Restoring Force Model for Composite-Shear Wall with Concealed Bracings in Steel-Tube Frame
Abstract
:1. Introduction
2. Composite-Shear Wall with Concealed Bracings in Steel-Tube Frame
3. Numerical Simulation of the Seismic Performances of Test Pieces
3.1. Numerical Simulations and Validation of Seismic Performances of Test Pieces
- (1)
- Computation model
- (2)
- Loading scheme
- (3)
- Constitutive relations and yield criteria
- (4)
- Finite Element Simulation Boundary Condition Setting
3.2. Analysis of the Computation Results and Validation
- (1)
- Failure morphology of the test pieces:
- (2)
- Hysteretic curve
- (3)
- Skeleton curve:
- (4)
- Effects of varying parameters on seismic performance of test pieces:
4. Establishment and Validation of the Restoring Force Model
4.1. Construction of the Skeleton Curve
4.2. Stiffness Degradation Curve
4.3. Establishment of the Restoring Force Model
- The loading curve is traced along the O-A-O-A1 path. The test piece is still in the elastic region, and A and A1 are the positive and negative yield points of the test piece, respectively.
- The loading and unloading curves are traced along the A-B-1-B1-2-B path. The test piece is in the elastoplastic region before reaching the ultimate load point. The coordinates of B and B1 are regarded as 0.5 times the coordinates of the peak load point in this segment. Moreover, 1 and 2 are the forward and reverse zero-loading points, respectively. Their ordinates are calculated from the unloading stiffness fitting curve.
- The loading and unloading curves are along the path B-C-3-C1-4-C. Within this segment, the test piece transitions from the hardening to the peak stage. C and C1 are the forward and reverse peak-loading points, respectively. Furthermore, 3 and 4 are the forward and reverse zero-loading points, respectively. Their ordinates are calculated from the unloading stiffness fitting curve.
- The loading and unloading curves are along the path C-D-5-D1-6-D. Within this segment, the bearing capacity of the test piece decreases rapidly, which indicates the failure stage. The coordinates of D and D1 are considered to be equal to 0.8 times those of the peak-loading points. Further, 5 and 6 are the forward and reverse zero-loading points, respectively. Their ordinates are calculated from the unloading stiffness fitting curve.
- The loading and unloading curves are along the path D-E-7-E1-8-E. The bearing capacity of the test piece reaches the ultimate limit. E and E1 are the respective points at which the forward and reverse loads decrease suddenly. Moreover, 7 and 8 are the forward and reverse zero-unloading points, respectively. Their ordinates are calculated from the unloading stiffness fitting curve.
- The loading and unloading curves are along the E-F-9-F1-10-F path. During this stage, the bearing capacity of the test piece remains constant as a function of displacement. The abscissas of F and F1 are regarded to be equal to 0.8 times that of the peak load point. Further, 9 and 10 are the forward and reverse zero-loading points, respectively. Their ordinates are calculated from the unloading stiffness fitting curve.
- The loading and unloading curves are along the path F-G-11-G1-12-G. The test piece has now undergone failure. G and G1 are the failure loading points, and 11 and 12 are the forward and reverse zero-loading points, respectively. Their ordinates are calculated from the unloading stiffness fitting curve.
- Points B, D, F, G, B1, D1, F1, and G1 shown in the figure represent sudden decreases in the load. The coordinates of these points are determined based on the rules listed above.
4.4. Validation of Restoring Force Model
5. Conclusions
- In previous studies [34,35], low-cyclic, reversed loading tests were performed on six 1/2 scale composite-shear wall test pieces with concealed bracings and steel tube frames. Based on these results, the study performed low cyclic reversed loading simulations of 28 virtual test pieces in ABAQUS. The stress contour, failure morphology, hysteretic curve, and skeleton curve of each test piece were obtained from numerical simulations. By performing regression analysis on the stiffness degradation data, the study obtained the stiffness degradation function, and then developed a quadric-linear restoring force model for a composite shear wall with a steel tube frame and concealed bracings.
- The study analyzed the effects of different controlling parameters on the seismic performance of the structure by modifying the wallboard thickness, strength of the recycled concrete, and axial compression ratio of the composite shear wall model with concealed bracings and a steel tube frame. The results indicated that the bearing capacity of the composite shear wall decreased as a function of the axial compression ratio. However, increasing the wallboard thickness and the strength of the recycled concrete leads to increased bearing capacity and lateral stiffness of the composite-shear wall.
- The composite-shear wall with a steel-tube frame and concealed bracings exhibited excellent seismic performance. This structure can be used as an earthquake-resistant component to construct buildings with high-seismic intensity in rural areas.
Author Contributions
Funding
Informed Consent Statement
Conflicts of Interest
References
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Test Piece No. | Type of Concealed Bracing | Thickness of Wallboard | Axial Compression Ratio | Spacing between Reinforcement Bars | Reinforcement Ratio of the Distribution Bars |
---|---|---|---|---|---|
MX-1 | Concealed steel bar bracing | 60 mm | 0.39 | 100 mm | 0.33% |
MX-2 | Concealed steel plate bracing | 60 mm | 0.39 | 100 mm | 0.33% |
MX-3 | Concealed steel bar bracing | 60 mm | 0.39 | 150 mm | 0.22% |
MX-4 | Concealed steel plate bracing | 60 mm | 0.39 | 150 mm | 0.22% |
MX-5 | Concealed steel bar bracing | 60 mm | 0.39 | 200 mm | 0.16% |
MX-6 | Concealed steel plate bracing | 60 mm | 0.39 | 200 mm | 0.16% |
Strength Grade | Amount of the Materials Used in the Recycled Concrete (kg m−3) | ||||||
---|---|---|---|---|---|---|---|
Cement | Fly Ash | Mineral Powder | Sand | Recycled Aggregate | Water | Water Reducer | |
C40 | 369 | 79 | 79 | 841 | 841 | 181 | 3.5 |
Type of Steel | Plate Thickness (Diameter)/mm | Yield Strength fy/MPa | Tensile Strength fu/MPa | Elongation δ/% | Elastic Modulus E/MPa |
---|---|---|---|---|---|
Distribution bar/Concealed steel bar bracing | 5 | 680 | 786 | 5.5 | 2.09 × 105 |
Frame steel plate/Connected steel lathings/Concealed steel plate bracing | 4 | 309 | 467 | 25.27 | 2.11 × 105 |
Square steel tube | 4 | 375 | 477 | 23.23 | 2.18 × 105 |
Test Piece No. | Type of Concealed Bracing | Strength of Recycled Concrete | Thickness of Wallboard (mm) | Axial Compression Ratio | Spacing between the Distribution Bars (mm) |
---|---|---|---|---|---|
MX-1-1 | Concealed steel bar bracing | C40 | 60 | 0.38 | 100 |
MX-1-2 | Concealed steel bar bracing | C30 | 60 | 0.38 | 100 |
MX-1-3 | Concealed steel bar bracing | C25 | 60 | 0.38 | 100 |
MX-1-4 | Concealed steel bar bracing | C40 | 50 | 0.38 | 100 |
MX-1-5 | Concealed steel bar bracing | C40 | 40 | 0.38 | 100 |
MX-1-6 | Concealed steel bar bracing | C40 | 60 | 0.3 | 100 |
MX-1-7 | Concealed steel bar bracing | C40 | 60 | 0.5 | 100 |
MX-2-1 | Concealed steel plate bracing | C40 | 60 | 0.38 | 100 |
MX-2-2 | Concealed steel plate bracing | C30 | 60 | 0.38 | 100 |
MX-2-3 | Concealed steel plate bracing | C25 | 60 | 0.38 | 100 |
MX-2-4 | Concealed steel plate bracing | C40 | 50 | 0.38 | 100 |
MX-2-5 | Concealed steel plate bracing | C40 | 40 | 0.38 | 100 |
MX-2-6 | Concealed steel plate bracing | C40 | 60 | 0.3 | 100 |
MX-2-7 | Concealed steel plate bracing | C40 | 60 | 0.5 | 100 |
MX-3-1 | Concealed steel bar bracing | C40 | 60 | 0.38 | 150 |
MX-3-2 | Concealed steel bar bracing | C30 | 60 | 0.38 | 150 |
MX-3-3 | Concealed steel bar bracing | C25 | 60 | 0.38 | 150 |
MX-3-4 | Concealed steel bar bracing | C40 | 50 | 0.38 | 150 |
MX-3-5 | Concealed steel bar bracing | C40 | 40 | 0.38 | 150 |
MX-3-6 | Concealed steel bar bracing | C40 | 60 | 0.3 | 150 |
MX-3-7 | Concealed steel bar bracing | C40 | 60 | 0.5 | 150 |
MX-4-1 | Concealed steel plate bracing | C40 | 60 | 0.38 | 150 |
MX-4-2 | Concealed steel plate bracing | C30 | 60 | 0.38 | 150 |
MX-4-3 | Concealed steel plate bracing | C25 | 60 | 0.38 | 150 |
MX-4-4 | Concealed steel plate bracing | C40 | 50 | 0.38 | 150 |
MX-4-5 | Concealed steel plate bracing | C40 | 40 | 0.38 | 150 |
MX-4-6 | Concealed steel plate bracing | C40 | 60 | 0.3 | 150 |
MX-4-7 | Concealed steel plate bracing | C40 | 60 | 0.5 | 150 |
Young’s Modulus | Poisson’s Ratio | Dilation Angle | Eccentricity | fbo/fco | k | Viscosity Parameter |
---|---|---|---|---|---|---|
34,500 | 0.2 | 30° | 0.1 | 1.16 | 0.667 | 0.009 |
Assembly Number | Peak Displacement (mm) | Peak Load (kN) |
---|---|---|
MX-1 | 14.56 | 1166.75 |
MX-2 | 13.78 | 1076.78 |
MX-3 | 14.22 | 1079.90 |
MX-4 | 12.18 | 1016.27 |
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Wei, D.; Suizi, J. Restoring Force Model for Composite-Shear Wall with Concealed Bracings in Steel-Tube Frame. Buildings 2022, 12, 1315. https://doi.org/10.3390/buildings12091315
Wei D, Suizi J. Restoring Force Model for Composite-Shear Wall with Concealed Bracings in Steel-Tube Frame. Buildings. 2022; 12(9):1315. https://doi.org/10.3390/buildings12091315
Chicago/Turabian StyleWei, Ding, and Jia Suizi. 2022. "Restoring Force Model for Composite-Shear Wall with Concealed Bracings in Steel-Tube Frame" Buildings 12, no. 9: 1315. https://doi.org/10.3390/buildings12091315