I have a bridge structure, which is only loaded vertically, why do I have to constrain it horizontally in the span and transverse directions?
The constraints that you apply to a model are completely independent of the loads that you apply. We will have to use some equations here to describe how it works. The overall static analysis solution is defined as:
F = Ku F is a vector of applied loads u is a vector of displacements we want to solve for K is the stiffness matrix
You will notice there is no constraint definition here. That is a clue.
If we think of a series of springs, each only having axial stiffness Ki forming an FE model, then we will assemble all of the spring element stiffnesses together to make an overall model stiffness. The diagram below shows how.
Now we have everything to solve for forces pulling at each end – or do we?
The stiffness matrix written here is singular, that means we cannot solve it. The reason is that the structure is free to move in the axial direction. It has what we call a Rigid Body Motion. Now we can solve for this in dynamic analysis – but not statics.
There is no reference to loading here; the stiffness matrix just doesn’t care what the loadings are. It doesn’t matter if all is in perfect balance, the stiffness matrix will be singular.
So we have to constrain the model to eliminate all of the rigid body modes. In the spring case we just ground, or fix one end. In the case of your bridge you will need to constrain the end support regions so that they cannot slide horizontally.
If you still need some guidance, try clicking the hyperlinks for fuller definitions