tapered vs. non-tapered light pole
- Thread starter anbm
- Start date
fmtjfw
Senior Member
- Location
- Fairmont, WV, USA
It probably weighs less for the same strength given the same height
gar
Senior Member
- Location
- Ann Arbor, Michigan
120818-1216 EDT
From a mechanical perspective you have a cantilevered beam (fixed at one end). If the beam is of uniform cross-section and a fixed force is applied to the free end of the beam, then the stress in the material will be a maximum at the fixed end and zero at the free end.
For minimum material cost you would want to make the stress nearly uniform throughout the pole. This implies a tapered pole.
Why does the stress vary along a uniform pole? Because the tangential force in the material is a function of the lever arm length from the point of force application to the point of interest. The support end has the longest lever arm from the free end, and therefore the highest stress. Stress is perpendicular force divided by area. Wrought iron is in the range of 30,000 #/sq-in, and steel is from the same range to 230,000 #/sq-in.
This same reasoning applies to why I beams are stronger and stiffer for the same weight of material compared to a flat plate.
On a side subject see http://en.wikipedia.org/wiki/John_A._Roebling for some interesting history. Roebling built the Brooklyn Bridge with iron wire instead of steel because it was less impacted by corrosive elements than steel. Thus, the cables had to be larger than if steel was used. The Brooklyn and Cincinnati bridges are still standing 1883 and 1866. I do not know if the cables have ever been replaced.
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From a mechanical perspective you have a cantilevered beam (fixed at one end). If the beam is of uniform cross-section and a fixed force is applied to the free end of the beam, then the stress in the material will be a maximum at the fixed end and zero at the free end.
For minimum material cost you would want to make the stress nearly uniform throughout the pole. This implies a tapered pole.
Why does the stress vary along a uniform pole? Because the tangential force in the material is a function of the lever arm length from the point of force application to the point of interest. The support end has the longest lever arm from the free end, and therefore the highest stress. Stress is perpendicular force divided by area. Wrought iron is in the range of 30,000 #/sq-in, and steel is from the same range to 230,000 #/sq-in.
This same reasoning applies to why I beams are stronger and stiffer for the same weight of material compared to a flat plate.
On a side subject see http://en.wikipedia.org/wiki/John_A._Roebling for some interesting history. Roebling built the Brooklyn Bridge with iron wire instead of steel because it was less impacted by corrosive elements than steel. Thus, the cables had to be larger than if steel was used. The Brooklyn and Cincinnati bridges are still standing 1883 and 1866. I do not know if the cables have ever been replaced.
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