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

[chigozie]

Every physical system vibrates (the so-called free vibration). This is due to the fact that the atoms and molecules that make up that system are always losing and or gaining energy as such always changing energy level-thus in motion. This vibration is not noticeable due to the natural damping that accompanies that system. As that system vibrates, it does so at particular frequencies –known as the natural frequencies. To locate these frequencies, we may have to resort to the technique of modal Analysis. For simple systems, simple modal analysis could yield the desired result, but if we have to contend with complex systems, finite element analysis will have to be performed in order to determine the dynamic response. The natural vibration of the system does not constitute any problem per say. Problems usually arise with the input of energy into the system (the forced vibration). This is usually verified when the energy input pulsates (non steady state) like is witness in the event of wind loading on structures. Like was said previously, one of the main problems that had to be confronted and resolved in the realization of this structure is that of wind loading. So how is it to be solved (assuming that we are making our own independent preliminary design or assessment of the structure)? We could adopt the criteria as defined in the codes that specified the minimum gust duration to be employed in the analysis. In the alternative, we decide on the reference period or the life span of the structure (Vn). We could also adopt the standard 50years return period for wind loading for building structures. Based on importance factor (If) and the use coefficient (Cu), we calculate the design period Vr (Vr = If * Cu *Vn ), then calculate the return period Tr (Tr = Vr/-In (1- pr), if we do not want to use the 50years return period or if it is not justified to use the 50years return period. Note that in the above equation for the calculation of the return period, Pr is the probability of exceeding the design load in the life span of the structure). With any of the approaches and the physical conditions of the site, we chose the basic wind speed for our design (say V = 40m/s). Then calculate the characteristic wind pressure Wk = 0.625S^2V^2; S depends on the exposure condition and the form of our structure. (particularly the plan area and height of our structure).Since we are building inside a town and our structure has its plan dimension greater than 50m and height greater than 50m (remember that it is in excess of 800m height), then our S is about 2 (we are using the British standard and the euro codes that did not include such a height (800m), as such we had to do some interpolation from the included height-which though may not represent the actual fact but which is enough for this stage of our design) for which our Wk = 0.625(2)^2(40)^2 = 4000 N/m^2. We approximate our structure to a triangular one and assume that wind attack face is on one of the sides. The height to breadth ratio is over 40 (as such we adopt the infinity ratio), so the total force coefficient is 2.1 for which the modified Wk = 2.1 x 4000 N/m^2 = 8400 N/m^2 or 8.4 KN/m^2. If we assume a rectangular face of 134m height on each set-back with varying widths (as the structure tappers from the bottom to the top) for each structural lift then, the surface area of each lift = 134m multiplied by 90% of the width of the lift directly underneath, except for the ground floor for which the full 100% width has to be used in the calculation (we assume that the structure is split into 6 lifts of 800/6 = 134m). (We will come back to this later).
The effect of the wind loading on the structure, apart from the fact that it causes torsional and bending stresses, is that it makes none regular force inputs into the structural system. These force inputs on the structure force it to deflect and to take up differing modal shapes. Since the forces are not at steady states but varying with time (due to none steady force input as already mentioned, vortex shading etc) the structure oscillates (vibrates). The maximum vibration is given by Dmax = P/[K^2(1-N^2/n^2)^2 + 4 pi^2N^2u^2]^0.5. K is the spring constant (if we assume that the masses of the structure are concentrated on the beams and that the beams are supported on columns built in at the ends, then K = 24EI/L^3), n is the natural frequency of the structure, N is the frequency of applied wind loading (P). The natural frequency of the structure is given by n =1/2pi (K/M)^0.5, M being the mass of the structure and u being the damping coefficient of the structure. An inspection of the vibration equation will show that if N =n, then the term n (the natural frequency of the structure) will disappear from the equation as such, apart from damping, the structure will be taken over by the wind-thus attains resonance. In such a situation, the structure vibrates wildly with the wind and the deflection tends to infinity (theoretically) except for damping. If this persists, a phenomenon known as “lock-in” could develop. In that case, the vibration is self propagating and eventually, the vibration will overcome damping and the structure will vibrate indefinitely and collapse. So, we have to demonstrate (through our calculation) that this condition will not be reached in the design by showing that the natural frequency of the structure is always below (in worst case, above the range of expected frequencies due to wind loading. One of the problems is that the critical velocity at which this resonance could occur may be below or above our chosen or calculated wind design speed as such we could be looking for that point outside the design wind speed range. If this is the case, then the above calculation could only serve for the bending and torsional stress analysis-thus, the base shear and bending designs; as such, we have to calculate the natural frequency of the structure and match it to the expected range of wind loading that could be imposed on the structure in its service life.
But how do we calculate the frequency of the wind loading at which our structure gets into trouble as to compare it with the natural frequency of the structure, given that in this case, we are not looking for it at a given point but over what could turn out to be a wide range?
Regards
Teddy

[chigozie]

The designers of this building (the Burj) had the option of using a steel structure (which has many advantages over other options) a reinforced concrete one and including, may be other options but opted for the reinforced concrete. Which and what could have informed their decision?
Again:-
Given our level of knowledge/understanding of structures, the environment and their behaviours, is it possible to build a structure that will beat the present record holder (the Burj). what and where engineeristically speaking will be our limit vertically. Is it to the sky (like it is said "the sky is the limit")
What is your opinion?
Regards
Teddy

[chigozie]

The mitigation of wind-induced excitations in tall building is one of the most important design considerations that should be met with right from the conception stage of any such a building. In that respect, different options have to be considered; of which the shape of the building is one of them. Reshaping of a structure does not involve only the plan modification but and also could involve elevational modification. The shape of a building could be aerodynamically modified by changing the taper of the cross-section. For one, this modification alters the flow pattern around the building. In so doing, it does not only provide the wind front a longer distance to travel and longer time to complete its percourse (thus dilution of the effect. Remember, power is the ability to do work i.e. work done per unit time, as such the longer it takes to complete a circle of work, the less power that that force system could exercise on the receiving system), but also creates room for spin offs-thus reduces the power input-as such wind-induced vibration of tall buildings. Further, a tapered tall building that spreads the vortex-shedding over a broad range of frequencies, more effectively reduces cross-wind responses. There have been several studies into this. In one of the studies, to investigate the tapering effect on the reduction rate of wind-induced vibration and responses of differing models of tapered tall buildings to this forced vibration, models of differing sizes were tested. High-frequency force-balance test was conducted on six types of building model having differing taper ratios - 2·5%, 5%, 7·5%, 10%, 15%. The results of the analysis were compared with that for a basic building model of square cross-section. Tests were conducted under two typical atmospheric boundary layers conditions, representing suburban and urban areas. The effect of wind direction was also considered. (Copyright © 2007 John Wiley & Sons, Ltd). The results of the test show clearly that there is much to gain in shaping the structure. Tapering distributes the dynamic behavior of the structure as such it becomes difficult to achieve a particular wind speed at which all parts of the structure will attain resonance. Apart from vibration, the structure is subject to another serviceability limit condition demand- base shear and bending moment, mainly due to same lateral loading.
There are several structural configurations geared towards countering the effect of lateral loading on a structure. For low rise buildings, the moment resisting frames or the shear wall approach could proof ideal. But after a certain height, it becomes impracticable to use the moment resisting frame. This is due to the fact that despite the fact that it becomes too expensive to achieve the construction following this approach, the lateral deflection (drift) that could be verified would be so great and unacceptable that that approach would have to be abandoned. For tall buildings such as the one in consideration (the Burj), it becomes imperative and unavoidable to resort to the shear wall approach; and when this shear wall is sort of located at the core of the structure, it is referred to as the “core structure” Due to the massiveness of the core structure, its robustness, its centralization, as such the location of both the geometric center, center of mass and center of rigidity within same range, structural eccentricity is as much is possible avoided. Though every attempt would be made as much as it is structurally possible to avoid this eccentricity, certain amount of eccentricity would definitely result due construction error, due to non homogeneity of structural components etc. The effect of the resultant eccentricity is to subject the structure to twist. If a building is subject to twist, as all are (implicitly), the torsional stiffness of the core, in a “core-only” structure could constitute a significant part of the total torsional resistance of the entire building. The torsional behavior of cores is a topic that is relatively of interest to many engineers. The proportion of the height, length, and thickness of the core walls of a typical building obligates us to analytically treat the core structure as a thin-walled structure. Consequently, when the core structure twists, originally plane sections of the core warp. Because the core is restrained from warping by the foundation, and to an extent by the floor slabs/beams, warping stresses somewhat similar to axial stresses are induced throughout the height of core walls. In buildings that are predominantly dependent on a core for torsional and lateral resistance (as is the Burj), it is imperative that consideration be given to warping effects. (Due to functional necessity, the core structure is usually an open one as such is susceptible to warping). For the fact that the core structure would be subject to enormous labor in a major event, all other parts of the structure that could be employed toward countering this twisting effect –thus the accompanying stresses had to be mobilized. For this, the columns, walls etc had to be properly linked up to the core structure- the main and dominant structure that bears the brunt. Since large torques are to be transmitted, robust links between the columns and the core structure had to be used. That is one of the reasons why deep beams were aggressively deployed in the structural configuration.
Regards
Teddy