First, the moment distribution from the bottom to the top of the pole
needs to be determined so that the maximum can be identified. The pole can be considered as a simple cantilevered beam
which makes finding the moment diagram simple. If a cut is made at an arbitrary location, x, then the moment at that location is
M_{aa} =
(300 lb) (12 - x ft)(12 in/ft)
= 43.2 - 3.6x kip-in
The maximum in the bottom section is 43.2 kip-in at the ground. The maximum for the top section is 21.6 kip-in at the mid-point joint.
The moment of inertia for both sections are,
I_{top} = πd^{4}/64 = π2^{4}/32
= 0.7854 in^{4}
I_{bottom} = π/64 (3^{4} -
2.5^{4}) = 2.059 in^{4} |