IntermediateTopic 49 of 112Civil & Structural
Plastic analysis
Collapse load found using plastic hinge mechanisms.
In depth
Ductile structures reach collapse when enough plastic hinges (M=M_p) form a mechanism. Collapse load found by equilibrium and kinematic (virtual work) methods; upper and lower bound theorems. Shape factor f=M_p/M_y (1.5 for rectangle, 1.12 for I-sections). Allows economical design for redistribution.
Key points
- Load factor λ
- Mechanism types: beam, sway, combined
- Uniqueness theorem
ExampleA fixed-end beam with UDL collapses at w=16M_p/L².
What is Plastic analysis?
Collapse load found using plastic hinge mechanisms.
Why is it important to understand plastic analysis?
Plastic analysis finds the collapse load of ductile structures, which can be much higher than the first yield load and is used for steel frames.
What is a plastic hinge?
A section where the moment reaches the plastic moment capacity and the member can rotate freely, forming a hinge in the mechanism.
What is a collapse mechanism?
A pattern of plastic hinges that allows the structure to deform freely, and the lowest load giving such a pattern is the collapse load.
How is Plastic analysis used in practice?
Typical applications include finding the collapse load of a portal frame under wind and gravity, checking the redistribution of moments in a continuous steel beam and designing a steel structure that uses its full capacity safely.
What should I learn before Plastic analysis?
Study "Virtual work and energy methods" first (topic 48 of 112 in Civil & Structural). It covers the groundwork this topic builds on.
What are the key points of Plastic analysis?
Load factor λ. Mechanism types: beam, sway, combined. Uniqueness theorem.
Can you give an example of Plastic analysis?
A fixed-end beam with UDL collapses at w=16M_p/L².
What comes after Plastic analysis?
The next topic is "Limit state design", which builds directly on this one.
How difficult is Plastic analysis?
It is classed as Intermediate in Civil & Structural (topic 49 of 112). It is an intermediate topic. Work through the beginner topics in Civil & Structural first.