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Safety Factor of WTC Steel Columns
#1
I have concluded a preliminary study of the safety factor of the twin tower steel columns at floor one based on an assumed gross building weight of 500,000 tons and A36, 36ksi yield strength steel.

The FOS is 1.54 for the steel at floor 1.

See attached graphic.

Note: if the gross weight of the building decreases the FOS increases and if the gross weight increases the FOS decreases.

I am replacing the graphic with a revised one showing MORE steel in the tree columns and a different OAL safety factor at floor one. The FOS would not change for any other floor.


Attached Files
.pdf   FOS r2.pdf (Size: 221.63 KB / Downloads: 1)
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#2
I don't know what to make of the silence of some of the more opinionated posters here about the strength of the twin towers such as Fetzer, Lemkin, Boldwyn, Kyle and of course Jack White.

Not a comment and no one has stepped forward to show how this work is flawed.

Of course, the FOS of the steel is not even an issue in a gravity driven progressive destruction of the floors.

But it was used as some sort of reason why it was impossible for the columns to be crushed... and it was quoted as never less than 4 or 5 and Fetzer and Boldwyn paraded the number 20 for the factor of safety. Just a nonsense argument with false information.

Anyone could have done this... it's basic math.... and all from the public record.

But this is a lesson of what happens when you decided to check the provenance of evidence claims for yourself and determine that several of those claims are made up out of whole cloth.

Trust but verify!
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#3
I for one am ignoring your posts and disappointed at the Forum, in general, for letting you more or less feel comfortable to attempt to take over the 911 part of this Forum with your snake oil. I don't buy your entire attack on the 911 Truth Movement - as that is what I see it as.
"Let me issue and control a nation's money and I care not who writes the laws. - Mayer Rothschild
"Civil disobedience is not our problem. Our problem is civil obedience! People are obedient in the face of poverty, starvation, stupidity, war, and cruelty. Our problem is that grand thieves are running the country. That's our problem!" - Howard Zinn
"If there is no struggle there is no progress. Power concedes nothing without a demand. It never did and never will" - Frederick Douglass
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#4
Jack is in hospital at the moment. Can't speak for any one else.
"The philosophers have only interpreted the world, in various ways. The point, however, is to change it." Karl Marx

"He would, wouldn't he?" Mandy Rice-Davies. When asked in court whether she knew that Lord Astor had denied having sex with her.

“I think it would be a good idea” Ghandi, when asked about Western Civilisation.
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#5
Magda,

Thanks for that information. I hope a speedy and complete recovery for Jack. Come back Jack!
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#6
Attached is the Excel worksheet which computes the weight of the facade steel. I've revised the graphic in the previous post adding more weight to the tree columns and making their wall thickness 5".

Methodology:

Although the facade were 36' tall x 10' wide pre fab panel assemblies I broke out the columns by floors. Therefore the column length is given as 12" and for the mechanical floors it is 14'. The mech floor facade panels were actually 42' tall. The corner assemblies were 24' tall (two floors) and 10' wide with with there spandrels bent at 45° to joint to the facade panels. The spandrels were treated as a separate item.. 10' x 4.25' for all but the mech floors which were 10'x5' and were assumed to be thicker.

The facade panels not only incremented in wall thickness and weight, but were assembled in an offset pattern beginning and ending at each mechanical floor section. This meant that there would be panels of two different wall thicknesses spanning three floors as the wall thickness "transitioned". So the panels just above and below the mech floors would have a 1 floor high panel, a two floor high panel then a 3 floor high panel and repeat symmetrically about the center. Refer to the graphic to see how the wall thicknesses were "mesh" and transitioned over 3 floors

The increment for wall thickness was .125 with the thinnest wall being .25" at the top floors and the thickest at floor 10 being 2.375". These thicknesses made the total facade cross sectional area and weight about 20% greater than the core columns. The facade did support about 10% more of the axial loads than the core and it also had to be stronger because of the wind shear.

The core columns decremented by .125 wall thickness as they went up and so the approach was the reverse... increment the thickness beginning at .250 at a similar rate. However, if the rate of change was less, the wall thickness at the bottom columns on floor 10 would be less than 2.375" and the weight less for the entire facade steel. The scheme presented makes sense... but the RATE of decrement could be different... yielding a lower overall mass.... but not by much. It HAS to be larger than the core... and we KNOW the core column sizes which are published online.

To compute the weight if a facade assembly... find the column weight at the floor chosen and multiply it by 6 then add 3 times 1,100 pound for the spandrels.

Example: How much did the facade panel weight at floor 96?

1 - 12' column weighs 1,151#
1 spandrel weighs 1,116#

1,151 x 6 = 6,906#
1,116 x 3 = 3,348#

6,906 + 3,348 = 10,254#

total weight of one 36' tall x 10' wide face panel at flr 96 = 10,254# = 5.127 tons (short)



Attached Files
.pdf   Facade Calc r2.pdf (Size: 14.61 KB / Downloads: 1)
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#7
The safety factor is for AXIAL loads... the weight of the building and contents - all dead and live loads will factor into the safety factor.

The steel strength is determined by its cross sectional area and the TYPE of steel used. In the base of the twin towers the steel was A36 which means it can support 36,000 #/in before failing. This is called the "yield strength".

To determine the total load the steel in the towers' columns can support you sum up the cross sectional area at the base and multiply it by the type of steel which in this case was A36.

Based on the areas I computed the tower's A36 steel columns (core plus facade) could support 825,708 tons. The factor of safety for AXIAL loads would be the ratio of the ACTUAL building weight to the 825,708 tons. If the building weighs 825,708 the factor of safety = 1. If the building weighs 412,854 the FOS = 2. It's that simple.

But we need to know how much DID the buildings weigh? The popular commonly expressed weight is 500,000 tons giving a 1.65 FOS.

But what if there was LESS steel in the facade... less cross sectional area? The ACTUAL load distribution between the core and the facade columns was about ~52% of the weight was carried by the facade and ~48%. Since we DO know the area of the core columns and if we assume this load distribution and the area of steel to support the loads.. the facade steel would be about 1/10 more cross sectional area than the core steel. The core steel area was 122.17 sq ft at the base so the facade would have to be 122.7 x 110% = 135 sq ft. so the total area would be 257.17 sq ft. This could support 666,507 tons.

If the building weighed 500,000 tons the FOS would THEN be 1.33. If it weighed 400,000 tons the FOS would be 1.66

So we have two variables: weight of building and total area of facade columns. However we can see that the FOS falls within a range from 1.33 - 1.66. The average being 1.5. The typical steel frame highrise has a FOS of 1.42 so the twin towers appears to be a bit "stronger" than your average highrise by about 5% as far as AXIAL loads are concerned.

It should be noted that this is the AVERAGE FOS of ALL the columns at the base. Some columns may have higher FOS and some lower depending on the loads they carry in proportion to their cross sectional area.

We've heard numbers for FOS of 4, 5 and even 20. This is simply nonsense and not based in reality. The steel would have had to have been 3 to 12 times heavier or the building 3-12 times lighter. And you can see that the numbers don't add up.

Of course this FOS discussion is moot, because the failure was NOT the columns, but the floors!
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#8
Why investigate the factor of safety in the Twin Towers?

There are many reasons why we would want to determine the factor of safety for the steel. The most obvious would be to see if sufficient loads could be applied via load redistribution to fail the (a column)... and cause local failure of the floors around that column.

Another consideration is that the higher the FOS is the less likely is the possibility for a progressive failure to propagate to other columns.

A simple example illustrates the notion of how FOS relates to progressive failure of the columns. In the example let's use 40 columns each carrying identical load with a FOS of 1. If one columns is destroyed or fails for ANY reason... there load it carried is then redistributed to the remaining 39 columns. Before failure each column supported 1/40th of the load and after failure the remaining 39 supported 1/39th of the load. With an FOS each column could ONLY support 1/40 of the load so when a single column fails ALL REMAINING are being loaded PASSED their yield strength and will FAIL from buckling almost immediately. YIKES.

If the FOS was 2 using the same example, each column could support 1/20 of the load. This means that if 19 columns were to fail the remaining 21 would then be supporting 1/21th of the load and the structure would stand. If one more column failed the remain 20 would carry 1/20th of the load and be at their limit. One more column and the remaining 19 would be OVER their limit and fail instantly.

So with an FOS or 1.5 if one column more than 1/3 of the columns fail the remaining columns will buckle immediately.

There are additional factors to consider in progressive column failure scenarios. One is that load redistribution will move to the closest columns to the failed one. And since not all columns ARE of the same load bearing characteristics more information is needed to understand whether and under what conditions will the adjacent columns fail. For example in the twin towers' core the four corner columns were much stronger and carried 2 or 3 times the load of some of the other core columns. So failure of the corner columns would lead to a rapid overloading and failure of adjacent weaker columns.

Look at the attached Column Percentage of Area chart for the core columns on flrs 80-83 (one 36' three story column). Note that the four corner columns contain 4.61% and 4.73% of the core area and carry the same percentage of the core loads. If those 4 columns are "failed" the adjacent columns will immediate see load increases as the loads from the 4 failed columns are redistributed to them. Let's assume the 2 adjacent columns share the new load from the failed columns. They would then carry an additional .5 x 4.61 = 2.3% or .5 x 4.75 = 2.38%. Here are the load percentages for the adjacent columns before and after failure of the corner columns 501 & 1008

502 before failure = 2.81%
502 after failure = 5.31% (it's now loaded at 1.9x its former load)
601 before failure = 1.56%
601 after failure = 3.86% (it's now loaded at 2.5x its former load)

908 before failure = 1.63%
908 after failure = 3% (it's now loaded at 1.8x its former load)
1007 before failure = 2.91%
1007 after failure = 5.28% (it's now loaded at 1.8x its former load)

So in each of these cases IF THE FOS WAS LESS THAN 1.8 the adjacent columns would fail... if they couldn't "offload" some of the additional loads transferred to the by the failure of the corner columns 501 and 1008.

We've seen that the FOS was likely in the 1.65 or lower range. This means that taking out (failure) of the 4 corner columns will lead to the failure (buckling) of the two adjacent columns and then those adjacent to them and so on! TAKE OUT 4 CORNER CORE COLUMNS AND THERE WILL BE A RAPID PROGRESSIVE FAILURE MOVING INWARD TO THE CENTER OF THE CORE AND ALL COLUMNS WILL BUCKLE IF THE FOS IS AROUND 1.65.

It's likely that the adjacent columns CAN redistribute the new loads to adjacent columns. But suppose 4 additional columns were to fail such as 503, 506, 1005 and 1006? If you run the numbers you will see that these 8 column failures with lead to a rapid redistribution and buckling of the entire core... with a FOS of about 1.65.

This understanding was crucial to those who would want to collapse the core at an upper floor so that the floors would have no core side support and drop down onto the intact floors below and initiated the ROOSD.

The ROOSD could be initiated at ANY level, requiring only 4-6 descending floor masses to initiated it. With the steel being thinner the higher you go and column failure from around floor 100 or below would do the trick and require MUCH less incendiaries or explosive energy.

The collapsing core would in addition to pulling the core side of the floors attached to the core down with it, would spring the facade panels or cause them to slip past the lower ones still connected to intact floors with those floors connected to the intact core. The initiation of the ROOSD floor destruction would deliver fractured floors (4-6) onto intact floors when as few as 4-8 key core columns were made to fail.

This is why the FOS is key to understanding of how to engineer the destruction of the towers.


Attached Files
.pdf   core column weight.pdf (Size: 21.46 KB / Downloads: 1)
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