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Introduction to FE Analysis

Tutorial CD

Introduction to FE Analysis

Tutorial CD

to constrain it horizontally in the span and transverse directions?

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.

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.

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