Finding the kinematic degree of indeterminacy?

[mneox]

I am currently looking at this website: http://www.public.iastate.edu/~fanous/ce332/displ/homepage.html

And this example that they went through: http://www.public.iastate.edu/~fanous/ce332/displ/homepage.html

Why does that structure only have one degree of kinematic indeterminacy? I understand that the fixed end has no DOFs, but wouldn't roller supports have 2 DOFs?

Could someone explain this concept to me

I get how to find DOFs if there were axial deformations, but what do I do when we neglect them?

 

[jbsteele]

The structure you are looking at has only one degree of kinematic indeterminacy because the roller supports only have one degree of freedom. The roller support can only move in one direction, so it does not introduce additional degrees of freedom. When we neglect axial deformations, we look at how many independent equations of constraint the structure has. If it has fewer than the number of unknowns, then there is an indeterminacy. In this example, the fixed end has no DOFs, so that means that the structure has just one equation of constraint. Since there is one unknown (the displacement of the roller support), there is one degree of indeterminacy.