The initial global processing was carried out solely for forces without considering the reinforcement design. Subsequently, the preliminary design of pile cap blocks was executed, and then the full global processing was performed. In the second phase of structural processing, loads and displacements were computed, and the structural elements were designed.
3.1 Global Stability Analysis
It is known that the global stability check must be carried out for all ULS combinations and guarantee the stability of the structure in all of them. The maximum values obtained for the parameters α, γz and FAVt are shown in Fig. 2.
In Fig. 2(a), the values obtained in the 0º and 180º directions exceeded the limit (α = 0.6), indicating a potential classification of hinged supports. However, as the building lacks a symmetric truss structure, α might not be a suitable parameter for assessing its stability. It is recommended to analyze using other parameters, particularly considering the complexity of being a structure with more than 4 floors.
[3] states that the γz parameter is a measure of global stability in a building, where values slightly above 1.0 suggest stability, and values exceeding 1.5 indicate an unstable structure. For reinforced concrete buildings, a γz value higher than 1.3 indicates high instability, and it is preferable to design structures with a value equal to or lower than 1.2. In this study, FAVt was adopted by the software to assess stability and estimate second-order effects, as its values were higher than γz, as shown in Fig. 2(b) and Fig. 2(c). According to [3], the obtained result in Fig. 2(c) (FAVt = 1.08) is considered satisfactory, indicating a structure with fixed supports (γz ≤ 1.10), low second-order effects (less than 10% of the respective first-order forces), and overall stability.
According to ABNT NBR 6118:2023 [8], limit values are set for the lateral movement of buildings to prevent adverse effects on non-structural elements like walls. The limit value is H/1700 for the top of the building and Hi/850 between consecutive floors, where H is the total height of the building, and Hi is the gradient between two consecutive floors. The obtained horizontal displacement results are presented in Table 4.
Table 4
Maximum horizontal displacements
DIsPLACEMENT | MAXIMUM VALUE (cm) | limit (cm) |
Top of the building | 0.18 (H/9855) | 1.03 |
Interfloor | 0.05 (Hi/5832) | 0.37 |
It can be observed that the maximum values obtained during processing are below the established limits and therefore meet the regulatory requirements.
3.2 Serviceability Limit State Analysis
In the initial SLS analysis, deflections and crack openings of beams and slabs were observed using the NLG as it is more refined and precise than the LG. For inclined elements, such as stairs, TQS® recommends caution when analyzing them with NLG, and therefore, these elements were preferably analyzed using LG. Several elements showed excessive displacements and Table 5 shows all the slabs with deflections exceeding the limit.
To simplify execution, trussed slabs were modeled without continuity, treating them all as having two sides simply supported. Analysis and structure launching revealed that symmetrical floor slabs L104, L105, L118, and L119 exhibited significant displacements due to numerous walls. Even after modifying trusses to TR16 and TR20, deflections remained above the limit. A more effective solution involved reducing the span of these slabs, allowing some walls to be directly supported by beams. Consequently, slabs like L103 and L104 were split, as depicted in the design modification in Fig. 3, with a similar approach applied to other symmetrical slabs.
In typical floor slabs directly supporting walls, the absence of transverse reinforcement, despite substantial shear forces from concentrated wall loads, underscores the need to reinforce ribs for shear in these areas.
Table 5
Slabs with deflections over the limit
FLOOR LEVEL | ELEMENT | DEFLECTION (cm) | Limit (cm) | RATIO (%) |
NLG | lG | NLG | lG |
Typical floor | L101 | 0.86 | 1.05 | 0.22 | 390.91 | 477.27 |
L102 | 0.81 | 1.00 | 0.22 | 368.18 | 454.55 |
L103 | 1.06 | 1.72 | 1.26 | 84.23 | 136.51 |
L104 | 2.64 | 3.10 | 1.66 | 159.04 | 186.75 |
L105 | 2.65 | 3.11 | 1.66 | 159.64 | 187.35 |
L106 | 1.07 | 1.73 | 1.26 | 84.92 | 137.30 |
L113 | 0.79 | 1.09 | 1.07 | 73.83 | 101.87 |
L114 | 0.78 | 1.09 | 1.07 | 72.90 | 101.87 |
L117 | 1.08 | 1.73 | 1.26 | 85.71 | 137.30 |
L118 | 2.56 | 3.05 | 1.66 | 154.22 | 183.73 |
L119 | 2.62 | 3.08 | 1.66 | 157.83 | 185.54 |
L120 | 1.07 | 1.73 | 1.26 | 84.92 | 137.30 |
L121 | 0.94 | 1.37 | 0.22 | 427.27 | 622.73 |
L122 | 0.89 | 1.30 | 0.22 | 404.55 | 590.91 |
Rooftop | L401 | 0.51 | 0.60 | 0.22 | 231.82 | 272.73 |
L402 | 0.48 | 0.57 | 0.22 | 218.18 | 259.09 |
L421 | 0.56 | 0.66 | 0.22 | 254.55 | 300.00 |
L422 | 0.54 | 0.63 | 0.22 | 245.45 | 286.36 |
[17] note that such reinforcements are uncommon due to challenges in their placement, leading to an increased calculation-resistant shear force (VRd1) by augmenting the useful height (d) of slabs. To simplify execution and avoid stirrups, slabs were tested with TR16 and TR20, some still requiring transverse reinforcement. Although truss lateral diagonals contribute to shear resistance, TQS® does not consider this. Ultimately, using TR12 eliminated the need for transverse reinforcement by increasing the concrete cover thickness from 4 cm to 6 cm in all typical floor slabs. Table 6 details beams with deflections above the limit.
Table 6
Beams with deflections over the limit
FLOOR LEVEL | ELEMENT | DISPLACEMENT (cm) | Limit (cm) | RATIO (%) |
NlG | lG | NLG | lG |
Typical floor | V101 | 1.37 | 1.67 | 0.54 | 253.70 | 309.26 |
V102 | 1.53 | 1.85 | 0.54 | 283.33 | 342.59 |
V116 | 1.39 | 1.69 | 0.54 | 257.41 | 312.96 |
V117 | 1.54 | 1.87 | 0.54 | 285.19 | 346.30 |
V122 | 1.07 | 1.30 | 0.29 | 368.97 | 448.28 |
V123 | 0.97 | 1.18 | 0.29 | 334.48 | 406.90 |
V126 | 1.19 | 1.44 | 0.29 | 410.34 | 496.55 |
V127 | 1.08 | 1.30 | 0.29 | 372.41 | 448.28 |
Rooftop | V401 | 0.81 | 0.95 | 0.54 | 150.00 | 175.93 |
V402 | 0.89 | 1.04 | 0.54 | 164.81 | 192.59 |
V416 | 0.82 | 0.95 | 0.54 | 151.85 | 175.93 |
V417 | 0.90 | 1.05 | 0.54 | 166.67 | 194.44 |
V422 | 0.63 | 0.74 | 0.29 | 217.24 | 255.17 |
V423 | 0.57 | 0.67 | 0.29 | 196.55 | 231.03 |
V426 | 0.70 | 0.81 | 0.29 | 241.38 | 279.31 |
V427 | 0.63 | 0.73 | 0.29 | 217.24 | 251.72 |
The beams failing the deflection assessment were all located in the en suite bathroom, attributed to the cantilever beam V123 and its symmetrical counterparts fixed to beam V103. V103, part of the bracing substructure, exhibited considerable displacement, causing solid slabs L101, L102, L121, L122, L401, L402, L421, and L422 to exceed deflection limits. To address this, beam V123 was extended to become V127, supported on an internal beam for better force distribution, as illustrated in Fig. 3(b). This modification aimed to alleviate displacements since the supporting beam (V103) lacked sufficient stiffness to absorb the large negative bending moment from cantilever beam V123.
The most significant displacements were observed on the staircases, measuring 0.73 cm on the first run and 0.78 cm on the second run. As the length of the span between the staircase supports is 360 cm, the L/250 deflection limit for the staircase is 1.44 cm and, therefore, the displacements in the staircases are within the limit established by the standard in the Excessive Deflection Limit State (ELS-DEF) test.
For the second round of processing, several crack openings were identified exceeding the 0.3 mm threshold, specifically on the typical floor, ranging from 0.31 to 1.00 mm, in slabs L103, L106, L117, and L120. Symmetrical beams V121 and V128 of the typical floor had peak openings of 0.31 mm. However, after implementing the aforementioned modifications, the cracking issue was successfully addressed.
In the upper tank, due to the aggressive environment, with the presence of chlorine and prone to shrinkage effects and temperature variation, more conservative crack opening limits of 0.2 mm were adopted, based on [18]. The wk values obtained on each side of the elements are shown in Table 7. It is evident that cracking has been effectively managed, guaranteeing the durability of the tank structure and the impermeability of the walls and slabs.
Table 7
wk values in the upper tank
element | DirECTION | SITE | Md (tfm∙m− 1) | Nd (tf∙m− 1) | As,cal (cm2∙m− 1) | As,ef (cm2∙m− 1) | wk (mm) |
Cover | X | Bottom | 0.30 | 1.63 | 1.50 | 1.55 | 0.02 |
Top | 0.58 | 1.30 | 1.77 | 1.96 | 0.06 |
Y | Bottom | 0.15 | 1.22 | 1.50 | 1.55 | 0.00 |
Top | 0.42 | 0.82 | 1.50 | 1.55 | 0.07 |
Bottom | X | Bottom | 1.26 | 2.61 | 3.07 | 3.11 | 0.09 |
Top | 1.51 | 2.40 | 3.60 | 3.92 | 0.13 |
Y | Bottom | 0.67 | 1.65 | 2.25 | 2.51 | 0.05 |
Top | 1.19 | 2.09 | 2.83 | 3.11 | 0.08 |
Walls 1 and 2 | X | Left | 0.21 | 1.93 | 2.25 | 2.51 | 0.00 |
Middle | 0.11 | 1.77 | 2.25 | 2.51 | 0.00 |
Right | 0.21 | 1.93 | 2.25 | 2.51 | 0.00 |
Y | Left | 1.19 | 3.33 | 3.01 | 3.35 | 0.11 |
Middle | 0.80 | 3.10 | 2.25 | 2.51 | 0.09 |
Right | 0.42 | 0.85 | 2.25 | 2.51 | 0.01 |
Walls 3 and 4 | X | Left | 0.21 | 1.84 | 2.25 | 2.51 | 0.00 |
Middle | 0.09 | 2.22 | 2.25 | 2.51 | 0.00 |
Right | 0.21 | 1.84 | 2.25 | 2.51 | 0.00 |
Y | Left | 1.51 | 4.23 | 3.87 | 5.02 | 0.07 |
Middle | 1.07 | 3.62 | 2.78 | 3.35 | 0.09 |
| Right | 0.58 | 1.15 | 2.25 | 3.11 | 0.01 |
3.3 Analysis of Column Dimensioning
With regard to the columns, all the elements were dimensioned and the results are shown in Table 8.
Table 8
COLUMN | SECTION (cm) | σ (kgf∙cm− 2) | λ | ρ (%) | STEEL RATE (kg∙m− 3) | n | STIRRUPS |
Φ (mm) | c/ (cm) |
P1 | 20x30 | 6.7 to 40.4 | 36 to 56 | 0.52 to 0.52 | 69.1 | 4 | 5 | 12 |
P2 | 20x30 | 13.5 to 91.1 | 36 to 56 | 0.52 to 0.52 | 68.5 | 4 | 5 | 12 |
P3 | 20x30 | 6.2 to 39.4 | 36 to 56 | 0.52 to 0.52 | 69.1 | 4 | 5 | 12 |
P4 | 20x30 | 6.2 to 39.3 | 36 to 56 | 0.52 to 0.52 | 69.1 | 4 | 5 | 12 |
P5 | 20x30 | 13.5 to 93.5 | 36 to 56 | 0.52 to 0.52 | 68.5 | 4 | 5 | 12 |
P6 | 20x30 | 6.8 to 38.7 | 36 to 56 | 0.52 to 0.52 | 69.1 | 4 | 5 | 12 |
P7 | 20x50/20x30 | 2.7 to 55.4 | 14 to 55 | 0.52 to 0.59 | 77.6 | 6/4 | 5 | 12 |
P8 | 20x40/20x30 | 2.9 to 53.5 | 14 to 55 | 0.52 to 0.59 | 77.6 | 6/4 | 5 | 12 |
P9 | 20x50 | 7.3 to 41.8 | 22 to 55 | 0.47 to 0.47 | 65.3 | 6 | 5 | 12 |
P10 | 20x30 | 18 to 145.2 | 27 to 57 | 0.52 to 4.91 | 272.1 | 6/4 | 8/5 | 20/12 |
P11 | 20x40/20x30 | 6.4 to 62.5 | 14 to 55 | 0.52 to 0.59 | 77.6 | 6/4 | 5 | 12 |
P12 | 20x40/20x30 | 6.7 to 59.2 | 14 to 55 | 0.52 to 0.59 | 77.6 | 6/4 | 5 | 12 |
P13 | 20x30 | 18.1 to 128.3 | 27 to 57 | 0.52 to 2.09 | 140.7 | 4 | 6.3/5 | 20/12 |
P14 | 20x50 | 7.4 to 41.4 | 22 to 55 | 0.47 to 0.47 | 65.3 | 6 | 5 | 12 |
P15 | 20x50/20x30 | 17.4 to 70.6 | 16 to 58 | 0.47 to 0.52 | 66.0 | 6/4 | 5 | 12 |
P16 | 20x50/20x30 | 18.1 to 67.4 | 16 to 58 | 0.47 to 0.52 | 66.0 | 6/4 | 5 | 12 |
P17 | 20x50 | 7.3 to 40.9 | 22 to 55 | 0.47 to 0.47 | 65.3 | 6 | 5 | 12 |
P18 | 20x30 | 18.6 to 150.6 | 27 to 57 | 0.52 to 4.91 | 272.1 | 6/4 | 8/5 | 20/12 |
P19 | 20x30 | 18.6 to 133.1 | 27 to 57 | 0.52 to 3.27 | 220.6 | 4 | 8/5 | 20/12 |
P20 | 20x50 | 7.2 to 40.5 | 22 to 55 | 0.47 to 0.47 | 65.3 | 6 | 5 | 12 |
P21 | 20x50/20x30 | 15.4 to 58.1 | 22 to 56 | 0.47 to 0.52 | 65.4 | 6 | 5 | 12 |
P22 | 20x50/20x30 | 16 to 59.4 | 22 to 56 | 0.47 to 0.52 | 65.4 | 6/4 | 5 | 12 |
P23 | 20x30 | 6.8 to 41.2 | 36 to 56 | 0.52 to 0.52 | 69.1 | 4 | 5 | 12 |
P24 | 20x30 | 13.6 to 92.3 | 36 to 56 | 0.52 to 0.52 | 68.5 | 4 | 5 | 12 |
P25 | 20x30 | 5.9 to 37.6 | 36 to 56 | 0.52 to 0.52 | 69.1 | 4 | 5 | 12 |
P26 | 20x30 | 5.9 to 37.6 | 36 to 56 | 0.52 to 0.52 | 69.1 | 4 | 5 | 12 |
P27 | 20x30 | 13.5 to 94 | 36 to 56 | 0.52 to 0.52 | 68.5 | 4 | 5 | 12 |
P28 | 20x30 | 6.8 to 39.1 | 36 to 56 | 0.52 to 0.52 | 69.1 | 4 | 5 | 12 |
Note: σ = Tension of calculation; λ = Slenderness index; ρ = Geometric reinforcement ratio; Steel rate = Mass of steel per volume of concrete; n = number of longitudinal bars; Φ = stirrups diameters; c/ = spacing between stirrups. |
Table 8 indicates that columns P10, P13, P18, and P19 had significantly higher geometric reinforcement ratios (ρ) compared to others, resulting in an excessive steel rate exceeding 100 kg∙m⁻³ according to [19] relative to the concrete volume. These columns exhibited geometric reinforcement ratios in the lapping region exceeding 8%, as per ABNT NBR 6118:2023 [15]. To address this, the cross-sectional area of four columns was increased from 20 x 30 cm to 20 x 40 cm, bringing the geometric reinforcement ratios in the lapping region to 4.52%, 2.15%, 6.28%, and 2.76%, respectively, now conforming to the standard's limit.
3.4 Adopted Solutions
This topic discusses the major errors pointed out by the software. Table 9 shows the major errors issued.
Table 9
Major errors pointed out by the software
FLOOR LEVEL | ERROR |
Foundation | Block incompatible with bending stress(es) and/or their direction |
Foundation | Block heights outside limits |
Foundation | Pile force greater than load capacity |
Error 1 arises when moments are transferred to the pile, requiring their operation under bending. According to [20], connections between columns and foundations depend on the block type: a block with one pile is treated as having hinged connections in all directions, while a block with two piles is considered fixed in the direction of the two piles, forming a moment-resisting structure. In the transverse direction, a hinged connection is considered. The error occurred because all connections were treated as fixed during the design, leading to moments being transferred to the piles. Blocks B1, B3, B4, B6, B23, B25, B26, and B28, all with one pile, were identified with this error. To address this, the connections were modified based on [20] proposal, adopting hinged connections in both x and y directions. This ensures that moments arriving at the base of the columns are absorbed by the tie beams, representing a viable and economical solution.
Error 2 was identified in blocks with a useful height lower than the minimum required, as presented in Table 10. To address Error 2, the solution involved increasing the height of the blocks to meet the minimum useful height, with 50 cm blocks adjusted to 55 cm and 55 cm blocks increased to 60 cm.
Error 3 indicates instances where the force on the pile exceeds its load capacity. Blocks with this error are detailed in Table 11.
Table 10
Block heights outside limits
BLOCK | h (cm) | USEFUL HEIGHT (cm) | MINIMUM HEIGHT (cm) |
B2 = B5 | 50 | 36.4 | 36.8 |
B10 = B18 | 55 | 39.7 | 44.2 |
B13 = B19 | 55 | 40.0 | 42.6 |
B24 = B27 | 50 | 36.6 | 36.8 |
Table 11
Blocks with pile force greater than load capacity
BLOCK | h (cm) | n | TYPE | BEFORE | AFTER |
STRESS/PILE (tf) | n | TYPE | STRESS (tf) |
FEq | Fmx | Fmn | Fmx |
B2 = B5 | 50 | 3 | Hexagonal | 87.79 | 29.26 | 10.13 | 3 | Hexagonal | 25.40 |
B9 = B14 | 55 | 2 | Rectangular | 51.26 | 25.63 | 13.26 | 3 | Hexagonal | 25.40 |
B15 = B16 | 60 | 3 | Hexagonal | 80.65 | 26.88 | 17.14 | 4 | Rectangular | 25.40 |
B17 = B20 | 55 | 2 | Rectangular | 50.83 | 25.42 | 13.16 | 3 | Hexagonal | 25.40 |
B18 = B19 | 60 | 4 | Squared | 102.79 | 25.70 | 18.68 | 5 | Squared | 25.40 |
B21 | 60 | 3 | Hexagonal | 76.59 | 25.53 | 10.55 | 3 | Hexagonal | 25.40 |
B24 = B27 | 50 | 3 | Hexagonal | 85.62 | 28.54 | 10.62 | 3 | Hexagonal | 25.40 |
Note: FEq = Maximum characteristic total equivalent normal force multiplied by the number of piles; Fmx = Maximum characteristic normal force in the most stressed pile; Fmn = Minimum characteristic normal force in the least stressed pile. |
In certain blocks, the maximum demanding force (Fmx) on one of the piles exceeded its load capacity of 25.40 tf. The initial solution involved rotating the blocks to alter the pile arrangement, preventing overloading. Blocks B2, B5, B21, B24, and B27, after rotation, no longer exhibited Fmx greater than the pile's load capacity. However, for the remaining blocks, even after rotation, Fmx still exceeded 25.40 tf. In these cases, the block types had to be modified by adding a pile, as indicated on the right side of Table 11.
3.5 Final Processing
The final structure is represented in Fig. 4. Figure 5 provides a depiction of the final design, illustrating the layout and dimensions of the elements throughout the structure.
In the final processing of the structure, after making all the corrections, the following results were obtained for the distribution of vertical loads per floor, shown in Table 12.
Table 12
FLOOR LEVEL | FLOOR | APPLIED LOAD (tf) | AREA (m2) | AVERAGE LOAD (tf∙m− 2) |
Tank | 7 | 56.12–2.40 = 53.72 | 29.20 | 1.922 |
Machine room | 6 | 31.74–1.68 = 30.06 | 8.10 | 3.918 |
Rooftop | 5 | 170.80–17.06 = 162.74 | 295.31 | 0.609 |
Typical floor | 4 | 313.42–17.17 = 296.24 | 295.31 | 1.061 |
Typical floor | 3 | 313.42–17.17 = 296.24 | 295.31 | 1.061 |
Typical floor | 2 | 313.42–17.17 = 296.24 | 295.31 | 1.061 |
Ground floor | 1 | 287.22–76.68 = 210.54 | 272.66 | 1.053 |
Elevator shaft | 0 | 37.57–0.32 = 37.25 | 6.34 | 5.926 |
Total | | 1.532.71–149.66 = 1.383.04 | 1.497.53 | 1.023 |
The average vertical load on the building is 1.023 tf∙m⁻², indicating a relationship between applied vertical loads per unit area. TQS® recommends a range of 0.70 to 1.70 tf∙m⁻², aligning the obtained value with good design practices. There is also a notable reduction in maximum displacements in cantilevers, such as slab L101, decreasing from 0.86 cm to 0.08 cm.
A comparison was made between considering the continuity of trussed slabs and treating them as simply supported, replacing negative reinforcement at supports with an equivalent welded mesh. Table 13 demonstrates that considering simply supported trussed slabs and using Q138 welded mesh as replacement for negative reinforcement is more economically viable when comparing the steel consumption of the two solutions. Figure 6 illustrates a cross-section of the truss layout on the slab.
Table 13
Comparison of steel consumption in trussed slabs
STEEL | REINFORCEMENT | TYPICAL FLOOR | ROOFTOP | Total (kg) |
WEIGHT (kg) | WEIGHT (kg) |
considering the continuity of the slabs | |
CA-50 | Negative | 847 | 260 | |
CA-60 | Q61 mesh | 254 | 254 | |
TOTAL | 1101 | 514 | 1615 |
CONSIDERING ALL SLABS TO BE SIMPLY SUPPORTED | |
CA-60 | Q138 mesh | 576 | 576 | 1152 |
Out of the initially planned 28 columns, it was possible to dimension 26 with minimal reinforcement. In the final stage, the drawings were issued and refined using the Quick Reinforcement Editor. Finally, Table 14 shows the summary of material consumption generated by the software TQS®.
Table 14
Summary of consumption by material and by element
CONSUMPTION | COLUMNS | BEAMS | SLABS | FOUNDATIONS | OTHER | TOTAL |
Volume of Concrete (m3) | 30.39 | 90.80 | 102.77 | 17.95 | 6.99 | 248.90 |
Formwork area (m2) | 463.84 | 957.60 | 278.44 | 62.75 | 39.31 | 1.801.94 |
Steel (kg) | 2.169 | 6.338 | 3.615 | 1.154 | 1.222 | 14.498 |
Steel rate (kg∙m− 2) | | | | | | 9.68 |