Develop Plastic Analysis for Obtaining the Collapse Mechanism of Determinate and Indeterminate Structures

 

Plastic analysis is a powerful method used in structural engineering to determine the collapse mechanism of determinate and indeterminate structures. It allows engineers to understand the behavior of structures beyond their elastic limits and identify the critical failure mode or mechanism. Here's an overview of the steps involved in developing a plastic analysis for obtaining the collapse mechanism of structures:

1. Structural Modeling: Create a structural model of the determinate or indeterminate structure using appropriate structural analysis software or manual calculations. Consider the geometry, materials, supports, and loading conditions of the structure.

2. Load Analysis: Determine the design loads acting on the structure, including dead loads, live loads, and other applicable loads such as wind or seismic loads. Apply the appropriate load combinations and factors of safety as per the design codes and standards.

3. Plastic Hinge Locations: Identify the potential plastic hinge locations in the structure. Plastic hinges are regions where plastic deformation occurs due to the redistribution of moments and forces beyond the yield point of materials.

4. Plastic Moment Capacity: Determine the plastic moment capacity of the structural members or sections at the potential plastic hinge locations. This involves evaluating the yield strength and the shape factor of the members or sections.

5. Plastic Analysis Procedure: Perform a step-by-step plastic analysis to determine the sequence of plastic hinge formation and progression in the structure. Start with the formation of the first plastic hinge and determine the corresponding moments and forces. Then, identify the subsequent plastic hinge locations and calculate the moments and forces at each hinge.

6. Collapse Mechanism: Analyze the results of the plastic analysis to identify the collapse mechanism of the structure. The collapse mechanism is the pattern of plastic hinge formation and progression that leads to the ultimate failure of the structure. It helps in understanding the load-carrying capacity and behavior of the structure under extreme conditions.

7. Structural Redundancy: In the case of indeterminate structures, consider the effects of structural redundancy. Redundancy refers to the ability of a structure to redistribute loads and resist collapse even after the formation of one or more plastic hinges. Evaluate the redistribution of moments and forces due to redundancy and its impact on the collapse mechanism.

8. Design Optimization: Based on the results of the plastic analysis, optimize the design of the structure to ensure the desired collapse mechanism and structural performance. This may involve adjusting member sizes, reinforcement layouts, or connection details to enhance the overall structural capacity and ductility.

It's important to note that plastic analysis should be conducted by experienced structural engineers familiar with the behavior of materials and the design principles of plasticity. It requires a deep understanding of structural mechanics, material behavior, and the limitations of plastic analysis methods. The results of the analysis should be interpreted and verified in accordance with relevant design codes and standards to ensure the structural safety and integrity of the designed structure.