How can I compute the thickness of a pole of a given material that is needed to carry a given load?

I want to compare those values for different materials, e.g. wood (pine, cork) and plastic polymers (HDPE,PP). So I want to compute the max load for a given material and cross section. Can I say that the max load is prportional to the cross area? and is this also true when I use hollow poles? Another question is what happen when the pole is loaded for limited amount of time. Can I tell when a pole that is loaded with, say, 20% more then its max load, will crush when loaded for 30 minutes every day?

And a question I'm very interested in is which cheap material will give me max strength per its density?

• vertical, indeed. May 9, 2018 at 11:23

The normal stress due to axial loading states $\sigma=P/A$ where P is value of the load and A is the normal cross sectional area.

The formula for normal stress due to bending moment states $$\sigma=My/I$$which can be elaborated as saying that normal stress depends on the moment (M), the thickness of the bar (y) and moment of inertia (I).

The shear stress due to axial loading states $\tau_{ave}=P/A$

The shear stress due to bending moment has formula $$\tau_{ave}=VQ/It$$ where V is the load, Q is first moment of area, I is moment of inertia and t is thickness of the bar.

Combining all these different kinds of stress we can conclude that the pole will fail in at least one of those scenarios. To make sure the pole won't break you need to make sure that the maximum yield stress is greater than maximum stress experienced in all four of these categories $$\sigma_{max}>\sigma$$ and $$\tau_{max}>\tau$$ Simple calculations for 4 of these stresses will tell you which material to use.

In conclusion, the material you choose depends on the Load itself, thickness, cross sectional area, first moment of area and moment of inertia of the pole you are using.

The time also matters since all materials are prone to fatigue which weakens it. Some materials are more likely to experience higher fatigues than others but it requires very complex analysis to identify the correct choice.

• Thanks for the dtaile answer. So for axial loading alone a pine wood with a stress of 1200psi and cross area of 10 inch^2 the max load is simply 12000lb? This sounds strange. May 7, 2018 at 13:03
• @OMGsh No the max stress is not what you get from calculating formula but it is what you get from material property tables online. I will try to clean up my explanation and make it more detailed tonight. May 7, 2018 at 13:06
• @OMGsh if you could attach an exact diagram of how the structure is loaded it would help a lot. May 7, 2018 at 13:52
• The structure is just a given weight placed on top of a tube. The number 1200psi was taken from somewhere online. Even in its week direction a wood has stres of 300psi so 10sqinch would carry 3000lbs. May 7, 2018 at 18:59
• Also need to consider buckling of the pole which could fundamentally change the conclusions for thin walled or narrow poles. May 8, 2018 at 15:44