I am installing a 24 ft 4×4 square quarter inch thick steel tube 4 ft into the ground with a concrete base of 28 inch diameter and just over 48 inches deep, so 20 ft of the post is above the ground. This post will be have heavy horizontal loads pulling it from the top of the post. I`m curious if the concrete base is deep enough and if reinforcement is required to keep the concrete from failing.
Thank you,
Best Answer
Whether your concrete base will survive is irrelevant, because your beam will fail.
See: https://www.amesweb.info/StructuralAnalysisBeams/Stresses_Steel_Hollow_Structural_Sections.aspx
Input:
Output: 
Notice the highlighted field of the output. That's the stress you'll be putting on the connection with the ground, (assuming it's rigid). The yield strength of steel (where it stops bending back when unloaded) is 36,300 psi, You'd be overloading this beam 1.5 times. It will fail.
Consult an engineer to design something for your purposes.
EDIT: I've done a recalc with a cantilevered beam calculator in response to the comments below. The result is essentially identical, and any difference between the two calculations is likely rounding. Simply put, two different calculators, with two different sets of input, give the same result:
I = 8.82813 in^4, and the 2 inches is the distance from the edge to the center.
There are two things to note in the results:
Further EDIT: The Plastic Modulus for this section is 5.28 in^4 Multiply that by the yield strength gives a Plastic moment of 190,000 in.lbf, which is ~16000 ft.lbf, which is LESS than the moment at the support of 20000 ft.lbf.
TLDR: You're loading the entire structure into the plastic region, turning it into a plastic hinge. This WILL fail.