Cantilever beam bending with partial UDL

[SamT92]

Hi Folks,

Apologies if this seems like a simply problem to many but some help would be appreciated.

Basically I have a Cantilever beam (5mm solid bar) with a partial UDL along the beam. See image for further detail.

Can someone tell me how to calculate the reaction and moment about A and the deflection and stress seen along the beam.

 

[BAretired]

Ma = w(L-a)(L+a)/2
Mb = w(L-a)[sup]2[/sup]/2
Mx = w(a<x<L)(L-x)[sup]2[/sup]/2

Rotation at any point x is the area under the M/EI diagram between A and x.
Deflection at any point x is the moment of the M/EI diagram between A and x about point x.

A simpler method which is probably sufficiently accurate is to resolve the uniform load into two concentrated loads, one at A, the other at L and use expressions for two point loads.

BA