# INSPECT-SPSW: INelastic Seismic Performance Evaluation Computational Tool for Steel Plate Shear Wall Modeling in OpenSees

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## Abstract

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## 1. Introduction, Significance, and Limitations

_{y}= 30 ksi) and ASTM A572 Gr. 50 (F

_{y}= 50 ksi) materials were chosen for infill plates and boundary elements (VBEs and HBEs). SPSW-ID and SPSW-CD denote the resulting models of each approach, whereas the ID and CD abbreviations refer to, in order, the indirect design and the capacity design methods. A displacement-controlled pushover analysis was performed for both designs. The maximum chosen lateral drift was 4%, corresponding to a 14.4 in. for lateral roof displacement. The theoretical base shear was more than the obtained analytical estimation, with only 2.3% in the case of SPSW-CD, while the SPSW-ID case reached 13%. In addition, a cyclic displacement loading (3% as the maximum drift with 0.5% increments) was applied for both designs. As a result, the SPSW-CD model exhibits a beam rotation range of −0.03 to +0.0075 radians, while the SPSW-ID model’s rotation range was from 0.0 to 0.06 radians. Considerably, the special moment-resisting frame’s (SMRF) beam rotation demands 0.03 radians. Based on these results, the total (elastic and plastic) HBE rotations exceeded 0.03 radians when the model achieved 3% lateral drift in the cyclic loading program. Furthermore, the overall plastic strength was lower than the estimated values of code equations. The practical results of adding plastic hinges along beam spans were significant accumulated plastic incremental rotations and partial yielding on the infill plates.

_{y}) and was accompanied by plate tearing till reaching 1.8% axial strain (i.e., 10.7 δ

_{y}). Then, the flange fibers for frame boundary elements were modeled for a 0.04-radian rotation capping point and gradual strength reduction until 0.10-radians.

_{d}), and structural system overstrength factor (Ω

_{o})]. The archetypes were named based on the following convention: SW520GK = steel walls; the number of stories equal to 5; panel aspect ratio 2.0; high seismic weights (intensive gravity forces on the leaning column); designed as κ

_{balanced}(the second approach). Additionally, V

_{d}, W

_{P-Δ}, W

_{SPSW,}and W

_{total}refer to the design base shear, weights assigned to the P-Delta leaning column, weights on the SPSW elements, and the total seismic weights for base shear calculations (= W

_{SPSW}+ W

_{P-Δ}), respectively. All reference models adopted the capacity design methods corresponding to the recommendations of AISC seismic provisions [25] in designing boundary elements to avoid the formation of in-span hinges, as recommended in one of their previous studies [27]. The numerical model used is shown in Figure 5. Dual strips with an axial hinge for each strip were adopted for infill plates. Otherwise, concentrated fiber flexural hinges at the edges of frame elements were modeled to simulate frame element degradation. To include P-Delta effects, “gravity-leaning-column” elements are modeled near the SPSW model. These elements have no contribution to the lateral resistance, so their cross-sectional area properties were multiplied by a tributary value of 100 (an assumption of the number of columns for the gravity system).

#### 1.1. Research Significance

#### 1.2. INSPECT-SPSW Limitations and Potential Future Extensions

## 2. Software Description

## 3. Results and Illustrative Examples

#### 3.1. Verification with a Numerical Study

^{−5}). The purpose of this small value is to simulate zero-strength during compressive fields first, then a reset to the compression onset point before tension reloading, and to reload in tension till the maximum plastic strain is reached in earlier cycles. Based on a side comparison for all nonlinear modeling material options in OpenSees [51] on a simple cantilever structure, it was decided to model all VBE and HBE segments as beamWithHinges (BWH) with plastic Hinge length (Lp) set to 0.9 of the elements’ section depth at Beam-column connections and one-tenth of that value at in-span connections (with infill strips elements). Plastic zones were assigned to a very concentrated fiber section. The cross-sections were vertically divided into 65 fibers (16 fibers on both the flanges and 33 on the web), as all fibers have similar tributary areas. Assessment of the models’ collapse potential through monotonic pushover curves included estimating system overstrength (Ω

_{o}) and period-based ductility (μ

_{T}). These parameters are defined as follows:

_{max}and V

_{d}represent the ultimate and design base shear strength, respectively. While the δ

_{u}and δ

_{y, eff}are the maximum and effective yield top displacements.

#### 3.2. Modeling of Experimental Specimens

#### 3.2.1. Single Story SPSW: Vian and Bruneau Specimen

_{y}) to 9 ε

_{y}, then a plateau until 10.7 ε

_{y}, and finally, a direct failure to reflect the experimental cracks. The infill hinges’ compression behavior was modeled as elastic-perfectly plastic with relatively small stress (0.25 of the tensile yielding stress) to add the small contribution of infill plates in compression resistance. The nonlinear behavior for fibers in the flexural hinges of beams was assumed to be tension-compression symmetric with 2% strain hardening from ε

_{y}to 0.02 strain. Its deterioration stage was defined from 0.022 to 0.036 strain values accompanied by a 40% strength reduction from the ultimate stress, and then it plateaus. The numerical model produced similar behavior to the experiment, as shown in Figure 9. The peak base shear equaled 2135 kN and occurred at 2.6% inter-story drift. Gradually, infill strips started to reach failure strain one by one, and the strength of flexural hinges in beams began to degrade, causing a 20% reduction from the ultimate base shear at 3.2% drift.

#### 3.2.2. Two-Story SPSW: Qu et al. Specimen

_{y}to 0.018 strain, and a gradual deterioration to a zero stress for 0.025 strain accompanied with little compression strength (0.2 of yielding stress). Two models were defined for the frame elements’ material nonlinearity with 2% strain hardening from the yield strain (ε

_{y}) to a strain value of 0.028 and a failure strain of 0.073. The first model did not experience strength degradation until it reached failure strain. The second model assumed a gradual deterioration in material strength that reaches up to 40% of peak stress at 0.046 strain. The hinges of intermediate beam RBSs were assumed to follow the deteriorated behavior, whereas the non-deteriorated model was used to identify plastic hinges of columns and other beams. The numerical results were almost similar to the experimental program. The modeled system achieved 4194 kN as a maximum base shear at 2.9% first story drift. Directly after the peak, the first story strips began to fail, and the strength of intermediate beam RBSs decreased from 3.7% drift. The collapse was determined at a 5.2% amplitude drift, and the final base shear was 45% less than the capping point with failures in some of the second-story panel strips. Figure 10 shows the resulting pushover curve compared to the experiment.

#### 3.2.3. Three-Story SPSW: Choi and Park Specimen

_{y}= 240 MPa) was used for infill plates, while frame members were fabricated from SM490 steel (Korean Standard, F

_{y}= 330 MPa). Deliberately, columns were designed with a minimal width-thickness ratio to prevent premature local buckling, achieve more significant deformations, and minimize the contribution of the moment-resisting frame action of the boundary elements in the global resistance (to determine the connection methods’ efficiency). H-shaped steel sections H 150 × 150 × 22 × 22, H 150 × 100 × 12 × 20, and H 250 × 150 × 12 × 20 were assigned to columns, intermediate and top beams, respectively. The flange and web plate elements of built-up cross-sections had met the width-thickness limits from the AISC seismic provisions [25]. The single top force cyclic program results showed that the peak occurred at 3.3% top story drift (110.5 mm top displacement) with 1961 kN maximum base shear. Before reaching the ultimate base shear, a beginning of WT in all plates was observed. However, their effect on the overall resistance propagates at a 4.4% top story drift condition until the maximum value of 5.2% (176.5 mm top displacement) with extreme infill cracks at 37% reported base shear degradation. In the numerical model, all axial hinges were assumed to have a strain hardening of 2% beyond yield. This strain-hardening continued till the peak stress reached 0.02 strain in the tension behavior and a small contribution in compression strength (5% of the tensile yielding stress). After the capping point, intermediate story strips were assumed to lose strength, gradually reaching zero stress at 0.042 strain. Conversely, infill strips’ strength was modeled to be steady in other stories. Flexural zero-length plastic hinges were added with a distance, d/2, from frame connection joints at the ends of all beam and column-base connections, using the zeroLengthSection nonlinear element command. This distance was chosen according to several performance-based guidelines (e.g., ASCE-SEI 41-17 [58]). The nonlinear behavior of frame element material involves tension-compression symmetry and no deterioration after 0.03 strain capping point. This model achieved 1971 kN maximum base shear strength for 129 mm top displacement and maximum deformation of 173 mm with 37% base shear reduction. Figure 11 highlights the similarity in the behavior among experimental works and the assumed numerical model regarding the cyclic pushover curve.

#### 3.2.4. Four-Story SPSW: Driver et al. Specimen

_{y}. Except for the first story, all infill elements would not lose this stress. This model achieved 3057 kN maximum base shear at 2.0% first story drift and 15% strength reduction at 4.1% drift, matching the experimental pushover profile, see Figure 12.

## 4. Discussion and Impact

_{T}, boundary elements FBE, or a combined case), and the status of each structural element’s strength through-loading cycles can be obtained directly. These graphical components would allow designers to assess the inelastic behavior of the whole model, understand the causes of numerical failure, and take enhancement actions more efficiently. A variety of users can take advantage of this design by verifying or mapping experimental results to numerical models, enhancing existing designs, or measuring the effect of a significant element on the overall system’s stability and performance. For example, in two arbitrary models shown in Figure 13 and Figure 14, the strength deterioration resulted from the second story W

_{T}in the first model

_{,}while the second model exposed FBE in the intermediate beam. The animation viewer indicated the status of each element’s resistance with a specific color and each element’s properties over time (force-deformation for axial hinges and moment-rotation for flexural hinges).

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**The strip model by Thorburn et al. [20].

**Figure 2.**The modified strip model by Shishkin et al. [26].

**Figure 3.**Frame-joint arrangement for moment-resisting connections in the modified strip model by Shishkin et al. [26].

**Figure 5.**Nonlinear model for collapse simulation [27]; example structural model of a three-story archetype.

**Figure 8.**Comparison of monotonic pushover analysis curves published by R. Purba and M. Bruneau [30] and solved by INSPECT-SPSW for the SW320 model.

**Figure 9.**Comparison between numerical and experimental pushover curves for the single-story specimen by Vian and Bruneau [54].

**Figure 10.**Comparison between numerical and experimental pushover curves for the two-story specimen by Qu et al. [55].

**Figure 11.**Comparison between numerical and experimental pushover curves for the three-story specimen by Choi and Park [56].

**Figure 12.**Comparison between numerical and experimental pushover curves for the four-story specimen by Driver et al. [57].

**Figure 13.**Visualizing the failure mechanism in INSPECT-SPSW; (

**a**) web tearing failure; (

**b**) frame flexural deterioration failure.

**Figure 14.**Representing elements’ local behavior; (

**a**) axial force-deformation relation for an axial hinge in a monotonic pushover; (

**b**) flexural moment-section rotation relation for a flexural plastic hinge through cyclic pushover.

User Control | Main Functions |
---|---|

Model | creates general model parameters: number of stories, plate width, floor heights, base fixation model, number of plate strips, and the method to calculate tension stress angle. |

Materials | defines nonlinearity parameters: materials stress-strain curves and frame element models. |

Cross-section selections | selects the used W-shape sections from the entire database of sections. |

Cross-section properties | defines frame cross-section properties for frame elements and infill plates. |

Drawing | assigns selected sections and frame elements model for each story infill plate and boundary elements. |

Gravity load | defines gravity loads for SPSW and the leaning column for each story. |

Modal analysis | Sets the number of mode shapes, runs a TCL script for modal analysis, and shows the modal analysis results regarding Eigenvalue, period time, frequency modal mass participation factor, and the deformed mode of all solved modes. |

Spectral response | Sets design spectral response acceleration parameter at short periods and 1-s period (S_{DS}) and (S_{D1}), response modification coefficient (R-factor), Importance factor (I), and system overstrength (Ω_{o}) for calculating spectral response, natural period (T), seismic response coefficient (${C}_{s})$ and design base shear (${V}_{d})$. |

Lateral loads | identifies the type of lateral load (monotonic pushover, cyclic loading, or time history dynamic analysis) and sets the sub-parameters, such as maximum drift displacement control, damping coefficients, or cycling loading record. |

Lateral analysis | triggers an event to generate a TCL script for lateral analysis, notifying the user if the analysis process is successful or not, providing the reason for failure, and reading analysis output files to restore it within the objects scheme. |

Final results | All analysis outputs include a pushover curve, node deformations, support reactions, normal, shear forces and bending moment diagrams, connections rotations, and infill strips stress-strain curves. |

**Table 2.**Results of cyclic pushover analyses for some SPSW experimental tests and solved numerically by INSPECT-SPSW.

Specimen | Scale | Measured Drift | Results | ${\delta}_{y}$ (%) | ${V}_{max}$ (kN) | ${\delta}_{u}$ (%) | $\Delta V$ (%) |
---|---|---|---|---|---|---|---|

TS1 | Full scale (1/1) | Inter-story drift | experimental | 2.5 | 2115 | 3.0 | 18 |

numerical | 2.6 | 2135 | 3.2 | 20 | |||

TS2 | Full scale (1/1) | first story drift | experimental | 3.0 | 4245 | 5.2 | 44 |

numerical | 2.9 | 4194 | 5.2 | 45 | |||

TS3 | one-third scale (1/3) | top story drift | experimental | 3.3 | 1961 | 5.2 | 37 |

numerical | 3.1 | 1971 | 5.0 | 37 | |||

TS4 | half-scale (1/2) | first story drift | experimental | 2.2 | 3135 | 4.0 | 15 |

numerical | 2.0 | 3057 | 4.1 | 15 |

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**MDPI and ACS Style**

AlHamaydeh, M.; Maky, A.M.; Elkafrawy, M.
INSPECT-SPSW: INelastic Seismic Performance Evaluation Computational Tool for Steel Plate Shear Wall Modeling in OpenSees. *Buildings* **2023**, *13*, 1078.
https://doi.org/10.3390/buildings13041078

**AMA Style**

AlHamaydeh M, Maky AM, Elkafrawy M.
INSPECT-SPSW: INelastic Seismic Performance Evaluation Computational Tool for Steel Plate Shear Wall Modeling in OpenSees. *Buildings*. 2023; 13(4):1078.
https://doi.org/10.3390/buildings13041078

**Chicago/Turabian Style**

AlHamaydeh, Mohammad, Ahmed Mansour Maky, and Mohamed Elkafrawy.
2023. "INSPECT-SPSW: INelastic Seismic Performance Evaluation Computational Tool for Steel Plate Shear Wall Modeling in OpenSees" *Buildings* 13, no. 4: 1078.
https://doi.org/10.3390/buildings13041078