Foxy82
Member
- Country
England
I don't pretend to be a structural engineer, or an architect (not even a fountain designer like the Italian guy you referenced in your earlier post).
But, have you ever read up on dynamic loading?
Static vs. Dynamic
Even though there was still ~80% of undamaged structure below the impact zone, this does NOT mean it was "progressively stronger". High-rise structures are NOT designed to handle dynamic loads in the gravity direction.
Dynamic, as opposed to static, means there are moving parts transferring load, or that the load itself changes direction or magnitude. A good example is aircraft landing gear, which retracts when it hits the ground to transfer loads into the rest of the landing gear mechanism.
When designing a landing gear, you do not design it to handle only the weight of the aircraft, but rather some multiplication of the aircraft's weight. A typical landing gear design will safely handle 4-5X the aircraft's weight. High-rise structures are not designed to the same limits as landing gears because they aren't expected to handle dynamic loads in the direction of gravity. In the case of the WTC towers, a floor collapsing onto the floor below was the dynamic load, and the sign that global progressive collapse had begun.
Failure modes
The structural elements failed in a few ways:
Material yielding - simply means the loads exceed the strength of the material and the structural member will literally shear, tear, bend, or deform to give way to the load.
Buckling - a specific type of failure where the vertical load exceeds the critical buckling force and causes a column to bend in different directions depending on how the ends are constrained. Short columns tend to fail at the material yield limit, while long slender columns tend to buckle before bending to the material yield limit before failing.
Critical buckling force is calculated by F = (pi2 E) / (KL/r)2 , where E is Young's Modulus, and KL is the effective length of the column, and KL/r is the slenderness ratio (r = radius of gyration). A thin column has small radius of gyration and a stocky column has large radius of gyration. The slenderness ratio determines elastic or inelastic mode of buckling failure.
Catenary failure - this is when beams (horizontal members) "sag" under the weight from above it has to support due to the loss or failure of a column underneath. This has the double action of pulling in adjacent columns inward while also pulling downward.
Sequence of events leading to failure
Now knowing these concepts, here is the sequence of events leading up to structural failure:
As an act of terrorism, a plane crashed into the building substantially changing the structural integrity of the overall frame.
The plane was loaded with jet fuel that in turn ignited office furnishings that had been concentrated in a corner by the force of impact.
The collision disrupted/loosened/knocked off fireproofing of structural members, especially the main span floor trusses that ran between the exterior wall and the interior core.
Over time the floor trusses began heating and losing their structural integrity, including sagging into a catenary mode. This eventually failed one end of their gravity/lateral mode connections. The failure to either end would be problematic for the unsupported length of the building's columns, and lowering its vertical load carrying capacity. The failure at the exterior wall is most likely due to heat and bolt sizing. Perhaps, those floor trusses then collapsed onto the lower level spread heat/fire to the adjacent stories and added to the heat exposure of the exterior columns, increasing their KL/r ratio beyond their design limit for steel at a given temperature. Or possibly, that failure mode might have initiated at a mid-story column splice.
The lack of support to the exterior columns continued until failure was initiated. A seam-like failure indicated a failure may have been imminent and only needed one to fail for all to fail.
Progressive collapse is initiated which is unstoppable once initiated.
Again, not an engineer, but the above seems a pretty convincing argument?
