# Assessing Effectiveness of Shape Memory Alloys on the Response of Bolted T-Stub Connections Subjected to Cyclic Loading

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## Abstract

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## 1. Introduction

## 2. Finite Element Models

_{0}, M

_{max}, and $\theta $

_{max}defining the reference moment of the T-stub, maximum moment, and maximum rotation, respectively. As a result, the maximum error of numerical modeling was approximately 3.47% compared with the experimental results. Figure 4 illustrates the force–displacement curve and Von Mises distribution for the experimental specimen (G310-T19-B400). The stresses concentrated on the T-stub through the beam rotation, and the critical stress and local deformation were revealed in beam flanges and bolts, respectively. Nu and Ex are the abbreviation forms of the numerical and experimental values, respectively.

#### The Capability of SMA Material

## 3. Analyzing the Moment–Rotation Curve

_{max}, ED, and RD was revealed when there was an increasing trend in the value of L1. For instance, in the SP03 model, ED capacity was reduced compared with the SP02 model (reference model) by about 20%. Similar reductions for the SP06 and SP07 models were observed by a decrease in yield stress of the bolt. A leap in F

_{yt}, t

_{f}, or bolt pretension led to enhancing the ED, M

_{max}, and RD values. For example, the values of ED, M

_{max}, and RD had increments of 1.5%, 3%, and 6%, respectively, where t

_{f}was increased to 23 mm.

_{max}and ED values in the SP15 model could be seen when the T-stub section was equipped with SMA. While an increment trend in the values could be seen when the T-stub was equipped with triangular stiffeners, the maximum ED increased by approximately 55%.

#### Assessment of Response Curve Variables

_{max}showed a downward trend by the change in F

_{yt}and t

_{f}and also when the T-stub or bolt was equipped with SMA material.

_{max}showed an upward trend of 24%, although its lowest value had a decreasing trend of 11.5% compared with the SP02 model, where the number of beam bolts changed from six to two.

_{max}) because of the inherent elastic, resilient, and reversible properties of the SMA material. However, it improved the flexibility and ductility of the DST connection.

_{max}values increased. Stiffeners enhanced the stiffness of the DST connection, and the connection would sustain 5% drift with negligible strength degradation.

## 4. Failure Indexes

#### Failure Modes

_{frd}is the design flexural resistance of the T-stub flanges, B

_{Rd}is the design axial resistance of the single bolt, m is the distance between the bolt axis and the section corresponding to the flange-to-web fillet where the formation of a plastic hinge can be expected, and n is the distance between the bolt axis and the location of the prying force.

## 5. Effects of SMA on Stiffener, T-Stub, and Bolt Column

#### 5.1. Monitoring Behavioural Curve

_{max}) for SP26 were higher than those of SP02. This validated the usage of stiffeners, either steel or SMA materials. It consistently increased the initial stiffness (Ki) and ultimate strength (F

_{max}) of the connection (each by 113.52% and 15%), while the first yield point of the connection was delayed (higher post-yield or residual stiffness).

_{max}experienced a percentage decrease of 27.4% and 11.8%. This reduction showed that SP15 was more flexible and ductile when compared with the original specimen (SP02), whereas the T-stub section could rebound or return to its preliminary position due to the inherent SMA material specifications. These results conclusively supported the reasons for using SMA material.

_{max}when compared with SP14, from 19% to 30%. Equipping the connection with the SMA T-stub section and changing the number and thickness of stiffeners led to changes in the M

_{max}value. This increase was between 19.6% to 34.6% when compared with the SP15 model. As shown in Figure 13, for non-reference models where the column bolt or T-stub section was equipped with SMA property, a change was seen in the number or thickness of the stiffeners simultaneously. The ED capacity of the SP24 and SP25 models increased when compared with the SP14 and SP15 models.

#### 5.2. Equivalent Viscous Damping Ratio

#### 5.2.1. Ductility Capacity and Failure Modes

#### 5.2.2. Bolt Force, Strain Energy, and Frictional Energy

## 6. Conclusions

_{max}when compared with the reference model.

- Investigating the use of different types and thicknesses of stiffeners to determine their impacts on the connection’s performance.
- Examining the effects of different T-stub thickness, yield strength, and bolt preload to improve the ultimate moment and ED capacity of the connection.
- Evaluating the behavior and performance of the connection with different types of loading conditions, such as cyclic, static, and dynamic loading.
- Conducting more comprehensive tests, such as shake table testing, to evaluate the real-world performance of the connection in seismic situations.
- Performing a detailed cost–benefit analysis of using different materials and designs to optimize the practicality and cost-effectiveness of the connection.
- Investigating the behavior of the DST connection under different loading conditions such as cyclic loading, static loading, and dynamic loading.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**MRF under cyclic loading. (

**a**) The MRF deflection diagram of the MRF, (

**b**) moment diagram, (

**c**) exterior connection, and (

**d**) installed substructure in numerical modeling, reproduced with permission of Gerami et al. [43].

**Figure 5.**(

**a**) The arrangement of bolt holes on connected T-stub to beam. (

**b**) General schematic of different parameters in T-stub profile.

**Figure 7.**(

**a**) Strain energy-displacement curve. (

**b**). Force- displacement curve (

**c**) Von Mises distribution.

**Figure 9.**Stress concentration on SP18 model. (

**a**) General view, (

**b**) bolt, and (

**c**) T-stub under cyclic loading.

**Figure 14.**Illustration of total energy dissipation ${\mathrm{E}}_{\mathrm{D}}$ and maximum strain energy ${\mathrm{E}}_{\mathrm{So}}$ [119].

Components | Fy (MPa) | Fu (MPa) |
---|---|---|

Bolt | 912.7 | 976.1 |

T-stub | 399.61 | 435.85 |

Beam or column | 399.61 | 435.85 |

Sample Model | M_{0} (KN.m) | $\mathit{\theta}$_{max} (%)
| M_{max} (KN.m) | |
---|---|---|---|---|

G260-T15-B350 | PS1Ex | 257.62 | 0.087 | 451.22 |

PS1Nu | 251.88 | 0.09 | 442.48 | |

Error percent | 2.23 | 3.45 | 1.937 | |

G310-T15-B400 | PS2Ex | 197.42 | 0.098 | 402.4 |

PS2Nu | 195.23 | 0.1 | 399.61 | |

Error percent | 1.11 | 2.041 | 0.69 | |

G260-T19-B350 | PS3Ex | 411.11 | 0.037 | 454.36 |

PS3Nu | 408.34 | 0.038 | 435.85 | |

Error percent | 0.674 | 2.7 | 4.07 | |

G310-T19-B400 | PS4Ex | 329.86 | 0.13 | 448.68 |

PS4Nu | 324.52 | 0.125 | 443.17 | |

Error percent | 1.62 | 3.84 | 1.23 | |

G260-T21-B350 | PS5Ex | 458.08 | 0.023 | 502.84 |

PS5Nu | 452.34 | 0.024 | 495.51 | |

Error percent | 1.253 | 4.37 | 1.46 | |

G310-T21-B400 | PS6Ex | 411.78 | 0.0385 | 447.97 |

PS6Nu | 407.47 | 0.04 | 440.73 | |

Error percent | 1.05 | 3.9 | 1.62 |

Sample Model | t_{f}(mm) | F_{yt}(T-Stub) (KN) | Bolt Pretension (KN) | * No (Bolt Beam) | F_{yb}(Bolt) (KN) | L_{1}(mm) | L_{2}(mm) | Stiffener of T-Stub (mm) | Equipped SMA Material |
---|---|---|---|---|---|---|---|---|---|

SP01 | 19 | 538.5 | 165 | 6 | 912.7 | 50 | 150 | …. | …. |

SP02 | 19 | 538.5 | 165 | 6 | 912.7 | 100 | 100 | …. | …. |

SP03 | 19 | 538.5 | 165 | 6 | 912.7 | 150 | 50 | …. | …. |

SP04 | 19 | 538.5 | 165 | 2 | 912.7 | 100 | 100 | …. | …. |

SP05 | 19 | 538.5 | 165 | 4 | 912.7 | 100 | 100 | …. | …. |

SP06 | 19 | 538.5 | 165 | 6 | 950.7 | 100 | 100 | …. | …. |

SP07 | 19 | 538.5 | 165 | 6 | 874.7 | 100 | 100 | …. | …. |

SP08 | 19 | 620 | 165 | 6 | 912.7 | 100 | 100 | …. | …. |

SP09 | 19 | 458 | 165 | 6 | 912.7 | 100 | 100 | …. | …. |

SP10 | 23 | 538.5 | 165 | 6 | 912.7 | 100 | 100 | …. | …. |

SP11 | 15 | 538.5 | 165 | 6 | 912.7 | 100 | 100 | …. | …. |

SP12 | 19 | 538.5 | 190 | 6 | 912.7 | 100 | 100 | …. | …. |

SP13 | 19 | 538.5 | 140 | 6 | 912.7 | 100 | 100 | …. | …. |

SP14 | 19 | 538.5 | 165 | 6 | * | 100 | 100 | …. | Bolt column |

SP15 | 19 | * | 165 | 6 | 912.7 | 100 | 100 | …. | T-stub |

SP16 | 19 | 538.5 | 165 | 6 | 912.7 | 100 | 100 | 3PL169 × 15 | …. |

SP17 | 19 | 538.5 | 165 | 6 | 912.7 | 100 | 100 | 3PL169 × 25 | …. |

SP18 | 19 | 538.5 | 165 | 6 | 912.7 | 100 | 100 | PL169 × 15 | …. |

SP19 | 19 | 538.5 | 165 | 6 | 912.7 | 100 | 100 | PL169 × 25 | …. |

Specimen | SP01 | SP02 | SP03 | SP04 | SP05 | SP06 | SP07 | SP08 | SP09 | SP10 |
---|---|---|---|---|---|---|---|---|---|---|

M_{max}(KN.m) | 455.25 | 450.9 | 427.82 | 399.14 | 447.83 | 453.94 | 448.2 | 455.36 | 444.46 | 465.3 |

ED(KN.m) | 142.9 | 138 | 110.2 | 87.96 | 136.7 | 139.9 | 135.9 | 140.81 | 135.34 | 140 |

RD(mm) | 28.65 | 27.18 | 25.44 | 27.58 | 27 | 27.23 | 26.3 | 27.65 | 26.81 | 28.9 |

Specimen | SP11 | SP12 | SP13 | SP14 | SP15 | SP16 | SP17 | SP18 | SP19 | |

M_{max}(KN.m) | 440.46 | 452.56 | 449.17 | 417 | 399.73 | 541.81 | 557.5 | 523.47 | 545.2 | |

ED(KN.m) | 137 | 140.9 | 134.8 | 142.05 | 84.75 | 192.1 | 213.6 | 181.8 | 196.85 | |

RD(mm) | 26.83 | 28.18 | 26.58 | 25.92 | 18.73 | 27.38 | 28.25 | 26.33 | 27.84 |

Specimen | SP01 | SP02 | SP03 | SP04 | SP05 | SP06 | SP07 | SP08 | SP09 | SP10 |
---|---|---|---|---|---|---|---|---|---|---|

Ki (KN.m) | 21,709 | 24,072 | 24,845 | 21,148 | 19,860 | 19,851 | 20,354 | 21,056 | 19,638 | 19,758 |

Kr (KN.m) | 10,712 | 7130 | 3710 | 12,476 | 5918 | 5720 | 6729 | 5994 | 6410 | 5980 |

F_{max} (KN) | 737.62 | 777.43 | 781.47 | 688.17 | 772.12 | 775.76 | 774.37 | 785.11 | 766.31 | 776.38 |

Specimen | SP11 | SP12 | SP13 | SP14 | SP15 | SP16 | SP17 | SP18 | SP19 | |

Ki (KN.m) | 20,255 | 20,654 | 20,062 | 12,147 | 17,471 | 34,440 | 48,684 | 29,242 | 35,300 | |

Kr (KN.m) | 5917 | 3500 | 6037 | 4168 | 4417 | 4302 | 3747 | 5883 | 6589 | |

F_{max} (KN) | 776.65 | 780.27 | 774.43 | 719.13 | 689.2 | 934.16 | 961.2 | 902.54 | 940 |

Sample Model | $\overline{\mathbf{\sigma}}$ | ${\mathbf{\sigma}}_{\mathbf{m}}$ | PEEQ | PI | MI | Plasticity Index | TI | RI |
---|---|---|---|---|---|---|---|---|

SP01 | 694.2 | −567.499 | 1.09814 | −1.0538 | 1.2891 | 463.1547 | −0.8175 | 3.7428 |

SP02 | 694.2 | −497.691 | 0.511864 | −0.9242 | 1.2891 | 215.8853 | −0.7169 | 1.5003 |

SP03 | 667.68 | −470.156 | 0.341547 | −0.8730 | 1.2399 | 144.0518 | −0.7042 | 0.9821 |

SP04 | 694.2 | −419.191 | 0.241981 | −0.7784 | 1.2891 | 102.0586 | −0.6038 | 0.5986 |

SP05 | 694.2 | −468.181 | 0.566258 | −0.8694 | 1.2891 | 238.8266 | −0.6744 | 1.5572 |

SP06 | 694.2 | −497.293 | 0.511835 | −0.9235 | 1.2891 | 215.8730 | −0.7163 | 1.4990 |

SP07 | 676.48 | −484.384 | 0.508633 | −0.8995 | 1.2561 | 214.5225 | −0.7161 | 1.4889 |

SP08 | 694.2 | −509.196 | 0.470578 | −0.9456 | 1.2891 | 198.4723 | −0.7335 | 1.4140 |

SP09 | 694.2 | −488.235 | 0.544232 | −0.9066 | 1.2891 | 229.5369 | −0.7033 | 1.5629 |

SP10 | 694.2 | −499.25 | 0.51937 | −0.9271 | 1.2891 | 219.0510 | −0.7192 | 1.5274 |

SP11 | 694.2 | −493.445 | 0.492601 | −0.9163 | 1.2891 | 207.7608 | −0.7108 | 1.4307 |

SP12 | 694.2 | −498.05 | 0.527099 | −0.9249 | 1.2891 | 222.3108 | −0.7174 | 1.5462 |

SP13 | 646.8 | −469.976 | 0.486086 | −0.8727 | 1.2011 | 205.0130 | −0.7266 | 1.4457 |

SP14 | 694.2 | −494.392 | 0.472123 | −0.9181 | 1.2891 | 199.124 | −0.7122 | 1.374 |

SP15 | 1309.81 | −347.098 | 0.025471 | −0.6445 | 2.4323 | 10.7427 | −0.265 | 0.03790 |

SP16 | 596.152 | −386.19 | 0.07693 | −0.7171 | 1.1071 | 32.4463 | −0.6478 | 0.2033 |

SP17 | 553.96 | −357.88 | 0.030672 | −0.6646 | 1.0287 | 12.9363 | −0.646 | 0.0808 |

SP18 | 665.99 | −433.944 | 0.170127 | −0.8058 | 1.2367 | 71.7532 | −0.6516 | 0.4521 |

SP19 | 614.55 | −420.317 | 0.101485 | −0.7805 | 1.1412 | 42.8026 | −0.6839 | 0.2831 |

Specimen | SP01 | SP02 | SP03 | SP04 | SP05 | SP06 | SP07 | SP08 | SP09 | SP10 |
---|---|---|---|---|---|---|---|---|---|---|

Failure mode | Mode 3 | Mode 3 | Mode 3 | Mode 2 | Mode 3 | Mode 3 | N/A | Mode 3 | Mode 3 | Mode 3 |

Specimen | SP11 | SP12 | SP13 | SP14 | SP15 | SP16 | SP17 | SP18 | SP19 | |

Failure mode | Mode 2 | Mode 3 | N/A | N/A | N/A | Mode 3 | Mode 3 | Mode 3 | Mode 3 |

Sample Model | t_{f}(mm) | No (Bolt Beam) | No (Bolt Column) | L_{1} (mm) | Thickness of Stiffener (mm) | Number of Stiffener | Type of Stiffener | Equipped SMA Material |
---|---|---|---|---|---|---|---|---|

SP20 | 19 | 6 | 4 | 100 | 15 | 3 | B | Stiffener |

SP21 | 19 | 6 | 4 | 100 | 15 | 3 | B | T-stub |

SP22 | 19 | 6 | 4 | 100 | 15 | 3 | B | Bolt column |

SP23 | 19 | 6 | 4 | 100 | 15 | 3 | A | Stiffener |

SP24 | 19 | 6 | 4 | 100 | 15 | 3 | A | T-stub |

SP25 | 19 | 6 | 4 | 100 | 15 | 3 | A | Bolt column |

SP26 | 19 | 6 | 4 | 100 | 25 | 3 | B | Stiffener |

SP27 | 19 | 6 | 4 | 100 | 25 | 3 | B | T-stub |

SP28 | 19 | 6 | 4 | 100 | 25 | 3 | B | Bolt column |

SP29 | 19 | 6 | 4 | 100 | 25 | 3 | A | Stiffener |

SP30 | 19 | 6 | 4 | 100 | 25 | 3 | A | T-stub |

SP31 | 19 | 6 | 4 | 100 | 25 | 3 | A | Bolt column |

SP32 | 19 | 6 | 4 | 100 | 15 | 1 | B | Stiffener |

SP33 | 19 | 6 | 4 | 100 | 15 | 1 | B | T-stub |

SP34 | 19 | 6 | 4 | 100 | 15 | 1 | B | Bolt column |

SP35 | 19 | 6 | 4 | 100 | 15 | 1 | A | Stiffener |

SP36 | 19 | 6 | 4 | 100 | 15 | 1 | A | T-stub |

SP37 | 19 | 6 | 4 | 100 | 15 | 1 | A | Bolt column |

SP38 | 19 | 6 | 4 | 100 | 25 | 1 | B | Stiffener |

SP39 | 19 | 6 | 4 | 100 | 25 | 1 | B | T-stub |

SP40 | 19 | 6 | 4 | 100 | 25 | 1 | B | Bolt column |

SP41 | 19 | 6 | 4 | 100 | 25 | 1 | A | Stiffener |

SP42 | 19 | 6 | 4 | 100 | 25 | 1 | A | T-stub |

SP43 | 19 | 6 | 4 | 100 | 25 | 1 | A | Bolt column |

Specimen | SP20 | SP21 | SP22 | SP23 | SP24 | SP25 | SP26 | SP27 | SP28 | SP29 | SP30 | SP31 |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Ki (KN.m) | 52,452 | 40,758 | 40,550 | 53,813 | 50,839 | 46,142 | 51,400 | 49,365 | 43417 | 637,812 | 62,677 | 33,782 |

Kr (KN.m) | 6024.2 | 4966.7 | 6976.2 | 2995.2 | 2860 | 5901.1 | 6049 | 2787.5 | 6061.4 | 2888.4 | 2964.7 | 6884.8 |

F_{max} (KN) | 903.91 | 859.88 | 893.02 | 905.02 | 873.7 | 884.59 | 898.64 | 874 | 898.98 | 936.24 | 927.67 | 933.52 |

Specimen | SP32 | SP33 | SP34 | SP35 | SP36 | SP37 | SP38 | SP39 | SP40 | SP41 | SP42 | SP43 |

Ki (KN.m) | 48,168 | 45,036 | 39,201 | 48,720 | 43,267 | 41,326 | 49,444 | 44,392 | 39,722 | 55,153 | 55,666 | 48,044 |

Kr (KN.m) | 2613.2 | 3571 | 2794.3 | 3436.8 | 3510.3 | 2870 | 2998.6 | 3402 | 3082.3 | 2572 | 2989.2 | 2778.7 |

F_{max} (KN) | 875.46 | 826.82 | 850.24 | 869.38 | 830.87 | 856.18 | 875.46 | 824.27 | 854.91 | 912.73 | 880.57 | 916.7 |

Specimen | SP20 | SP21 | SP22 | SP23 | SP24 | SP25 | SP26 | SP27 | SP28 | SP29 | SP30 | SP31 |
---|---|---|---|---|---|---|---|---|---|---|---|---|

${\theta}_{y}$ (rad) | 0.012 | 0.013 | 0.012 | 0.011 | 0.013 | 0.011 | 0.013 | 0.012 | 0.01 | 0.013 | 0.011 | 0.011 |

${\theta}_{u}$ (rad) | 0.0349 | 0.0349 | 0.0348 | 0.0345 | 0.0349 | 0.0344 | 0.0349 | 0.0349 | 0.0349 | 0.0348 | 0.0349 | 0.0349 |

M_{y} (KN.m) | 385.92 | 373.61 | 382.11 | 385.37 | 376.4 | 376.19 | 382.45 | 375.51 | 384.48 | 399.42 | 392.52 | 395.94 |

$\mu =\frac{{\theta}_{u}}{{\theta}_{y}}$ | 2.99 | 2.68 | 2.88 | 3.11 | 2.67 | 3.17 | 2.68 | 2.78 | 3.33 | 2.66 | 3.04 | 3.24 |

Failure mode | 3 | 3 | N/A | 3 | 3 | N/A | 3 | 3 | N/A | 3 | 3 | N/A |

Specimen | SP32 | SP33 | SP34 | SP35 | SP36 | SP37 | SP38 | SP39 | SP40 | SP41 | SP42 | SP43 |

${\theta}_{y}$ (rad) | 0.01 | 0.01 | 0.012 | 0.01 | 0.009 | 0.013 | 0.011 | 0.008 | 0.012 | 0.011 | 0.009 | 0.012 |

${\theta}_{u}$ (rad) | 0.0348 | 0.0345 | 0.0341 | 0.0334 | 0.0347 | 0.0347 | 0.0348 | 0.0347 | 0.0346 | 0.0348 | 0.0347 | 0.0346 |

M_{y} (KN.m) | 377.55 | 359.25 | 369.42 | 375.06 | 361.01 | 372 | 377.55 | 358.14 | 371.45 | 391.08 | 382.6 | 387 |

$\mu =\frac{{\theta}_{u}}{{\theta}_{y}}$ | 3.32 | 3.84 | 2.81 | 3.25 | 3.61 | 2.68 | 3.11 | 3.97 | 2.85 | 3.07 | 3.82 | 2.74 |

Failure mode | 3 | 3 | N/A | 3 | 3 | N/A | 3 | 3 | N/A | 3 | 3 | N/A |

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## Share and Cite

**MDPI and ACS Style**

Torabipour, A.; Asghari, N.; Haghighi, H.; Yaghoubi, S.; Urgessa, G.
Assessing Effectiveness of Shape Memory Alloys on the Response of Bolted T-Stub Connections Subjected to Cyclic Loading. *CivilEng* **2023**, *4*, 105-133.
https://doi.org/10.3390/civileng4010008

**AMA Style**

Torabipour A, Asghari N, Haghighi H, Yaghoubi S, Urgessa G.
Assessing Effectiveness of Shape Memory Alloys on the Response of Bolted T-Stub Connections Subjected to Cyclic Loading. *CivilEng*. 2023; 4(1):105-133.
https://doi.org/10.3390/civileng4010008

**Chicago/Turabian Style**

Torabipour, Ahmadreza, Nima Asghari, Homa Haghighi, Shaghayegh Yaghoubi, and Girum Urgessa.
2023. "Assessing Effectiveness of Shape Memory Alloys on the Response of Bolted T-Stub Connections Subjected to Cyclic Loading" *CivilEng* 4, no. 1: 105-133.
https://doi.org/10.3390/civileng4010008