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it would be nice to have more details and pictures on your structure to help figure out what is your question.
if you take some structure, like a pen, with some stiffness, and you apply a force stretching it, you would get some stress level due to its geometry. Let's say stresses are 10MPa. Let's say, if it is a polymer, it would stretch by 10mm.
Now let's change the material/stiffness to a pen made of steel. Apply the exact same force. Stress levels will be exactly the same. Displacements though, would decrease a lot, probably by 1/100th.
The force acting on the strcuture is still the same, and the acting stresses are the same. Of course, depending on the material properties, if stresses go to high, the material may or may not fail…
My point is, if you've changed stiffness of all your springs at once, the force distribution and load path wouldn't change, so i wouldn't expect a change in stress distribution. Now, if you change them differently, this could change the load path, and then, change the stress distribution.