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Cantilever beam bending with partial UDL

Cantilever beam bending with partial UDL

Cantilever beam bending with partial UDL

(OP)
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.

RE: Cantilever beam bending with partial UDL

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

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

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