I was talking with a friend tonight about the collapse of the Twin Towers, and he proposed that the collapse was due to the fact that steel has very poor compressive strength as compared to tensile strength. In his view this lack of compressive strength is the key to the buildings collapse.

Note: My friend believes that 9/11 was probably an inside job, but questions the controlled demolition hypothesis.

I pointed out to him that the "pancake" theory of the global collapse does not postulate that weakness of the core columns was a critical factor, and that the global collapse was not a result of buckling of core columns, but, rather was due to the overload of the concrete slabs on individual floors from the pressure of the floors falling upon them from above.

The collapse, according to NIST, was initiated due to weakening of core columns on floors affected by fire. Therefore, the compressive strength of the columns is not the key factor in the collapse scenario.

I would like to point out that I am not personally committed to the controlled demolition hypothesis. I am genuinely interested in reasoned arguments which support the official theory.

(: hereward

It has been noted that Dr Greening’s report is now available having undergone some alteration.
However there remain serious flaws within the assumptions made and these are having the effect of rendering the conclusions almost worthless.
The main flaw in this report, regarding the collapse is contained within the authors derivation and use of the strain energy requirements to collapse a single floor.

This flaw has as its source the assumptions implied within the bottom paragraph of page 19. The author states, “As noted in Section 4.2 the 236 perimeter and 47 core support columns have an effective cross sectional area of …..10.15 m^2.………we conclude that the supports at a given floor would fail if the downward compressive load exceeded about 4000MN.”
The author then goes on to compute a “collapse safety factor of about 3” for that storey.

The author is stating that the same amount of force would be required to produce failure in any of the storeys. This is plainly wrong since the upper storeys were made of relatively light material section and in some portions, I-section columns, whereas the bottom storeys comprised relatively heavy section box columns.
The author seems to apply a belief that the tower support structures were of the same cross sectional area throughout the height of the tower.

A similar flaw occurs when the author discusses strain energy. Firstly and most importantly he uses the same value, 600MJ, for each of the storeys within the structure. There is no way this can be true and the values would lie over a wide range. For instance the 100th storey normally carries the ten storeys and the hat truss above and would be built with this in mind. The tenth floor would carry 100 upper storeys and the hat truss, so its geometry would reflect this. The author’s use of a constant value for this strain energy requirement does not reflect the situation which actually did exist.

Neither does the author take regard of the elastic strain energy absorbed by storeys other than the topmost storey of the lower section. To be able to cause a failure in those storey columns a force would have to be exerted by the falling upper section and this force would also act on all of the storeys below the impact and also on those above the impact point. The initial impact force exerted and thus the force required to cause buckling failure at the upper levels would not be sufficient to cause these failures at lower levels, but the effect of the force would still be some elastic deflection of all other storeys. The size of the deflection caused would vary from storey to storey and would be in the same ratios as the static load ratios for each storey. The energy requirement for this energy would vary dependent upon the number of storeys remaining but would always be a prerequisite to continued collapse.
The effect of ignoring this phenomenon is to ignore a large energy requirement that has to be satisfied before the collapse can continue. The energy ignored would be the difference between the average of the applied load over one storey’s resultant elastic deflection, and the average of the applied load over all storeys resultant elastic deflection.

The author examines the distance over which the failure load would act and these figures he gives are around 0.11 metres (p31)from a storey height of 3.7m. So he contends that after less than 3% of its length the columns would thereafter offer no further resistance to the falling mass. This contradicts accepted theory most notably contained within BZ that a minimum 3% vertical deflection would be required to even initiate buckling points. BZ show that the required force reduces from that point but it does not at any time fall below 25% of the initial failure value.
The author justifies his use of these small values of deflection by stating that actual failure occurred in the fixings between column sections rather than column failure itself . But this cannot be the case because we know from BZ that buckling points would only appear after 3% vertical deflection. There would be no buckle points at the vertical deflections used by the authors. Buckle points or a horizontal deflection of the column midpoint are necessary for the downward acting mass force to be able to gain a moment through which to apply a force on the fixings.
No buckling=> no moment=> no force=> no failure.
The author at one point suggests he is using compressive failure modes. Again the contention that total and catastrophic failure, resulting in an inability to transmit any force whatsoever, would occur after a deflection of only 3% is contradictory to accepted knowledge of compressive failures, which exhibit deformations of up to 40% with varying load requirements before ultimate failure results in an inability to carry any load whatsoever.

Neither do his own figures tie together
His figure of a failure load for storey 80 was 4000MN.(p19) This force acting over a distance of 0.11 metres would give a maximum energy requirement of 440MJ. But this is in contradiction to his figure for energy requirements to collapse one storey, being 600 MJ.
For these two figures to be satisfied it would be required that the force acted over a distance of a minimum of 0.15metres and in actuality a greater distance than this since the load would be zero at time = 0 rising to a maximum. The author gives no reason for this discrepancy.

Let us now examine the actual value of strain energy requirement for collapse. The author has identified the strain energy requirement for the first 3% of the vertical deflection of the buckling columns. We know from BZ that the remaining 97% of the vertical deflection will require a further energy input of some ten times this amount. So using a very rough approximation we can argue that the energy requirement is of the order of some ten times greater than the value used by the author. Even if we included a factor to allow a pessimistic view of early fracture and did this by allowing that only half of this additional requirement has to be met, we can see that the new value would still be of the order of some five times greater than the value used by the author.
To demonstrate the relative size of the energies involved let us assume for the moment that the aircraft was travelling slightly faster than the author has assumed, and let that assumption be that the velocity was 240ms^-1 rather than the 220ms^-1. This is not an absurd suggestion since it reflects the velocity given by the NIST report. We now see that the aircraft impact energy would be increased from the 3.0 x 10^9 J which the author uses to about 3.6 x 10^9 J. Thus an additional 600MJ would be available and according to the authors figures this would be sufficient to take out all of the perimeter columns and all the core columns on one entire storey. This would be in addition to the damage which we did witness being caused. Is this realistic? The aircraft velocity increased by a mere 20ms^-1, now has the energy to destroy an additional entire storey? This in itself casts doubt upon the relative size of these figures.

So what can be salvaged from this report? The author has demonstrated that the collapse times which were actually observed on the day, were consistent with a value of strain energy requirement to collapse each floor of around 600 - 800 MJ. Thus it can be shown that only by application of strain energy requirements of this order could the observed collapse times have been achieved. Since the values of strain energy were demonstrably higher than those used by the author we must conclude that since the observed collapse times were achieved then some mechanism must have applied in order for the energy requirements to be reduced to the levels used by the author. Without the removal of that ability the collapse times could not have been achieved.

Gordon Ross 23rd February 2006