What is the formula for calculating the maximum deflection of a bike axle?

[Buchanskii]

My Question...

To find the maximum deflection of this axle, can the formula:

(W*a/24*E*I)*(3*l^2-4*a^2)

Will the total length simply be 370mm(wheel to wheel), or will I have to include the total length of the axle?

 

[Studiot]

Welcome Buchanskii.

The effective span will be the clear distance between the wheel flanges. You do not include the length that is within the wheels themselves.

So yes 370 is good.

I am troubled by your formulae but can't help without more information about the cross section and so on. Do the collars noted as F indicated loads from the bicycle frame?
Is this bicycle in fact a tricycle?

 

[Buchanskii]

Hi Studiot, thanks for your help - much appreciated. Sorry about the small Picture aswell, still learning :0

It is Indeed a tricycle; don't know why I put Bicycle. The two collars are attached to the frame in the form of bearing housings, which will support the load of the driver and the frame.

The Inertia of the frame I've worked out as 19000mm^4 using pi*D^4/64 (as it's a solid cylindrical shaft)

Load of approximately 700N

E aluminium 70GPA

a being distance between wheel and load.

Just was wondering about the length, a fellow student put doubt into my mind.