Plastic analysis of structures is applicable to structures made of ductile materials only.

Ductile materials have the ability to undergo significant deformation before failure, which means they can withstand large amounts of plastic deformation. This is in contrast to brittle materials, which fail suddenly and without warning once their ultimate strength is exceeded. Plastic analysis is based on the assumption that the structure will undergo large plastic deformations before failure.

Here are the reasons why plastic analysis is applicable to structures made of ductile materials only:

1. Plastic Deformation Capacity: Ductile materials have a high plastic deformation capacity, which allows them to undergo substantial deformation before failure. This is important because plastic analysis involves predicting the behavior of a structure beyond its elastic limit and into the plastic range.

2. Redistribution of Moments: Plastic analysis assumes that plastic hinges will form in the structure when it reaches its plastic limit state. These plastic hinges allow for the redistribution of moments, which helps in achieving a more efficient use of the overall structural capacity. Brittle materials, on the other hand, do not exhibit plastic deformation and cannot redistribute moments.

3. Energy Dissipation: Ductile materials have the ability to absorb and dissipate energy during plastic deformation. This energy dissipation helps to prevent sudden and catastrophic failure of the structure. Brittle materials, being unable to undergo plastic deformation, do not possess this energy dissipation capability.

4. Ductility Requirements: Plastic analysis is often used in the design of structures that require a certain level of ductility, such as earthquake-resistant buildings. Ductility is a desirable characteristic in seismic design because it allows the structure to absorb and dissipate energy during an earthquake, reducing the risk of collapse.

In summary, plastic analysis is applicable to structures made of ductile materials because of their high plastic deformation capacity, ability to redistribute moments, energy dissipation capability, and the ductility requirements of certain structural designs.