Did anybody do any kind of mathematical or experimental analysis to test how significant such a jolt would be? I don't deny that the columns were misaligned during the collapse, but I did my own back-of-envelope, first approximation calculations of the collapse of the Towers, as follows."Why both D Chandler and T Szamboti are wrong to expect a sudden jolt or significant deceleration"
AND the reason - yet again - in one sentence - "Because the Top Block did not drop to impact on the lower tower with columns in alignment"
AND I've already posted a pretty picture that is a large part of the necessary proof. Look and THINK:
Both Chandler and Szamboti expected the line of the perimeter - the yellow arrows - to hit its other part. Clearly it wasn't going anywhere near where the "Jolt" (Szamboti) OR "deceleration" (Chandler) would come from.
The force the section of the Towers that were above the damaged zone normally exerted on the section below the damaged zone can be approximated by taking the mass of those floors and multiplying it by gravitational acceleration. The entire building had a mass of about 450 x 10^6 kg, and about 10% of each Tower was above the impact zone, so I estimate about 45x10^6 kg of mass above the impact zone. This should be a conservative estimate; the real value probably is a bit larger, and would be different for each Tower.
F=ma = 45x10^6 kg * 9.8 m/s^2 ~= 441x10^6 Newtons
This is the gravity or static load that the portion of the Towers below the impact zones resisted from the portion above the impact zones on a normal day.
When the portion of the Towers above the impact zone began moving, they began moving pretty much as a rigid block, at least for a few meters, until they actually impacted the lower floors. Each floor was separated from the next by 3 or 4 meters. I don't know how fast they accelerated or what velocity they reached in this time, but I conservatively estimated 1/2 free fall acceleration for 3 meters, giving the falling section a velocity of 5.4 m/s by the time it reached the next lowest floor, using standard free fall velocity calculation.
The force the upper section was capable of generating on impact with the lower section would depend on the stopping distance or stopping time required to stop the falling mass. I'm assuming that the ultimate limit of stopping distance would be the distance the bolts holding each floor together could be distorted before shearing. If you wanted to assume that the columns were aligned, you would need to decide how far the columns could deflect before they broke. According to NIST's "Overview of the Structural Design of World Trade Center 1, 2, and 7 Buildings" (File Name 910105.pdf), "The typical bolt used in the simple shear connections was 22 mm (7/8 in) diameter ASTM A325... The bolt used for heavier brace and moment connections was a 25 mm (1 in) diameter ASTM A490." ("Overview of the Structural Design of World Trade Center 1, 2, and 7 Buildings." Unnumbered page; P 25 in the PDF.) I made several calculations using different values of stopping time (in the millisecond range) and stopping distances (in the millimeter range). An example calculation:
Where m is mass, g is gravitational acceleration, h is height of fall and s is the stopping distance.
Assuming the bolts could bring the falling upper section to a stop in 6 millimeters without shearing,
F= mgh/s = (45x10^6 kg * 4.9 m/s^2 * 3 m) / 6x10^-3 m = 110 x 10^9 N
The ratio of the impact force to the normal static load is
110x10^9 / 441 x 10^6 = 249
If, instead, the falling section fell at standard 1g, then the impact force becomes
(45x10^6 kg * 9.8 m/s^2 * 3 m) / 6x10^-3m = 221x10^9 N
and the ratio becomes 501 times the usual static load.
My results tell me that for the lower section to withstand the collapse of the falling material above them, they would have to have withstood about 250 times the static force they normally supported. As the bolts (and the rest of the building) would not be able to resist this much force, they would have broken before reaching that value. If the columns had been aligned and impacted straight on to each other, they would have to have deflected by a few meters without breaking to resist the force of the material falling on them.
As each floor broke apart, it would add to the falling mass of debris. Whatever wasn't ejected to the sides probably would contribute to the mass impacting the next floor, and all of it would continue accelerating, increasing the amount of force applied, until it reached equilibrium. Any jolt would have been momentary, lasting milliseconds, similar to the jolt or deceleration that a football player experiences when running through a paper banner. I don't believe you would notice very much! Just as you don't notice each detonation inside the piston chambers of a car revving its engine, you wouldn't notice the jolt as the falling section impacts the next floor.
Other people have also performed similar calculations, using different assumptions for the variables, but all of them concluding that the Towers could not possibly have withstood the force of impact of the falling material (and none of them assume the columns were aligned):
New Mexicans for Science and Reason, "How Does a Building Crush Itself?," By Dave Thomas
"Static v. Dynamic Loading: Why the WTC Towers Fell So Fast"
"Why Did the World Trade Center Collapse? Science, Engineering, and Speculation"