21-05-2011, 12:27 PM
(This post was last modified: 22-05-2011, 04:16 AM by Jeffrey Orling.)
Jason,
Thank you for being open minded about this matter. Steel framed have the beams / girders actually which carrry the floor loads connected to the SIDE of the columns in almost all cases. The reason why is simple. Let me illustrate with an example.
Let's look at the a point lot down in the structure. The floor load is relatively small, even if it is for an large portion of a floor and is carried by a single girder which needs to be affixed to a column which transfers the load to the foundation. That column is carrying the load of all the columns above it... and their portion of the floor loads attached to them And this is why the column cross section is progressively larger moving down the structure. If you placed the a girder on top of a column, then you would have to place the next column on top of the girder and so one. The girder then, is having the entire load above placed on its end... the portion of the girder which is on top of the column. If you examine the cross sectional area of the girder... the web... will see how small it is compared to the column above and below it. The web would be crushed ... too small to support the load.
We often weld in web stiffeners to assist a H shaped beam to support the loads when there are concentrated vertical loads placed on it mid span. A steel beam works by placing the compression and tension material as far apart and using a relatively thin tall web to separate them. A wood or concrete beam has a uniform cross section typically which is why you CAN rest a solid wood beam directly on a solid wood column (with the same compressive yield strength.
So there is no other way to erect a multi story steel frame than to attached the loads (girders) to the sides of the columns.
There were several contributing factors which assisted the gravity driven collapse phase.
1. the floor system was column free... this made the floors long span and placed all the columns to support them at the outside edge of the building and at the perimeter of the core. This required that all the floor loads be directed by the beams... there were no girders... to the few columns that would carry the floor loads. At the facade the floor beams truss joists were attached to every other column at the facade. The other columns received the axial loads via the spandrel plates which connected all the facade columns together. On the core side the floor trusses were connected to a channel section at 80" oc (truss spacing) which was then connected to the perimeter core columns... 8 of them on one side and 6 on the other with the corner core columns carrying loads from bother sides. The core side had several possible failure points... the truss seats themselves, the channel which supported them... the beam stub outlookers.. which were very short beams connecting the channels to the columns and the bolts and welds of all the connections. As you progress from the floor to the column the yield strength of the component must increase as it carries the aggregate load of what ever is connected to it.
2. To make the floor structure long span... it had to be deep. The deeper a beam is the less it deflects per given load.. hence longer spans have deeper beams. Deeper beams make the entire structure taller... and would make the floor system very heavy as well. Heavy means more steel, more expense, and larger columns and also more expense... and connection and erection issues. The floor system was an off site pre assembled approach.
To make the floor system lighter and thin enough a truss system was used. A steel truss is like H beam in that it has a compression chord at top and a tension chord on the bottom which "do the work" separated by diagonals... in the case of the towers' floor trusses - 1" Ø bars. This allowed for wire pipes and ducts... "building "service" to run perpendicular to the trusses without cutting holes in them which is also expensive and weakens a beam or girder and must be done in its center and of a limited size as well, else the beam action is lost.
The trusses are light, very light, and the floor which they supported was made as light as possible too - no stone aggregate concrete. Concrete needs a form to pour it on. The floor system instead used light weight 22 ga (the lightest used for this) corrugated metal decking to support the concrete pour. The decking ran parallel to the trusses for economy reasons and to allow conduits for wiring to be run in the concrete. This was the weaker direction to orient the decking. Additional cross trusses were inserted perpendicular to the main pre assembled trusses which tied the entire system together... giving the entire floor a membrane action. Everything working together us a composite. A composite floor is made stronger by composite action and so the individual components of a composite can be made weaker and lighter and cheaper as long as the composite performs to spec.
And so it is why the WTC twin tower floors (components) were so (relatively) light... and therefore inexpensive and easy to erect. And as we saw easy to come apart when off spec loading occurred. And not only that... To reduce the weight and the cost the PANYNJ requested and were granted a design load reduction for the long span open office floor. NYC code calls for 100 pounds per square foot and the PANYNJ were allowed to use a design of 58#/SF.. a 42% reduction. Their claim was that normal conditions in offices rarely see loads of 100#/SF. The request was granted. The tower floors were designed to be 42% weaker than all other office floors in NYC.
3. By relocating the columns out of the main floor space the entire floor area was more vulnerable to failure not just an area within one - 4 column bay as we see in all other steel frame designs. This column free floor space design was touted as more flexible for designers of the fit out of the tenant floors, AND more economical to build... and quick too.
It must be emphasized that the was no expectation that ANY floor would see sufficient imposed loads to fail it. Tenants are not allowed to exceed the load allowances... even in elevators. If these loading limits are observed there is no reason to expect any structural failure.
As explained in many of my posts, the collapse was inevitable ONCE the threshold load was exceeded... a load which PANYNJ had authorized be reduced 58#/PSF which made this failure point lower. But the designers never expected that a single floor could support 4, 5, 10 or 14 floor weights and their contents. If this load was imposed on ANY floor in that building... or ANY BUILDING for that matter is would fail and collapse.
And that is precisely what happened in Phase II... Phase I delivered the over design imposed load onto the floor system in the undamaged section of the tower... first to the top most floor... 96 or so... and then the runaway collapse (ROOSD) ensued. As stated we don't know how those 14 top floors were "destroyed" and converted into the imposed load for floor 95. It doesn't seem likely that office fires could leading to such a destruction. But the destruction of those floors could be a "mini" (not so mini actually) destruction up top 14 floors engineered with explosives and or cutter charges to the relatively small steel sections above floor 96. If the objective was to "free" the mass to crush the floors progressively... then calculations involved the creating the minimum threshold mass to initiate the ROOSED... and that may be as few as 4 or 5 floors!
The much more difficult concept to grasp is the fate of the core columns and this was made more difficult because we can see what happened to most of them except at the end after the floors had collapsed and the facade peeled away.
A steel frame is able to stand erect because it is braced by beams affixed to the sides of columns. Without and floors a steel frame is a 3 dimension lattice. A frame can be made rigid with very stiff joints or use of diagonal bracing... or as in wood studs application of a membrane - wall sheathing - to the studs. Diagonals are very "inconvenient" for any number of reasons in tall structures... but they are often used to stiffen the entire structure to resist wind loads which are enormous and act laterally not axially on the columns
The towers relied and rigid non rotating connections of the beams/bracing to the columns called moment connections. The bracing beams had their webs welded and bolted with angles to the columns. The welds and bolts carried the full load of the connections.
Perhaps the most difficult concept to understand and rarely encountered is "self buckling" of a column. Euler, a physicist, discovered that a column's strength... the axial load it can support is not ONLY determined by its cross sectional area and type of material... different materials have different compressive strengths... but by its unsupported length.
He described three classes of columns - short - medium and long and this were expressed in ratios of the length to their cross sectional area. Short columns are the strongest... long are the "weakest" for a given cross sectional area.
But there is a upper limit for long columns. Long columns made of steel cannot be longer than 150 times their shortest cross sectional dimension. So a column which is 12x24 inches in plan can not not longer than 150x12" or 150 feet tall. If one attempts to erect a column of these proportions it will buckle at a point below its mid height. It will fail from its own weight. It will "self buckle". This is "Euler Buckling".
Columns, are made as small as possible in cross sectional area to "do the job" and this makes them cheaper, uses less real estate and so forth... but they have to have sufficient area for floor beam connections to be made as well.
In the case of steel high rise frames the bracing is at each floor level and so the columns are considered short and therefore quite strong. The core column 501 which had a short axis dimension of 22" and a floor height of 144". The slenderness ratio was about 1/7. The actual column length was 36'. But the effective length was 12'
However in a high rise one column is placed on top of the next and so core column 501 was 1362 feet high made up of 38 columns... most 36' long and a few at 42 feet... with bracing at each 12'. So again each segment was a short column. Even at the top where the cross section has been reduced to a 12" wide flange the slenderness ratio was 12 and this still made it a short column and not subject to self buckling.
When the floors collapsed, they destroyed the beams and girders which carried them. Those beams and girders were overwhelmed by the same excessive (to their design spec) imposed loads. It's likely that their connections failed rather than the beams bending and deflecting or shearing. They would shear if the connections were stronger than the beam itself. And this DID occur in some cases.
As the floors collapsed past the columns... leaving them without their lateral bracing... the effective unbraced length grew. After the collapse of 16 floors... say from 96 to 76 for example... the unbraced length of the 20 floor tall unbraced column was 192 feet and the short axis was about 18" 1/160 which EXCEEDED the slenderness ratio limit for a tall column which is 150. Therefore this 20 floor high unbraced section of column HAD to buckle from "Euler buckling". This of course was made even easier because it was already created from 36' long sections and the welds at the column joints failed and the sections were sprung out of column beginning at below half its unsupported height. Having collapsing material assault it laterally only added to its inherent instability.
The only columns which survived at all were the largest in cross section. And they only survived as long as they did because the bracing was still attached to the next column. This can be seen in the spire columns of rows 500 and 600. The bracing made these pairs effectively a column of about 15' by 22" in plan view... but this didn't help much and even those massive core columns buckled and failed... springing off their 36' long sections below mid height. CC501 weighed almost 1100 tons up to the 78 floor and when it buckled perhaps as much as 400 tons above its mid height accelerated straight down at free fall... with nothing to support, resist or stop it.
The columns had very little strength relatively in the lateral direction... without the bracing. Even without Euler buckling coming into play... there was enormous lateral loads coming from the collapsing debris of the 90+ floors above as the facade acted like a chute containing it. But this was a futile effort by the facade and the collapse rubble exerted a lateral force which pushed the facade over and acted in a similar manner on the core columns. So the floors did not ONLY collapse passing the columns, stripping off the lateral bracing... but it also exerted lateral forces ON the columns (absent the lateral bracing) which contributed to their fracturing apart at those same weak points... the welds applied to the outer perimeter which connected them. Understand that if CC col 501 for example, a floor 18 had a cross sectional area of 5.08 feet, the weld connecting it to the column above it was only about 150" in length an it's cross section was at most a foot or two in area. This is why the columns were found (seen in the debris) in "neat" sections broken at their welds.
It's likely that the lateral pressure from the debris was a factor as well as the Euler buckling. The latter was the mechanism for the "spire" columns which survived the floor collapse and were stronger and less likely to yield to the lateral forces. The debris might have actually braced the bottom of the spire columns... but the Euler buckling ruled and they self buckled and sprung or toppled.
Thank you for being open minded about this matter. Steel framed have the beams / girders actually which carrry the floor loads connected to the SIDE of the columns in almost all cases. The reason why is simple. Let me illustrate with an example.
Let's look at the a point lot down in the structure. The floor load is relatively small, even if it is for an large portion of a floor and is carried by a single girder which needs to be affixed to a column which transfers the load to the foundation. That column is carrying the load of all the columns above it... and their portion of the floor loads attached to them And this is why the column cross section is progressively larger moving down the structure. If you placed the a girder on top of a column, then you would have to place the next column on top of the girder and so one. The girder then, is having the entire load above placed on its end... the portion of the girder which is on top of the column. If you examine the cross sectional area of the girder... the web... will see how small it is compared to the column above and below it. The web would be crushed ... too small to support the load.
We often weld in web stiffeners to assist a H shaped beam to support the loads when there are concentrated vertical loads placed on it mid span. A steel beam works by placing the compression and tension material as far apart and using a relatively thin tall web to separate them. A wood or concrete beam has a uniform cross section typically which is why you CAN rest a solid wood beam directly on a solid wood column (with the same compressive yield strength.
So there is no other way to erect a multi story steel frame than to attached the loads (girders) to the sides of the columns.
There were several contributing factors which assisted the gravity driven collapse phase.
1. the floor system was column free... this made the floors long span and placed all the columns to support them at the outside edge of the building and at the perimeter of the core. This required that all the floor loads be directed by the beams... there were no girders... to the few columns that would carry the floor loads. At the facade the floor beams truss joists were attached to every other column at the facade. The other columns received the axial loads via the spandrel plates which connected all the facade columns together. On the core side the floor trusses were connected to a channel section at 80" oc (truss spacing) which was then connected to the perimeter core columns... 8 of them on one side and 6 on the other with the corner core columns carrying loads from bother sides. The core side had several possible failure points... the truss seats themselves, the channel which supported them... the beam stub outlookers.. which were very short beams connecting the channels to the columns and the bolts and welds of all the connections. As you progress from the floor to the column the yield strength of the component must increase as it carries the aggregate load of what ever is connected to it.
2. To make the floor structure long span... it had to be deep. The deeper a beam is the less it deflects per given load.. hence longer spans have deeper beams. Deeper beams make the entire structure taller... and would make the floor system very heavy as well. Heavy means more steel, more expense, and larger columns and also more expense... and connection and erection issues. The floor system was an off site pre assembled approach.
To make the floor system lighter and thin enough a truss system was used. A steel truss is like H beam in that it has a compression chord at top and a tension chord on the bottom which "do the work" separated by diagonals... in the case of the towers' floor trusses - 1" Ø bars. This allowed for wire pipes and ducts... "building "service" to run perpendicular to the trusses without cutting holes in them which is also expensive and weakens a beam or girder and must be done in its center and of a limited size as well, else the beam action is lost.
The trusses are light, very light, and the floor which they supported was made as light as possible too - no stone aggregate concrete. Concrete needs a form to pour it on. The floor system instead used light weight 22 ga (the lightest used for this) corrugated metal decking to support the concrete pour. The decking ran parallel to the trusses for economy reasons and to allow conduits for wiring to be run in the concrete. This was the weaker direction to orient the decking. Additional cross trusses were inserted perpendicular to the main pre assembled trusses which tied the entire system together... giving the entire floor a membrane action. Everything working together us a composite. A composite floor is made stronger by composite action and so the individual components of a composite can be made weaker and lighter and cheaper as long as the composite performs to spec.
And so it is why the WTC twin tower floors (components) were so (relatively) light... and therefore inexpensive and easy to erect. And as we saw easy to come apart when off spec loading occurred. And not only that... To reduce the weight and the cost the PANYNJ requested and were granted a design load reduction for the long span open office floor. NYC code calls for 100 pounds per square foot and the PANYNJ were allowed to use a design of 58#/SF.. a 42% reduction. Their claim was that normal conditions in offices rarely see loads of 100#/SF. The request was granted. The tower floors were designed to be 42% weaker than all other office floors in NYC.
3. By relocating the columns out of the main floor space the entire floor area was more vulnerable to failure not just an area within one - 4 column bay as we see in all other steel frame designs. This column free floor space design was touted as more flexible for designers of the fit out of the tenant floors, AND more economical to build... and quick too.
It must be emphasized that the was no expectation that ANY floor would see sufficient imposed loads to fail it. Tenants are not allowed to exceed the load allowances... even in elevators. If these loading limits are observed there is no reason to expect any structural failure.
As explained in many of my posts, the collapse was inevitable ONCE the threshold load was exceeded... a load which PANYNJ had authorized be reduced 58#/PSF which made this failure point lower. But the designers never expected that a single floor could support 4, 5, 10 or 14 floor weights and their contents. If this load was imposed on ANY floor in that building... or ANY BUILDING for that matter is would fail and collapse.
And that is precisely what happened in Phase II... Phase I delivered the over design imposed load onto the floor system in the undamaged section of the tower... first to the top most floor... 96 or so... and then the runaway collapse (ROOSD) ensued. As stated we don't know how those 14 top floors were "destroyed" and converted into the imposed load for floor 95. It doesn't seem likely that office fires could leading to such a destruction. But the destruction of those floors could be a "mini" (not so mini actually) destruction up top 14 floors engineered with explosives and or cutter charges to the relatively small steel sections above floor 96. If the objective was to "free" the mass to crush the floors progressively... then calculations involved the creating the minimum threshold mass to initiate the ROOSED... and that may be as few as 4 or 5 floors!
The much more difficult concept to grasp is the fate of the core columns and this was made more difficult because we can see what happened to most of them except at the end after the floors had collapsed and the facade peeled away.
A steel frame is able to stand erect because it is braced by beams affixed to the sides of columns. Without and floors a steel frame is a 3 dimension lattice. A frame can be made rigid with very stiff joints or use of diagonal bracing... or as in wood studs application of a membrane - wall sheathing - to the studs. Diagonals are very "inconvenient" for any number of reasons in tall structures... but they are often used to stiffen the entire structure to resist wind loads which are enormous and act laterally not axially on the columns
The towers relied and rigid non rotating connections of the beams/bracing to the columns called moment connections. The bracing beams had their webs welded and bolted with angles to the columns. The welds and bolts carried the full load of the connections.
Perhaps the most difficult concept to understand and rarely encountered is "self buckling" of a column. Euler, a physicist, discovered that a column's strength... the axial load it can support is not ONLY determined by its cross sectional area and type of material... different materials have different compressive strengths... but by its unsupported length.
He described three classes of columns - short - medium and long and this were expressed in ratios of the length to their cross sectional area. Short columns are the strongest... long are the "weakest" for a given cross sectional area.
But there is a upper limit for long columns. Long columns made of steel cannot be longer than 150 times their shortest cross sectional dimension. So a column which is 12x24 inches in plan can not not longer than 150x12" or 150 feet tall. If one attempts to erect a column of these proportions it will buckle at a point below its mid height. It will fail from its own weight. It will "self buckle". This is "Euler Buckling".
Columns, are made as small as possible in cross sectional area to "do the job" and this makes them cheaper, uses less real estate and so forth... but they have to have sufficient area for floor beam connections to be made as well.
In the case of steel high rise frames the bracing is at each floor level and so the columns are considered short and therefore quite strong. The core column 501 which had a short axis dimension of 22" and a floor height of 144". The slenderness ratio was about 1/7. The actual column length was 36'. But the effective length was 12'
However in a high rise one column is placed on top of the next and so core column 501 was 1362 feet high made up of 38 columns... most 36' long and a few at 42 feet... with bracing at each 12'. So again each segment was a short column. Even at the top where the cross section has been reduced to a 12" wide flange the slenderness ratio was 12 and this still made it a short column and not subject to self buckling.
When the floors collapsed, they destroyed the beams and girders which carried them. Those beams and girders were overwhelmed by the same excessive (to their design spec) imposed loads. It's likely that their connections failed rather than the beams bending and deflecting or shearing. They would shear if the connections were stronger than the beam itself. And this DID occur in some cases.
As the floors collapsed past the columns... leaving them without their lateral bracing... the effective unbraced length grew. After the collapse of 16 floors... say from 96 to 76 for example... the unbraced length of the 20 floor tall unbraced column was 192 feet and the short axis was about 18" 1/160 which EXCEEDED the slenderness ratio limit for a tall column which is 150. Therefore this 20 floor high unbraced section of column HAD to buckle from "Euler buckling". This of course was made even easier because it was already created from 36' long sections and the welds at the column joints failed and the sections were sprung out of column beginning at below half its unsupported height. Having collapsing material assault it laterally only added to its inherent instability.
The only columns which survived at all were the largest in cross section. And they only survived as long as they did because the bracing was still attached to the next column. This can be seen in the spire columns of rows 500 and 600. The bracing made these pairs effectively a column of about 15' by 22" in plan view... but this didn't help much and even those massive core columns buckled and failed... springing off their 36' long sections below mid height. CC501 weighed almost 1100 tons up to the 78 floor and when it buckled perhaps as much as 400 tons above its mid height accelerated straight down at free fall... with nothing to support, resist or stop it.
The columns had very little strength relatively in the lateral direction... without the bracing. Even without Euler buckling coming into play... there was enormous lateral loads coming from the collapsing debris of the 90+ floors above as the facade acted like a chute containing it. But this was a futile effort by the facade and the collapse rubble exerted a lateral force which pushed the facade over and acted in a similar manner on the core columns. So the floors did not ONLY collapse passing the columns, stripping off the lateral bracing... but it also exerted lateral forces ON the columns (absent the lateral bracing) which contributed to their fracturing apart at those same weak points... the welds applied to the outer perimeter which connected them. Understand that if CC col 501 for example, a floor 18 had a cross sectional area of 5.08 feet, the weld connecting it to the column above it was only about 150" in length an it's cross section was at most a foot or two in area. This is why the columns were found (seen in the debris) in "neat" sections broken at their welds.
It's likely that the lateral pressure from the debris was a factor as well as the Euler buckling. The latter was the mechanism for the "spire" columns which survived the floor collapse and were stronger and less likely to yield to the lateral forces. The debris might have actually braced the bottom of the spire columns... but the Euler buckling ruled and they self buckled and sprung or toppled.