Heiwa
You have claimed on the "gravity collapse" thread that:
When challenged for a detailed analysis of this, you cross-referenced your own paper wherein it is noted:
I believe this analysis to be insufficiently detailed and, in particular, incorrect.
NIST tested the steel recovered from WTC (which in itself is of interest, as CTers usually claim it was all whisked away to China with unseemly haste). NIST NCS STAR 1-3D (http://www.fire.nist.gov/bfrlpubs/fire05/PDF/f05158.pdf) confirms a range of actual values:
- Core webs ranged from as low as 31.1 to 41.9 ksi, ie. 86 to 116% of specificed strength.
- Core flanges ranged from 32.4 to a high 53.4 ksi, ie. 90 to 146% of specified strength.
Setting to one side the 31.1 and 32.4 ksi results, inasmuch as a small proportion of columns below failure point are unlikely to lead to any wider problem, let's take the lower maximum of 116% specified value.
Now, the NIST Demand to Capacity Ratios (DCR) are based upon specified strengths and NIST themselves note that there is effectively spare capacity up to actual (but varying) yield point/strength.
Core columns in WTC typically had a Demand to Capacity Ratio (DCR) of 0.83, ie a safety factor of 1/0.83=1.20. Now let's assume assume that the steel has an additional 16% beyond minimum yield value. This would reduce the DCR to 1.16/.83=1.4.
In other words we could increase the loads in these areas by up to 40% before yield point was reached and plastic (permanent) deformation begins. Of course this figure has lots of variables - most of the steel webs did not have such a high yield factor, some areas had DCRs well in excess of 0.83, and so on.
What we don't do is then add any significant additional allowance for tensile strength because (a) yield failure is already occuring and (b) gravity loads will be compressive, not tensile.
As I frequently mention elsewhere on the forums, one thing we also have to appreciate is that the structure of WTC is complex; in addition to dead and live loads, it will be dealing with (for example) transverse and shear loadings from the wind. There will be a degree of torsion due to differential loading. And so on. We would therefore have to look at the exact steelwork design in considerable detail before we could determine a safety factor for each. That's why engineers earn a lot of cash, and why complex modelling software was developed.
Nevertheless it is clear that the actual capacity of the core is not going to be anything like 300% or 3:1 before irreversible damage and failure begin to occur.
But in any event the above calculations all assume an intact core, and we know from the various NIST studies and eyewitness evidence that the cores suffered damage - around a third. This will obviously have reduced loadbearing capacity still further, and a simple pro-rata reduction of (say) 30% is likely to be wrong because the damage is concentrated in localised areas and hence these areas will be susceptible to accelerated failure under loads.
Now, Heiwa, can you produce similar calcs and figures to back up the "FoS>3" position you've adopted, or is it as substantial as your structural calculations?
You have claimed on the "gravity collapse" thread that:
Heiwa said:
When challenged for a detailed analysis of this, you cross-referenced your own paper wherein it is noted:
Heiwa said:
I believe this analysis to be insufficiently detailed and, in particular, incorrect.
NIST tested the steel recovered from WTC (which in itself is of interest, as CTers usually claim it was all whisked away to China with unseemly haste). NIST NCS STAR 1-3D (http://www.fire.nist.gov/bfrlpubs/fire05/PDF/f05158.pdf) confirms a range of actual values:
- Core webs ranged from as low as 31.1 to 41.9 ksi, ie. 86 to 116% of specificed strength.
- Core flanges ranged from 32.4 to a high 53.4 ksi, ie. 90 to 146% of specified strength.
Setting to one side the 31.1 and 32.4 ksi results, inasmuch as a small proportion of columns below failure point are unlikely to lead to any wider problem, let's take the lower maximum of 116% specified value.
Now, the NIST Demand to Capacity Ratios (DCR) are based upon specified strengths and NIST themselves note that there is effectively spare capacity up to actual (but varying) yield point/strength.
Core columns in WTC typically had a Demand to Capacity Ratio (DCR) of 0.83, ie a safety factor of 1/0.83=1.20. Now let's assume assume that the steel has an additional 16% beyond minimum yield value. This would reduce the DCR to 1.16/.83=1.4.
In other words we could increase the loads in these areas by up to 40% before yield point was reached and plastic (permanent) deformation begins. Of course this figure has lots of variables - most of the steel webs did not have such a high yield factor, some areas had DCRs well in excess of 0.83, and so on.
What we don't do is then add any significant additional allowance for tensile strength because (a) yield failure is already occuring and (b) gravity loads will be compressive, not tensile.
As I frequently mention elsewhere on the forums, one thing we also have to appreciate is that the structure of WTC is complex; in addition to dead and live loads, it will be dealing with (for example) transverse and shear loadings from the wind. There will be a degree of torsion due to differential loading. And so on. We would therefore have to look at the exact steelwork design in considerable detail before we could determine a safety factor for each. That's why engineers earn a lot of cash, and why complex modelling software was developed.
Nevertheless it is clear that the actual capacity of the core is not going to be anything like 300% or 3:1 before irreversible damage and failure begin to occur.
But in any event the above calculations all assume an intact core, and we know from the various NIST studies and eyewitness evidence that the cores suffered damage - around a third. This will obviously have reduced loadbearing capacity still further, and a simple pro-rata reduction of (say) 30% is likely to be wrong because the damage is concentrated in localised areas and hence these areas will be susceptible to accelerated failure under loads.
Now, Heiwa, can you produce similar calcs and figures to back up the "FoS>3" position you've adopted, or is it as substantial as your structural calculations?
