.3249 | 0.018 |
300 | 9.53 | 0.3623 | 0.3623 | 0.000 |
275 | 9.53 | 0.4007 | 0.4008 | 0.017 |
250 | 9.53 | 0.4401 | 0.4401 | 0.000 |
225 | 9.53 | 0.4803 | 0.4803 | 0.000 |
200 | 9.53 | 0.5212 | 0.5213 | 0.015 |
175 | 9.53 | 0.5630 | 0.5630 | 0.000 |
150 | 9.53 | 0.6059 | 0.6060 | 0.012 |
125 | 9.53 | 0.6508 | 0.6508 | 0.000 |
100 | 9.53 | 0.6998 | 0.6999 | 0.011 |
75 | 9.53 | 0.7599 | 0.7599 | 0.000 |
50 | 9.53 | 0.8545 | 0.8546 | 0.008 |
25 | 9.53 | 1.0965 | 1.0965 | −0.002 |
400 | 12.7 | 0.2999 | −0.0049 | −101.644 |
375 | 12.7 | 0.2810 | 0.0057 | −97.989 |
350 | 12.7 | 0.2625 | 0.0185 | −92.967 |
325 | 12.7 | 0.2445 | 0.0334 | −86.337 |
300 | 12.7 | 0.2269 | 0.0505 | −77.756 |
275 | 12.7 | 0.2100 | 0.0696 | −66.856 |
250 | 12.7 | 0.1939 | 0.0908 | −53.192 |
225 | 12.7 | 0.1787 | 0.1140 | −36.233 |
200 | 12.7 | 0.1647 | 0.1392 | −15.461 |
175 | 12.7 | 0.1666 | 0.1666 | 0.030 |
150 | 12.7 | 0.1966 | 0.1966 | 0.000 |
125 | 12.7 | 0.2299 | 0.2300 | 0.026 |
100 | 12.7 | 0.2692 | 0.2693 | 0.022 |
75 | 12.7 | 0.3218 | 0.3218 | 0.000 |
50 | 12.7 | 0.4138 | 0.4139 | 0.014 |
25 | 12.7 | 0.6799 | 0.6799 | 0.000 |
hs (mm) | ts (mm) | (mm) | (mm) | RD (%) |
---|---|---|---|---|
250 | 6.35 | 0.1646 | −0.0107 | −106.521 |
225 | 6.35 | 0.1894 | −0.0125 | −106.616 |
200 | 6.35 | 0.2163 | −0.0119 | −105.515 |
175 | 6.35 | 0.2458 | −0.0088 | −103.560 |
150 | 6.35 | 0.2793 | −0.0025 | −100.899 |
125 | 6.35 | 0.3188 | 0.0079 | −97.515 |
100 | 6.35 | 0.3670 | 0.0255 | −93.060 |
75 | 6.35 | 0.4245 | 0.0578 | −86.382 |
50 | 6.35 | 0.4853 | 0.1277 | −73.678 |
25 | 6.35 | 0.5790 | 0.3262 | −43.656 |
250 | 8.00 | 0.0612 | 0.0612 | 0.000 |
225 | 8.00 | 0.0545 | 0.0466 | −14.532 |
200 | 8.00 | 0.0702 | 0.0345 | −50.940 |
175 | 8.00 | 0.0882 | 0.0252 | −71.435 |
150 | 8.00 | 0.1086 | 0.0193 | −82.190 |
125 | 8.00 | 0.1323 | 0.0180 | −86.411 |
100 | 8.00 | 0.1611 | 0.0234 | −85.485 |
75 | 8.00 | 0.1989 | 0.0415 | −79.146 |
50 | 8.00 | 0.2556 | 0.0911 | −64.347 |
25 | 8.00 | 0.3690 | 0.2500 | −32.246 |
250 | 9.53 | 0.1404 | 0.1404 | 0.000 |
225 | 9.53 | 0.1192 | 0.1192 | 0.000 |
200 | 9.53 | 0.1003 | 0.1003 | 0.040 |
175 | 9.53 | 0.0839 | 0.0839 | 0.000 |
150 | 9.53 | 0.0705 | 0.0705 | 0.043 |
125 | 9.53 | 0.0612 | 0.0612 | 0.000 |
100 | 9.53 | 0.0793 | 0.0581 | −26.796 |
75 | 9.53 | 0.1066 | 0.0662 | −37.923 |
50 | 9.53 | 0.1515 | 0.1009 | −33.415 |
25 | 9.53 | 0.2566 | 0.2269 | −11.580 |
200 | 12.7 | 0.2107 | 0.2107 | 0.000 |
175 | 12.7 | 0.1864 | 0.1864 | 0.027 |
150 | 12.7 | 0.1645 | 0.1646 | 0.030 |
125 | 12.7 | 0.1462 | 0.1462 | 0.000 |
100 | 12.7 | 0.1326 | 0.1327 | 0.038 |
75 | 12.7 | 0.1280 | 0.1280 | 0.000 |
50 | 12.7 | 0.1436 | 0.1437 | 0.028 |
25 | 12.7 | 0.2282 | 0.2282 | 0.000 |
hs (mm) | ts (mm) | (mm) | (mm) | RD (%) |
---|---|---|---|---|
250 | 6.35 | 0.0252 | 0.0227 | −9.905 |
225 | 6.35 | 0.0326 | 0.0303 | −6.882 |
200 | 6.35 | 0.0416 | 0.0394 | −5.405 |
175 | 6.35 | 0.0528 | 0.0499 | −5.527 |
150 | 6.35 | 0.0668 | 0.0620 | −7.203 |
125 | 6.35 | 0.0847 | 0.0759 | −10.436 |
100 | 6.35 | 0.1080 | 0.0928 | −14.077 |
75 | 6.35 | 0.1369 | 0.1176 | −14.100 |
50 | 6.35 | 0.1710 | 0.1692 | −1.093 |
25 | 6.35 | 0.3169 | 0.3170 | 0.009 |
200 | 8.00 | 0.0336 | 0.0130 | −61.399 |
175 | 8.00 | 0.0277 | 0.0177 | −35.960 |
150 | 8.00 | 0.0268 | 0.0246 | −8.427 |
125 | 8.00 | 0.0362 | 0.0339 | −6.272 |
100 | 8.00 | 0.0494 | 0.0469 | −5.022 |
75 | 8.00 | 0.0689 | 0.0668 | −3.063 |
50 | 8.00 | 0.1055 | 0.1055 | 0.019 |
25 | 8.00 | 0.2184 | 0.2184 | 0.000 |
175 | 9.53 | 0.0497 | 0.0128 | −74.139 |
150 | 9.53 | 0.0422 | 0.0156 | −62.989 |
125 | 9.53 | 0.0379 | 0.0212 | −44.093 |
100 | 9.53 | 0.0380 | 0.0305 | −19.700 |
75 | 9.53 | 0.0463 | 0.0463 | 0.000 |
50 | 9.53 | 0.0788 | 0.0788 | 0.013 |
25 | 9.53 | 0.1750 | 0.1750 | −0.006 |
125 | 12.7 | 0.0678 | 0.0226 | −66.603 |
100 | 12.7 | 0.0616 | 0.0266 | −56.913 |
75 | 12.7 | 0.0630 | 0.0374 | −40.638 |
50 | 12.7 | 0.0799 | 0.0629 | −21.252 |
25 | 12.7 | 0.1497 | 0.1410 | −5.851 |
hs (mm) | ts (mm) | (mm) | (mm) | RD (%) |
---|---|---|---|---|
150 | 6.35 | 0.0283 | 0.0162 | −42.640 |
125 | 6.35 | 0.0369 | 0.0190 | −48.563 |
100 | 6.35 | 0.0488 | 0.0254 | −47.961 |
75 | 6.35 | 0.0648 | 0.0391 | −39.698 |
50 | 6.35 | 0.0992 | 0.0729 | −26.592 |
25 | 6.35 | 0.2115 | 0.1882 | −11.049 |
150 | 8.00 | 0.0263 | 0.0263 | 0.000 |
125 | 8.00 | 0.0253 | 0.0253 | 0.040 |
100 | 8.00 | 0.0306 | 0.0283 | −7.800 |
75 | 8.00 | 0.0445 | 0.0381 | −14.398 |
50 | 8.00 | 0.0743 | 0.0650 | −12.604 |
25 | 8.00 | 0.1642 | 0.1578 | −3.886 |
125 | 9.53 | 0.0350 | 0.0350 | 0.057 |
100 | 9.53 | 0.0349 | 0.0349 | 0.000 |
75 | 9.53 | 0.0420 | 0.0420 | 0.000 |
50 | 9.53 | 0.0651 | 0.0649 | −0.384 |
25 | 9.53 | 0.1464 | 0.1464 | 0.000 |
100 | 12.7 | 0.0539 | 0.0539 | −0.019 |
75 | 12.7 | 0.0539 | 0.0539 | 0.000 |
50 | 12.7 | 0.0707 | 0.0707 | 0.014 |
25 | 12.7 | 0.1383 | 0.1383 | 0.000 |
hs (mm) | ts (mm) | (mm) | (mm) | RD (%) |
---|---|---|---|---|
150 | 6.35 | 0.0211 | 0.0212 | 0.047 |
125 | 6.35 | 0.0251 | 0.0251 | −0.040 |
100 | 6.35 | 0.0324 | 0.0325 | 0.031 |
75 | 6.35 | 0.0462 | 0.0462 | −0.022 |
50 | 6.35 | 0.0768 | 0.0768 | 0.013 |
25 | 6.35 | 0.1771 | 0.1771 | 0.006 |
125 | 8.00 | 0.0295 | 0.0263 | −10.885 |
100 | 8.00 | 0.0306 | 0.0299 | −2.290 |
75 | 8.00 | 0.0404 | 0.0404 | −0.025 |
50 | 8.00 | 0.0663 | 0.0663 | 0.000 |
25 | 8.00 | 0.1499 | 0.1499 | −0.007 |
100 | 9.53 | 0.0386 | 0.0341 | −11.580 |
75 | 9.53 | 0.0433 | 0.0411 | −4.948 |
50 | 9.53 | 0.0638 | 0.0637 | −0.266 |
25 | 9.53 | 0.1390 | 0.1390 | −0.007 |
75 | 12.7 | 0.0598 | 0.0537 | −10.224 |
50 | 12.7 | 0.0713 | 0.0674 | −5.445 |
25 | 12.7 | 0.1334 | 0.1312 | −1.634 |
hs (mm) | ts (mm) | (mm) | (mm) | RD (%) |
---|---|---|---|---|
175 | 4.75 | 0.0199 | 0.0166 | −16.566 |
150 | 4.75 | 0.0224 | 0.0178 | −20.651 |
125 | 4.75 | 0.0269 | 0.0212 | −21.176 |
100 | 4.75 | 0.0346 | 0.0277 | −19.763 |
125 | 6.35 | 0.0256 | 0.0250 | −2.265 |
100 | 6.35 | 0.0303 | 0.0283 | −6.796 |
75 | 6.35 | 0.0417 | 0.0383 | −8.017 |
50 | 6.35 | 0.0690 | 0.0648 | −6.118 |
25 | 6.35 | 0.1594 | 0.1562 | −1.989 |
100 | 8.00 | 0.0360 | 0.0360 | 0.000 |
75 | 8.00 | 0.0417 | 0.0417 | 0.000 |
50 | 8.00 | 0.0645 | 0.0637 | −1.318 |
25 | 8.00 | 0.1422 | 0.1422 | −0.007 |
75 | 9.53 | 0.0487 | 0.0487 | −0.021 |
50 | 9.53 | 0.0664 | 0.0664 | 0.000 |
25 | 9.53 | 0.1376 | 0.1376 | 0.000 |
50 | 12.7 | 0.0785 | 0.0785 | −0.013 |
25 | 12.7 | 0.1361 | 0.1361 | 0.000 |
hs (mm) | ts (mm) | (mm) | (mm) | RD (%) |
---|---|---|---|---|
150 | 4.75 | 0.0220 | 0.0220 | 0.000 |
125 | 4.75 | 0.0248 | 0.0248 | 0.000 |
100 | 4.75 | 0.0309 | 0.0309 | 0.032 |
75 | 4.75 | 0.0432 | 0.0432 | −0.023 |
100 | 6.35 | 0.0324 | 0.0324 | 0.000 |
75 | 6.35 | 0.0414 | 0.0414 | 0.000 |
50 | 6.35 | 0.0665 | 0.0665 | −0.015 |
25 | 6.35 | 0.1525 | 0.1525 | −0.007 |
75 | 8.00 | 0.0464 | 0.0462 | −0.539 |
50 | 8.00 | 0.0661 | 0.0661 | −0.015 |
25 | 8.00 | 0.1408 | 0.1408 | 0.000 |
75 | 9.53 | 0.0589 | 0.0576 | −2.224 |
50 | 9.53 | 0.0706 | 0.0701 | −0.581 |
25 | 9.53 | 0.1376 | 0.1375 | −0.065 |
50 | 12.7 | 0.0910 | 0.0895 | −1.714 |
25 | 12.7 | 0.1395 | 0.1386 | −0.667 |
hs (mm) | ts (mm) | (mm) | (mm) | RD (%) |
---|---|---|---|---|
125 | 4.75 | 0.0257 | 0.0245 | −4.779 |
100 | 4.75 | 0.0303 | 0.0286 | −5.638 |
75 | 4.75 | 0.0415 | 0.0395 | −4.816 |
100 | 6.35 | 0.0377 | 0.0377 | −0.053 |
75 | 6.35 | 0.0433 | 0.0427 | −1.410 |
50 | 6.35 | 0.0661 | 0.0651 | −1.468 |
25 | 6.35 | 0.1478 | 0.1473 | −0.318 |
75 | 8.00 | 0.0543 | 0.0543 | 0.000 |
50 | 8.00 | 0.0692 | 0.0692 | −0.014 |
25 | 8.00 | 0.1409 | 0.1409 | −0.007 |
50 | 9.53 | 0.0774 | 0.0774 | 0.000 |
25 | 9.53 | 0.1406 | 0.1406 | −0.007 |
hs (mm) | ts (mm) | (mm) | (mm) | RD (%) |
---|---|---|---|---|
100 | 4.75 | 0.0315 | 0.0315 | 0.000 |
75 | 4.75 | 0.0415 | 0.0414 | −0.024 |
75 | 6.35 | 0.0472 | 0.0472 | 0.000 |
50 | 6.35 | 0.0675 | 0.0675 | 0.000 |
25 | 6.35 | 0.1466 | 0.1466 | −0.007 |
50 | 8.00 | 0.0708 | 0.0708 | 0.000 |
25 | 8.00 | 0.1422 | 0.1422 | −0.007 |
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Case | Thickness (T) | Shorter Base (A) | Longer Base (B) | Height (H) | Length (L) |
---|---|---|---|---|---|
1 | 2 | 35 | 60 | 65 | 955.90 |
2 | 3 | 35 | 60 | 65 | 637.26 |
3 | 4 | 35 | 60 | 65 | 477.95 |
4 | 5 | 35 | 60 | 65 | 382.36 |
5 | 6 | 35 | 60 | 65 | 318.63 |
6 | 2 | 40 | 60 | 65 | 932.78 |
7 | 3 | 40 | 60 | 65 | 621.86 |
8 | 4 | 40 | 60 | 65 | 466.39 |
9 | 5 | 40 | 60 | 65 | 373.11 |
10 | 6 | 40 | 60 | 65 | 310.93 |
11 | 2 | 40 | 65 | 70 | 878.09 |
12 | 3 | 40 | 65 | 70 | 585.39 |
13 | 4 | 40 | 65 | 70 | 439.04 |
14 | 5 | 40 | 65 | 70 | 351.23 |
15 | 6 | 40 | 65 | 70 | 292.70 |
16 | 2 | 40 | 60 | 70 | 881.92 |
17 | 3 | 40 | 60 | 70 | 587.95 |
18 | 4 | 40 | 60 | 70 | 440.96 |
19 | 5 | 40 | 60 | 70 | 352.77 |
20 | 6 | 40 | 60 | 70 | 293.97 |
21 | 2 | 35 | 65 | 65 | 950.02 |
22 | 3 | 35 | 65 | 65 | 633.35 |
23 | 4 | 35 | 65 | 65 | 475.01 |
24 | 5 | 35 | 65 | 65 | 380.01 |
25 | 6 | 35 | 65 | 65 | 316.67 |
Number of Hat-Stiffeners | hs (mm) | ts (mm) | (mm) | (mm) | RD (%) | RD (%) |
---|---|---|---|---|---|---|
1 | 200 | 12.7 | 0.1647 | 0.1392 | −76.39 | −80.04 |
25 | 6.35 | 1.7712 | 1.7712 | 153.90 | 153.90 | |
2 | 225 | 8.00 | 0.0545 | 0.0466 | −92.19 | −93.32 |
25 | 6.35 | 0.5790 | 0.3262 | −17.00 | −53.24 | |
3 | 250 | 6.35 | 0.0252 | 0.0227 | −96.38 | −96.74 |
25 | 6.35 | 0.3169 | 0.3169 | −54.56 | −54.56 | |
4 | 125 | 8.00 | 0.0253 | 0.0253 | −96.38 | −96.38 |
25 | 6.35 | 0.2115 | 0.1882 | −69.68 | −73.03 | |
5 | 150 | 6.35 | 0.0211 | 0.0211 | −96.97 | −96.97 |
25 | 6.35 | 0.1771 | 0.1771 | −74.61 | −74.61 | |
6 | 175 | 4.75 | 0.0199 | 0.0166 | −97.15 | −97.62 |
25 | 6.35 | 0.1594 | 0.1562 | −77.15 | −77.61 | |
7 | 150 | 4.75 | 0.0220 | 0.0220 | −96.84 | −96.84 |
25 | 6.35 | 0.1525 | 0.1525 | −78.14 | −78.14 | |
8 | 125 | 4.75 | 0.0257 | 0.0245 | −96.31 | −96.49 |
25 | 6.35 | 0.1478 | 0.1473 | −78.82 | −78.88 | |
9 | 100 | 4.75 | 0.0315 | 0.0315 | −95.48 | −95.48 |
25 | 6.35 | 0.1466 | 0.1466 | −78.98 | −78.98 |
Number of Hat-Stiffeners | hs (mm) | ts (mm) | (mm) | (mm) | RD (%) | RD (%) |
---|---|---|---|---|---|---|
1 | 250 | 9.53 | 0.0958 | 0.0958 | −86.26 | −86.26 |
250 | 4.75 | 1.7735 | 1.7735 | 154.23 | 154.23 | |
2 | 150 | 6.35 | 0.1381 | 0.1266 | −80.20 | −81.84 |
25 | 6.35 | 0.5371 | 0.5371 | −23.01 | −23.01 | |
3 | 150 | 4.75 | 0.1244 | 0.1244 | −82.17 | −82.17 |
25 | 6.35 | 0.4497 | 0.4497 | −35.53 | −35.53 | |
4 | 125 | 4.75 | 0.1650 | 0.1650 | −76.34 | −76.34 |
25 | 9.53 | 0.6344 | 0.6345 | −9.06 | −9.04 | |
5 | 100 | 4.75 | 0.2259 | 0.2259 | −67.61 | −67.61 |
25 | 8.00 | 0.6014 | 0.6014 | −13.79 | −13.79 |
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Alves, M.A.; Rodrigues, E.M.; Rocha, L.A.O.; dos Santos, E.D.; Almeida, W.R.; Isoldi, L.A. Numerical and Geometrical Evaluation of Steel Plates with Transverse Hat-Stiffeners Under Bending. Metals 2025, 15, 647. https://doi.org/10.3390/met15060647
Alves MA, Rodrigues EM, Rocha LAO, dos Santos ED, Almeida WR, Isoldi LA. Numerical and Geometrical Evaluation of Steel Plates with Transverse Hat-Stiffeners Under Bending. Metals. 2025; 15(6):647. https://doi.org/10.3390/met15060647
Chicago/Turabian StyleAlves, Mariana Alvarenga, Eduarda Machado Rodrigues, Luiz Alberto Oliveira Rocha, Elizaldo Domingues dos Santos, William Ramires Almeida, and Liércio André Isoldi. 2025. "Numerical and Geometrical Evaluation of Steel Plates with Transverse Hat-Stiffeners Under Bending" Metals 15, no. 6: 647. https://doi.org/10.3390/met15060647
APA StyleAlves, M. A., Rodrigues, E. M., Rocha, L. A. O., dos Santos, E. D., Almeida, W. R., & Isoldi, L. A. (2025). Numerical and Geometrical Evaluation of Steel Plates with Transverse Hat-Stiffeners Under Bending. Metals, 15(6), 647. https://doi.org/10.3390/met15060647