Engineering of the FIU pedestrian bridge, which collapsed

[Peter Dow]

Wikipedia - Florida International University pedestrian bridge collapse

The Florida Department of Transport has released the engineering design and construction plans for the FIU pedestrian bridge, which can be downloaded from this link.

 

Florida Department of TRANSPORTATION - Denney Pate signed and sealed FIU bridge construction plans - 2016 & 2017

https://cdn2.fdot.gov/fiu/13-Denney-Pate-signed-and-sealed-FIU-bridge-construction-plans.pdf

 

My analysis of these engineer's plans have revealed that my earlier suspicion that member 11 was dangerously under-reinforced has been confirmed, to such a degree that the collapse of member 11 (and consequently the whole bridge) under the compression load after the bridge was placed on the piers but before destressing was to be expected.

 

The engineering plans, signed off by the "Engineer of Record", W. Denney Pate of FIGG, were at dangerously at fault and so the construction team by simply following the plans faithfully would have guaranteed the collapse of the bridge.

 

The first point of concern to note from the engineering plans is that the plan's P.T. bar tensioning begins once the concrete reaches a strength of only 6,000 psi or more, as this quote shows -

 

"CONSTRUCTION SEQUENCE - STAGE 2 - SUPERSTRUCTURE PRE-CASTING

2. AFTER CONCRETE COMPRESSIVE STRENGTH HAS REACHED 6000 PSI, STRESS POST-TENSIONING  OF THE MAIN SPAN IN THE FOLLOWING SEQUENCE ..."

 

6,000 psi is less than the final full strength of the concrete was expected to be (at least 8,500 psi) when it has fully set and in this case proceeding with the construction while the concrete was not fully hard was a contributing factor to the collapse.

 

The next point of concern to note is that the engineer's plans recommend a P.T. bar setting for the 2 P.T. bars in member 11 which together total a P.T. bar tension of 560 KIP.

 

 

The results of my truss calculations show that the dead weight of the bridge exerts on member 11

* a tension force of 304 KIP while the bridge is being transported and

* a compression force of 1367 KIP when the bridge is placed on the piers, which is a point of concern to note.

 

 

The P.T. bar tension of 560 KIP on member 11 is somewhat higher than it needs to be - I have suggested that a P.T. bar tension of 390 KIP would have been plenty.

 

Now let us consider what all those forces together in the sequence they were applied mean for the compression force on the reinforced concrete of member 11.

 

I have considered 5 different stages, A, B, C, D and E. The bridge collapsed as a result of damage to the concrete member 11 sustained in stage D, so the bridge never got to stage E in good order, sadly, but inevitably given the plans followed.

 

Stage A

The concrete has hardened to at least 6,000 PSI and so post-tensioning is about to begin but at this stage the mainspan is still resting on the ground, so there are no troublesome forces on member 11, no P.T. bar tension, no bridge dead weight and so the reinforced concrete is not being compressed very much at all except under its own weight and that of the canopy immediately above it, but we will ignore that for now.

 

Stage B

The P.T. bars of member 11 have been tensioned to the recommended amount - a total of 560 KIP and that tension force on the P.T. bars is being provided by an equal and opposite compressive force of 560 KIP on the reinforced concrete. But the mainspan is still on the ground so not much in the way of dead weight of the bridge to worry about yet.

 

Stage C

The mainspan has been lifted onto the transporters and now the dead weight of the bridge is exerting an external tension force of 304 KIP on member 11. This has the effect of reducing the compressive force on the reinforced concrete of member 11 by 304 KIP down to 256 KIP.

 

Stage D

In this case, "D" for danger and for "Doom".

This is when things take a turn for the worse. The bridge gets placed on the piers and now the dead weight of the bridge is applying a compression force of 1367 KIP on to member 11.

 

So now the reinforced concrete has to take the full compression force of 560 KIP from the P.T. bars under tension plus the 1367 KIP dead weight of the bridge to suffer a whopping 1927 KIP of compression force, which is more than member 11 is able to cope with, especially so if the concrete has not reached is full strength of at least 8500 PSI, as is shown in this table from my concrete column calculator and this bar chart.

 

 

 

Therefore the collapse of member 11 must be expected if the strength of the concrete was only 8,000 psi or less and the plans only require that the strength of the concrete at this stage be at least "6,000 psi".

 

A point of concern to note is that the plans only call for 8 number 7 (diameter 7/8" inch, area 0.6 square inches each, axially orientated reinforcing bars), just barely 1% of a reinforcement ratio for that size of concrete member. The compression strength of member 11 was 99% concrete by areal cross-section.

 

Another point of concern to note is that plans only call for member 11 to be of size 24 inches by 21 inches in cross section. Whereas the equivalent member at the south side of the bridge, member 2 was 150% wider, 36 inches by 21 inches and although it was carrying a higher dead weight from the bridge, member 2 survived intact.

 

 

Member 11 was not thick enough, it wasn't reinforced with steel bar enough, it was not strong enough to survive the forces it was subjected to during stage D.

 

The P.T. bars, 1.75" diameter steel bars, didn't contribute to the long term compression strength of member 11, but actually contributed to ruining the long term compression strength in stage D.

 

 

As I have noted there, W Denney Pate's drawings don't draw a section through member 11 with only 2 P.T. bars, only section B-B "(TYP. FOR ALL MEMBERS WITH P.T. BARS)" which draws 8 reinforcement bars. Bars marked here "7S11" are 8 size 7 (7/8" diameter) bars confirmed by the table on page 98, SHEET B-98, SUPERSTRUCTURE REINFORCEMENT BAR LIST AND NTSB images.

 

The plans specify an inadequate reinforcement and inadequate compression strength of the reinforced concrete of member 11 to withstanding the compression load of 1927 KIP before destressing the P.T. bars, which would have cracked, crumbled and weakened the member 11 during Stage D. This was catastrophic damage which would sooner or later cause the member 11 to fail.

 

Possibly at Stage D the cracked and crumbled concrete of member 11 was temporarily still being precariously held together by static friction increased by the additional compression on the concrete provided by the tense P.T. bars. (Sort of like if you crush a biscuit between your hands, the crumbs don't fall out until you release your grip.)

 

This would explain why the bridge did not collapse immediately when placed on the piers but only when destressing of member 11 began and the already cracked concrete lost some of its static friction cohesion by the reduction in compression and only then did the member 11 shatter, collapsing the bridge.

 

Member 11 was carrying the full weight of the structure. There is no redundancy in the FIU bridge design whereby other concrete columns can take the load if truss member 11 fails. It was all on member 11. When member 11 goes, the whole bridge goes down.

 

This picture shows "the smoking gun" - far too small and far too few reinforcement bars, marked "<-B->".

 

The picture also shows the broken stirrup reinforcement bars, which too, were inadequate to the task expected of them.

 

Stage E.

After destressing is complete. We don't know for sure if this stage was actually completely entirely but even if it had been, by that time the damage which had been done in Stage D was revealing itself and the member 11 was failing and bridge had begun the process of collapsing.

 

There was no way to complete stage E successfully because member 11 was on a hair trigger to collapse because of the severe damage to the concrete sustained in stage D.

 

The inadequate strength of member 11, alone, could be entirely responsible for the collapse of the bridge.

 

Additionally, I have concerns about the failure of the bottom joint under shear fracture where member 11 connects to the deck and member 12.

 

 

 

To my mind the responsibility for the collapse of the bridge lies with he who wrote those plans - W. Denney Pate.

 

Nevertheless, I believe that others too had a responsibility not to allow citizens to pass or drive under any bridge under construction, before it has been completed and certified as safe.

 

A collapsed bridge is a pity. A collapsed bridge falling onto citizens is a crime.

 

Peter Dow's 'Truss Forces - The weak points of the bridge and the forces they failed under' picture album on Flickr

 

Peter Dow's 'Mug Shots - FIU Bridge Collapse - Key personnel responsible' album on Flickr

[studiot]

Thank you for posting this information. +1

 

It will take some time to digest it.

 

Aberdeen huh?

 

I've just collected someone from Aberdeen at Bristol airport.

[Peter Dow]

1 minute ago, studiot said:

Thank you for posting this information. +1

It will take some time to digest it.

No problem.

2 minutes ago, studiot said:

Aberdeen huh?

Yes. I am to Aberdeen what Andrei Sakharov was to the Soviet Union - a scientist, excluded by the academic establishment of Aberdeen and persecuted by the UK police state and courts for my pro-human rights political activism.

4 minutes ago, studiot said:

I've just collected someone from Aberdeen at Bristol airport.

"Bristol" huh? Aberdeen is known as the "oil capital" of Europe with ambitions to become the "energy capital" of Europe. Has Aberdeen sent our engineers to build a Severn Estuary tidal energy scheme yet? We can if the UK would like to pay for one such?

[Strange]

2 hours ago, studiot said:

Thank you for posting this information. +1

 

It will take some time to digest it.

 

Aberdeen huh?

 

I've just collected someone from Aberdeen at Bristol airport.

Oh god. Don't encourage him. Please.

[studiot]

2 hours ago, Peter Dow said:

This would explain why the bridge did not collapse immediately when placed on the piers but only when destressing of member 11 began and the already cracked concrete lost some of its static friction cohesion by the reduction in compression and only then did the member 11 shatter, collapsing the bridge.

 

Please explain why concrete in such heavy compression as you describe is 'cracked' ?

[Peter Dow]

5 minutes ago, studiot said:

Please explain why concrete in such heavy compression as you describe is 'cracked' ?

Concrete is known to be strong under compression and weak under tension.

Although concrete is indeed strong under compression it is not infinitely strong and it will fracture under a sufficiently strong stress.

https://en.wikipedia.org/wiki/Compressive_strength

https://en.wikipedia.org/wiki/Properties_of_concrete

https://en.wikipedia.org/wiki/Concrete_fracture_analysis

[studiot]

Just now, Peter Dow said:

Concrete is known to be strong under compression and weak under tension.

Although concrete is indeed strong under compression it is not infinitely strong and it will fracture under a sufficiently strong stress.

https://en.wikipedia.org/wiki/Compressive_strength

https://en.wikipedia.org/wiki/Properties_of_concrete

https://en.wikipedia.org/wiki/Concrete_fracture_analysis

I know that , but any Engineer would (should) shy away from describing the failure of concrete in compression as cracking.

It doesn't.

It suffers crushing failure if at all.

 

But don't forget how difficult it is for any material to fail in compression.

In order for that to happen it has to be in triaxial compression, otherwise some other form of failure occurs.

The 'compression' failure of concrete cubes, for instance is (uniaxial compression) is a diagonal shear failure, and the BS rules out cube failures which depart significantly from this pattern.

[Peter Dow]

Well I am not shy.

[studiot]

You have described member 11 as under-reinforced.

 

How does (by what mode) an underreinforced concrete member fail?

 

Edit, further why was it in so much compression?

Ties are usually much longer than struts so it looks like a tie in the diagram, not a strut?

Edited April 26, 2018 by studiot

[Peter Dow]

1 hour ago, studiot said:

You have described member 11 as under-reinforced.

For the compression load it was being subjected to at "Stage D", when placed on the piers but before the P.T. bar could be destressed, "under-reinforced" certainly.

I calculated the Maximum Allowable Design Factored Load for member 11, a 24" x 21" concrete column with 1% steel reinforcement (and 2 ducts) for various compression strengths from 6000 psi to 8500 psi and found these values.

 

When the bridge is set on the piers but before the PT bars are destressed, the compression force on the reinforced concrete of member 11 is 1927 kip.

560 kip (from the P.T. bar) + 1367 kip (from the dead weight of the bridge) = 1927 kip

1927 kip is too much force for this member 11 to withstand, party because it has so little reinforcement.

With more steel reinforcement, member 11 could easily have withstood 1,927 KIP.

But it didn't have enough reinforcement so the concrete of the member suffered damage.

1 hour ago, studiot said:

How does (by what mode) an underreinforced concrete member fail?

Well let's stick to member 11 rather than discuss all concrete members, shall we?

Damage was done at stage D - cracking, crumbling, crushing, fracturing, shearing - use any term you like or get on your high horse about any term you don't like,  I don't mind - inelastic deformation or permanent damage - in the normal way damage is done to a concrete column that is suffering more compression load than it can survive by merely elastic deformation.

However I don't claim that the member "failed" at that stage D, before destressing had begun.

It appears that the member did not fail until the P.T. bars were being destressed, when strength which the P.T. bar was contributing to, was lost - strength which had been necessary to prevent the member from failing. I speculate that this was strength from static friction cohesion.

Imagine you have three books - you stack them together and put one hand under the stack and another on top. So long as you press the books sufficiently firmly together, static friction will allow you to hold the books together and you can turn the orientation of the stack so that the books are orientated vertically. However, if you destress your hold, then static friction will lessen and the books will fall.

 

Edited April 26, 2018 by Peter Dow

[Peter Dow]

1 hour ago, studiot said:

Edit, further why was it in so much compression?

Ties are usually much longer than struts so it looks like a tie in the diagram, not a strut?

Well I didn't work out the forces by how "it looks" but by using an online truss calculator to calculate the forces.

The force on a truss member depends on its location in relation to where the support nodes are and on the overall weight the truss is carrying.

During transit on the transporter, the support is not at the ends, but on the penultimate end nodes, so member 11 serves as a tie, experiencing tension of 304 kip.

When sited on the piers then support nodes are at the very ends, so member 11 serves as a strut, experiencing compression of 1367 kip.

 

which explains the 1367 kip compression on member 11 when the main-span is placed upon the piers

Which calculates the 304 kip tension on member 11 when the main-span is being carried by the transporter, which in turn explains why the P.T.bar tension force has to be greater than 304 kip, but not why it needs to be as much as 2 x "280 kip" or "560 kip" or 184% the size of the tension force it must resist, when something smaller would do.

 

 

I think I shall attach my images in case there is a future problem with my Flickr account.

 

[Raider5678]

5 hours ago, studiot said:

How does (by what mode) an underreinforced concrete member fail?

1

Typically it's not by compression.

Tension is concrete's weakest strength I believe.

[studiot]

 

19 hours ago, Peter Dow said:

Well let's stick to member 11 rather than discuss all concrete members, shall we?

Damage was done at stage D - cracking, crumbling, crushing, fracturing, shearing - use any term you like or get on your high horse about any term you don't like,  I don't mind - inelastic deformation or permanent damage - in the normal way damage is done to a concrete column that is suffering more compression load than it can survive by merely elastic deformation.

 

Better let's keep the discussion professional shall we?

 

I'm trying to make sense of your calculations, but have not yet tried to wade through the 110 page pdf you linked which presumably has the information required to make my own calcs?

 

At the moment I am at the following stage with your figures.

 

Area M11 =  24 x 21 = 504 sq ins

Area steel = 8 x 0.6  = 4.8 sq ins

Aread duct = 14 sq ins

area concrete = 485.2 sq ins

 

Applied load = 1927000 lbs force

If this was applied to the concrete alone compressive pressure = 1927000 / 485.2  = 4000 psi (just under)

 

Granted I have not applied any factors, but a failure investigation must investigate ultimate conditions of collapse.

[Peter Dow]

3 hours ago, studiot said:

Better let's keep the discussion professional shall we?

Whose profession? Sakharov's? Those who are worthy of nomination for the Sakharov prize for freedom of thought?

Or the profession of those who persecuted Sakharov, those who are not worthy?

3 hours ago, studiot said:

I'm trying to make sense of your calculations, but have not yet tried to wade through the 110 page pdf you linked which presumably has the information required to make my own calcs?

 

At the moment I am at the following stage with your figures.

 

Area M11 =  24 x 21 = 504 sq ins

Area steel = 8 x 0.6  = 4.8 sq ins

Aread duct = 14 sq ins

area concrete = 485.2 sq ins

Agreed and that's easy to work out.

3 hours ago, studiot said:

Applied load = 1927000 lbs force

That takes a lot of working out and there are many modelling assumptions and simplifications on the way but that's the figure I worked out for the total compression load on member 11 at stage D, when the bridge was on the piers but before P.T bar destressing had taken place, sure.

3 hours ago, studiot said:

If this was applied to the concrete alone compressive pressure = 1927000 / 485.2  = 4000 psi (just under)

 

Granted I have not applied any factors, but a failure investigation must investigate ultimate conditions of collapse.

I acknowledge your calculation but it was not a calculation that I found useful. It is not appropriate to use your calculation to deduce that concrete of a compressive strength of only "4,000 psi" would be allowable or acceptable for an engineer to design such a size of member to sustain such a load.

There are, as you allude to, many "factors" to include in the recommended engineering design methods, equations and codes.

For my concrete column calculations, I adapted the method described in this pdf file

http://faculty.arch.tamu.edu/media/cms_page_media/4198/NS22-1cncrtdesign_3.pdf

See "Criteria for Column Design", page 14 / 43 of the pdf, labelled "Page 372" of the Texas A&M book / document which the pdf is an extract from.

See also "Example 19", page 36 / 43 of the pdf labelled "Page 394".

The equations there specify factors multiplying together to increase the minimum acceptable concrete strength for a "concrete only" design by a combined factor of about 2.26 = (1 / (0.65 x 0.8 x 0.85),.

So more like 2.26 x1,927,000/485.2  = 8985 psi would be required to design a concrete-only column of those dimensions to carry that load.

I have just today included the factor for the rebar compressive strength and rearranged the design equation to solve for f'_c  "concrete design compressive strength" and calculated 8,289 psi - see the attached image files.

Edited April 27, 2018 by Peter Dow

[studiot]

2 hours ago, Peter Dow said:

Agreed and that's easy to work out.

These are your figures, so I'm glad you 'agree' them.

2 hours ago, Peter Dow said:

That takes a lot of working out and there are many modelling assumptions and simplifications on the way but that's the figure I worked out for the total compression load on member 11 at stage D, when the bridge was on the piers but before P.T bar destressing had taken place, sure.

Again this is your figure, so I'm glad you 'agree' it.

 

I am quite capable of working out the forces in a relatively simple lattice girder like this one.
I did, however, ask you a question about the necessary information and I would have thought the least you could do would be to point me to the right page instead of being sarcastic.

 

I also understand the working of ~RC struts and in particular their failure modes, something you seem abnormally reluctant to discuss.

So no more half lectures please.

 

You are presumably aware that the ultimate strength of grade C60 steel is half as strong again at 90,000 psi?

 

You have however claimed that the actual stress applied to member M11 exceeded then concrete strength of 6000 psi, when the calculation you accepted shows it to be only 2/3 of that figure.

Since you obviously missed it last time I will repeat this.

We do not expect a component to come near to failure under normal working loads, which is why we derate things by applying factors.

So consideration of factored loads is not appropriate in a failure investigation.

Have you ever conducted any failure investigations?

I have and I can assure you that the procedure is quite different from the normal design one.

We are not asking does it conform to the code (although that question will inevitably be asked as well) when we are trying to determine what happened.

 

 

 

 

Edited April 27, 2018 by studiot

[Peter Dow]

I see you have posted (or edited) 12 minutes ago.

Before I reply to your more recent post, I have more to add to my last post.

The calculation I had done was for a Maximum Allowed Design Factored Load of 1,927 kip.

When I calculate, as I should, for a service load of 1,927 kip, the required concrete design compressive strength required reach ridiculously high values -  for example,10,000 psi for a load factor of 1.2 - see attached image.

This demonstrates that a 21" x 24" concrete column member with 1% areal rebar and 2 x 3" diameter ducts is a non-starter to bear a service load of 1,927 kip.

Edited April 27, 2018 by Peter Dow

[studiot]

On ‎4‎/‎26‎/‎2018 at 6:37 PM, Peter Dow said:

 

So now the reinforced concrete has to take the full compression force of 560 KIP from the P.T. bars under tension plus the 1367 KIP dead weight of the bridge to suffer a whopping 1927 KIP of compression force,

 

So are you now saying that you didn't mean this claim you made, so big and bold?

Are you , in fact, now saying these are not the actual forces involved?

 

For example a post tensioning force is not applied 'factored' . You jack until the required force is physically as measured.

 

Incidentally ,code minimum steel is 0.4% here, if the Florida state code is anything like ours, and up to a maximum of 6%.
So unless substantially greater loads than 1927 KIP were applied M11 was not technically under-reinforced.

Edited April 27, 2018 by studiot

[Peter Dow]

1 hour ago, studiot said:

I am quite capable of working out the forces in a relatively simple lattice girder like this one.
I did, however, ask you a question about the necessary information and I would have thought the least you could do would be to point me to the right page instead of being sarcastic.

The "right page"? If you are doing your own calculation, then is it not for you to decide what is the "right page"?

I have given page numbers on many of images which are snapshots from that 110 page pdf. There is a page index on page 2, however the sheet numbers don't correspond to the pdf document numbers, the pages are not in the correct order and there is no way to search for text, so finding your way around that document is a pain, sorry.

I didn't even use that pdf, which was only released recently, to build a model for my truss calculations, but the 2015 MCM Design build proposal pdf, which contains the proposal documentation, which is here if you are interested.

http://facilities.fiu.edu/projects/BT_904/MCM_FIGG_Proposal_for_FIU_Pedestrian_Bridge_9-30-2015.pdf

That document is at least searchable by text, which is something, though it lacks any information on the P.T. bars for member 11 which were an after thought.

(continues later)

 

1 hour ago, studiot said:

You are presumably aware that the ultimate strength of grade C60 steel is half as strong again at 90,000 psi?

Hmm but the concrete column design equation variable fy is the yield strength, not "ultimate" and example 13 says "Grade 60 (fy = 60 ksi)."

The engineering plans (on page 3 of the pdf, sheet B-2), specify "All reinforcing steel shall be ASTM A615 Grade 60", so I think I am right to use 60,000 psi for my calculations, but I stand to be corrected if you know better?

1 hour ago, studiot said:

You have however claimed that the actual stress applied to member M11 exceeded then concrete strength of 6000 psi, when the calculation you accepted shows it to be only 2/3 of that figure.

Your equation which I acknowledged calculates an average stress, which is not the same as the "actual" stress, which is too complicated to be so easily calculated.

1 hour ago, studiot said:

Since you obviously missed it last time I will repeat this.

We do not expect a component to come near to failure under normal working loads, which is why we derate things by applying factors.

So consideration of factored loads is not appropriate in a failure investigation.

It is an appropriate consideration in my failure investigation.

1 hour ago, studiot said:

Have you ever conducted any failure investigations?

Oh, all my adult life, I have investigated the UK which is one big failure in oh so many different ways.

1 hour ago, studiot said:

I have and I can assure you that the procedure is quite different from the normal design one.

We are not asking does it conform to the code (although that question will inevitably be asked as well) when we are trying to determine what happened.

Well speak for yourself. I, "inevitably", have determined that Pate's design is dangerously, recklessly and culpably out of code as regards the critical component member 11 which failed - and that's all a jury needs to know to convict of involuntary manslaughter.

1 hour ago, studiot said:

So are you now saying that you didn't mean this claim you made, so big and bold?

Are you , in fact, now saying these are not the actual forces involved?

I haven't withdrawn my figures, no.

1 hour ago, studiot said:

For example a post tensioning force is not applied 'factored' . You jack until the required force is physically as measured.

Understood. The post tensioning force however - in this case 560 kip - contributes to the service load, as does the force from the rest of the truss - the dead weight of bridge - 1367  kip (as does the pedestrian live load but I am ignoring that for now).

The service load requires to be factored and the factored load must be less that the Maximum Allowable Design Factored Load.

1 hour ago, studiot said:

Incidentally ,code minimum steel is 0.4% here, if the Florida state code is anything like ours, and up to a maximum of 6%.
So unless substantially greater loads than 1927 KIP were applied M11 was not technically under-reinforced.

What makes it technically "under-reinforced" is the calculation of Maximum Allowable Design Factored Load, which is pitifully too little to cope with a service load of anything like 1,927 kip.

If it had been a higher percent, the relevant technical difference it would make would be to the calculation of Maximum Allowable Design Factored Load, not to the percentage per se.

You misunderstand if you have, or you think I should have, a bee in my bonnet about reinforcement percentages. I am interested in performance.

Edited April 28, 2018 by Peter Dow

[Peter Dow]

1 hour ago, studiot said:

So unless substantially greater loads than 1927 KIP were applied M11 was not technically under-reinforced.

Rubbish. M11 could not service a 1927 kip service load therefore it was under-reinforced and too small. M11 was under-designed in many ways.

[studiot]

Well on the subject of a failure investigation here are the four areas that I would investigate. (one more than usual due to the construction technique).

 

1) Inadequate design.

2) Inadequate materials.

3) Inadequate Workmanship.

4) Misadventure during construction.

As to calculations,

15 hours ago, Peter Dow said:

The "right page"? If you are doing your own calculation, then is it not for you to decide what is the "right page"?

I have given page numbers on many of images which are snapshots from that 110 page pdf. There is a page index on page 2, however the sheet numbers don't correspond to the pdf document numbers, the pages are not in the correct order and there is no way to search for text, so finding your way around that document is a pain, sorry.

I was simply looking for some dimensions, without which calculation cannot proceed.

That was too much to ask huh? Despite the rules of this forum, I must wade through a 110 page doc?

Thus I have been using your calculated forces.

As such it is clear to me that even without any reinforcement at all the concrete of M11 was capable of surviving the  maximum load you calculated.

However you calculated a fancy spreadsheet that omitted two vital pieces of information.

Firstly no mention of the links was made.
These are provided to prevent bursting, which is the normal mode of compressive failure of short compressive members.
The links also aid construction.

Secondly no mention of length was made.
This is required to determine the actual amount of reinforcement necessary to prevent bending and to satisfy the codes.

 

But you have put in a lot of work and somewhere in those drawings I saw a note about the "shear failure at the connection".

I have already queried the possibility of shear failure, and no connection details have been provided.

 

But the big question is torsion.
I note the form of the bridge is an inverted T.

As such imbalanced loads (perhaps due to failue area 4) would introduce significant torsion in the members, which may not have been allowed for in the detailing.

As I'm sure you are aware, the combination of torsional effects with shear and bending stress can be many times that of direct stresses from normal (=standard) loading.

[Peter Dow]

Now considering member 2, which survived intact,

member 2's "SECTION C-C" -

- has 12 x size 8 (diameter 1", area 0.785 sq-in) reinforcing bars and member 2's P.T. bar force setting is

560 kip (same as member 11).

My truss calculation results were -

in transit tension of 458 kip

in situ compression of 1920 kip

Now let us consider what all those forces together in the sequence they were applied mean for the compression force on the reinforced concrete of member 2.

At the critical "Stage D", when the bridge is placed on the piers but before the P.T. bars can be destressed, the reinforced concrete of member 2 has to take the full compression force of 560 KIP from the P.T. bars under tension plus the 1920 KIP dead weight of the bridge to suffer a total of 2480 KIP of compression force, but member 2 was able to cope with that load of 2480 kip, so I calculated the maximum allowable design factored load to find out how strong the concrete must have been, in this table from my concrete column calculator and this bar chart.

Therefore the survival of member 2 may be expected, during Stage D anyway, if the strength of the concrete was 7,000 psi or more, albeit a reasonably safe load factor (at least 1.2) is not to be enjoyed until the concrete hardens to at least 8,285 psi.

Simply applying commonly used engineering design equations for concrete columns suggests clearly why member 2 survived but member 11 failed. Pate's under-design of member 11 was significantly further out of code than was his design of member 2.

Attached image files ...

 

Edited April 29, 2018 by Peter Dow
Attaching image files

[Neil Obstat]

It seems to me they blew it when they decided to make member M2 out of concrete instead of solid steel! 

It ought to be a RED FLAG when a reinforced concrete member is expected to withstand 1.2 times its maximum full strength (8.5 kpsi) when it's only at 6,000 psi test.

But even if M2 were steel, and presuming the rest of the span had survived intact, they'd STILL have an ugly bridge. 

Even after the installation of the FAKE diagonal tubing that was going to adorn the area above the span, still UGLY!

An ugly bridge with ALL the support for the whole thing depending on a critical path of a series of lousy BOLTS, any ONE of which failing causes the bridge to collapse.

IMHO a prideful attempt to have an unusual appearance was the problem from the beginning. 

We live in a time when appearances are valued far too highly.

AND the harried distraction of SPEED of construction leads to expecting too much of concrete which requires TIME to cure completely.

Imagine the implications:

A lousy design, if it had been completed (with M2 made of steel), then hundreds of students would have come walking across it to celebrate its "grand opening" with colored lights shining on the stupid diagonal tube decorations overhead, with traffic below on the highway honking and perhaps having collisions, then the students would start jumping up and down chanting some stupid song .......... and BOOM! Truss member M11 explodes and the whole thing comes crashing down just the same, but this time everyone standing on it comes down with the bridge. Not good.

 

Edited June 5, 2018 by Neil Obstat

[studiot]

Hello, Neil and welcome.

Don't know anything about your background, but steel also has it's share of problems.

I remember a 380 metre viaduct set on twin continuous welded steel girders that the erectors failed to make a proper dimensional weld allowance for.

They were 115mm short when the girders reached the far abutment.

That would have been a more spectacular failure if I hadn't come up with a solution.