Effect of Stiffeners on Mechanical Behavior of T-Stubs Based on Experiment and Numerical Simulations
Abstract
:1. Introduction
2. Materials and Methods
2.1. Fabrication and Design of Specimens
2.2. Loading Device and Loading System
2.3. Arrangement of Strain Measuring Points
3. Loading Test Results and Analysis
3.1. Test Phenomenon and Failure Mode
3.2. Stiffness, Bearing Capacity, and Deformation
3.3. Bolt Stress
4. Finite Element Analysis
4.1. Modeling and Verification
4.2. Effect of Preload Force
4.3. Development Process of Bolt Internal Force
- Point A: Yielding at the root of the T-stub flange;
- Point B: Yielding at the corresponding position of the flange bolt of the T-stub;
- Point C: Bolt bending moment peak, yielding of bolt half sections;
- Point D: Lowest bending moment of the bolt, yielding the diagonal full section.
4.4. Analysis of Internal Force Parameters of Bolts
- As shown in Figure 15a,d, with the increase in flange thickness, the flexural stiffness of the flange increased, which reduced the prying of the flange to the bolt. Furthermore, the bolt axial force, bending moment, and prying force gradually decreased. The bolt axial force decreased by 6.1% as flange thickness increased from 12 mm to 16 mm, and the bolt axial force decreased by 6.1%. As thickness increased, the bolt axial force tended to decrease smoothly. The bending moment is influenced by flange thickness, and the bending stress accounted for 27.9% to 52.7% of the total stress without stiffener ribs. After the arrangement of stiffener ribs, it accounted for 19.9% to 44.3% of the total stress, and the bending stress was reduced by approximately 8% compared with the overall.
- As shown in Figure 15b,e, without stiffener ribs, the transverse spacing ratio e2/e1 increased from 0.57 to 1.75, and the difference in bolt axial force, bending moment, bending moment stress ratio, and prying force did not exceed 5%, which shows that the bolt internal force was unaffected by the transverse spacing ratio without stiffener ribs. After placing the stiffening ribs, the internal force of the bolt of the T-stub part was reduced with the increase of the transverse spacing ratio, which was because of the force diversion caused by the stiffening ribs, resulting in the warpage of the T-stub flange in the direction of the vertical stiffening ribs. The bending stress ratio of the FE series specimens was 53% and the prying force ratio was 23%, whereas the bending stress of the ES series accounts for approximately 39.9–47.3% of the total stress, and the prying force ratio was approximately 5.8–~13.2%. Hence, the stiffening ribs can reduce the bending moment and prying force of the bolts; however, the prying force effect cannot be eliminated in the case of a small transverse distance ratio e2/e1.
- As shown in Figure 15c,f, the internal force of the bolts decreased with increasing longitudinal distance ratio n/m in both the ribbed and unribbed cases, indicating that the larger the n/m, the less pronounced the prying of the flange. Compared with the unribbed T-piece, the prying force ratio of the ribbed T-piece was reduced by 12.2% to 15.6%, and the bending stress ratio was reduced by approximately 8%.
5. Conclusions
- In the case of no stiffener rib, the internal force of the bolt and transverse distance ratio are unrelated, and the internal force of the bolt is mainly influenced by the flange thickness and longitudinal distance ratio. Under the same load, the thinner the flange and the smaller the longitudinal distance ratio, the greater the bolt axial force, bending moment, and prying force.
- When the flange thickness increases from 12 mm to 20 mm, the bolt prying force decreases by 26.0% when there is no stiffener rib, but the bolt prying force decreases by 58.1% when there are stiffener ribs. This indicates that compared with the T-stub without stiffener ribs, the reduction in bolt prying force is greater with the increase in flange thickness for the T-stub with stiffener ribs. Furthermore, without stiffener ribs, the overall bolt prying force accounts for approximately 20% of the bolt force. The arrangement of stiffener ribs can reduce this to lower than 10%.
- With or without stiffener ribs, the bolt bending moment is generated by the uneven force on both sides. In the elastic range, the overall bending stress of the bolt was high, and the influence of the bolt bending moment on the bolt load capacity should be considered in the design.
- Compared with the T-stub without stiffener ribs, the bolt internal force with stiffener ribs is mainly affected by the thickness of the flange, transverse distance ratio, and longitudinal distance ratio of the bolt. Under the same load, the smaller the flange thickness, transverse distance ratio, and longitudinal distance ratio, the larger the bolt axial force, bending moment, and prying force.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Specimen No. | Geometric Dimensions | Bolt Specification | Stiffener Rib Arrangement | |||||
---|---|---|---|---|---|---|---|---|
t /mm | m/ mm | n/ mm | e1/ mm | e2/ mm | n/m | |||
T1 | 12 | 65 | 65 | 55 | 55 | 1 | 10.9M16 | no |
T2 | 8 | 65 | 65 | 55 | 55 | 1 | 10.9M16 | no |
T3 | 20 | 65 | 65 | 55 | 55 | 1 | 10.9M16 | no |
T4 | 12 | 75 | 55 | 55 | 55 | 1.36 | 10.9M16 | no |
T5 | 12 | 55 | 75 | 55 | 55 | 0.73 | 10.9M16 | no |
T6 | 12 | 65 | 65 | 55 | 55 | 1 | 10.9M16 | no |
T7 | 12 | 65 | 65 | 55 | 55 | 1 | 10.9M16 | yes |
Pickup Location | Yield Strength fy (MPa) | Ultimate Strength fu (MPa) | Elastic Modulus E (MPa) | Elongation Δ (%) |
---|---|---|---|---|
8 mm Steel Plate | 306.17 | 447.71 | 197,526.5 | 41.41 |
12 mm Steel Plate | 462.56 | 550.09 | 198,431.9 | 28.58 |
16 mm Steel Plate | 378.10 | 526.31 | 207,600.4 | 31.55 |
20 mm Steel Plate | 377.33 | 523.55 | 205,644.9 | 29.06 |
10.9M16 | 1053.61 | 1128.24 | 210,000 * | 14.31 |
Specimen No. | Ki/kN·mm | Ki/K1 | Fy,i/kN | Fmax,i/kN | Fmax,i/Fmax,1 | Δy/mm | Δu/mm |
---|---|---|---|---|---|---|---|
T1 | 375.17 | 1.00 | 104.05 | 266.14 | 1.00 | 0.65 | 31.17 |
T2 | 68.31 | 0.18 | 46.02 | 200.10 | 0.75 | 1.07 | 39.55 |
T3 | 570.74 | 1.52 | 196.10 | 291.15 | 1.09 | 0.6 | 3.15 |
T4 | 352.32 | 0.94 | 94,05 | 235.12 | 0.88 | 0.51 | 30.88 |
T5 | 386.82 | 1.03 | 140.07 | 291.15 | 1.09 | 0.4 | 26.56 |
T6 | 4190.58 | 11.17 | 346.66 | 534.27 | 2.01 | 0.65 | 27.16 |
T7 | 4782.28 | 12.75 | 549.55 | 646.33 | 2.43 | 0.22 | 9.17 |
Specimen No. | Geometric Dimensions | Bolt Diameter | Stiffener Rib Arrangement | ||||||
---|---|---|---|---|---|---|---|---|---|
t /mm | m/ mm | n/ mm | e1/ mm | e2/ mm | n/m | e2/e1 | |||
FT1 | 12 | 65 | 65 | 55 | 55 | 1 | 1 | 10.9M16 | no |
FT2 | 16 | 65 | 65 | 55 | 55 | 1 | 1 | 10.9M16 | no |
FT3 | 20 | 65 | 65 | 55 | 55 | 1 | 1 | 10.9M16 | no |
TS1 | 12 | 65 | 65 | 55 | 55 | 1 | 1 | 10.9M16 | yes |
TS2 | 16 | 65 | 65 | 55 | 55 | 1 | 1 | 10.9M16 | yes |
TS3 | 20 | 65 | 65 | 55 | 55 | 1 | 1 | 10.9M16 | yes |
FE1 | 12 | 65 | 65 | 40 | 70 | 1 | 1.75 | 10.9M16 | no |
FE2 | 12 | 65 | 65 | 55 | 55 | 1 | 1 | 10.9M16 | no |
FE3 | 12 | 65 | 65 | 70 | 40 | 1 | 0.57 | 10.9M16 | no |
ES1 | 12 | 65 | 65 | 40 | 70 | 1 | 1.75 | 10.9M16 | yes |
ES2 | 12 | 65 | 65 | 55 | 55 | 1 | 1 | 10.9M16 | yes |
ES3 | 12 | 65 | 65 | 70 | 40 | 1 | 0.57 | 10.9M16 | yes |
FM1 | 12 | 50 | 80 | 55 | 55 | 1.6 | 1 | 10.9M16 | no |
FM2 | 12 | 65 | 65 | 55 | 55 | 1 | 1 | 10.9M16 | no |
FM3 | 12 | 80 | 50 | 55 | 55 | 0.63 | 1 | 10.9M16 | no |
MS1 | 12 | 50 | 80 | 55 | 55 | 1.6 | 1 | 10.9M16 | yes |
MS2 | 12 | 65 | 65 | 55 | 55 | 1 | 1 | 10.9M16 | yes |
MS3 | 12 | 80 | 50 | 55 | 55 | 0.63 | 1 | 10.9M16 | yes |
Model No. | Axial Force (kN) | Bending Moment (N·m) | Prying Force (kN) | Axial Stress (N·mm−2) | Bending Stress (N·mm−2) | Bending Stress ratio | Prying Force Ratio |
---|---|---|---|---|---|---|---|
FT1 | 70.45 | 157.01 | 20.45 | 350.56 | 390.65 | 0.527 | 0.225 |
FT2 | 66.17 | 82.77 | 16.17 | 329.25 | 205.93 | 0.385 | 0.196 |
FT3 | 65.14 | 50.48 | 15.14 | 324.13 | 125.61 | 0.279 | 0.189 |
TS1 | 54.82 | 87.07 | 4.82 | 272.81 | 216.64 | 0.443 | 0.081 |
TS2 | 52.87 | 41.54 | 2.87 | 263.10 | 103.35 | 0.282 | 0.052 |
TS3 | 52.02 | 25.79 | 2.02 | 258.83 | 64.18 | 0.199 | 0.037 |
FE1 | 72.84 | 164.67 | 22.84 | 362.46 | 409.72 | 0.531 | 0.239 |
FE2 | 70.45 | 157.01 | 20.45 | 350.56 | 390.65 | 0.527 | 0.225 |
FE3 | 71.80 | 161.88 | 21.80 | 357.30 | 402.76 | 0.530 | 0.233 |
ES1 | 53.25 | 70.80 | 3.25 | 264.98 | 176.16 | 0.399 | 0.058 |
ES2 | 54.82 | 87.07 | 4.82 | 272.81 | 216.64 | 0.443 | 0.081 |
ES3 | 58.99 | 105.95 | 8.99 | 293.56 | 263.60 | 0.473 | 0.132 |
FM1 | 61.90 | 126.85 | 11.90 | 308.02 | 315.60 | 0.506 | 0.161 |
FM2 | 70.45 | 157.01 | 20.45 | 350.56 | 390.65 | 0.527 | 0.225 |
FM3 | 84.57 | 201.14 | 34.57 | 420.81 | 500.45 | 0.543 | 0.290 |
MS1 | 52.11 | 74.78 | 2.11 | 259.29 | 186.06 | 0.418 | 0.039 |
MS2 | 54.82 | 87.07 | 4.82 | 272.81 | 216.64 | 0.443 | 0.081 |
MS3 | 59.11 | 100.62 | 9.11 | 294.16 | 250.34 | 0.460 | 0.134 |
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Chen, S.; Feng, B.; Wang, L.; Zhang, Y.; He, J. Effect of Stiffeners on Mechanical Behavior of T-Stubs Based on Experiment and Numerical Simulations. Buildings 2023, 13, 986. https://doi.org/10.3390/buildings13040986
Chen S, Feng B, Wang L, Zhang Y, He J. Effect of Stiffeners on Mechanical Behavior of T-Stubs Based on Experiment and Numerical Simulations. Buildings. 2023; 13(4):986. https://doi.org/10.3390/buildings13040986
Chicago/Turabian StyleChen, Shizhe, Bo Feng, Lu Wang, Ying Zhang, and Jianian He. 2023. "Effect of Stiffeners on Mechanical Behavior of T-Stubs Based on Experiment and Numerical Simulations" Buildings 13, no. 4: 986. https://doi.org/10.3390/buildings13040986