**ORIGINAL ARTICLE **

RASI, José Roberto ^{[1]}, CAUNETTO, Donizete ^{[2]}, BROETTO, Jonathan Figueiredo ^{[3]}

RASI**, **José Roberto. CAUNETTO, Donizete. BROETTO, Jonathan Figueiredo. **Structural alternatives in suspended bottoms of tubular metal tanks with two cells for water reserve.** Revista Científica Multidisciplinar Núcleo do Conhecimento. Year 05, Ed. 06, Vol. 12, pp. 111-135. June 2020. ISSN: 2448-0959, Access link: https://www.nucleodoconhecimento.com.br/civil-engineering/structural-alternatives

## SUMMARY

With the increasing demand for water reserve due to the implementation of new allotments and horizontal condominiums, which met the need for the minimum dynamic pressure of 100 kPa, the tanks began to have internal physical divisions (vertical cells) whose upper cell has the bottom quota suspended at a height that guaranteed the manometric pressure necessary to meet this standard. Due to the lack of specific Brazilian technical standards for water storage in a metal reservoir, it has been used as a sizing parameter for metal reservoirs with several vertical water storage cells, the AWWA D100 in its entirety or only partially, mainly due to axial efforts in the coasts (virolas) to determine permissible stresses to buckling (*FL*). This article addresses the problem of choosing the most appropriate type of vertical metal bottom suspended and commishes the results of five different types of bottoms, sized according to AWWA D100-05. Within the typology of the 5 funds analyzed, the most economical fund was the segmented spherical fund.

Keywords: Metal tank, AWWA D100 standard, suspended funds.

## 1. INTRODUCTION

This article addresses the problem of choosing the most appropriate type of vertical metal bottom suspended and commishes the results of five different types of bottoms, sized according to AWWA D100-05.

With the implementation of new allotments and horizontal condominiums due to the incentives of government housing policy, mainly by the housing program of the Ministry of Cities, Minha Casa Minha Vida Program (Pereira, 2017), which caused a great increase in the demand of drinking water storage tanks, mostly above ground, cylindrical and with varying diameter and heights, called water castle.

Due to the need for minimal dynamic pressure in the public supply network, that according to NBR 12.218/1994, must be 100 kPa (10.20 m.c.a.), the tanks now have internal physical divisions (vertical cells) whose upper cell has the bottom dimension suspended at a height that guaranteed manometric pressure necessary to meet this standard, since normally the land quotas do not offer for the tank to be supported.

According to Trees (1911), the bottoms of suspended metal tanks can be of various types, such as flat, conical, and spherical or spherical segmented.

Visal (2017) states that storage tanks operate without pressure (or very little), called atmospheric tanks, differentiating them from pressure vessels. They are usually cylindrical in shape, perpendicular to the ground with a flat bottom and a fixed or floating ceiling.

The design and construction of atmospheric cylindrical tanks require the knowledge of specific technical standards, materials and labor appropriate for each type of application and involve a number of other special care because anomalies and irregularities in these equipment can cause great financial losses or even loss of life (Nunes, 2013).

According to Gomes (2017), the standards commonly used in Brazil for metal tank projects and constructions are NBR 7821, API 650 and AWWA D100.

NBR 7821/1983 – Welded Steel Tanks for Oil and Derivatives Storage, of the Brazilian Association of Technical Standards (ABNT) and the American regulatory standard API 650 – 2013 – Welded Steel Tanks for Oil Storage – of the American Petroleum Institute (API), are specific to the reserve of oil and derivatives.

The American Water Works Associations’ AWWA D100-05 – Welded Carbon Steel Tanks for Water Storage standard aims to provide minimum requirements for the design, construction, inspection and testing of new welded carbon steel tanks for atmospheric pressure water storage.

Within the sizing requirements, the AWWA D100 presents three methods for determining the permissible buckling stress (FL) for cylindrical sections, which allows the verification of the maximum compression stress due to axial load and axial load due to wind loading applied to the coasts.

Due to the lack of specific Brazilian technical standards for water storage in a metal reservoir, it has been used as a sizing parameter for metal reservoirs with several vertical water storage cells, the AWWA D100 in its entirety or only partially, mainly due to axial efforts in the coasts (virolas) to determine permissible stresses to buckling (FL).

## 2. GOALS

General Objective

The general objective of this article is the dimensioning of several types of suspended bottoms of the upper vertical metal tank cell composed of two cells, within the recommendations of AWWA D100-05, using the Autodesk Simulation Mechanical 2018 software.

Specific Objectives

The specific objectives are:

- Determine the axial stresses on the sides of the metal tank lower cell, resulting from axial and lateral loadings and compared them to the permissible stress to buckling according to what prescribes 3.4 – Column, Strut, and Shell Stability Formulas from AWWA D100 – 05.
- Determine the vertical displacements of the suspended backgrounds.
- Determine the total weight of the proposed suspended funds by quantifying the area and thicknesses of the sized plates and support structures.

## 3. MATERIAL AND METHOD

The tank presented in this article is a metallic reservoir, for water reserve, composed of two cells, with a capacity of 150.00 m³ each (total of 300.00 m³), with metal cone cover (Figure 1), with five types of suspended bottoms (Figures 2A; 2B; 2C; 2D and 2E).

Figure 1: Metal tank of two cells with a capacity of 300.00 m³.

Typology of the 5 suspended funds proposed:

Fig.: 2A – Flat bottom radial beams and mast

Fig.: 2B – Flat bottom radial beams without mast

Fig.: 2C – Flat bottom orthogonal beams

Fig.: 2D – Conical background

Fig.: 2E – Segmented spherical background

The actions considered are those of wind, stored water (hydrostatic action), ceiling overload and the structure’s own weight (Figure 3A), released in the Autodesk Simulation Mechanical software.

Figure 3A – Uploads

Figure 3B – Launch of uploads in the software

According to Andrade junior (1998), the wind action is calculated according to NBR 6123 – Forces due to the Veto in Buildings (1987) and, as a general rule, it is assumed that the wind can act in any horizontal direction. As the structure of the tank is asymmetric in relation to the Z axis, perpendicular to the wind direction, it is considered that the wind can focus perpendicularly to any geratriz of the tank.

The static component of wind pressure, which acts perpendicularly on an area element, is given by:The external pressure coefficients *C _{pe}* are expressed for the body type of the structure, assuming for the application of AWWA D100-05 that

*C*=

_{pe}*Cf*(Table 1).

Wher*e *q is the wind pressure at a point where air stagnation occurs, obtained from expression 2:The *V _{0}* Speed is called basic speed, corresponds to a gust of 3 seconds, exerted on average once in 50 years, measured 10 m above the ground, in a flat and open place. NBR 6123 (1987) presents the basic isopletas, in m/s. For our examples,

*V*= 40 m/s was adopted.

_{0}The topographic factor *S _{1}* is used to evaluate the relief of the land around the building and adopted equal to 1.0 for our examples.

Factor* S _{2}* considers the combined effect of terrain roughness, wind speed variation with height above terrain, and building dimensions. Factor

*S*

_{2}is obtained through expression 4:

Where: Z = height above ground,

*F*= Wind gust factor,

_{r}*b*= meteorological parameter,

*p*= terrain roughness function and time interval. For the tank height of 16.0 m, roughness II, class A, one has

*S*= 1.05.

_{2}Factor *S _{3 }*is a statistical factor that considers the degree of safety required and the useful life of the structure, considering the installations of reservoirs with low human occupation factor (Andadre Junior, 1998), the value of 0.95 was used.

According to Haffez* et al* (2011), it is assumed that the tanks are subjected to uniform wind pressure (*q*), acting along the Z axis, as shown in figures 3^{rd} and 3B. AWWA D100-05 recommends the use of drag coefficient (*Cf*), according to the shape of the structure, according to Table 1. For tubular tanks with cylindrical shape, the adopted *Cf *is 0.6.

Table 1 – Drag coefficient Cf

Have:

V_{k }*= *40 . 10 . 1,05 . 0,95 = 39,90 m/s

*q *= 0,613 . 39,90^{2} = 975,90 N/m² ou 99,51 kgf/m²

Δ_{p }= 0,6 . 975,90 = 585,54 N/m² ou 58,71 kgf/m².

The hydrostatic action generates effects that act in the radial and vertical directions and result in lateral pressure on the side and pressure at the bottom of the reservoir.

The design overhead applied to the ceiling, according to AWWA D100-05 item 3.1.3.2, should be 750 N/m² (15 lb/ft²).

The own weight of the structure is automatically released by the Autodesk Simulation Mechanical 2018 software, considered the specific weight of the steels used in tank sizing.

The thickness of the feroline pressure ferolas due to the hydraulic pressure of the tank must be calculated according to sec equation 3-40. 3.7 AWWA D100-05 – Cylindrical Shell Plates (equation 7):Where:

*t* = hull design thickness (ferrule), in mm

*h _{p}*

_{ }= liquid height, in m

*D* = tank diameter, in m

*S* = Permissible steel voltage, in Mpa

*E* = Welding efficiency

*G* = Specific liquid weight (for water = 1)

The minimum thickness of the cylindrical strand in contact with water should be in line with Table 2 according to the Sec. 3.2 of AWWA D100-05. For the 5.73 m nominal diameter tank, the minimum prescribed thickness is 4.76 mm.

Table 2 – Drag coefficient Cf

AWWA D100-05 classifies the structural materials to be used in tanks into 3 classes, depending on the flow limit (Fy). Table 3 shows this classification.

Table 3 – Material class as a function of Fy

The material used in the coasts, bottoms and ceiling is ASTM A36, characterized by a modulus of elasticity (E) equal to 205,000 Mpa, Poisson coefficient (μ) equal to 0.30, density (γ) of 77,000 N/mm³, flow voltage f_{y} = 250.00 Mpa and last f_{u} voltage = 400.00 Mpa. The material used in the support structures of the suspended funds (beams W and C) is the ASTM A572 (grade 50) with flow voltage f_{y} = 345.00 Mpa and last f_{u} voltage = 450.00 Mpa. They are classified as Class 2 material.

Table 4 shows the main permissible stresses prescribed by AWWA D100-05, depending on the class of materials and applications in the reservoirs.

Table 4 – Permissible voltages in applications

For the verification of stability due to the buckling of the tank’s coast, the AWWA D100-05 prescribes 3 methods of analysis. For this work, Method 1 was used, which is a simplified procedure based on membrane analysis techniques. For Class 2 materials, the thickness/radius ratio of the reservoir to which buckling changes from elastic to inelastic (*t/R*)_{c }is 0.0025372. The permissible stress for buckling for Class 2 material is given by the following formulas:

When 0 ≤ *t/R* ≤ (*t/R*)_{c} means that buckling occurs in the elastic regime and the permissible stress for buckling is given by equation 8:_{
}

When (*t/R*)_{c} ≤ t/R ≤ 0.0125 means that buckling occurs in the inelastic regime and the permissible stress for buckling is gWhen t/R > 0.0125, it means that buckling occurs in plastic and the permissible stress for buckling is constant and is worth:Table 5 – Welding efficiency values is presented partially from Table 15 Weld design values – tank plate joints, where only the welding values are presented. For the work on canvas, double frontal chamfer welding with full padding was considered.

Table 5 – Welding efficiency values in %

## 4. RESULTS

Numerical modeling and analysis were done using a commercial software of analysis and structural design Autocad Simulation Mechanical 2018. Each ferrule of the tank was modeled as a shell element with constant design thicknesses, with isotropic properties and with a medium plane centrally positioned. At the top of the tank, there is a circular vertical ring modeled with L profile rigidly attached to the elemnetos. The finite element dimensions are 0.20 x 0.20 m (discretization). For each tank type, according to the typology of each suspended bottom, a 3D finite element model was created (Figure 4).

Figure 4: Discretized metal tank

Starting from the minimum thickness according to Table 2, for the sizing of the strandwas also verified the thickness due to circumferential pressure, using the equation (7) and the thickness due to buckling, with the determination of the permissible stress (*FL*), using the equations (8) and (9) and the axial stresses of the strands determined by the Mechanical Simulation software and compared with the calculated permissible stresses (*FL*). ́The required thickness of each ferrule is the largest thickness within the 3 criteria.

Table 6 shows in detail the Van Misse, Circumferential tension and axial tension in each ferrule of the 5 tanks studied with different types of suspended funds.

Table 6 – Sizing of the coasts according to AWWA D100 – 05

Figure 5 shows the tank with the thicknesses required for each ferrule of the side.

Figure 5: Tank with the final thicknesses of the strand

Figures 6A, 6B, 6C and 6D show the results of the analyses with Van Misse stresses, circumferential stresses and axial stresses in each ferrule for the tank with bottom of cell 2, with radial W beams and central mast. The values obtained fed table 6. Equal analysis were made on the other 4 tanks that complete this work.

Fig. 6A: Van Misse Tensions in 3D Cut

Fig. 6B: Van Misse Tensions

Fig. 6C: Circumferential tensions

Fig. 6D: Axial strains

The suspended funds analyzed in this work, with the exception of the bottom with radial beams and central mast (Figure 2A), were designed as self supported and supported only on the side of the tanks. The results of the analyses are presented below.

The suspended bottom with radial beams type W and central mast, whose geometry is shown in Figure 7, where it has the same nominal diameter of the tank, D = 5,730.00 mm, number of support beams = 18 pieces, beam profile W = 310 x 28.3, beam material W = ASTM A572 – grade 50, diameter of the central mast = 640.00 mm, central mast thickness = 6.35 mm, central mast plate material = ASTM A36, bottom plate thickness = 7.95 mm (5/16″), bottom plate material = ASTM A36.

Bottom loading = hydrostatic pressure h = 5.80 m.c.a.

Figure 7: Background layout with radial beams and central mast

The stresses on the bottom plate and the support beams are shown in Figures 8A and 8B.

Figure 8A: Stresses on the suspended bottom Maximum voltage = 90.0 Mpa

Figure 8B: Stresses on the support beams Maximum voltage = 64.9 MPa

Figure 8C: Vertical off sets (mm)

Figure 8D: Axial stresses on mast Maximum voltage= 37.6 Mpa

The suspended bottom with radial beams type W and without central, whose geometry is shown in Figure 9, where it has the same nominal diameter of the tank, D = 5,730.00 mm, number of support beams = 18 pieces, beam profile W = 310 x 44.5, beam material W = ASTM A572 – grade 50, circumferential support beam U 6″ first soul, beam material U = ASTM A572 – grade 50, bottom plate thickness = 7.95 mm (5/16″), bottom plate material = ASTM A36.

Bottom loading = hydrostatic pressure h = 5.80 m.c.a.

Figure 9: – Background layout with radial beams and without mast

Figure 9A – Stresses on the suspended bottom Maximum voltage = 87.4 Mpa

Figure 9B – Stresses on the support beams Maximum voltage = 89.2 MPa

Figure 9C – Vertical offsets (mm)

The suspended bottom with orthogonal beams (grid) type W and without central, whose geometry is shown in Figure 10, where it has the same nominal diameter of the tank, D = 5,730.00 mm, number of support beams = 10 pieces, beam profile W = 360 x 72, beam material W = ASTM A572 – grade 50, circumferential support beam U 6″ first soul, beam material U = ASTM A572 – grade 50, bottom plate thickness = 9.53 mm (3/8″), bottom plate material = ASTM A36.

Bottom loading = hydrostatic pressure h = 5.80 m.c.a.

Figure 10: – Background layout with orthogonal beams (grille) and without mast

Figure 10A – Stresses on the suspended bottom Maximum voltage= 79.9 Mpa

Figure 10B – Stresses on the support beams Maximum voltage = 85.7 MPa

Figure 10C – Vertical off sets (mm)

The cone-shaped suspended bottom, whose geometry is shown in Figure 11 (cut), where it has the same nominal diameter of the tank, D = 5,730.00 mm, thickness of the bottom plate = 9.53 mm (3/8″), bottom plate material = ASTM A36. Bottom loading = hydrostatic pressure h = 5.80 m.c.a.

Figure 11: – Tapered bottom scheme in cut

Figure 11A – Stresses on the suspended bottom Maximum voltage = 90.8 Mpa

Figure 11B – Vertical displacements (mm) Maximum voltage = 7.359 mm

The suspended bottom in semi sphere or segmented spherical bottom format whose geometry is shown in Figure 12 (cut), where it has the same nominal diameter of the tank, D = 5,730.00 mm, thickness of the bottom plate = 4.75 mm (3/16″), bottom plate material = ASTM A36. Bottom loading = hydrostatic pressure h = 5.80 m.c.a.

Figure 12: – Schematic of the cut-segmented spherical background.

Figure 12A – Stresses on the suspended bottom Maximum voltage = 88.32 Mpa

Figure 12B – Vertical displacements (mm) Maximum voltage = 7.359 mm

The weights of the suspended funds were calculated without determining clippings or use of flaps and leftovers, calculating only the surfaces of plates multiplied by weight / m². Table 7 shows the general summary of the weights of the 5 types of suspended funds and these differences can be seen in the total weight x fund type chart in Figure 13.

Table 7 – Suspended fund weights

Figure 13 – Comparisons of fund weights

The vertical maximum offsets of the suspended bottoms are shown comparatively in Figure 14.

Figure 14 – Comparisons of vertical maximum displacements

## 5. CONCLUSIONS

From the results obtained, it is concluded that the segmented spherical suspension fund is the most economically viable and also the most technically recommended, because it presents the smallest vertical displacement, under complete loading.

The cone-type suspended bottom is also economically viable but has vertical displacement under somewhat excessive loading, and it should be checked if it interferes with the pipes. The vertical displacement could be decreased with the use of triangular reinforcement plates, supporting the bottom on the side sides.

The suspended bottom supported by orthogonal beams is totally uneconomical.

## REFERENCES

ABNT – Associação Brasileira de Normas Técnicas, NBR 7.821, Tanques soldados para armazenamento de petróleo e derivados. Rio de Janeiro, RJ. Abril de 1983.

ABNT – Associação Brasileira de Normas Técnicas, NBR 6.123, Forças devido ao vento em edificações. Rio de Janeiro, RJ. Junho de 1988.

ABNT – Associação Brasileira de Normas Técnicas, NBR 12.218, Projeto de rede de distribuição de água para abastecimento público. Rio de Janeiro, RJ. Julho de 1994.

ANDRADE JUNIOR, L. J. Análise estrutural das chapas metálicas de silos e reservatórios cilíndricos. Dissertação de mestrado. Escola de Engenharia de São Carlos. Universidade de São Paulo, 1998.

API – *American Petroleum Institute*, API 650, *Welded Steel Tanks for Oil Storage*, decima terceira edição, Washington D. C., Março de 2013.

AWWA – *American Water Works Association, AWWA D100-05, Welded Steel Tanks for Water Storage*. Edição atualizada. Denver, Colorado. Maio 2005.

GOMES, E. F. Soldagem em reservatórios metálicos para armazenamento de água. Trabalho de conclusão de curso. Curso de especialização em Engenharia de soldagem. Universidade Federal de Minas Gerais, 2017.

HAFEEZ, G., EL ANSARY, A. M. & EL DAMATTY, A. A. *Effects of winds load son the stability of conical tanks. **Can. J. Civ. Eng. 38, Published by NCR Research Press, *2011.

PEREIRA, P. M. F. Análise dos conjuntos habitacionais do programa Minha Casa, Minha Vida na cidade de Monte Alegre de Minas- MG. Dissertação de mestrado. Faculdade de Geografia. Universidade Federal de Uberlândia, 2017.

TREES, M. J. Design of elevated steel tanks. Thesis. University of Illinois, Urbana-Champaign, 1911.

VISAL, B. & SIBIN, B. *Design and analysis of storage tanks.* *International Journal of Innovative Research in Science, Engineering and Technology. **Vol. 6, Issue 5. *maio 2017.

^{[1]} Master’s degree in Structures and Civil Construction; Specialization in Industrial Constructions; Specialization in Environmental Engineering; Specialization in Safety Engineering; Civil Engineer, and Mechanical Operation Engineer.

^{[2]} Specialization in Structural Engineering and Civil Engineering.

^{[3]} Civil Engineer.

Sent: March, 2020.

Approved: June, 2020.