Tapered beam Deflection 5

[TP29]

Hello,
I'm hoping someone here can help. I have a question concerning my dinghy mast that have been puzzling me for some time now and I have been unable to find any reference book or website that covers this topic. I am a Chartered Engineer, but not a structural one, so know the basics of structural theories but confess that this is beyond me.

If a sailboat mast of uniform section is unstayed then it can be considered as a cantilever beam and I am able to calculate the deflection using simple beam theory (assume for now that the sail applies a UDL to the mast). How do I calculate the deflection, but when the mast section is uniformly tapered (so that the 'I' value decreases linearly from root to tip)? Clearly the deflection will be greater - can I replicate this by simply applying a uniformly increasing load to a non-tapered section? If not, how else can I calculate the deflection? It must be possible to do this using hand calcs rather than FEA, surely. For the sake of detail, I should add that the mast section is a hollow cylinder and that the taper applies in all axes iso that the section remains round. I guess this makes it a high aspect ratio frustum of a cone.

Many thanks in advance for any suggestions, but be warned - if I get a good response I may pose another question!

 

[transmissiontowers]

You can get a demo/student edition of GTStrudl for free with a joint limit of around 50 (can't remember for sure) that has a stepwise tapered beam function and cable elements that might solve your problem.

_____________________________________
I have been called "A storehouse of worthless information" many times.

 

[prex]

TP29,
if you get less deflection in a tapered beam for the same inertia at the fixed end and the same load distribution, then you better double check your results: this would be a physically inconsistent situation violating the principle of energy conservation.

prex

http://www.xcalcs.com

Online tools for structural design

 

[TP29]

Thanks for the links to the freebie software, I will give these a go. I think Broekie's revised formulae (thanks again) probably is the integral of Prex's equation, with x = L. I will try and check this later on.