EBT Allowable deflection in beam

[40818]

Right, once and for all i seek consenus on a grey area which will no doubt provide debate.

For a simple engineering theory of bending, what would you take as an allowable deflection for a give thickness, radius of curvature, etc.

I have read of values from 0.5t through to 2t in various books, but i do not know where they get these values from. As far as i'm aware, Timoshenko's Strength of Materials Chapter V shows that it is related to the radius of curvature rather than thickness. So you can have deflections in the order of say 10 times the thickness and the values you calculate using MY/I will be reasonable as long as the radius of curvature is large compared to the inital beam dimensions.

Though the whole theory tends to turn to mush when we consider short deep beams that tend to dominate primary aircraft structure.

Any ideas on the acceptable limitations and whats been approved before? And this just shouldn't be resticted to aero, but engineering as a whole.

Comments please.

 

[RPstress]

For inaccuracy of My/I there are at least two main effects usually at work: behaviour non-linear with load due to membrane stresses, and non-linear strain distribution due to curvature, which also becomes significantly non-linear with load as radius of curvature/thickness ratio gets lower.

Plus, of course, any material non-linearities due to yielding, or elastic E not being constant. Also you can have y being wrong due to Ec<>Et.

Roark has a section on wide and/or deep beams. ETB can be surprisingly innaccurate for short deep beams.

Inaccuracy due to membrane effects depends on edge/end conditions. If no in-plane constraint at all, then even quite big deflections will be linear.

In the past we've only ever had to justify this sort of thing based on particular cases, so we'd do a check with large-deflection non-linear FE or ESDU for a 10% load increase. Similar with ETB not applying due to curvature: check curved beam formula for the given structure.

So, no general limits from me, I'm afraid.

 

[rb1957]

also consider that a beam with a large deflection looks (and acts) more like an arch ... it would react transverse loads with axial loads (like a membrane) ...