Member Discrete Element Method for Static and Dynamic Responses Analysis of Steel Frames with Semi-Rigid Joints
Abstract
:Featured Application
Abstract
1. Introduction
2. Member Discrete Element Method (MDEM)
2.1. Particle Motion Equations and Internal Forces
2.1.1. Particle Motion Equations
2.1.2. Particle Internal Forces
2.2. MDEM for Modelling Geometric Nonlinearity
2.3. MDEM for Modeling Facture Behavior
3. Member Discrete Element Modeling for Semi-Rigid Connections
3.1. Virtual Zero-Length Spring Element
3.2. Semi-Rigid Connection Models
3.3. Cyclic Behavior Modelling of Semi-Rigid Connections
3.4. Computational Procedures for Static and Dynamic Analysis of Steel Frames with Semi-Rigid Joints
4. Examples
4.1. Geometrically Nonlinear Analysis of a Column with Elastic Support
4.2. Static and Dynamic Response of a Beam with Elastic Ends
4.3. Static and Dynamic Response Analysis of Steel Frames with Linear Semi-Rigid Connections
4.4. Snap-Through Buckling Analysis of the Williams Toggle Frame with Linear Semi-Rigid Connections and Supports
4.5. Static Analysis of a Steel Portal Frame with Bilinear Semi-Rigid Connections
4.6. Dynamic Analysis of the Two-Span, Six-Story Vogel Steel Frame with Nonlinear Semi-Rigid Connections
5. Conclusions
- (1)
- This paper presented an effective numerical approach for static and dynamic behavior simulation of steel frames with semi-rigid joints based on the Member Discrete Element Method (MDEM). In the MDEM, a structure is discretized into a set of finite rigid particles, as well as geometric nonlinearity and fracture behaviors can be naturally captured. A virtual spring element without actual length is applied to simulate the semi-rigid connection. On this basis, the modified formula of the contact element stiffness at the semi-rigid connection is derived. Finally, the numerical approach proposed is verified by complex behaviors of steel frames with semi-rigid connections such as geometric nonlinearity, snap-through buckling, dynamic responses and fracture. In addition, compared with other numerical approaches taking the FEM as a representation, the approach proposed is simple and feasible for simulating the semi-rigid connections because the zero-length spring element is not directly involved in the calculation.
- (2)
- The comparison of the analysis results of the proposed approach and the existing researches shows that the modified MDEM can accurately capture linear and nonlinear behaviors of semi-rigid connections. Some common conclusions can be drown as follow: the semi-rigid connections may significantly reduce structural stiffness, and structural bearing capacity under static loading will be overestimated if the semi-rigid connections are ignored; When the frequency of dynamic load applied is close to structural fundamental frequency, resonance occurs in the frames with rigid or linear semi-rigid connections, but not in the frame with nonlinear semi-rigid connections, the reason is that the hysteresis damping of the nonlinear connection causes energy dissipation. Fracture behavior analysis also indicates that frames with semi-rigid connection possess more anti-collapse capacity.
- (3)
- The MDEM can avoid the difficulties of finite element method (FEM) in dealing with strong nonlinearity and discontinuity. A unified computational framework is applied for static and dynamic analyses. The method is simple and generally good, which is an effective tool to investigate complex behaviors of steel frames with semi-rigid connections. In the follow-up study, material nonlinearity will be taken into account to simulate the collapse process of steel frames with semi-rigid connections under strong earthquake or impact loading action.
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Semi-Rigid Connection Types | Configuration | Formulas |
---|---|---|
Elastic support | ||
Couple-bar joint | (for two same bars) | |
Beam-column joint | (for semi-rigid connections on the beam) |
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Ye, J.; Xu, L. Member Discrete Element Method for Static and Dynamic Responses Analysis of Steel Frames with Semi-Rigid Joints. Appl. Sci. 2017, 7, 714. https://doi.org/10.3390/app7070714
Ye J, Xu L. Member Discrete Element Method for Static and Dynamic Responses Analysis of Steel Frames with Semi-Rigid Joints. Applied Sciences. 2017; 7(7):714. https://doi.org/10.3390/app7070714
Chicago/Turabian StyleYe, Jihong, and Lingling Xu. 2017. "Member Discrete Element Method for Static and Dynamic Responses Analysis of Steel Frames with Semi-Rigid Joints" Applied Sciences 7, no. 7: 714. https://doi.org/10.3390/app7070714