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Deflection of a pole with end load and UDL

Erin Hayward-Lang


Hi, i'm modelling a radio antenna pole and wanted to calculate the deflection/deformation

The pole is 6m tall with an antenna on top, i've calculated the wind loading on both the antenna and the pole, assuming it will be modelled as a point force at the top and uniformly distributed load down the pole. I've seen relevant equations but not sure if i can combine them. For ref, at 120mph winds, the force on the antenna is approx 335N and the entire pole has a force of approx 1480N. The pole is slightly tapered but this could probably be overlooked for purpose of calculation 

Also im not entirely sure how bending moments work if that is relevant

(I'm a 19 year old physics student and mechanics definitely isnt my strong point - just incase this question sounds silly) 😊 thank you

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So what is the question? Do you want the tip deflection? Do you want the deflection at every point along the length? Do you want the bending moment at the anchor? What is the question?


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The main point you are asking is can the results from different loading be added. For a static analysis, yes. Just think about applying a load at the tip and using the correct equation you will get a deflection. If you have doubled the load it would deflect twice as much. If you applied two loads each equal to the first load you would have the same deflection as a single load of twice the first. There are many reference books that will provide the equations for beams. A pole in this case is a vertical beam. Cantilever is the type of beam. As far as the taper, it could make a difference. The force at a point will decrease with decreasing diameter but the contribution to the moment at the base will increase as the distance (moment arm increases). Bending moment is very relevant.  It may be the most relevant value. From the bending moment (lb-ft, lb-in, etc) and the cross section of the pole you can determine the stress in the material. If you are addressing vibrations, Dr D. would be a good source for this info. If you are a physics major, what is your area of strength/interest if not mechanics.?  

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