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Hi.

I am new here (I am from Denmark), so I hope I found the right place... :-)

Well, I have a situation where I have a cantilevered beam and first this beam was straight, but then the architect found out about the size of the beam... Then I suggested to make the beam with variating height - so yes, it is my own fault that I put myself in an difficult enginnering problem. But problems are to be solved, right? Well at attached file you get an idea of the issue. I have calculated this beam as follows:

1) To determine that the strength is ok, I calculated the momentum and the cross sectional properties in a number of sections, and derived the bending stress and shear stress. This seemed ok.

2) To get an idea if the stiffness of the beam is ok, I calculated the deflection for a normal cantilevered beam, using the area moment of inertia in a section in the middle of the height-variating part of the beam - and added a factor 1,2 to have some margin.

The question is now: Does there exist formulars for correct calculation of the deflection of such kind of beam?

Maybe the moment and shear stress curves are even not completely correct for this kind of beam?

Does there exist (free, low price or demo) engineering / FEM software that can calculate this beam?

I am new here (I am from Denmark), so I hope I found the right place... :-)

Well, I have a situation where I have a cantilevered beam and first this beam was straight, but then the architect found out about the size of the beam... Then I suggested to make the beam with variating height - so yes, it is my own fault that I put myself in an difficult enginnering problem. But problems are to be solved, right? Well at attached file you get an idea of the issue. I have calculated this beam as follows:

1) To determine that the strength is ok, I calculated the momentum and the cross sectional properties in a number of sections, and derived the bending stress and shear stress. This seemed ok.

2) To get an idea if the stiffness of the beam is ok, I calculated the deflection for a normal cantilevered beam, using the area moment of inertia in a section in the middle of the height-variating part of the beam - and added a factor 1,2 to have some margin.

The question is now: Does there exist formulars for correct calculation of the deflection of such kind of beam?

Maybe the moment and shear stress curves are even not completely correct for this kind of beam?

Does there exist (free, low price or demo) engineering / FEM software that can calculate this beam?