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

 

Plastic analysis is a method used to determine the collapse mechanism of both determinate and indeterminate structures. The collapse mechanism refers to the sequence of plastic hinge formations in a structure, leading to its ultimate failure. Here's a step-by-step process for developing a plastic analysis to obtain the collapse mechanism:

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

2. Determine Plastic Hinge Locations: Identify potential plastic hinge locations in the structure. These are regions where plastic deformation is expected to occur. For determinate structures, hinge locations are typically at the supports or at critical sections of members. In indeterminate structures, hinge locations can occur at multiple locations.

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

4. Equilibrium Analysis: Perform an equilibrium analysis of the structure under the given loading conditions. Determine the bending moments, shear forces, and axial forces in the members using equilibrium equations and compatibility conditions.

5. Plastic Analysis Procedure: Start with an assumed collapse mechanism and plastic hinge sequence. Assign plastic moments to the members at the identified hinge locations. Distribute the moments to satisfy equilibrium conditions and compatibility of deformations.

6. Compatibility Analysis: Check the compatibility of deformations at the plastic hinges. Ensure that the rotations and displacements at the hinges are compatible with the assumed collapse mechanism. Adjust the plastic moments and hinge locations if necessary.

7. Collapse Mechanism Evaluation: Evaluate the stability and collapse mechanism of the structure based on the plastic analysis results. Analyze the distribution of plastic moments, member forces, and deformations to identify the collapse mechanism. This involves considering the progression of plastic hinges and the redistribution of forces.

8. Structural Redundancy: In the case of indeterminate structures, consider the effects of structural redundancy. Account for the ability of the structure to redistribute loads and resist collapse even after the formation of plastic hinges. Analyze the redistribution of moments and forces due to redundancy and its impact on the collapse mechanism.

9. Iterative Analysis: Iterate the plastic analysis process, adjusting the assumed collapse mechanism and plastic hinge locations, until a stable and realistic collapse mechanism is obtained.

10. Design Considerations: Based on the collapse mechanism obtained, evaluate the structural integrity and capacity. Ensure that the structure satisfies the required strength, stiffness, and stability criteria. Consider design factors such as ductility, member sizes, reinforcement details, and connection capacities.

It is essential to note that plastic analysis requires expertise and should be performed by experienced structural engineers. The results of the analysis should be verified against relevant design codes and standards to ensure the safety and integrity of the structure.

 

The Remembering

 

In the context of plastic analysis for obtaining the collapse mechanism of determinate and indeterminate structures, remembering plays a significant role. Here's an explanation of how remembering is applied in this process:

1. Recall Structural Behavior: Remembering involves recalling the fundamental principles of structural behavior and plasticity. This includes understanding the response of materials and structures beyond their elastic limits, the concept of plastic hinges, and the redistribution of moments and forces.

2. Previous Experience: Engineers draw upon their previous experience with similar structures and collapse mechanisms. They remember the lessons learned from past projects and apply that knowledge to the current analysis. This helps in identifying potential plastic hinge locations, predicting collapse modes, and making informed decisions during the analysis process.

3. Design Codes and Guidelines: Remembering involves familiarizing oneself with the relevant design codes and guidelines. Engineers recall the specifications and provisions outlined in these documents, including the requirements for plastic analysis, load combinations, material strengths, and detailing practices. This ensures that the analysis and design are in accordance with established standards.

4. Structural Mechanics: Remembering the principles of structural mechanics, such as equilibrium equations, compatibility of deformations, and force/moment distributions, is crucial for conducting an accurate plastic analysis. Engineers recall these concepts and apply them in the analysis process to ensure that the structure remains in equilibrium and the deformation patterns are consistent with the assumed collapse mechanism.

5. Lessons Learned: Remembering also involves incorporating lessons learned from previous failures or design challenges. Engineers recall instances where the collapse mechanism differed from initial assumptions or where unexpected behaviors occurred. By remembering these lessons, engineers can avoid repeating past mistakes and improve the accuracy of their analysis and design.

6. Continuous Learning: Remembering is an ongoing process that involves continuous learning and staying updated with the latest research, advancements, and case studies related to plastic analysis and collapse mechanisms. Engineers strive to expand their knowledge and improve their understanding of structural behavior to enhance the quality and reliability of their analysis.

By actively remembering and applying the lessons learned from previous experiences, design codes, and continuous learning, engineers can effectively perform plastic analysis and obtain accurate collapse mechanisms. This ensures the safety, efficiency, and integrity of the designed structures.