Case Studies of Plastic Analysis

1. Case Studies of Plastic Analysis Elastic and Plastic Analysis Using Dr. Frame Case Studies of Plastic Analysis

2. Basic Concept  • Plastic Analysis • Stress remains constant while the strain increases. • The plastic hinge forms. • Collapse occurs when sufficient plastic hinges have formed to convert the structure to a mechanism. • Plastic analysis: determining the minimum load that causes the structure to collapse. • Elastic Analysis • Element is assumed to obey Hooke’s law and recover to original state on removal of load. • Elastic Analysis: determining the maximum load that cause one point in any member section to reach the yield stress or elastic critical buckling stress. Case Studies of Plastic Analysis

3. Basic Concept  • Effect of the axial force: 1. Both tensile and compressive force reduce the plastic moment 2. Reduced plastic moment formula: • Plastic Moment • Simple plastic moment formula: Mp = ZFy • Effect of the shear force: 1. Tresca and Von-Mises yield criteria 2. In I-beams, the reduction in the plastic moment is negligible until the shear force is over 50% shear capacity of the web Case Studies of Plastic Analysis

4. About Dr. Frame • Plastic Hinge Objects • Installation and removal of plastic hinges • Before yielding: blue rectangles • After yielding: solid red circles during loading, open red circles during unloading • Simple linear interaction relation to account for axial force effect • Second-Order Analysis • Load-Dependent EI Case Studies of Plastic Analysis

5. Case Model Beam: W 310 x 60 Column: W 250 x 67 Case Studies of Plastic Analysis

6. Analysis Result: Case 1 • Combined mechanism λe = 5.35 λc = 7.70 Case Studies of Plastic Analysis

7. Analysis Result: Case 2 • Combined mechanism λe = 3.11 λc = 4.73 Case Studies of Plastic Analysis

8. Analysis Result: Case 3 • Sway mechanism λe = 1.43 λc = 1.95 Case Studies of Plastic Analysis

9. Analysis Result: Case 4 • Sway mechanism λe = 2.07 λc = 2.96 Case Studies of Plastic Analysis

10. Analysis Result: Case 5 • Sway mechanism λe = 2.12 λc = 3.06 Case Studies of Plastic Analysis

11. Discussion  • Reduction in plastic moment capacity due to axial force • “Column 1”in all cases are investigated. W250x67: Np = 2992.5 kN Mp = 315.35 kNm • The bigger axial force, the bigger reduction in plastic moment capacity. Case Studies of Plastic Analysis

12. Discussion  • Comparison of linear analysis and second-order analysis in Case 1, Case 3 • The collapse load factor reduces. • The P-Δ effect is more significant in multistory frame. Case Studies of Plastic Analysis

13. Discussion  • A handy plastic analysistool -- Dr. Frame • Model and observe plastic behavior in structure interactively • Get the order of plastic hinges formation and the final collapse mechanism easily and visually Case Studies of Plastic Analysis

14. Plastic Hinge Formation  Case Studies of Plastic Analysis

15. Plastic Hinge Formation  Case Studies of Plastic Analysis

16. Conclusion The location of plastic hinges in frames to form a mechanism varies with the type of loading, shape and other physical properties of the frame. Dr. Frame is a very handy program to perform plastic analysis for framed structures of complicated shape and with a high degree of redundancy. • The plastic moment reduction due to axial force must be considered in the plastic analysis, especially when the axial force N exceeds 15% Np. • For more accurate result, one needs to do the second-order analysis accounting for the P-Δ effects and load-dependent EI. Case Studies of Plastic Analysis