Simplle question

[6060-842]

ok first time posting so please be gentle...

Have a small bracket ( 90 degree bend) fixed at the top plane with a force on the front plane (see sketch)
To calculate max stress and deflection woukd you use something like Roarks equations for treat like a cantilever beam

 

[rb1957]

short answer ... no.

first, how is this angle attached to the "rest of the world" ? I suspect some fasteners ?

second (and you probably can't answer this) how stiff is the structure (that the angle mounts on) ? Particularly in torsion, as that's what your load will do to it.
Simple assumption is to assume it is stiff enough and move on with the solution.

third, at the interface with "the rest of the world" there will be shear (500N) and a moment, torsion about the axis of the angle, due to the couple between the applied load and the angle's reaction. this moment will be reacted by prying forces (or "heel and toe") between the angle flange and the supporting structure. This moment is divided between the fasteners in some manner ...
a) if two fasteners reasonably equally spaced from the load then 50% each is a good assumption,
b) if more than 2 then some other distribution,
c) lazy, conservative, approach would be to put all of the moment at each fastener ... just to show that the loadpath is good for it.

4th, there will be some bending of the angle, like a beam, with the load causing bending as in a beam. There are many secondary effects, but this is just homework ... but then homework wants yo to pick up on the secondary effects ...

 

[GregLocock]

I find it often helps to sketch out what I think the likely deflected shape is. Assuming perfect fixity you'd have a distributed rotation about the fixing to the wall (your cantilever in bending), and the front face would bow inwards quite a lot at the bottom in the middle and not much at the top and sides. I'd also add a coordinate system so that it is easier to describe. Since it is a linear system you can first work out the cantilever and then a plate encastre at one edge with a point load on it. That's all in Roark.

 

[Ron247]

Is it an equal leg angle?

 

[rb1957]

but if the base is truly continuously fixed to "the rest of the world", then only the standing leg would deflect (out-of-plane).

But I think OP means that the base is discretely attached (at 2 or more points), and then it could behave like a beam;
and I think OP uses "fixed" to mean that the flange is supported so prying forces can develop (to react the offset moment).