We will start with an easy case in order to avoid calculations that
would take up a few pages.
Force "F" is putting pressure onto
the centre of the rail. At this very point the bend "f" is being calculated.
The rail length is
measured in "l"
Please see above an example which is commonly used in mechanical engineering. The related formula is:
This formula is used to calculate the bend at any part of the
rail. We, however, are only interested in the bending at the centre
of the rail. This slightly simplifies the the formula as follows:
We could get started if we only know the meaning of "E" and "ly".
"E" stands for the so-called modulus of elasticity. As this is a
material constant and we know the material (aluminium), we also know "E".
The "E" of aluminium is 70,000 N/mm2.
And then we have "ly", the so-called moment of inertia which is
entirely depending on the cross-section. As we do know our profiles
(surprise,surprise), we also know "ly".