Compatible Truss-Arch Model for Predicting the Shear Strength of Steel Shape-Reinforced Concrete (SRC) Beams
Abstract
:1. Introduction
2. Proposed Model
2.1. Model Description
2.2. Truss-Arch Modeling of Composite Truss
2.3. Stress Decomposition of Steel Shape
2.4. Calculation Process
- (1)
- Input the geometric dimensions, reinforcement details, and the properties of concrete and steel;
- (2)
- Calculate the shear resistance of the truss and arch actions Vct + Vca by Equations (1)–(7);
- (3)
- Calculate the shear resistance of the vertical steel web Vss by Equations (9)–(15);
- (4)
- Calculate the overall shear strength of SRC beams by Vct + Vca + Vss.
3. Results and Discussions
3.1. Test Database
- (1)
- The compressive strength of concrete varies from 23.3 MPa to 46.6 MPa;
- (2)
- The yield strength of steel web varies from 265 MPa to 332 MPa;
- (3)
- The steel shape ratio varies from 2.16% to 6.62%;
- (4)
- The shear span-to-depth ratio varies from 0.84 to 2.00;
- (5)
- The width of the cross-section varies from 150 mm to 450 mm;
- (6)
- The height of the cross-section varies from 240 mm to 650 mm;
- (7)
- The stirrup ratio varies from 0.00% to 0.52%.
3.2. Comparison between Tested and Calculated Results
4. Conclusions
- (1)
- Multiple shear mechanisms, which consist of a vertical steel web and a composite truss, exist to resist the applied shear load. In the proposed model, the shear strength of the composite truss is evaluated using the traditional truss-arch model, and a stress decomposition based on von Mises yielding criterion is conducted within the steel shape to decouple its shear contribution. Finally, the total shear strength can be determined by superimposing the shear contributions of these two mechanisms;
- (2)
- Through verification with 50 available test results for SRC beams, the proposed model demonstrated its superiority. The predictions generated by the proposed model (with an AVG of 0.98 and a CoV of 0.10) exhibited significantly better agreement with the test results when compared with existing shear equations. For instance, the JGJ 138 equation had an AVG of 0.81 and a CoV of 0.18, the ANSI/AISC 360 equation had values of 0.73 and 0.27, and the Eurocode 4 equation had values of 0.74 and 0.31, indicating that the established model can effectively and reliably predict the shear strength of SRC beams.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Ref. | Specimen ID | Steel Shape | fyw/MPa | ρss /% | L/mm | b/mm | h/mm | ρsv /% | ρsl /% | fc/MPa | fys/MPa | fyw/MPa | Ve/kN | Vu/kN |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
[8] | BH1 | H450 × 200 × 9 × 14 | 312 | 3.80 | 460 | 450 | 550 | / | 1.32 | 40.10 | / | 312 | 2423 | 2364 |
BH2 | H390 × 200 × 10 × 16 | 330 | 4.03 | 460 | 450 | 550 | / | 1.32 | 40.10 | / | 330 | 2399 | 2353 | |
BH3 | H300 × 200 × 13 × 15 | 313 | 3.84 | 460 | 450 | 550 | / | 1.32 | 40.10 | / | 313 | 2109 | 2216 | |
BH4 | H200 × 200 × 20 × 12 | 280 | 3.36 | 460 | 450 | 550 | / | 1.32 | 40.10 | / | 280 | 1766 | 1999 | |
BWH2 | H390 × 200 × 10 × 16 | 330 | 4.03 | 460 | 450 | 550 | / | 1.32 | 40.10 | / | 330 | 2399 | 2353 | |
BWH2A | H390 × 200 × 15 × 16 | 312 | 4.76 | 460 | 450 | 550 | / | 1.32 | 40.10 | / | 312 | 2281 | 2578 | |
BWH2B | H390 × 200 × 20 × 16 | 303 | 5.48 | 460 | 450 | 550 | / | 1.32 | 40.10 | / | 303 | 2605 | 2802 | |
[10] | SRC1-00 | H300 × 150 × 6.5 × 9 | 332 | 2.16 | 975 | 350 | 600 | / | 1.45 | 28.90 | / | 332 | 772 | 686 |
SRC1-00-T | H300 × 150 × 6.5 × 9 | 332 | 2.16 | 975 | 350 | 600 | / | 1.45 | 28.90 | / | 332 | 751 | 686 | |
SRC1-00-E | H300 × 150 × 6.5 × 9 | 332 | 2.16 | 975 | 350 | 600 | / | 1.45 | 28.90 | / | 332 | 799 | 686 | |
SRC1-00-D | H300 × 150 × 6.5 × 9 | 332 | 2.16 | 975 | 350 | 600 | / | 1.45 | 28.90 | / | 332 | 695 | 686 | |
SRC1-50 | H300 × 150 × 6.5 × 9 | 332 | 2.16 | 975 | 350 | 600 | 0.09 | 1.45 | 27.70 | 380 | 332 | 861 | 798 | |
SRC1-25 | H300 × 150 × 6.5 × 9 | 332 | 2.16 | 975 | 350 | 600 | 0.18 | 1.45 | 32.20 | 380 | 332 | 877 | 885 | |
SRC1-17 | H300 × 150 × 6.5 × 9 | 332 | 2.16 | 975 | 350 | 600 | 0.26 | 1.45 | 28.90 | 380 | 332 | 923 | 835 | |
D1-N | H198 × 99 × 4.5 × 7 | 325 | 3.16 | 338 | 200 | 350 | 0.52 | 0.36 | 24.50 | 407 | 325 | 408 | 373 | |
D2-FS | H198 × 99 × 4.5 × 7 | 325 | 3.16 | 338 | 200 | 350 | 0.52 | 0.36 | 23.90 | 407 | 325 | 415 | 366 | |
D3-WS | H198 × 99 × 4.5 × 7 | 325 | 3.16 | 338 | 200 | 350 | 0.52 | 0.36 | 23.90 | 407 | 325 | 395 | 366 | |
DB1-15-NS | H198 × 99 × 4.5 × 7 | 325 | 3.16 | 338 | 200 | 350 | 0.52 | 0.36 | 23.30 | 407 | 325 | 391 | 359 | |
DB2-15-NS | H198 × 99 × 4.5 × 7 | 325 | 3.16 | 338 | 200 | 350 | 0.52 | 0.36 | 24.50 | 407 | 325 | 409 | 373 | |
DB3-NTNS | H198 × 99 × 4.5 × 7 | 325 | 3.16 | 338 | 200 | 350 | / | 0.36 | 23.70 | / | 325 | 396 | 316 | |
DB4-15-FS | H198 × 99 × 4.5 × 7 | 325 | 3.16 | 338 | 200 | 350 | 0.52 | 0.36 | 23.90 | 407 | 325 | 414 | 366 | |
DB5-15-WS | H198 × 99 × 4.5 × 7 | 325 | 3.16 | 338 | 200 | 350 | 0.52 | 0.36 | 23.90 | 407 | 325 | 398 | 366 | |
[11] | PPSRC1 | H500 × 200 × 9 × 14 | 317 | 3.37 | 650 | 450 | 650 | 0.16 | 0.84 | 24.30 | 393 | 317 | 2170 | 1898 |
PPSRC2 | H500 × 200 × 9 × 14 | 317 | 3.37 | 975 | 450 | 650 | 0.16 | 0.84 | 24.30 | 393 | 317 | 1600 | 1388 | |
[12] | B1-1.5 | I16 | 312 | 4.97 | 390 | 200 | 260 | 0.28 | 1.21 | 27.09 | 298 | 312 | 304 | 287 |
B1-1.5p | I16 | 312 | 4.97 | 390 | 200 | 260 | 0.28 | 1.21 | 39.47 | 298 | 312 | 367 | 341 | |
B2-1.0 | I16 | 312 | 4.97 | 260 | 200 | 260 | 0.28 | 1.21 | 34.23 | 298 | 312 | 495 | 437 | |
B2-1.5 | I16 | 312 | 4.97 | 390 | 200 | 260 | 0.28 | 1.21 | 34.23 | 298 | 312 | 342 | 315 | |
B2-2.0 | I16 | 312 | 4.97 | 520 | 200 | 260 | 0.28 | 1.21 | 34.23 | 298 | 312 | 255 | 261 | |
B3-1.0 | I16 | 312 | 5.13 | 260 | 200 | 260 | 0.28 | 1.21 | 44.98 | 298 | 312 | 467 | 533 | |
B3-1.5 | I16 | 312 | 5.13 | 390 | 200 | 260 | 0.28 | 1.21 | 44.98 | 298 | 312 | 373 | 383 | |
B3-2.0 | I16 | 312 | 5.13 | 520 | 200 | 260 | 0.28 | 1.21 | 44.98 | 298 | 312 | 322 | 300 | |
[13] | SRRAC-1 | I16 | 265 | 6.62 | 342 | 150 | 300 | 0.05 | 1.13 | 30.00 | 393 | 265 | 379 | 400 |
SRRAC-2 | I16 | 265 | 6.62 | 342 | 150 | 300 | 0.05 | 1.13 | 26.40 | 393 | 265 | 366 | 382 | |
SRRAC-3 | I16 | 265 | 6.62 | 228 | 150 | 300 | 0.05 | 1.13 | 27.60 | 393 | 265 | 499 | 510 | |
SRRAC-4 | I16 | 265 | 6.62 | 342 | 150 | 300 | 0.05 | 1.13 | 27.60 | 393 | 265 | 371 | 388 | |
SRRAC-5 | I14 | 265 | 6.62 | 456 | 150 | 300 | 0.05 | 1.13 | 27.60 | 393 | 265 | 280 | 338 | |
SRRAC-6 | I16 | 283 | 5.78 | 342 | 150 | 300 | 0.05 | 1.13 | 27.60 | 393 | 283 | 339 | 378 | |
[23] | SRRC1 | I14 | 327 | 4.92 | 240 | 180 | 240 | 0.31 | 1.18 | 34.31 | 339 | 327 | 319 | 305 |
SRRC2 | I14 | 327 | 4.92 | 336 | 180 | 240 | 0.31 | 1.18 | 34.31 | 339 | 327 | 239 | 239 | |
SRRC3 | I14 | 327 | 4.92 | 432 | 180 | 240 | 0.31 | 1.18 | 34.31 | 339 | 327 | 184 | 207 | |
SRRC4 | I14 | 327 | 4.92 | 240 | 180 | 240 | 0.31 | 1.18 | 35.26 | 339 | 327 | 343 | 309 | |
SRRC5 | I14 | 327 | 4.92 | 336 | 180 | 240 | 0.31 | 1.18 | 35.26 | 339 | 327 | 245 | 242 | |
SRRC6 | I14 | 327 | 4.92 | 432 | 180 | 240 | 0.31 | 1.18 | 35.26 | 339 | 327 | 172 | 207 | |
SRRC7 | I14 | 327 | 4.92 | 240 | 180 | 240 | 0.31 | 1.18 | 36.03 | 339 | 327 | 325 | 313 | |
SRRC8 | I14 | 327 | 4.92 | 336 | 180 | 240 | 0.31 | 1.18 | 36.03 | 339 | 327 | 245 | 245 | |
SRRC9 | I14 | 327 | 4.92 | 432 | 180 | 240 | 0.31 | 1.18 | 36.03 | 339 | 327 | 178 | 208 | |
SRRC10 | I14 | 327 | 4.92 | 240 | 180 | 240 | 0.31 | 1.18 | 44.20 | 339 | 327 | 368 | 359 | |
SRRC11 | I14 | 327 | 4.92 | 240 | 180 | 240 | 0.31 | 1.18 | 46.61 | 393 | 327 | 368 | 373 | |
SRRC12 | I14 | 327 | 4.92 | 240 | 180 | 240 | 0.31 | 1.18 | 33.20 | 393 | 327 | 343 | 299 |
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Zhang, X.; Xue, Y.; Liu, Y.; Yu, Y. Compatible Truss-Arch Model for Predicting the Shear Strength of Steel Shape-Reinforced Concrete (SRC) Beams. Buildings 2023, 13, 1391. https://doi.org/10.3390/buildings13061391
Zhang X, Xue Y, Liu Y, Yu Y. Compatible Truss-Arch Model for Predicting the Shear Strength of Steel Shape-Reinforced Concrete (SRC) Beams. Buildings. 2023; 13(6):1391. https://doi.org/10.3390/buildings13061391
Chicago/Turabian StyleZhang, Xu, Yicong Xue, Yaping Liu, and Yunlong Yu. 2023. "Compatible Truss-Arch Model for Predicting the Shear Strength of Steel Shape-Reinforced Concrete (SRC) Beams" Buildings 13, no. 6: 1391. https://doi.org/10.3390/buildings13061391