Effect of wind in the design of reinforced concrete buildings

Resumo This paper presents the results from a parametric study carried in order to quantify how far errors in the design stage related to the consideration of the wind action may put at risk the response and safety of reinforced concrete buildings. Using an architectural model as reference and varying the number of floors of the building, the structural safety was evaluated as a function of the wind action intensity. Results showed that even for low-rise buildings, with 10 floors, ignoring the wind action can significantly jeopardize their behaviour and safety. Yet, for slenderer buildings, up to 30 floors, it can lead to catastrophic results, as the ruin of the structure by progressive collapse.

Effect of wind in the design of reinforced concrete buildings

Introduction
The progressive collapse is a partial or complete ruin mechanism of a structure caused by the located failure of a primary structural element (Li et al [1]).This leads to the redistribution of loads to the surrounding elements, which can collapse as well.In national and international literature there are several cases of serious structural accidents in buildings with concrete structure (Kamari et al [2], Schellhammer et al [3], King and Delatte [4], Gardner et al [5]).Souza and Araújo [6] highlight that in Brazil, the amount of structural accidents is increasing and that their origins are mainly related to mistakes in design and construction stages.This recurs in other countries too, and as example it can be cited the work of Kaltakci et al [7], that analysing the causes of accidents in buildings under construction in Turkey, got to the same conclusions.On January 29, 2011, in the city of Belem, Para, occurred one of the greatest structural accidents registered in Brazil in reinforced concrete buildings.On this day collapsed the residential building called Real Class, which was under construction, fatally victimizing three people.Figure 1 shows the building under construction and the landscape after its collapse.This building had constructed area of approximately 13,400 m² and was composed by 01 under-ground floor, 01 ground floor and 35 high floors, with about 105 m high.The building's tower had its weight estimated in 9 thousand tons, which were supported by 25 columns.The building's ruin occurred during a heavy rain, where intense winds were registered in the city.In slender structures, the wind is one of the main actions to be considered (see Dyrbye and Hansen [8]) and there are records of various structural accidents with this action as origin (see Sha and Malinov [9], Klinger et al [10] and Rao et al [11]).At the time of this accident, three different teams carried out studies about the case and the analyses developed by a professors' team of the Faculty of Civil Engineering from Federal University of Para indicated that the wind load was not properly considered in the design.This paper presents results of a parametric study done in order to show how errors in the consideration of the wind action during the design stage can jeopardize the behaviour and the safety in the Ultimate Limit State of reinforced concrete buildings.A typical architectural plan was used as reference to develop the structural and foundations designs, having as one of the variables the number of floors, varied between 10, 20 and 30 floors.The other variable of the study was the magnitude of the wind, which was initially assumed as zero, to define the geometry and the amount of steel reinforcement of the structural elements, which were designed according to the recommendations of ABNT NBR 6118 [12].Later, the wind action was considered as recommended by ABNT NBR 6123 [13] and the internal forces were used to verify the response in service and the safety of the structure and the foundations that were initially designed without wind consideration.The response in service and safety of columns and foundations is discussed.

Wind
In the structural design, the wind is physically represented by a speed profile reaching a building.Its characteristics and the effects it generates depend on the velocity of the wind, the geometry of the building, and of the protection caused by the terrain and surrounding obstacles.Rosa et al [14] warn that the environment has great influence on the wind loads in a given building and that its accurate consideration is only possible if there are experimental data from tests in wind tunnel.On the other hand, Elsharawy et al [15] point out that even low building may suffer significant influence of wind action, as in function of its plan geometry and columns positioning, wind action can induce torsional forces in the spatial frame.Although ABNT NBR 6123 [13] does not guide the use of automated weather stations data, the ABNT NBR 5422 [16] alludes to this procedure in the recommendations for transmission lines designs.In this case, the currently used values to define the country's wind isotachs can be verified by data from automatic stations, provided by institutions responsible for monitoring meteorological data.Figure 2 shows wind speed data provided to the city of Belem-PA by ICEA [17], in the period of 1951-2010.It is possible to realize that the basic wind speed (V 0 ) defined for Belem, which is 30 m/s, was exceeded three times in this period and that the average results seems to present increasing trend in function of time.It is known that pressure made by wind is not static.It suffers fluctuations (gusts) and depends on characteristics of its incidence on  [18]).These pressure fluctuations not only depend on the gust time, but also on the flow regime (turbulence) and can cause the structure to suffer dynamic oscillations, inducing fatigue.In design situations, standards recommend the adoption of gust speeds in structural design, since structures in general have higher fundamental frequency of vibration than natural wind frequency.The intensity of wind forces in a structure varies spatially and temporally and, in design, most standards adopt a simplified methodology where wind dynamic action is replaced by an equivalent static load.Through this procedure, it is attempted to represent the peak pressure caused by wind on the structure, being this pressure function of wind basic speed (V 0 ), and of S1, S2 and S3 parameters, as shown in Equation 1.This speed (V 0 ) was established for the entire country through probabilistic approach and is defined as the 3-second-speed gust, exceeded on average once in 50 years, measured 10 m above the ground, in open and flat field.Another important consideration on determining wind effects is the drag force, that in multistory buildings, describes the forces induced by the wind and should be calculated according to ABNT NBR 6123 [13] using Equation 2. (1) (2) Where: F a is the drag force, C a is the drag coefficient, obtained in function of the height and the plan dimensions of the building, q is the velocity pressure, A is the area of the reference surface.S1, S2 and S3 are parameters defined in ABNT NBR 6123 [13] The determination of the drag coefficient is made depending on wind turbulence conditions.The ABNT NBR 6123 [13] defines that a building can be considered in high wind turbulence when its height does not exceed twice the average height of buildings in the vicinity, extending these, toward and in the direction of the incident wind, in a minimum distance of: 500 m, for a building up to 40-mhigh; 1,000 m, for a building up to 55-m-high; 2,000 m, for a building up to 70-m-high; and 3,000 m, for a building up to 80-m-high.

Global stability
The verification of reinforced concrete columns in tall buildings is influenced by the overall stability of the building and can be negatively affected by 2 nd order effects obtained with the calculation considering the deformed structure.ABNT NBR 6118 [12] presents two approximate procedures for checking the possibility of dispensing the consideration of 2 nd order global forces: instability parameter α; and coefficient γ z .They are used to classify a structure as being composed by fixed or mobile nodes and, in the case of coefficient γ z , it is considered that a structure has fixed nodes if γ z ≤ 1.1.Feitosa and Alves [19] consider that the use of these parameters in design is convenient, since the precise consideration of 2 nd order effects may significantly increase analysis complexity.The coefficient γ z can be determined using Equation 3, and in the case of structures with mobile nodes, since γ z ≤ 1.3, 1 st order forces can be used to calculate the 2 nd order ones, being scaled up by 0.95γ z .If the structure presents γ z > 1.3, calculating 2 nd order effects must be made using the P-Delta analysis method. (3) Where: M 1,tot,d is the 1 st order moment, found by Equation 4, ΔM ,tot,d is the addition of moments after 1 st order analysis, determined by Equation 5. (4) Where: F hid is the horizontal force applied on i floor, h i is the floor's height h. (5) Where: P id is the acting vertical force on i floor, u i is the horizontal displacement of i floor.Effect of wind in the design of reinforced concrete buildings

Design of reinforced concrete columns
In buildings a column will usually be subjected to bending moments in addition to the axial compressive forces due to not only asymmetry of spans and loads, but also because of horizontal actions like the wind.In these cases, it is common for both design and verification of load capacity to use bending-axial load interaction diagrams.These curves are obtained assuming points with different strain states in the cross section and computing for each of these points the axial force and the resultant moment in the section, as shown in Figure 3a for combined bending and axial load.
In this figure, a random point A represents a combination of axial force and bending moment that would lead the column to ruin.In it, any combination of forces that results in a point inside the curve represents a safe load state and any point outside shows a combination of forces higher than the element's load capacity.Radial lines as line OA represent the load eccentricity and point B shows the combination of forces for a balanced failure.Above this point, the failure is controlled by compression and below it, controlled by tension.Combination of forces up the line OC indicate critical situations where the ruin can occur without tensile strains of the element (no cracking).
In the case of columns under compression plus biaxial bending it is possible to draw a three-dimensional interaction surface from the interaction diagrams for the two main axes, as illustrated in Figure 3b, for cases a and b.For case c, that combines moments in x and y directions, the resulting eccentricity's direction is defined by the angle λ, calculated with Equation 6. Flexure in this case occurs on an axis defined by the angle θ.In practice, the construction of this three-dimensional surface of interaction can be complicated even using computational methods.In this paper, it was made in a simplified manner, as described by Nilson et al [20] and presented in Equation 7. (

Computational modelling
The methodology consisted of, based on an architectural plan of a building's typical floor, designing the reinforced concrete structure and the foundations, entirely ignoring the wind action.This was done taking as variable the number of floors, generating spatial frames with 10, 20 and 30 floors, in order to highlight the relevance of the wind action in the design of reinforced concrete buildings.Later, the wind was considered in the computational models, following the recommendations from ABNT NBR 6123 [13], showing how the behaviour and the safety levels of both structure and foundations can be in risk if this horizontal action is not properly considered in the design stage.These analyses were done using the commercial software AltoQi Eberick V9.
In the analyses without wind, the dimensions of the columns were pre-designed considering their influence areas and assuming a constant vertical load on the floor.After this step, the structural design was regularly carried, yielding to the necessary dimensions and reinforcement ratios of the structural elements to safely support the vertical forces.Subsequently, the interaction diagrams of all columns were generated, based on sections and steel rein-forcement found in the analyses without considering the wind.The structural models were then analysed again, now considering the wind as established by ABNT NBR 6123 [13].From these analyses the combinations of actions in each of the columns were extracted, for the evaluation of the structural safety.Also, the horizontal displacements of the structure were analysed, in order to evaluate its performance in service, the γ z coefficient, as an indicative parameter of instability, besides the increase of the 2 nd order moments.Figures 4, 5 and 6 present the plans of the structures which were designed for models with 10, 20 and 30 floors, respectively, in the windless analyses.In these figures, columns selected for this article's presentation and discussion of results are highlighted with a red circle.A corner column (P1), a column near the floor's edge (P11) and an inner column (P6) were chosen.Tables 1, 2 and 3 present the dimensions of these columns' cross section and the steel reinforcement designed, for models with 10, 20 and 30 floors, respectively.

Criteria of ABNT NBR 6123 (1988)
The basic wind speed defined in ABNT NBR 6123 [13] as v 0 = 30 m/s to the city of Belem, Para.To calculate the drag coefficient, the flow regime was assumed as being of low turbulence and was calculated according to the Brazilian standard's abacuses knowing that the plan dimensions of the floor are 20.80 m x 19.20 m.The correction coefficients for characteristic speed were: n S 1 = 1.00, related to flat terrains;  Where: b, p and F r are constants defined in the Brazilian wind standard; z is the height aboveground.

Criteria of ABNT NBR 6118 (2014)
According to ABNT NBR 6118 [12], for the determination of the 2 nd order overall forces, the physical nonlinearity of materials can be considered in a simplified way to reticulated structures with at least four floors, admitting to the calculation of structural elements the stiffness values presented in Equations 9, 10 and 11.Slabs:

EI E I
Where: (EI) sec is the stiffness of the element; E c is the elastic modulus of concrete; I c is the moment of inertia of the gross cross section.For forces' determination, the combination of actions follows the formulas recommended by ABNT NBR 8681 [21], presented in Equation 12. ( Where: F d is the calculation value of the action, γ gi is the coefficient of permanent actions, F Gi,k is the characteristic value of permanent actions, γ q is the weighting coefficient of variable actions, F Q1,k is the characteristic value of the variable action considered as main action for the combination, Ψ oj F Qj,k is the reduced value of combining each of the other variable Effect of wind in the design of reinforced concrete buildings actions. For columns' safety evaluation, it was considered that the design strength (R d ) should exceed the design load (S d ), as shown in Equation 13. (

Serviceability Limit State (SLS)
The serviceability limit states are related to people's comfort and to the durability and good working conditions of the structure, considering both users and machines installed in the building.ABNT NBR 6118 [12] recommends for concrete structures that the following serviceability limit states are checked: crack formation limit state; crack opening limit state; excessive deformations limit state; decompression limit state; excessive compression limit state; and excessive vibration limit state.For this article, it was admitted that the excessive deformations limit state would be dominant in relation to the others and it was evaluated using as analysis parameters the global displacement of the structure and γ z coefficient, which is used to evaluate the importance of 2 nd order global effects.ABNT NBR 6118 [12] admits that in mobile nodes structures with 1.1 < γ z ≤ 1.3 it can be used to approximately determinate the 2 nd order global forces.Figure 7 presents the γ z variation in x and y directions in function of the number of floors.It is possible to see that ignoring the wind action would cause that even the smaller building, with only 10 floors, had coefficient γ z of 1.39, which requires that the 2 nd order effects are determined by P-Delta analysis method.In the most extreme case, of the 30-floor model, values of γ z up to 2.29 were found, indicating that the 2 nd order effects would be extremely high.Figure 8 presents the variation of total displacements per floor considering the wind action in x and y directions.ABNT NBR 6118 [12] recommends that displacements are maintained below limit values, to avoid damage to non-structural elements, like masonry walls.It recommends that in case of horizontal displacements of buildings, they are maintained at values in centimetres below

Ultimate Limit State (ULS)
The ultimate limit state is related to the collapse or any other ruin of the structure that leads to the interruption of its use.ABNT NBR 6118 [12] recommends for concrete structures to check the following ultimate limit states: loss of static equilibrium; end of the structure's load capacity, whole or in part, due to axial and tangential forces, assuming the redistribution of internal forces; end of the structure's load capacity, whole or in part, considering the 2 nd order effects; ultimate limit state caused by dynamic forces; ultimate limit state of progressive collapse; end of the structure's load capacity, whole or in part, considering exposure to fire; end of the structure's load capacity, considering seismic actions; other ultimate limit states that might occur in special cases.
In the analyses carried in this paper, it was considered that the wind would cause the most significant effects on the ultimate limit state of columns.This way, both the increase in 2 nd order moments and the possibility of ending the load capacity of columns under combined biaxial bending were evaluated.Figure 9 shows the increase in 2 nd order moments caused by the wind action in x and y directions of the building, as presented in Section 2.2, pointing out how important it is to correctly consider in design the actions caused by wind.Significant increases in 2 nd order moments were observed, which can really jeopardize the structure's safety.

Effect of wind in the design of reinforced concrete buildings
Columns P1, P6 and P11 were selected to illustrate the global response and for these elements diagrams of iteration were generated, as illustrated in Figure 3. Figure 13 shows the resistance envelopment for P1 in the case of the 10-floor building.In this and in the other figures, the dashed line indicates the design envelop, considering the all safety coefficients and the solid line shows the strength considering the characteristic resistances of steel and of concrete.It is possible to see that for 4 combinations of actions the design load was bigger than the design resistance.This indicates that for these cases of load, the design safety level would not be satisfied.
In the case of the 20-floor building, the diagrams of columns P1 and P11 are worth mentioning, which presented critical combination of actions, as show in Figures 14 and 15.In x direction of column P1, 4 combinations extrapolated the characteristic resistance of the column and other 2 the design one, whereas for the y direction only 1 combination was higher than the design strength.On the other hand, for column P11, only the y direction presented critical situations, with 4 combinations resulting in higher forces than the characteristic strength and 7 higher than the design one.This indicates that these columns would have a higher probability to ruin.
For the 30-floor model, it was observed that the most critical situations would also occur for columns P1 and P11 (see Figures 16 ), while for column P6 (see Figure 17) in all models, the iteration diagram showed that the acting force level would be lower than the design strength.The analyses carried out for the 30-floor building showed that also in the case of columns P1 and P11 the probability of ruin would be significant.In these cases, even more seriously, it is possible to realize that many of the critical points would be related to abrupt ruin modes, governed by crushing of concrete without cracking of the columns.

Conclusions
This study shows in an objective way how the wind action affects

Figure 3 -
Figure 3 -Iteration diagrams for reinforced concrete columns

Figure 4 -Figure 5 -Figure 6 -
Figure 4 -Plan of the structure for the 10-floor model

Figure 7 -Figure 8
Figure 7 -Variation of gamma z coefficient

Figure 11 -Figure 13 -
Figure 11 -Addition of load in the foundation of column P6

Figure 18 -
Figure 18 -Interaction diagrams for column P11 of 30 floors

Table 1 -
Dimensions and steel of columns studied for the 10-floor model

Table 2 -
Dimensions and steel of columns studied for the 20-floor model

Table 3 -
Dimensions and steel of columns studied for the 30-floor model