In Strength of Materials, let's recall that objects deform differently depending on the stress they may experience. For example, when we apply a pulling force to a steel rod by hand, it will not elongate significantly. However, when we use heavy machinery when applying a pulling force, it may reach a point where one can see a change in shape.
The same goes for structures. Depending on how big or small the force is, the structure's materials may behave linearly or nonlinearly.
In analysis, it's essential to differentiate the two.
Linear and Nonlinear Behavior
To fully understand the difference between linear and nonlinear analysis, we need to recall what these terms mean. To begin, let's view a typical stress-strain curve.
One key trend from this curve was the linear relationship between stress and strain, as seen from its origin to its yield point. During this stage, we say that the material obeys Hooke's Law.
In this stage, it can return to its original position when we remove the loads. In addition, the deformations of the object are relatively small. Other references would term this behavior as elastic.
As we apply larger loads on the object, we will eventually reach a point wherein it will pass the linear stage. At this phase, the material would be inelastic. The thing will not return to its original shape if we remove the loads. Meaning it will disobey Hooke's Law.
Linear and Nonlinear Analysis
Now that we have explained linear and nonlinear behavior - let's go back to structures and analysis.
As a general rule, when a structure observes an elastic behavior, it is said to be linear; however, if it is inelastic, it is a nonlinear structure.
In some unique cases, certain buildings may still be in the linear stage, but it has deformed significantly. Such structures are also nonlinear.
When we classify structures as linear or nonlinear, what does it mean for analysis? To answer that, it has something to do with their properties. A linear structure would have constant properties throughout time. When these become nonlinear, specific properties change over time. Engineers must factor in these changes because these may govern the design.
Examples of nonlinear analyses include plastic and buckling analysis.
Summary
When structures behave within the elastic range and have small deformations after all loads are applied, they are said to be linear.
When structures fall outside the elastic range, or there are huge deformations despite being in this stage, it is said to be a nonlinear structure.
