Structure Stability 2

[Hudhaifa]

Hi

The stability concept of a structure (frame/truss) is not very clear for me. I have found the following statement in one of the structural courses;

What do you think about the above statement?

 

[r13]

Obviously the displaced shapes are drawn from the understanding of the joint condition.

Yes. Pin support does not have rotational restrain, so member remains in displacement.

 

[AaronMcD]

This was always intuitive to me. If there is no initial first order stiffness, it is unstable. In other words, if I imagine all elements to be infinitely rigid sticks and it can still move delta-x, where delta-x approaches zero, it is unstable. Whenever I get a "structure is unstable" error, I look at all my boundary conditions and connections, and mentally try to "move" elements and find the instability. Often this is a "spinning" instability.

Even if it cannot move a real positive distance in second order analysis, it can be unstable in first order analysis as the deformed shape is not considered. For example, two, 2d elements attached end to end with a moment release, and pin connection at each end of the model. If you draw it deformed, the elements clearly must stretch. However, if you move the middle joint a distance approaching zero, the deformation approaches zero. It has no stiffness, and is therefore unstable in a first order analysis.

http://www.hellodwell.design

 

[AaronMcD]

@rb1957
conventionally, the open circle represents a pin connection, and the triangle represents a pin boundary. No symbol represents fixed connection or boundary. Circle at boundary (or triangle on top of 2 circles)represents a pin free to roll.

The bottom image is supposed to have a triangle pin boundary at the right support.

http://www.hellodwell.design