Constraints and Static Determinacy

[member 392791]

Hello,

Is it possible for a structure to be completely constrained and statically indeterminate, or partially constrained and statically determinate? Or does one come with the other automatically?

I am having difficulties determining if a structure is partially constrained or completely constrained, or improperly constrained.

 

[SteamKing]

I'm not sure what an 'improperly constrained' structure would look like.

To help you determine when a structure is statically determinant, you might review the following:

http://en.wikipedia.org/wiki/Statically_indeterminate
http://hcgl.eng.ohio-state.edu/~ceg431/CE431_Part2.pdf
http://www-classes.usc.edu/architecture/structures/Arch213A/213A-lectures/12-Determinacy.pdf

 

[nvn]

Is it possible for a structure to be completely constrained and statically indeterminate?

Yes.

Is it possible for a structure to be partially constrained and statically determinate?

No.

Or does one come with the other automatically?

No.

I am having difficulties determining if a structure is completely constrained, partially constrained, or improperly constrained.

A completely constrained structure is static (stable).

Partially constrained and improperly constrained structures are quite similar. They are both nonstatic (unstable). The only subtle difference between the two is, a partially constrained structure has an insufficient number of constraints, whereas an improperly constrained structure has a sufficient number of constraints, but the constraints are configured wrong, such that the structure is still nonstatic (unstable, moves).

 

[timthereaper]

Yes. Consider a bar fixed rigidly at both ends to opposing walls and a force applied in the middle of the bar. The bar is fully constrained, but the reaction forces can't be solved with just the equations of statics, making it statically indeterminate.

You could say that the beam in the above example is "overconstrained", and by that I mean that the bar could still be fully constrained without fixing both ends. A cantilever beam is fully constrained in translation and rotation as well, and that problem is statically determinate. I know that's not the exact meaning of "overconstrained", but I'm just trying to illustrate that point.

You also have cases where things are statically determinate but not fully constrained. Consider a beam on 2 rollers with a vertical force being applied downward. The system is statically determinate, meaning you can solve for the reaction forces at the rollers with just the equations of statics, but the system is underconstrained because any lateral force on the beam will cause it to move.