The world’s tallest building, the BURJ (Dubai)

[aslam]

Design and Analysis of Heavily Loaded Reinforced Concrete Link Beams for Burj Dubai

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[chigozie]

Like I said in my previous post, one of the main problems that had to be solved in the design and the realization of the building is that of containing the horizontal loads as induced by such agent as wind, seismic wave etc. Looking at this structure, one cannot afford not to recognize that it is a tall slender structure. This is recognized by the fact that if you should compare the vertical dimension to lateral the dimension, the ratio would be very great. But how great is this great to be as to be classified as slender?
If we should make a rough estimate, following the general guide and the formulae attributable to Euler for the classification of columns (this structure, acting as a whole, is like a column that is fixed at the base but free at the top), then the structural height of the building is twice that actual. So we would be talking of a structural height that is in excess of 2 x 800 = 1,600m (theoretically). If the structure was to have a uniform form (say cylindrical) from the base up to the roof top, then we can take the structure as a whole, calculate the ratio of its structural height to the radius of gyration of the structure, thus the slenderness ratio. This will definitely fall outside the 360 unit range that defined the extreme limit of long slender column. Again, since this structure is a reinforced concrete structure, if we should follow the guide as per BS 8110, the slenderness ratio will be the assumed actual height multiplied by 2 (800 x 2 = 1600 = structural height) then divided by the diameter (1600/D). If this is greater than 15 unit (which I am very sure that it is several time greater than), then the structure is a long slender column. We arrive at the conclusion, that in both cases, the structure could be likened to a very! very long slender column. This implies that (due to constructional error-thus inherent eccentricity) any little change in horizontal load will induce a large eccentricity to the structure which is self propagating-thus large out of balance moment, which will increase with every inch increase in height. This will create apart from other problems, that of instability. This is the point that ingenuity in the design and the realization of the project played a great part.
The structure, looking from the top towards the base, has the snail shell form; but looking from the elevations, it has the pyramidal form. The choice of the form did not make only architectural/aesthetic sense but also structural engineering sense. The structure benefited from two basic geometric configurations-the buttressing or the forting form which I will prefer to refer to as the “tripod or dorsal-born form” (on the plan) and the arching form which I will prefer to refer to as the “pyramidal form” (on the vertical plain). These were mainly employed for the provision of lateral and vertical stability to the structure. To counter the effect of wind loading, the structure employed:-
1) the oblong shapes i.e. the extended cylindrical shapes that are known to be one of the best structural shapes at relieving structures from dynamic hydraulic loading thus good for vortex shading )
2) The tapered helical form (running from the base to the summit). This form was achieved by the side stepping of the setbacks which created a continuous spiral curve from the base of the structure on to the summit. The effect was that it created a long passage through which the wind that impacts on the surface of the structure has to follow (instead of destalking directly on the leeward side of the structure at full strength thus producing the large horizontal forces). This elongated pathway which the wave front is forced to follow has the effect that the wind speed, thus the resultant forces are reduced due to damping/attenuation, natural decay, the resistances that it encounters on its pathway which are due to the friction offered by the pathway, interference of the incoming wind wave front on the wave front which was already traversing the pathway (they are moving at different velocities as such have differing wave fronts). On conclusion, since the wave front takes an inclined direction, it will be resolved into the vertical and the horizontal components, with the net effect that the horizontal component (that results in the horizontal deflection and twist of the structure-thus moment and the torsion on the structure) is grossly reduced in comparism to what it would have been if such a measure was not taken. The vertical component of force has an up-lifting effect on the structure which gravity-thus the weight of the structure could take care of conveniently. If the entrance force of the wave front is say 15KN and it flows at an angle of 35° to the horizontal (inclination of the pathway), depending on the roughness of the surface of the pathway as such the co-efficient of friction, the length of the pathway as such the time that it will take a wave front to traverse the pathway etc, let’s assume that the net force is now reduced to 13KN. If this force is resolved into the vertical and horizontal components, then the horizontal component that will have to be designed for (H) = 13 cos 35° = 0.82 x 13 = 10.65KN. This implies that this load has been reduced by 15 – 10.65 = 4.35 (29%)
One of the conditions set out in the codes is that a structure that is to withstand horizontal load has to be regular both in the lateral and vertical direction (the codes specified the respective limits). Does this structure meet up with that condition?
A casual look at the structure will lead to the illusion that it contravened this basic rule (in that it had sharp and well defined setback, contrary to the specification in the codes that the changes in dimension both in the vertical and the horizontal directions should be gradual). In actuality, this is not the case as each section that is terminated is terminated completely, without and part of it extending beyond that level as such will not introduce any eccentricity to the overall structure. Again, the setbacks fell within the 10% of the total area occupied by the structure at that level and 30% of the total area of the structure as at the base (plan). Looking at the structure which comprised basically of oblong shaped components (3 in number) fused together in torn around a cylindrical centre, there is no doubt that the building met this condition (there are no abrupt changes in dimensions within any of the components that formed the base structure (in the sense that the form is within the limits as defined in the codes), there are no penthouses-cantilevering floors, but each and every component terminated completely at the pre-chosen points-the setbacks).This practice has the structural effect that the flanges (the outflanking oblong wings) have tripod or buttressing effect on the core structure.

[chigozie]

CONTINUED FROM THE LAST POST

The world’s tallest building, the BURJ (Dubai)

On the other hand, the core structure which extended beyond the setbacks acted as restraint to the setbacks (i.e. the wings that have been terminated. In so doing, these setbacks could be analyzed as columns restrained at both ends-thus reducing their effective height (respective effective height = 0.75 x actual height) and as a result their slenderness ratio. The core structure that extended beyond the point of termination of the outflanking wings could be viewed as the critical lift for the lateral loading. This is due to the fact that the top end is free as such none restrained or supported. The structural layout went a long way to solving this problem in that this lift could be likened as having effective height that is the overall height minus the height of the terminated wings. This drastically reducing the structural effective height. So if the outflanking wings terminated at the height of 600m above the ground level, then the effective height of the extended part of the structure (the ultimate lift) will be 2(800-600) = 400m instead of 1600m!! Again all the changes in dimension were concentric-thus making the geometric center to more or less coincide with the center of mass/stiffness (so doing avoiding conscious introduction of eccentricity). These are only the preliminary conditions. The dynamic loading due to wind loading will definitely suffice considering the exposure condition (wind loadings become grievous with increase in heights, the shape factor etc). To meliorate on that problem (apart from the measures cited earlier), ingenious design had to be adopted as to shade the wind load before they could be applied to the structure. This is achieved by incorporating structures such as fenders, walls, fittings on the external surfaces of the building as to make the wind fronts to intercept themselves, forming interfering waves instead of constructive waves. This pattern of wave, sort of, (may I say), is self-destructive instead of constructive. This is analogous to fighting fire with fire. This process will not eliminate the load but will only reduce it. Given the complexity involved in these interactions and reactions, in actuality, the horizontal forces that would have to be confronted eventually are not easy to estimate as such one will have to resort to the help of computation analysis such as that done with the computational fluid dynamics (the CFD). In most cases, particularly those involving structure of primary importance (as this structure), the wind tunnel study of the behavior of the structure under likely wind loadings have to be carried out. This has the advantage that one could observe physically the behavior of the structure rather than relying wholly on computer simulation (as given by the CFD analysis).
We have to recall that this load is not the only horizontal load to be contended with. The seismic load may be the one that may pose the major problem, thus the critical load (if the structure is located in a seismic zone (and if yes), the characteristics of the site and seismic intensity). In that case, the structures that were incorporated into the building as to reduce the wind loading will not have any effect on the design horizontal loading due to earthquake.
Regards
Teddy

[chigozie]

In my second post on this topic (post #2), I estimated the load that a typical column (at the foundation level) carries at 1.05 x 66426.67 = 69748KN (including its own weight). This was based on direct multiplication of the load at a typical floor level with the estimated numbers of floors supported by the column; as such I multiplied the load of (the typical floor load) by (estmated number of floors above the foundation level) and arrived at a loading of 249.1 x 267 = 66426.67KN. Since this is a very tall building, efforts will be made to economize on the building materials coupled with the fact that the structure should be as light as possible (without compromising stability/rigidity), as to impose as little as possible load on the supporting structures particularly the foundation. Following this reasoning, light weight materials had to be used. These manifested in the form of fiber glass forms and panels (for the floors ) topped up with light weight aggregates for the floor slab.
Typical fiber glass forms/panels topped up with light weight aggregates for the floor slab has unit volume weight of 14 KN/M^3
So the design dead load for the floor work = 14 x 0.2 + 0.8 = 3.6 KN/M^2 (0.8 KN/M^2 = the weight of the light weight partitioning, the fittings etc). Thus the design dead load = 1.3 x 3.6 = 4.68KN/M^3

Due to the fact that it is most unlikely that all the loads (particularly the live load) will be imposed on the structure at the same time, the codes allowed for the reduction of the live loads following the procedures specified in the relevant codes. The BS 8110 allowed the reduction of the load in the proportion of 10% for any successive floor above the 2nd floor up to the maximum of 50% i.e. from the 6th floor upwards. Since this reduction could start from the second floor and comparing the total numbers of floors involved, this means practically that the live load for all the floors could be reduced by 50%. Following this reasoning, we have live load = 50% of 3 = 1.50KN/M^2, thus design live load = 1.50 x 1.50 = 2.25 KN/M^2. This implies that the reversed design vertical load/floor = 20.3 (4.68+ 2.25) = 145.9KN. Ratio of the reversed design load to that calculated before = 140.7/249.1 = 0.565 as such the reversed design load/column at the foundation level = 69748 x 0.565 = 39390.1KN. Compare the result with the actual load (of 37000 KN) as recorded on the foundation of the building (refer to the circled part of the image above). The difference between the estimated load (of 39390.1KN) and the load registered at the pile locations (of 37000 KN), though small and not outside the margin of error, could be accounted for. This is due to:-
· The density or concentration of pile/unit plan area of the buildings foundation as compared to the assumed column spacing used in my estimate.
· The fact that I was not using the actual loadings as to the actual structure in my estimate but was trying to make an independent estimate as could be done in the preliminary stage of any design.
· That I was conservative in my estimate as this is necessary as to consider a more critical condition than could be experienced in the actual structure.
Regards
Teddy

[Flexi]

Design and Analysis of Heavily Loaded Reinforced Concrete Link Beams for Burj Dubai
another interesting paper:

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regards
Flexi

[chigozie]

Heavily reinforced concrete beams formed part of the structural arrengement for this building. Considering the fact that the beams at each floor level are to support principally but only the floor directly resting on them, the fact that the floors are to not to carry special loads but serve mainly as offices, hotel accommodation etc (for which the typical live load is 2KN/M^2) and the fact that light weight materials were used for the floor construction, I do not see the need for employing heavily reinforced concrete beams for this structure (if the framing was optimised).
Please say what you think about it.
Regards
Teddy

[chigozie]

Could any one please clarify me if the contours traced are those of different soft wares superimposed one on the others or are they the contours traced by same software over the same site. If they are contours traced from the same software over same site (and not contours traced from different soft wares superimposed one on the others), I do not see the connection between the comments made at the footnote (on the right of the load contour) to the image (on the left) regarding the difference in pile load distribution.
Again, why should the settlements recorded at the least loaded points (green shade) be greater than those recorded at the more heavily loaded points(yellow, orange, red shade)?
Regards
Teddy

[aslam]

@ Teddy,

I think Graph of distance VS settlement is of only one software and not for all software.

Regarding values of settlement,

settlement/bearing pressure under raft depends also on type of soil (clayey, sandy c-@ soil etc) in addition to magnitude of load. And settlement/pressure distribution may be concave or convex depending upon type of soil which may be modelled in FEM software using soil subgrade for raft and soil spring for raft.

[chigozie]

Aslam writes:-
I think Graph of distance VS settlement is of only one software and not for all software.

Regarding values of settlement,

settlement/bearing pressure under raft depends also on type of soil (clayey, sandy c-@ soil etc) in addition to magnitude of load. And settlement/pressure distribution may be concave or convex depending upon type of soil which may be modelled in FEM software using soil subgrade for raft and soil spring for raft.

Comment:-

Please note that there were 2 issues raised in my post (one deals with the load distribution and the second with settlement). The first part does not refer to settlement but to load distribution on piles/raft and the soil spring (for raft).
As to the graphs, I have same hunch as you. It is supposed to be a contour graph traced by only a soft ware; but from the footnote (encircled), it seems obvious that the writer was comparing some soft wares (refer to the footnote). Excerpts are:-
· The difference between the pile load distributions could be attribute to a number of reasons including:-the FE REPUTE and PIGLET models take account of the pile-soil-pile interaction whereas SOM modeled the soil as springs connected to the raft and piles using an S-Frame analysis.
· The HCL FE analysis modeled the soil/rock using non-linear responses compared to the linear spring stiffnesses assumed in the SOM analysis.
· ………
This clearly shows that comparisms were being made as to the outputs of some soft wares (not only a soft ware since it will make no sense for one to compare the output of a soft ware with itself). It is for this that I was doubting the relevance of the statements if the graph displayed is that of the output of but only one soft ware (for which you are in agreement with me).
Again, settlement is proportional to load and the soil characteristics. Since we are talking of a relatively limited area (a very small one indeed), the issue in variation in soil characteristic does not play any part since it is most probable that the soil within the space occupied by the foundation has an assumed uniform characteristics (the graph confirmed this since the soil could not have such a well defined, sharp and regular variation as traced in the settlement graph). Based on this, I do not see the reason why the piles subjected to lesser load should suffer greater settlements.
What do you think about it?
Regards
Teddy

[chigozie]

If we adopt the load of 39390.1KN/column (as estimated in the latest review on the design load), and assume that the circular or the polygonal core structure was to support the transverse load due to horizontal forces (wind or seismic), then we could design the column as a laterally braced column (i.e. it is designed to support mainly vertical load). In that case, we cannot afford not to recognize the gravity of the vertical load that a typical column has to support, as such we have to try to minimize on the section dimension by employing high grade concrete and or steel. If we are to employ grade 75 concrete and 460 steel, then the combined strength of the concrete and the steel should be such that they will be able to equal or surpass that due to the external load. Let’s assume that the section will be made of only concrete (unreinforced), then the cross section of concrete required should be equal or greater than 39390.1 x 10^3/0.45 x 75 = 1167114.0mm^2!!. If we decided to use 800mm x 800mm reinforced column for the say the first ¼ total height of the building from the foundation, then the cross sectional area of concrete provided = 800 x 800 = 640000 mm^2, which implies that steel is to provide 1167114.0 - 640000 = 527114mm^2. If we use the steel/concrete modular ratio of 15, then area of steel reinforcement = 527114/15 = 35140.9mm^2. For 50mm diameter steel, number of steel strands = 35140.9/0.25pi (50)^2 = 18. Note that we did not include the effect of the reduction of the area of concrete due the presence of steel. This will not have much influence on the area of steel to be provided in as much as we used a modification factor of 0.45 instead of anything in the range of 0.5 to 0.6. The ratio of the area of steel to concrete = 35140.9/640000 = 0.055 = 5.5%. Though this is within the limits allowed in the codes, I would prefer to upgrade it (putting into consideration the fact that these columns will in actuality participate in the carrying the lateral load and also the fact that the structure will be subjected to twist, the grave consequences if something should go wrong, as such has to be well reinforced-that is, to 18 + 14 = 32 strands) to make 32/4 = 8 numbers on each face of the column. I do not know if 50mm diameter steel does exist, so let’s scale the dimension down to 32mm diameter. In this case, lets adopt 8% of the cross sectional area of concrete as the area of steel to be provided. This implies that the strands of steel to be provided = (8% of 640000)/0.25pi (32)^2 =64 strands. This could be provided in 2 rings of 8/6/per face and central core in cross of2 x 4 strands. (4 x 8 + 4 x 6 + 2 x 4 = 64)(Refer to the screen shot above).
Regards
Teddy