If we have a look on the slope, hum, this

straight line, the stiffness has a value of 10 Newtons

over 80 millimeters,

that is to say of 0.125

Newtons per millimeter.

For the record, we had, here, a slope of

0.25 Newtons per millimeter.

So, we can see that if we increase the length of the

system, doubling the length of the spring, we increase this length,

the stiffness of the system is divided by 2.

In this video, we can also see a configuration

with two springs, but instead of having

put them one below the other, we have put them one

next to the other, with a little device which enables to

hang up the load directly to both springs in the same time.

So, this time, we have a displacement, of only 20 millimeters

for 10 Newtons, of 40 millimeters for 20 Newtons, and of 60 for 30 Newtons.

Then, we have a

behavior with a much steeper slope, than before.

And, the stiffness, here,

is equal, we are going to see, 10

Newtons for 20 millimeters,

that is to say 0.5 Newtons per millimeter. So, what

we can see here, it is that if we increase the section of our spring,

or, if we double the number of springs, we also double the stiffness.

If we write the stiffness, we have thus seen that it

was inversely proportional to the length of the system, and then

that it is proportional to the number of springs, to be more

general, to the area of spring available, that is to say A.

And then, we are going to introduce, here, a constant

E, of which we are going to see the meaning very

soon, but for the moment, we are simply going to say

that R is equal to E times A over l.

That is to say proportional

to the section and inversely proportional to the length.

What we have seen, now, regarding the stiffness of a structure,

it is a behavior which on the one hand, followed straight lines.

Thus, a behavior which was

linear, where the lengthening increased proportionally

to the loads.

On the other hand, what we have seen

is that we could increase the load, or

decrease it, and that we are going to find again the

initial position of our springs, at the end.

This behavior, we call it an elastic behavior.

An elastic behavior, is when a structure

gets its shape back, its initial shape, when it is unloaded.

And actually,

here, we have got a behavior which was both linear and elastic.

Then, we call it a linear-elastic behavior.