For us a hard landing inspection is required typically if the touchdown rate is greater than 8 - 10 feet/sec. Being an experimental organisation -that's an equivalent parameter equal to 8 - 10 feet/sec pure vertical - not what you'd be looking at on the VSI. Once while doing some runway performance testing we came in at 12 feet/sec - teeth rattling!
The other thing to bear in mind is how close to MLW the aircraft is at TD - the greater the weight, the more inclined I'd be to have a structural inspection carried out.