Hanging a 4x4 could be done with carriage bolts. Depending on the movement required it would be one single bolt or an array of bolts, and the bolt's required sheer rating would depend on the total load divided by the number of bolts.
The sheer strength of a bolt assembly is calculated as follows:
- Tensile strength probably at least 100000psi (check the specs by the manufacturer)
- Multiply by 0.6 to get Shear strength
- Multiply by cross section area of major diameter of bolt (e.g. 0.5in bolt has 0.44in^2)
- Multiply by number of bolts (e.g. 2, 3 or 4)
- Divide by safety factor of 5x for dynamic use
100000 * 0.6 * 0.44 * 2/5 = 10560 lbs
If you have 1/4in bolts, it is 1/164 of the above number (1/2 the diameter, so 1/2^2 the area).
ItIf movement is alwaysnot a factor, it is wise to use multiple through bolts even if the permissible load exceeds the requirement with just one.
Of higher importance is the bearing ability of the wood, considering the species. I have seen numbers of about 400lbs per lag bolt in deck building, so likely more for a through bolt if that's what you are using.
Pre-drill and keep the holes at least 1in away from the wood edge.