Analysis and design of a vertical sectored tank

This article describes the conceptual design and the structural analysis of a vertical cylindrical partitioned tank for an international chemical company. Vertical cylindrical tanks are commonly used in the chemical industry worldwide as vessels to contain liquids. Most of these plants have reduced area for the installation of the container tanks. Many of them need to renew their manufacturing process according to the new technologies and requirements. In addition, in some cases, the preparation of mixtures is carried out on small surfaces. All this factors led to the idea of designing a vertical sectorised tank, considering that alternative hydrostatic pressure cases can lead to eccentric loads on the upper surfaces. Therefore, bending stresses and compression and tension stresses will occur. A Finite Element Method calculation was performed to determine the wall thickness fulfilling the structural requirements for two distinguishing design alternatives. This article describes the particular models designed and the detailed FEM simulation and mechanical calculation carried out to determine the optimized solution of partitioned tanks with a diamond‐shaped inner bracing system that manages to meet all the structural, manufacturing, constructive and environmental needs with a target thickness of 12 mm.


INTRODUCTION
Vertical cylindrical tanks are commonly used in the chemical industry worldwide as vessels for liquids. 1,2Usually, they are grouped by forming tank farms 3 inside the plant in an industrial estate.Vertical cylindrical tanks are welded, thin-walled steel structures. 4Without these structural elements, the industrial process would be inviable.
In the chemical industry, the plants that produce coatings are remarkable and are supposed to indicate worldwide economic growth. 5Coatings are used for automobiles and transportation, construction, canned drinks, furniture, and product finishes and recently are becoming relevant in nanotechnology. 6,7Production has stabilized in Europe and the USA, with indicators for the general economy, becoming increasingly technologically oriented. 8In 2016, the painting and coating industrial sector employed 295,400 workers in the USA.In 2017, product shipments for painting and coating producers in the USA were approximately $28.4 billion. 9Globally, the current (2018) automotive coating sector is valued at approximately $18 billion, and it is expected to reach $28 billion by 2022. 10 To obtain modern and better coatings on a large scale, two or more components are involved in the chemical mixture or final product. 11In the European Union, these aspects are also important in Spain, where there are not only national producers but also some international companies, mainly in site locations with automotive factories or food industries (around the main cities).In Spain, there are 339 significant painting companies whose economic data can be found in the following Reference 12.
These companies can prepare a large number of chemical products, in order to adapt to new market needs, in generally limited physical spaces.On this premise, the idea of using sectorised tanks was born.Furthermore, in the case under study, the promoter preferred to maintain the aesthetics of the existing tank farms, so they were designed in a cylindrical shape.Finally, due to external and internal corrosion, it was preferable to use stainless steel. 13he idea has been developed between an international company located in Valencia (Spain) (Figure 1), an engineering consultant and an academic research group.After meetings with tank contractors and on the basis of previous projects and designs prepared by consultants, the design was finalized.
The first designs, carried out by contractors, performed cylindrical tank performance calculations according to API-650 14 or EN 14015 15 and EN 1993-4.2. 16These calculations were appropriate for studying the nozzles and other components.However, the structural behavior of the compartmentalized tank did not match these calculations, mainly due to the asymmetric behavior of the hydrostatic pressures and the alternating loads.For this reason, the promoter contacted his engineering consulting firm and the authors.
Another important consideration for the company was that the liquids could be hazardous and contain contaminants.Hence, safety and tightness are necessary, and the calculations and analysis should properly reflect the reality.The company has important measures of security and has allocated resources for it.
There have been several reviews of single-unit tanks design for static and buckling modes which may be related to this one.The most influential computational analysis of steel tanks was published by Godoy in 2016. 3This fundamental work aims to show the tank design and simulation as a quasi-static problem, including the buckling under uniform external pressure, wind load, thermal loads, and foundation settlement.Further on, the effects on reinforcing steel tanks with intermediate ring stiffeners on wind buckling can be found in Reference 17.Likewise, and following with the main design type of single-unit tanks, there have been several publications carrying out a thorough structural analysis of accidental loads such as blast and fire. 18,19hus, the current state of the art of storage steel tanks is mainly focused on the structural design of single-body vertical tanks enabling to extent such structural performance to cylindrical four compartmented tanks.This article aims to get a deeper structural understanding of this special sectorised tanks showing the key design drivers that characterize its shell design and performance.

F I G U R E 1
General view of the chemical company factory.

General geometry
The general geometry of the designed vessel is a cylindrical tank with a self-supported conical roof and a stiffened conical bottom that is divided inside into four symmetric vertical compartments throughout four walls with a cross shape intersecting the middle axle of the tank (Figure 2).The cylinder height is 18 m, and the diameter is 4.6 m, which gives an H/D ratio of 3.913, corresponding to a slender tank. 3The external cylinder, whose thickness will be the object of this study and analysis, is projected by curved smooth welded courses, each 2 m in height and 7.128 m in length.As shown in Figure 2, the key distinguishing design of the sectorised tank is composed of 4 symmetrical inner walls (Figure 2A) which also could be reinforced with an inner bracing system (Figure 2B) to further assess its structural performance and thus optimize the tank's wall thickness.After further analysis and conversations with potential on contractors, the inner walls are solved with planar corrugated 10-mm-thick sheets with a repetitive height pattern of 0.674 m, as shown in Figures 2 and 3. F I G U R E 3 Detail of the corrugated sheet for the inner partitions.
The steel sheets are continuously welded at the inner extremes to a central vertical column comprising a square hollow section of 250 × 250 × 12 mm and externally reinforced with four channel section profiles of 250 × 60 × 12 mm, which all together form a cross-section.The corrugated shells are also welded to the bottom base until the intersection of the conical covering.At the opposite extreme, in the intersection with the cylinder, another four channels are introduced, as a transition element.The idea is that the inner walls previously welded to the channels at its extremes, should be welded afterwards to the rest of the tank, easing the assembly and welding process.
The bottom of the base has a conical surface with a height of 0.115 m at the center and an outer slope of 5%, made of smooth welded shells.The attachment of the conus to the horizontal concrete foundation base is made by means of 24 radial vertical stiffener plates.As shows Figure 4, such plates are separated by 15 • and its height is variable in accordance to the cone's shape.In addition, annular vertical reinforcement plates are introduced to diminish the free shell of the cone piece, and also, a small vertical pipe of 500 mm in diameter is placed in the central area, acting as a central column support.On the opposite side, at the intersection with the curved courses, there is an annular ring plate that is externally reinforced with an angular profile.
The tank is closed at the top with a self-supported conical covering with a central height of 0.492 m and a slope of 21% 3,20 and is welded to the cylinder, introducing an external reinforcement ring with an "L" cross-section.
Furthermore, the tank assembly is supported, anchored to the foundation by anchor bolt chairs. 21According to the static former calculations, 12 symmetrically chairs are placed around the perimeter.The chairs consist of a top plate, two gusset plates and anchor bolts of 30 mm in diameter.
The numerical simulation considers two sectorised design alternatives which differ in the presence or not of the horizontal bracing system that reinforces the inner main symmetrical walls of the tank as depicted in Figure 4.The Alternative 2 comprises the diamond-shaped bracing system which is made of successive rows of four circular hollow sections (CHS) of 125 mm diameter and 5 mm thickness.The rows are evenly distributed in height every 1.011 m as shows Figures 2D and 4.
The structural calculation results in a comparison of the mechanical performance of both alternatives and subsequently, an optimization approach of the tank wall thickness as key technical feature of the analysis and design of vertical sectored tanks.
F I G U R E 4 Geometric views: left, general view; top, partial section; right, inner partitions and bracing system; bottom, bottom tank section and stiffeners at the bottom.

Material properties
The whole tank is designed and will be constructed with stainless steel, except the anchor bolts, which will be constructed with structural carbon steel.Every part or element of the steel should comply with the specifications of Eurocode 3 and EN 10088. 22More concretely, the stainless steel components should comply with EN 1993-1-4 23 General rules for stainless steel.
The chosen stainless steel is austenitic, grade 1.4306 (equivalent to American AISI 304, and AISI 304 L steel.According to the mentioned Eurocode, its main mechanical characteristics are as follows: • Yield stress: f y = 200 N/mm 2 (nominal stress corresponding to a 0.2% remainder deformation).
• Ultimate stress: Moreover, according to point 2.1.3and further comments, 23 the following set of mechanical parameters is adopted: • Poisson coefficient for elastic behavior:  = 0.3.
• Transverse shear modulus: • Considering the frames, cables and bars (which affect the angular sections): Yield stress: f y = 180 N/mm 2 and ultimate stress: • Anchor bolts (6.8 class structural steel) with a yield stress: f y = 480 N/mm 2 and ultimate stress:

Numerical simulation
The structural analysis is performed with the finite element software SAP2000 (version 19.2.1). 24The structure is modeled by frame and shell elements.The shell element chosen combines membrane and bending behavior and includes the effects of the transverse shear deformation regarding the shell thickness (Mindlin/Reissner). 25Every node has 6 degrees of freedom.

Meshing
After a sensitivity analysis, the model meshing with finite elements follows an induced regular meshing pattern according to geometry and fitting.A study on the FE solution convergence is conducted for the sectorised tank mesh model considering different number of shell and frame elements until the difference between two consecutive models become negligible. 26For the external cylinder, the first row of finite elements has a height of 54.75 mm, and the width is obtained by dividing the perimeter into 144 angular sectors, every 2.5 • , which leads to a width of 100 mm.The following rows in the tank height to the ridge have a height of 84.25 mm for each element, providing 213 finite elements per column.The main characteristics of the model-derived meshing are 85,786 node numbers, 1756 restrained joints, 87,927 shell elements, 876 frame elements, and 505,308 degrees of freedom.
The bracing system, anchoring bolts, and stiffening rings were modeled with frame elements.At the base, the model gathers the support conditions of the radial stiffener plates and the bottom ring plates with a vertical grade reaction modulus of 100 N/mm 3 (concrete).The grade reaction value was selected after a thorough analysis to eliminate unrealistic perfect rigid base conditions. 21Other values were also tested, but the changes in the results were neglected.

Actions and load combinations
This subsection defines and describes the loads acting on the tank models.The self-weight, G, is taken from the specific weight of stainless steel, 7900 kg/m 3,23 implemented in the software and calculated according to the geometry.
As regards to hydrostatic pressure distribution, W, the specific weight of the fluid (mainly resins) takes its highest value of 1100 kg/m 327 according to the supplier's information.The individual effect of hydrostatic pressure is normally the worst calculation hypothesis among all the loads. 3,17Thus, it is widely known that such negative effects proportionally increase with the tank depth which in the particular case of sectorized design tanks also forces to consider alternate load cases as shows the sequence of Figure 5.
As for the maintenance live load above the top cover, S, t (Eurocode 1 EN 1991-4 28,29 ), a standard value of 1 kN/m 2 is adopted.In the case of the environmental load of the snow, N, a comprehensive value of 1 kN/m 2 is adopted which in overall fully integrates its spatial distribution in Spain.Finally, the wind's action is taken into account by including the wide spectrum of Southern Europe conditions and the final installation tank location on the East of Spain. 30Accordingly, a basic pressure value of 0.42 kN/m 2 , which corresponds to 26 m/s, is considered.
The wind loading requires a more in-depth analysis, according to References 28,31.The basic velocity should be increased to obtain the mean velocity value.According to Reference 31 and noticing that the chemical plant is located in an industrial state, the terrain category is III.Taking into account a roughness and exposure factor for the tank height, the exposition factor increases to 2.2.
For the pressure coefficients, several considerations 3,32,33 have been taken into account to consider the tank slenderness and the slope of the conical cover in order to consider the sectorized tank as, a silo structure with little differences. 4he pressure in a closed tank varies depending on its position on the circumference, the tank slenderness H/D = 3.91 which gives an inverse value of 0.256.Thus, the coefficients may be derived from the expression (1) referenced in 34 which results in a distribution of pressure coefficients around a circumference as shows Figure 6 for three different heights along the tank.
The adopted values are implemented in a spreadsheet and incorporated into the structural software as normal pressures acting on the finite elements of the courses.
The wind effect is studied for two main directions: one direction parallel to an inner wall and another direction parallel to the bisectrix of the 90 • angle by which the tank is divided by the inner walls (45 • ) (Figure 7).Thus, the number of load combinations increases.Wind actions applied to a group of tanks can be found in, 3,4 in this study, the sectorized tank will be considered isolated.
As concerns to the combination coefficients for ultimate limit state (ULS) and serviceability limit state (SLS), National (Spanish) specifications 35 are used.
Finally, a total number of 20 load hypothesis has been analyzed as summarizes Table 1 and from that, the worst load combinations have been considered to further asses the structural performance of sectorized tanks either with or without inner bracing systems.

F I G U R E 7
Wind loads hypothesis regarding the position of the tank.

TA B L E 1
Load cases adopted for Alternatives 1 and 2.

Design basis and verification
The first consideration is indicated in Eurocode 3 EN 1993-4-2: Tanks. 16In point 2.2, reliability differentiation, three different levels of rigor should be used, depending on the consequence class chosen, which also includes the structural arrangement and the susceptibility to different failure modes.The consequence class chosen is the third one: tanks storing liquids or liquefied gases with toxic or explosive potential and large-size tanks with flammable or water-polluting liquids in urban areas.This is an important fact, as in point 4.2.2, for this class, which is established using calculus and analysis with the finite element method shell type, as in the present work.
Second, partial factors of strength are followed according to point 2.9.2.2, considering a partial factor for the shell wall stability of g M1 = 1.10 and for rupture g M2 = 1.25: (3) Third, the serviceability limit states, in point 5.5, should be taken as deformations and deflections that adversely affect the effective use of the structure and deformation, deflections and vibrations that cause damage to non-structural elements.Deformations, deflections and vibrations should be limited to meet the previous criteria.Specific limiting values, appropriate for the intended use, should be agreed upon between the designer, the client, and the relevant authority, considering the intended use and nature of the liquids to be stored.However, a value is not provided.For this work, From a structural point of view, and based on experience, the appearance, stresses and strain compatibility, the following criteria are used: the maximum absolute displacement should not exceed 25 mm.This leads to a displacement of nearly 1/200 of the diameter and 1/780 of the height.
Fourth, similar values are indicated regarding Eurocode 3 EN 1993-1-4 for additional stainless steel 13 and partial safety factors.
As specified at point 4 of the Eurocode, a constant Young's modulus of 200,000 N/mm2 can be adopted, corresponding with a unitary strain of 2 per thousand, considering that E s barely varies until greater stress values of 100 N/mm 2 are reached.
Finally, concerning the result of the stress comparison in the ultimate limit state, a detailed analysis is performed.However, according to EN 1993-1-6 36 for linear analysis (LA) or geometrically nonlinear analysis (GNA) analysis, the stress results respond to the Von Mises absolute stress formulation, 4,21 which unifies the effects and maximum values that are more unfavorable and is commonly used for rupture or collapse criteria (plastic limit state) (LS3).

Type of analysis
The set of simulations follows the main guidelines and prescriptions of EN 1993-1-6. 36A wide discussion about the use of EN 1993-1-6 for shell tanks and buckling analysis can be found in References 3,4.The former calculations (EN 1993-1-6, 2.2) were performed with linear elastic shell analysis (LA).However, meaningful differences in the results, especially for deformations, were detected when performing the geometrically nonlinear elastic analysis (GNA).The type of analysis was P-Delta, which is appropriate for small deformations.In Figure 8, it can be seen that the load cases "1 + 3" and "1 + 2 + 3" present the highest differences regarding the maximum translation between the (LA) and (GNA) results.These differences increase when lower thicknesses of the shell courses are adopted.In the case of a tank without bracing, these differences are constant with thickness.For the case with a bracing system, these differences develop unevenly among the load cases under consideration.In conclusion, the geometric nonlinearity remarkably influences the results, and consequently, the linear method is left for further analysis.On the other hand, where compression stresses are predominant in any part of the shells (as in the sectors without hydrostatic pressure), the GNA analysis provides the elastic buckling load of a perfect structure, including changes in the geometry, which may be of assistance in checking the limit state of buckling (LS3).Also, a geometrically nonlinear elastic analysis with imperfections included (GNA) was performed for the stiffened tank with bracing reinforcement (Alternative 2).It is worth noting load case "1 + 2 + 3," which provides the absolute maximum translation values being found at the compressed unloaded quadrant (towards the inside of the cylindrical vessel).An imperfection case based on the initial geometry was generated in accordance with the buckling deformed shape, with a maximum amplitude value of 10 mm.The increase of translation displacements are negligible resulting in difference values of about1.2%,which fully justify not considering geometric imperfections in further steps analysis.

Comparison of thicknesses between Alternative 1 and 2
The initial designs and analysis performed aim to set the thickness of the different plate elements and bars making up the sectorized tank of the study.As previously stated, the structural design of a conventional cylindrical tank is featured by the proper design of the external cylinder wall and its courses.However, in the case of a compartmented tank, it is envisaged that the key design element it is also the outer wall thickness but, as the tank design comprises four sectorized inner walls, a deeper structural analysis will assess the optimization of the wall thickness.To fulfill this purpose, two design alternatives are considered.First, Alternative 1 is characterized by a sectorized tank that gradually varies its cylindrical course thickness to properly meet the deformation and stress requirements.Conversely, Alternative 2 introduces a diamond-shaped bracing system within the inner walls to partially restrain the free deformation of the cylinder and thus, optimizing the external wall thickness of the tank.

First alternative calculus and analysis description numerical simulation: Alternative 1
The presence of inner walls substantially modifies the sectorized tank behavior as compared to a single-body conventional tank.The symmetrical inner walls delimit four points through the cylinder section that strain the free outer displacement.The statically indeterminate situation created above the cylinder shells provides important bending moments in the joints between the shells, as occurs in the case of a continuous beam.The hydrostatic pressure in each quadrant leads to a membrane type behavior which is combined with the bending shell behavior caused by the stiffness of the connection between the cylindrical vessel and the inner walls that also provide a rotational restraint.The thickness trends in terms of deformation and stresses are observed in Figure 9. Shortly, the cylinder shell thickness of 18 mm represents the lower limit from which the shell stresses experience significant increases even beyond its strength limits.
With regards to buckling limit state, the tank is stable for the lower thickness analyzed (13 mm).

Numerical simulation: Alternative 2
The analysis consists of the implementation of a bracing system to the former model by adding CHS stainless steel frames to get Alternative 2. The inner diamond-shaped bracing system shares the length between the joint points of the vessel shells and the inner walls.The novel approach introduces significant changes in the mechanical behavior of the whole tank.Throughout these bracing frames, the points above the vessel shell are fixed.The structural system largely gains in non-translational performance, experiencing a great decrease in deformations as shown in Figure 10.These issues have beneficial impact on the stress behavior, significantly reducing the course thickness (Figure 10).The tank is stable with respect to buckling for the lowest thickness analyzed (5 mm).The minimum threshold of the cylinder thickness is set to be 12 mm which produces a maximum deformation (SLS) value towards the inner side of the unloaded quadrant of 5.435 mm (hydrostatic load case "1 + 2 + 3).
As regards to the inner wall sheets, in comparison with Alternative 1, the bracing system remarkably reduces the diaphragm effect of the walls for each quadrant.The wall stresses are due to hydrostatic pressure being almost similar for the different hydrostatic hypothesis acting on the loaded quadrants.

2.5.3
Final sectorised design model The two alternatives under consideration are technically feasible.In the case of Alternative 1, the optimum uniform thickness given to the shell courses is 18 mm.By comparison, the optimum value for Alternative 2, including the bracing system, is 12 mm.This latter option exhibits better mechanical behavior from a structural point of view.Likewise, Alternative 2 will also come out on top if construction, manufacture, and environmental considerations are taken into account.
On the one hand, the lower thickness improves manufacturing and welding while in terms of metallic material needs, F I G U R E 11 Maximum stress location scheme.

F I G U R E 12
Resultant translations for the hydrostatic pressure load cases (ULS) for Alternative 2 (bracing) at the external cylinder.
Left to right: 1, 1 + 2, 1 + 3, 1 + 2 + 3, and 1 reduces the carbon footprint of the tank assembly.On the other hand, the lighter structure means cost savings and better adjustment to the tight budgets of the industrial projects where sectorized tanks are used.

RESULTS AND DISCUSSION
On the basis of the above thickness approach of two distinguishing design models, this section summarizes the most important results obtained for the final model of 12 mm thickness and a set of inner diagonal frames corresponding to Alternative 2. The main results comprise the maximum absolute translations (X, Y , and Z) in mm (SLS) and the maximum Von Mises stresses in N/mm 2 (ULS) for each load combination.The maximum Von Mises stresses, after a rigorous analysis, are provided for different parts of the shell model (Figure 11): at the cylinder "tummy bellies" (T.B.), at the "welding seams" between the cylinder courses and the inner walls (W.S.), near or at the base (N.B.) for the bottom courses, and at the interior partitions (I.P.) (in the inner walls) as shown on the sketch of Figure 9.The worst calculation hypothesis in is due to axisymmetric hydrostatic pressure loading as can be either in the total displacement representation of Figure 12 and also, Figure 13 illustrates the cross-sectional deformation view at a height of 6 m where the axisymmetric effect is more noticeable.This trend is confirmed when assessing the stress distribution obtained for the different hydrostatic hypothesis as shown in Figures 14 and 15 which are numerically summarized in the stress values of Table 2.
As regards to the combinations that include the remaining gravitational loads (live loads and snow), Table 3 gathers the most significant results that are in full agreement with the key structural design values of Table 2.

TA B L E 2
Main results for the hydrostatic pressure combinations (the self-weight G is included).

Load combination
Absolute translation (mm) F I G U R E 16 Left: deformed shape for the V0 load case, normal to the surface translation.Upper right: planar section at a height of 18 m: the absolute maximum is 0.528 mm.Bottom right: planar section at a height of 9 m: the relative maximum is 1033 mm.For the 1 + 2 hydrostatic load case, the maximum translation at a height of 18 m is 1.63 mm (scaling results ×200).
The effect of wind is studied and calculated after implementing wind pressures on the finite element surfaces, according to Section 2.3.3.Among the different calculations made, the worst approach considers the situation of empty tank in order to quantify the wind effect and the global stability of the tank.For the two wind hypothesis studied, V0 and V45, the displacements values are below 0.5 mm at the maximum height of the tank and regarding mechanical stresses, the resulting values represent less than 10% of the above stresses for hydrostatic and gravitational combined loads (Figure 16).

CONCLUSIONS
The set of results presented above highlight the relevance and technical feasibility of using compartmentalized cylindrical tanks for containing liquids and resins in chemical industries.This need is becoming more and more pressing as space layout requirements in chemical and industrial projects is more restrictive and the range of chemical products to be contained is increasing.Thus, the initial approach of a sectorised tank seeks to understand its particular structural performance by comparing it with a single-body cylinder tank.Because of the effect of axisymmetric loads on each compartment, the structural behavior of partitioned tanks is different from the single cylindrical tank.
In terms of displacements, the deformation of single tanks mainly affects the circumferential perimeter of the cylinder which usually is under tension.However, in sectorised tanks, the axisymmetrical mechanical behavior significantly affects the cylinder shape losing its original form.With regard to stresses, the sectorised tanks present bending forces which implies that the rest of sections through the circumferential perimeter have to adapt to such deformations by forming inward and outward creases since its total length is fixed.
As a result, the standard specifications and design rules for cylindrical tanks must be readapted for the case of sectorised tanks with emphasis on simulating the inner wall structural response and alternative hydrostatic loading sequence within the tank.
This study has further explored two conceptual design alternatives for a sectorised tank of 18 m height and 4.6 m of diameter.The thickness of the cylinder courses has been the main variable into study to assess its structural performance.Among all the numerical simulations conducted, the hypothesis of hydrostatic pressure and alternative hydrostatic load distribution have been the most critical calculation cases.
In the case of Alternative 1 (sectorised tank with four inner symmetrical walls), the parametric study of thickness resulted in adopting a target value of 18 mn thickness for the cylinder courses.Conversely, in Alternative 2, a bracing system is added to the sectorised tank with four inner symmetrical walls to reinforce the connecting points between the cylindrical shell and the inner walls.By doing so, the mechanical behavior of the solution is much better than the previous case and the minimum thickness meeting all the structural requirements is set to be 12 mm.The impact of this outcome of thickness reduction is significant since means a total weight material reduction of 33% for the sectorized tank studied.The outstanding material savings achieved with Alternative 2 not only have an economic impact in the construction and installation budget of sectorised tanks but also represents a significant environmental milestone since the reduction of carbon footprint is equally proportional to the reduction in weight of raw material.Because of this, the incorporation of a bracing system to sectorised tanks can be considered as an eco-friendly design technique to reduce material consumption.
Regarding the complimentary wind load analysis, the worst scenarios studied for the case of empty tank resulted in stresses values of the order of 10% compared with hydrostatic loads.When wind is combined with the rest of loads, the stress differences against hydrostatic cases are negligible and of the order of less than 2%.Thus, it can be concluded that the effect of the wind pressure is minimal in terms of hydrostatic pressure values.
In summary, the effect of wind is small.Finally, the structural, functional and environmental relevance of incorporating a diamond-shaped bracing system in sectorised tanks is further studied by means of the slenderness ratio of cylindrical tanks in the range between 3 and 5. Slenderness ratios higher than 5 are unusual and in case of design, the key load is wind action and lateral movements produced which are beyond the scope of the results discussed herein.
Thus, the bracing system proposed in this study presents good structural behavior and cost material savings for slenderness ratios between 3 and 5 which practically solves all practical cases in the chemical industry providing a robust, efficient and eco-friendly solution for project designers, tank builders and installation engineers.
Basic tank geometry with 4 inner walls (Alternative 1), (B) Basic tank geometry with four inner walls + inner bracing system (Alternative 2), (C) Detail of inner wall geometry, and (D) Conceptual design of the inner bracing system (reinforcement).

F
I G U R E 5 Load case sequence for hydrostatic pressure loading.

F I G U R E 6
Wind external pressure coefficients versus wind direction in degrees (EN 1993-4-1:2007 Annex C).

F I G U R E 8 (
LA) versus (GNA) Comparison of the maximum displacement (ULS) versus thickness for the two considered alternatives (hydrostatic pressure load cases).

F
I G U R E 9 (GNA) Comparison of the maximum displacement (ULS) versus thickness and maximum shell stresses vs. thickness for Alternative 1 (without bracing) (hydrostatic pressure load cases).F I G U R E 10 (GNA) Comparison of maximum displacement (ULS) versus thickness and maximum shell stresses versus thickness for Alternative 2 (bracing) (hydrostatic pressure).
Main results for the hydrostatic pressure combinations plus all gravitational loads.