Heiwa:
First of all, your spring model won’t work because, as soon as the collapse of the Towers begins, the elastic limit of the structural steel is exceeded almost immediately. The elastic strain energy capacity of A36 steel is only about 20 J/kg compared to 36 J/kg for the energy released by the descent of an upper portion of a Tower through one floor height. If you take a total core column area at the 95th floor as 2 m^2 and the yield stress of the core column steel as 250 MPa you can calculate the time required for the elastic limit to be reached – it come out to less than 10 milliseconds. At that point you can say goodbye to your springs and say hello to plastic hinges.
Actually I think the perimeter columns were the Achilles’ heel of the Towers and the bolted column end-plate connectors were the weakest link in the structural integrity chain. If you look at the load-displacement curve for A325 bolts (See NIST NCSTAR 1-3D) you will find that these bolts fail after an elongation of only 0.3 inches, which requires an energy input of about 2000 J per bolt. This means that all the perimeter column bolts could be destroyed with an energy expenditure of a mere 2 MJ. This is theoretically possible if the deformation energy is directed to a small fracture zone within each bolt, however, in practice energy is dissipated not just within a bolt but also within the end plate and in the column itself. Nevertheless, it looks like all the perimeter column bolts could be fractured with an energy input of less than 50 MJ.
Appendix B of the FEMA Report on WTC 1 & 2 notes that as the perimeter columns lost lateral support they deformed out-of-plane from overloading eccentricities. It was estimated that as the eccentricity increased, the applied bending moment exceeded the bolt moment capacity when the eccentricity was about 4.5 inches, which would occur when a column was only about 2 deg off vertical.
A325 bolts were probably also the weakest link in the core columns, especially for the upper floors. The splice connections consisted of two splice plates connected to the columns by eight or twelve A325 bolts with an ultimate shear capacity of about 220 MPa. The splice plates were consistently stronger than the bolts so the columns mostly failed in tension through shearing of the bolts. This explains why very few buckled columns were found in the WTC rubble piles.
