The Collapse Stadium Roof

What were the most probable causes of this stadium to collapse? From these pictures and some basic structural engineering and mechanic of materials knowledge the engineer should be able to disgnose some probable causes that may cause the collapse. Please make your observation , apply the knowledge and make your diagnosis. It is also necessary to interview peoples on site during the collapse to know the sequence of events before collapse and to confirm our diagnosis.
The roof was made up of space trusses. It was a skeletal latticed shells.
American Society of Civil Engineers(ASCE) defined  a latticed structure is a structure in the form of a network of elements(as opposed to a continous surface). Rolled , extruded or fabricated sections comprise the member elements. Another characteristics of latticed structural system is that their load-carrying mechanism is three dimensional in nature.

The general behaviour of this thin, very long span structure may be explained easily and understood by the behaviour of thin shell , latticed shells and braced domes structure .

Member Behaviour

A compressive structural member buckles after reaching its critical stress and enters into post-buckling. The load carrying capacity of a buckled member is substantially less than that of a pre-buckled member. Under a constant applied load environment, the buckling of a member usually leads to inelastic post-buckling.The post-buckling behaviour of a truss member is greatly dominated by the selender ratio. A failure of a member in a redundant truss system may potentially result in the stress reversal in other members. Stress reversal in a buckled member is difficult to model exactly, and not much experimental data are available.
A collapse mechanism results from the redistribution of load when one member fails, causing a subsequent progressive overstress condition in other members. Initial lack of fit may cause prestressing in members, with subsequent unexpected failure at relatively low loads. Where member sizes are varied to allow as many members as possible to be fully stresses under worst case loading(optimised design), progressive collapse may not be possible. In this case, several members may fail simultaneously, thereby causing an apparent brittle(sudden) failure os the structure.
In practice, space truss structures have a high number of redundant members, but this does not necessarily confer a corresponding high factor of safety on the structure because the path to collapse may pass through through a small number of members. Collapse of such structures is not uncommon and can have dire safety and economic consequences. Analyses based on the static load redistribution condition of space trusses have shown that the loss of only one critical member can lead to total collapse of the structure at full service loadings.
Two practical methods for analyzing space trusses for progressive collapse include a) the member removal methods and b) the member residual strength method. Both methods essentially follow the same procedure as outlined below:
(1) Analyze the structure(using linear elastic procedures) to determine which member will fail first( i.e which member has the highest stress compared to the design capacity.)
(2) Depending on the method being used, either a) completely remove the member that has reached its maximum capacity and will fail due to overstress(member removal method) or b) limit the load capacity of the member after it reaches its maximum capacity(member residual strength method).
(3) Reanalyze the structure with the removed(zero strength) or reduced strength member, and identify the next member most likely to fail.
(4) Return to the second step and iterate until the structure’s capacity is signigicantly reduced(i.e , the structure is about to collapse or can no longer carry the design load.)

When applying the Member Residual Strength Method, the designer must decide what constitutes the residual strength of a member. For major structures, it is recommended that full scale member tests be performed, in tension and compression, to estimate the post-maximum load behaviour of the space truss members.

Dynamic Effects of member failure

In a truss-type structural system, when members are primarily carrying axial loads, member failure may take place by yielding(tension) or buckling of compression members. Besides due to external dynamic forces, a structural vibration, a tesion-yielded member may take up additional load due to strain hardening, whereas compressive buckled members lose strength and shed load to other members. The critical stress beyond which a member buckles is normally far less than yield stress.Therefore, a greater emphasis must be given for member failure under compression. Two major types of sudden member failure which have potential to cause dynamic effects in structure are:

(1) Brittle-type member failure. This type of failure may take place within the linear ealstic regime. When a member fails in this fashion, it is assumed that the member after failure does not have any load-carrying capacity. For material other than brittle, this type of failure can arise due to reasons such as material defects, fabrication or construction errors, impact and accident..
(2) Member failures due to buckling and post buckling. A compressive structural member, after its initial elastic buckling may enter into inelastic post-buckling. Depending upon the selenderness ratio and other factors, this process may be accompanied by sudden loss in load-carrying capacity of the member, thus giving rise to member snap/dynamic jump(a dynamic phenomenon)

Aerial View of the stadium

pic16

Pic 1

This lattice shell structure is very sensitive to movement of the supports.Any movement of the supports will cause redistribution of forces within the whole structure. Can the two concrete buttresses at both ends of the collpase roof and all the perimeter columns provide the required rigidity? Proof ?

Stadium before collapse

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Pic 2


Imagine if the collapse happened at this moment. Thousands of people will be killed and injured!

Stadium after collapse


Please look these pictures for clues. It showed some tell tale sign that need to be confirmed by measurements, analysis and testing

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Pic 3 What were the sequence of failures before total collapse?

pic2
Pic 4 Observed the remaining space trusses attached to the concrete buttress

pic1
Pic 5

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Pic 6

pic4
Pic 7 . The other concrete buttress. Observed similar pattern of failure

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Pic 8 Concrete Buttress

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Pic 9 See the large span between the concrete butress and the first column support along the perimater

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Pic 10

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Pic 11

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Pic 12
What were the possible forces acting on assemblage in the zone where the space truss snapped? These forces originated from :Vertcally- Dead Load, Rain water loading!In plane loading due to temperature effect, Horizontally(reversable)-wind loading and other dynamic loading such as ground movement!

pic41

What were the “Demand” of all possible worst forces at the end of space trusses near the concrete butresses? What were the “Capacities” of the steel members, connections and assemblage against those forces?

Pic12a

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Pic 12b

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Pic 13

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Pic 14

080214 15 Stadium

Pic15

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Pic 16

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Pic16a Click on the caption to enlarge the pic.

This photo showed the space frames were supported by connection at the column butress and the columns along the perimeter of the stadium. This column free portion on both side of the stadium looks unstable. The space frame was mainly supported by the columns placed along the perimeter of the stadium.(See photo 18,12,20 and 22.

Question:

What was the adequacy of these columns to support the worst loading from the space frame? Observe the size of the last perimeter steel column assemblage?

colum free
Pic 17

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Pic 18

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Pic 19

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Pic 20 The space truss were supported by steel columns along its perimeter and the two concrete buttresses at the tips.

080305 01 Stadium

Pic20a View during construction

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Pic21

Notice all column bases were dislodged at the its connection to the concrete stump. Need to observe the mode of failure of the base plate. It may be failure of the welds,shearing of bolts, prying of the plate due to inadequate thickness or snapping of hold down bolt in tension or any of their combination. I am sorry I dont have the photos of this column to concrete stump connections

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Pic 22

space truss

Pic 22a

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Pic23

This photo showed the inclined, curved space frame was supported only at two points i.e at the last perimeter columns and the concrete stump(see pic 12). The photos showed the column free span was very large maybe greater than 30 m.
The above configuration may create large torsional forces at the column stump supports. (compare pic 1 with pic 28).
What was the worst torque at the ends of the space trusses where it snapped?(see pic 7 & 8). What was the torsional capacities of the space trusses at that section?

Col Stump 1
Pic 24a

non scoreboard butress-enlarge2

Pic 24b

typical nodes

Typical Nodes

mero system 2

Typical Tubular members

Mero ball joint

Typical steel ball joints

HERE to see a more detail view of Pic 24b and what evidences can you get on the failure of this zone to help you in the failure investigation of this space trusses?

HERE to see a more detail view of Pic 21 and evidences on the perimeter columns after collapse

Here are the evidences from Pic 24b.Similarly evidences can be identified, categorised from other components of the structures.
From this pic it was observed ;
1. Buckling of inclined members(tube){Sign of load exceeding Buckling capacities}
2. Pullout of the threaded screws from the ball joints{Sign of very high tensile load in the tubular members exceeding its tensile capacities}

Why the two tubular members buckled and the other members threaded bolts were pullout of the steel ball joints?

This photo extracted from Pic23 shows Why the two inclined tubular members buckled and the other members threaded bolts were pullout of the steel ball joints.
The truss (self weight and any live load) P at an eccentricity e , any horizontal load resulted from wind pressure, the dominating effect of geometry and the ends restrains created large torsional forces at the supports. These forces must be resisted by the inclined and diagonal tubular members which were either in tension or compression. These forces exceeded the axial compressive and tensile capacities of the tubular members creating the observed phenomena.
It is believed the buckling of the tubular compression strut triggered the progressive collapse of the whole roof. A detailed structural analysis as stated in the Member Behaviour will proof this diagnosis.

Pic60c

Extracted from Pic23

3. ruptured of the members(tubes) and the nodes. {Sign of very high tensile load in the tubular members and the steel ball joints exceeding its tensile capacities}
a) Analyse the structure and determine the maximum axial forces in members. Confirm these members behave as intended i.e compression or tension. Thsese forces are the demand. (Note: In the vicinity of the cantilever around the perimeter columns the top boom will be in tension and the bottom boom will be in compression. The inclined diagonals may be in tension or compression. Similarly for members at the concrete butress supports.)
b) Determine the axial capacities(compression or tension) of these members.
c) Determine the factor of safety i.e ratio of capacities/Demand for the critical members.The member with lowest factor of safety will probably collapse first.
Do the 4 steps analysis as stated in Member Behaviour for progressive collapse .
Based on the observation, evidences,results of analysis and diagnosis it is then we do the elimination processes to zoom in the most probable cause of the collapse. It may be due a combination of causes.

Testing


We start by doing some actual 1) components and 2) representative samples tests cut from the collapse space truss components.
The representative sample tests will yield basic properties of the materials(steel tubes) such as the Yield Stress and Yield strain, % elongation, rupture stress and strain and so on.
These basic properties should be used to estimate the component compressive or tensile strength of the members.
Next we do the component test to determine and confirm the capacities of the tubular members especially in compression, tensile capacities of the threaded bolts and tensile and compressive capacities of the steel ball joints, and compression capacities of the sleeves and the end cones(see typical node above). See pg. 90 of ref. 10 for Load tests on space truss connections.

Probable Causes
Compare the results of Strucutral Analysis with what observed on site or evidences obtained from site. If the results dosnt telly with what observed on site, your analysis was wrong. Revised your structural analysis.
Compare the materials properties results obtained from tests with the what were in the drawings and specification.
Determine what does not comply with the specified Code of practices, drawings and specification.
In most cases, at the Diagnosis Stage, simple hand calculation will do (without using computer softwares etc). Softwares are only used to check and confirmed the diagnosis. The FUNDAMENTALS are the most important in the failures investigation . Understanding the fundamentals will guide us to answer a lot of key questions e.g What, Where, Why ,How the failure happened? It will help us on what to focus during the investigation and saving time on unncessary processes e.g there is no necessity to test the concrete strength of the buttresses or column stumps as the pictures showed all the steel ball connected to the conrete components were intact. We can eliminate the strength of the concrete in the investigation even by looking at the pictures. So the focus should be on the steel space frame and its components. Decisions on what type of analysis, type of tests, location of samples to be tested and frequency of sampling, selection of components to be tested shall be decided during the desk study .

from ref 3Allowable compressive stress versus selenderness l/r ratio; fy=240

from ref 3

Pic 24c

truss_butress detail
Pic 25

Both photos Pic24a & Pic 24b showed the space frame snapped at the ball joint connections. The ball joint connections fixed to the concrete stump were intact.

Questions:-

1. What are the magnitude forces in the members and joints at this point of failure under worst combination of loading acting on the whole roof structure?
2. What were the capacities of the members and connections at this point of failure?

Simillar questions should be asked for the columns and connections along the perimeter that support the roof structures

Since this part of the structures was subjected to cyclic loading the steel members and joints may fail by fatigue. Fatigue considerations are important because the consequent failure is generally sudden and at a stress level much lower than the ultimate stress.

Questions:-


Will the configuration and assemblage of members and joints as shown in fig 25 being able to withstand the worst forces at this location? Definitely it cant because it snapped at this point. Why? What did the assemblage indicated ?

The configuration and assemblage of members and connections as shown in fig 25 were not suitable for any reversal of loads such as wind or dynamic loading.

Shah Alam Stadium


38
Pic 26

shah_alam2
Pic 27
The latticed shell roofs were supported rigidly on all three sides

shah_alam_stadium

Pic 28

The shape(see the dominating effect of geometry in attached article) and the ends restrains are very important in this egg shell like structures.
Hold an A4 size paper along the shorter edges with you left and right hand respectively. Move your hands a bit towards each other so that the paper form a curves. The distnace between the fingures of the hands is the span of the “thin shell”; It can span thousands of time of its thickness.
Now hold the paper just along one of the longitudinal edge. The paper cant even supports its own weight.
The three edges must be designed to provide the required rigidity(see Shah Alam Stadium(pic 28).
Loads applied to the shell are carried by in general through a combination of bending and stretching(inplane membrane tension or compression of struts) actions, which generally vary from point to point.
For flat roof shell or latticed shells bending was the dominant effect.

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15 Responses to “The Collapse Stadium Roof”

  1. Razali Says:

    Prof,
    TQ very much for the photos and illustrations leading to a very clear area of concern; stability in long term performance. You have practically zeroed in on the designed stability of both ends of the structure leading to the main butresses. Torsion and resonance were the causes to the fall of the Tacoma Bridge. Are we not learning here??

    The Sultan Mizan Stadium is sited very close to the South China Sea and neighbour to the Kuala Terengganu Airport, hence the effect of wind forces from nature and from the decending/ascending flights should have been considered.

    Looking at the very long free standing span on both sides and the sheer simplicity of the end connections detailing, it is very much in doubt where this have been looked at specialist in structure.

    What is evident here is the age old differences between the Architect and the Engineers.. The architect wants a WAU BULAN design (Picture 1). Having wide roof ends embedded in the foundation (picture 28 will not give that shape.

    The picture tallies with that assumption.. The `Roof Wing Tip’ connecting to the butress failed completely (Pic 11). Maybe a record of wind and flights near the time of collapse would give a certain indication to the mechanism of collapse..

    • Engineer Says:

      These pictures tell a thousands words. Comapre the pic1 with pic 28(Stadium Shah Alam the capacity of which is double the collapse stadium). The space frame of the Shah Alam stadium were supported on 3 sides and were very stable. Any forces due to movement of the egg shell like roof will be transferred to the concrete buttresses(by inplane membrane) at both ends of the stadium(longitudinally).The Shah Alam stadium was very rigid.
      The pictures from the collapse stadium showed the space frame were supported by columns along the perimeter of the stadium and the concrete buttress at the ends(pic 1 and pic 20). These perimeter columns were very doubtful could provide the required rotational, lateral and vertical stiffness and rigidity.The stability were very doubtful(all columns base were dislodged. pic21).
      The roof is flater than Shah Alam Stadium so there was little ‘membrane’ effects. From the configuration of the roof and its supports,I suspect the roof had very large deflection at mispan of the stadium. The deflection causes the roof to sag at midsapan creating a large inplane forces at the concrete buttress. Any gust of strong wind will cause uplift reducing the deflection causing forces reversal(tension to compression) in the concrete buttresses. The ball joint connections were very welll designed, detail and constructed. So it failed just before those connections(see pic 24 & pic25).
      The diagnosis above need to be confirmed by thorough structural analysis simulating the condition as diagnosed and may be some testing .
      The pattern of collapse look like another possibility structural design failure .

      Until further evidence we can rule out failure due to construction.

  2. Razali Says:

    Prof,
    TQVM for the shell structure material. It give the general concept. Somehow it seems no mathematical representation is available. Is there such mathematical model to analyse structural capacity based on the concept??

  3. Engineer Says:

    In order to understand the response of the structure when subjected to any loading understing the CONCEPT is most basic requirement. It will also give you the ‘feel’ how the structure will behave. For example the response of this roof space trusses if all the perimeter column connection to the concrete column stump were pinned were different from those those connections were fixed or fully rigid connection. The next question is can you achieve fully rigid connection? How? Even if these connection can be designed to be rigid what happened at Ultimate load? Hinges formed at that loading may transform the fully rigid connection to pin connections.
    What will happen if these connections were pinned? The space trusses was just like a piece of rigid string supported vertically by the pinned jointed columns and horizontally supported by the two concrete buttresses. All horizontal load will be absorbed by these two buttresses. Like in this case the buttresses seemed to be rigid. What about the members and connections just before the buttresses? What are the worst forces in the said members and connections? What are the capacities?
    To determine the worst forces(demand) is easy. There are many cheap commercial structural softwares available for the analysis of space trusses. If you browse through the net you can get this many working software to analyze space truss structure even for free.Click here and Here. There are many of such site but my advice be careful when using software.
    Check and check and check the input, output data throroughly . Check also the equilibrium of forces of the whole structure i.e summation of forces must be zero and the stresses in the members are within stress strain curve elastic limit. Check the support conditions input and output.
    Forces in the members of space trusses are either in tension or compression.To determine the capacities , basic properties of the steel such as the stress-strain curve and its dimension as well ends conditions for compression members must be known. Tensile test on samples from site must be done . Sectional properties such as the x-sectional areas and moment of inertia and radius of gyration can be derived. Compression capacities may just be determined from moment of inertia of section and the effective length of members.
    Tension and compression capacities of the members can be derived based on code of practices used in the original design or specified. Tests on specimen taken from site should be used to verify, validate and confirmed the capacities.
    We need to carry out fatigue test on the ball joint to determine the fatigue strength.
    Assembladge similar to the one on the concrete butress can be made in the lab and tested to determine, verify and validate the end assmeblage capacities to resist the worst load it was subjected to including torsion. The loading should simulate the worst loading cases that this assemblage was subjected to. Due to reversal of wind direction, Cyclic loading should be considered.

  4. Engineer Says:

    At the end of my comments posted on the August 17, 2009 I said “Until further evidence we can rule out failure due to construction.”
    Looking at Pictures 12, 22a qnd 23 there are evidences that there might be some error in the construcion of the space truss especially at the ‘bifurcation’ zone before the concrete buttress.

  5. Razali Says:

    TQVM Prof,
    I understand the step by step elimination of probabilities to failure.

  6. Dmitry D Says:

    http://sites.google.com/site/robustness1/prezentacia-no-2

  7. Dmitry D Says:

    http://sites.google.com/site/robustness1/Home/1

  8. Dmitry D Says:

    http://www.mkrtychev.ru/load/stadion_quotzenitquot_na_krestovskom_ostrove_v_gs_peterburg/1-1-0-5

  9. Engineer Says:

    Mr Dmitry D,

    As I told you the application of non linear (both geometric and materials ) theory is very complicated to be applied practically in the design of structures, There are a lot of research to be needed in this areas . At the moment there are just guidelines to prevent progressive collapse such as in reference 13, section 3.6.1 to section 3.6.3. I had extracted these section in this webpage and translated to Russian as follows:-

    Поведение членов
    Сжимающие структурных пряжками члена после достижения критического напряжения и вступает в должность потери устойчивости. Грузоподъемность пряжками члена существенно меньше, чем предварительно пряжками члена. Под постоянной нагрузке окружающей среды, изгиб члена обычно приводит к неупругого после buckling.The после потери устойчивости поведения фермы члена значительно преобладали selender отношение. Неспособность члена в системе избыточные ферма может потенциально привести к напряжению вспять другими членами. Стресс вспять пряжками член трудно модель точно, и не так много экспериментальные данные.
    Механизм распада результате перераспределения нагрузки когда один из участников не удалось, вызывая последующие прогрессивные условия перенапряжение в другие члены. Первоначальные несоответствие может привести предварительного напряжения в члены, с последующим неожиданный сбой при относительно низких нагрузках. Где член размеры разнообразны, чтобы позволить столько членов, сколько возможно, чтобы быть полностью нагрузки в худшем случае загрузка (оптимизированный дизайн), прогрессивные коллапс не возможно. В этом случае, несколько членов могут не одновременно, тем самым вызывая явное хрупких (внезапно) неспособность ОС структуры.
    На практике, пространственная ферма структуры имеют большое число избыточных членов, но это не обязательно предоставлять соответствующую высоким коэффициентом запаса по структуре, так как путь к краху может пройти через небольшое число членов. Крах таких структур не является редкостью и может иметь тяжелые безопасности и экономических последствий. Анализ, основанный на статическом состоянии перераспределение нагрузки космических фермы, показали, что потери только один критический элемент может привести к полному развалу структуры при полной нагрузке службы.
    Два практические методы анализа космических ферм для прогрессивного распада являются: а) члены и методы их устранения и б) член методом остаточных сил. Оба метода существенно следовать той же процедуре как указано ниже:
    (1) Анализ структуры (с помощью линейной упругой процедуры), чтобы определить, какой член не удастся первым (т.е. какой член имеет высокие напряжения по сравнению с проектной мощностью.)
    (2) В зависимости от метода используются, либо а) полностью удалить члена, которое достигло своего максимального потенциала и не сможет из-за перенапряжений (член метод удаления) или б) ограничить грузоподъемность члена после достижения своего максимального потенциала (член методом остаточной прочности).
    (3) повторный анализ структуры с удален (нулевой прочности) или уменьшить член сила, и определить следующий член, скорее всего, на провал.
    (4) Вернуться на шаг и второй итерации, пока потенциал этой структуры является signigicantly снижается (т.е. структура скоро падет или более не может выполнять расчетной нагрузке.)
    При подаче заявления членов остаточная прочность методом, дизайнер должен решить, что представляют собой остаточные силы члена. Для крупных структур, но рекомендовано, чтобы быть выполнена полная испытаниях член масштаба, при растяжении и сжатии, чтобы оценить после максимальной нагрузки поведение членов пространственная ферма.
    Динамических эффектов член провал
    В ферма типа структурной системы, когда сотрудники в первую очередь проведение осевых нагрузок, член неудача может проходить путем выделения (напряжение) или потери устойчивости сжатия членов. Кроме того, благодаря внешнему динамические силы, структурные вибрации, принесло tesion-член может принять дополнительные нагрузки из-за деформационного упрочнения, а сжимающие пряжками члены теряют силу и пролить нагрузку к другим членам. Со стрессом, после которого члены пряжки, как правило, гораздо меньше, чем доходность stress.Therefore, больше внимания следует уделять члены неудачу при сжатии. Два основных типа внезапного отказа членов, которые могут явиться причиной динамические эффекты в структуре являются:
    (1) Хрупкая безотказную тип члена. Этот тип отказа может иметь место в рамках линейной ealstic режима. Когда член не таким образом, предполагается, что государство-член после неудачи не имеет грузоподъемность. Для материалов, помимо хрупкого, такого рода неудачи может возникнуть из-за причин, таких как наличие дефектов материала, изготовления или строительства ошибкам, последствия и аварии ..
    (2) Член неудачей из-за потери устойчивости и после потери устойчивости. Сжимающие структурных член, после ее первоначальной упругий изгиб может вступить в неупругом после потери устойчивости. В зависимости от соотношения selenderness и другие факторы, этот процесс может сопровождаться внезапной потере несущей способности государств-членов, тем самым вызывая член Snap / динамический переход (динамическое явление)

  10. flashuac Says:

    Спасибо за интересную статью! 🙂

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