There'll be differences from piping code to piping code, but the gist is as follows. An elbow consists of 2 elements, which are input with 3 nodes in succession. Let's say 10-20-30.

CAESAR converts this input "behind the scenes" to add nodes at the inlet side of the bend, middle of the bend, and outlet side of the bend. If you already have a node at the inlet and outlet weld points, CAESAR will throw up an error and ask you to correct the situation.

The two elements, however, are two sticks. When you provide geometrical data, CAESAR calculates the flexibility and stress intensification factors for movement of these two sticks relative to each other so as to represent a bend.

CAESAR simulates how much motion there exists based on a series of stiffness values and internal/external forces, and based on the derived motion, calculates an equivalent stress.

In the case of an elbow anchored on either end (10-20-30), the growth from 10-20 is resisted by the lateral stiffness from 20-30 and vice versa. The lateral load on 30 is equal to the axial load on 10 - this is a simple free body problem. Both are equal to the amount of load that's acting to compress node 10-20 axially, which the load is the balance between the lateral stiffness of 20-30 and the axial stiffness of 10-20, based on the change in length due to thermal expansion.