MATEC Web of Conferences 406, 06011 (2024) https://doi.org/10.
1051/matecconf/202440606011
2024 RAPDASA-RobMech-PRASA-AMI Conference
Finite element analysis of oil storage tank failure
under complex loading conditions
Themba Mashiyane1,3*, Lagouge Tartibu1, and Smith Salifu2
1Department of Mechanical and Industrial Technology, University of Johannesburg, South Africa
2Centrefor Nanoengineering and Advanced Materials, University of Johannesburg, South Africa
3Eskom Research, Testing & Development, Eskom SOC Ltd, Johannesburg, South Africa
Abstract: Storage tanks are vital components across industries, especially
in the power generation industry, where they are used for oil storage. The
internal pressure these tanks are able to withstand greatly affects their
longevity and behaviour under service conditions. This paper presents a
comprehensive computational study that utilizes Finite Element Analysis
(FEA) technique to investigate the failure mechanism of oil storage tanks
when subjected to complex loading conditions. In the simulation, FEA
software, Abaqus is employed to replicate the operational scenarios which
incorporate internal pressure from the stored liquid in the tank, internal
pressure developed during discharge and external pressure in the windward
direction. Realistic boundary conditions are applied to the tank to accurately
mimic real-case scenarios. The stress and strain contour plot shows that the
maximum stress (greater than the yield strength of the tank material) and
strain with values 485.4 MPa and 2.095 × 10−3, respectively were
developed on the surface of the tank in the windward direction. By post-
processing, the output database results obtained from the stress and strain
analysis in Abaqus using fe-safe, the tank was found to survive 1 429 hours
before failure under the specified operating conditions.
1 Introduction
The global demand for energy has fueled the expansion of oil and gas infrastructure, thus,
leading to the widespread utilization of large-scale storage tanks for the safe storage of
petroleum products [1]. Among these storage vessels, oil storage tanks play a critical role in
ensuring the stability and integrity of oil reserves [2]. However, the structural reliability of
these tanks becomes a significant concern due to the diverse environmental and operational
conditions they are subjected to [3]. One of the most critical failure modes posing a
substantial risk to oil storage tanks is buckling, particularly when the tanks experience
combined internal and external pressure scenarios [3]. Buckling failure in storage tanks
occurs when the applied load exceeds the structural capacity of the tank, hence, resulting in
sudden and catastrophic collapse of the tank.
_______________________
*Corresponding author: tmashiyane12@gmail.com.
© The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative
Commons Attribution License 4.0 (https://creativecommons.org/licenses/by/4.0/).
MATEC Web of Conferences 406, 06011 (2024) https://doi.org/10.1051/matecconf/202440606011
2024 RAPDASA-RobMech-PRASA-AMI Conference
Oil storage tanks are characterized as thin-walled cylinders, thus, they can exhibit buckling
in the form of deformation, distortion, or even rupture of the tank walls. The unplanned
failure of these tanks in the form of buckling tends to pose threats such as environmental
contamination, loss of valuable resources, and risks to human safety [1]. As a result of the
potential consequences of storage tank failure due to buckling, comprehending and
mitigating the risks associated with storage tank buckling is of utmost importance to
industries such as the oil and gas sector and power generation industry which rely hugely on
these essential storage facilities for their daily activities [4-6].
In order to gain a comprehensive understanding of the combined effects of internal and
external pressures on storage tanks, it is crucial to investigate the interaction between these
pressure scenarios. Internal pressures within storage tanks arise from the stored contents,
pressure build-up during discharge and faulty vents, while external pressures can result from
factors such as wind loads, seismic events, or adjacent storage tank operations. The
examination of these pressure interactions is vital for accurately assessing the structural
vulnerabilities of oil storage tanks and implementing robust design and maintenance
strategies [7].
Over the past decades, extensive research has been conducted to investigate the buckling
behaviour of oil storage tanks. Early studies, such as those by Donnell and Wan [8], explored
the impact of imperfections on the buckling behaviour of thin cylinders using large-deflection
shell theory. Subsequent research, such as Miller's comparative analysis on ring-stiffened
steel cylinders [9], provided insights into both elastic and inelastic buckling. Further
advancements include experiments conducted by Singer [10] and studies by Seung-Eock and
Chang-Sung [11], where they highlighted the influence of initial geometric imperfections on
the buckling behaviour of cylindrical shells.
Oftentimes, the buckling in storage tanks is commonly associated with external forces,
such as wind and seismic events [12, 13]. Nevertheless, contributions from researchers like
Uematsu et al. [14-16] have significantly advanced the understanding of wind-induced
buckling in storage tanks by investigating pre-buckling deflections and critical buckling wind
pressure. Numerical simulations have also played a crucial role in the buckling analysis of
storage tanks, with studies conducted by Schmidt et al. [17], Sosa and Godoy [18], and Jaca
and Godoy [19]. Their studies provided valuable insights and recommendations for post-
buckling strength design strategies and also highlighted the inadequacy of design steps in
predicting wind-induced buckling during construction.
This study aims to perform a comprehensive computational investigation by employing
the Finite Element Analysis (FEA) technique to analyze the failure of oil storage tanks by
buckling under complex loading conditions. By utilizing the FEA software Abaqus, the
simulation accurately mimics real-case scenarios, allowing for the application of realistic
boundary and loading conditions that depict a real-case scenario.
2 Methodology
The primary objective of this study is to investigate how the tank responds to both internal
and external pressure, by providing insights into its stress, strain, displacement, and buckling
characteristics under typical operating conditions. To achieve this, a finite element analysis
(FEA) approach is utilized with the aid of commercial software, Abaqus CAE.
The model development stage involves utilizing FEA software, Abaqus to develop a tank
model with specifications similar to those used in oil storage applications. The tank model is
developed using S355 low-carbon steel, and its dimensions are specified (as shown in Table
1) according to the requirements of the power generation company. S355 low-carbon steel
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MATEC Web of Conferences 406, 06011 (2024) https://doi.org/10.1051/matecconf/202440606011
2024 RAPDASA-RobMech-PRASA-AMI Conference
was selected due to its high strength, good ductility, and excellent weldability which makes
it essential for large structural applications like oil storage tanks. Material properties for the
tank and the diesel oil stored within it (as depicted in Table 2) are also specified in the
material properties specification section of Abaqus.
Table 1. Dimension of storage tank [20]
Shape of tank parts
Dimensions Cone top (m) Cylindrical section(m) Vent (m)
Height 0.770 10.077 0.156
Outer diameter 0.975 7.076 0.100
Inner diameter 1.015 7.096 0.120
Thickness 0.010 0.010 0.010
Table 2. Material properties of (a) storage tank and (b) diesel oil
(a) Material Properties of Tank Value
Modulus of Elasticity (GPa) 202.6
Poisson’s Ratio 0.28
Thermal Conductivity (W/(mK)) 14.85
Density (kg/m3) 480
Thermal Expansion (× 10−5 𝐾 −1 ) 1.30
Specific Heat Capacity (J/kgK 531
Yield Strength (MPa) 1139
(b) Properties of Oil Used in the Tank [21]
Density of diesel (kg/m3) 840
Specific volume of diesel (× 10−3m3/kg) 1.18
To ensure the accuracy of the FEA, a mesh convergence study (as shown in Figure 1(b))
is conducted. This study involves choosing an appropriate mesh type (quadratic tetrahedral
elements of type C3D10) and gradually reducing the mesh size until the desired results are
obtained without sacrificing computational efficiency and result integrity. For this study, the
stress developed in the tank was used as the basis for the convergence study. By gradually
reducing the mesh size from the default size, a constant stress value was opened at 0.10m
mesh size and below. Thus, a 0.10m mesh size with a lesser computational time but a similar
stress result was selected for the study. Quadratic tetrahedral elements were chosen for this
study due to their ability to handle complex geometry and their ability to strike a balance
between accuracy and computational efficiency. Loading and boundary conditions are
defined to reflect realistic operational scenarios for oil storage tanks. At the top of the tank,
displacement and rotational boundary conditions are applied in the X and Z axes, which
permit displacement along the Y axis (such that X=0, Y=1, and Z=0). On the other hand, the
base of the tank is fixed (Encastre) and does not experience any movement (X=0, Y=0, and
Z=0), as shown in Figure 1(a). The loading involves the incorporation of external pressure
from wind and internal pressure due to the height and density of the stored liquid, as well as
any potential pressure build-up during tank discharge or vacuum conditions.
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MATEC Web of Conferences 406, 06011 (2024) https://doi.org/10.1051/matecconf/202440606011
2024 RAPDASA-RobMech-PRASA-AMI Conference
Figure 1: (a) Applied loading and boundary conditions (b) Mesh convergence study plot
The analysis of the tank's behaviour involves two distinct steps within the FEA software.
A static general step is conducted to determine stress and strain under the specified
operational conditions, while a separate buckling step is introduced to identify potential mode
shapes and the buckling pattern induced by the combined internal and external pressure
scenarios. To evaluate the useful life of the tank under the specified conditions, post-
processing software, fe-safe is utilized. The output database obtained from the stress analysis
is imported into fe-safe, thus, enabling the prediction of the tank's lifespan based on nodal
stresses and strains.
3 Mathematical validation expression
To determine the pressure within a cylindrical storage tank, the following methods were
employed:
Pressure on Tanks: The internal pressure (𝑃𝐼 ) within the tank, resulting from the liquid it
contains, is computed using the formula:
𝑃𝐼 = 𝜌𝑔ℎ (1)
where 𝜌 represents the liquid density, 𝑔 is the acceleration due to gravity (9.8 m/s²), and ℎ
denotes the height of the cylindrical tank.
Wind Pressure: Wind exerts force on structures like cylindrical tanks due to the movement
of air molecules, termed wind pressure. This pressure can lead to structural deformation,
stress, and even failure if not properly considered in design and construction. The formula
for calculating the pressure exerted by wind on a structure based on wind speed (𝑉) is
expressed as:
𝑃 = 0.0025 × 𝑉 2 (2)
where 𝑉 is the wind speed in miles per hour (mph), and 𝑃 is the pressure in pounds per square
foot (psf).
Stress Developed in Thin-Walled Cylinder: Since the considered oil storage tank has a
diameter-to-thickness ratio exceeding 20, it falls into the category of a thin-walled cylinder.
Consequently, the hoop (circumferential) stress (𝜎) in such a cylinder is determined by the
formula:
𝑃 𝑑
𝜎 = 2𝑡𝐼 (3)
and the stress developed in the longitudinal direction is given as:
𝑃 𝑑
𝜎 = 4𝑡𝐼 (4)
where 𝑃𝐼 is the internal pressure, 𝑑 represents the diameter, and 𝑡 signifies the thickness of
the cylinder or tank.
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MATEC Web of Conferences 406, 06011 (2024) https://doi.org/10.1051/matecconf/202440606011
2024 RAPDASA-RobMech-PRASA-AMI Conference
4 Results and discussion
The findings from the finite element analysis (FEA), as illustrated in Figure 2, offer critical
insights into how the filled oil storage tank behaves under various loading conditions. In the
direction facing the wind, a notably high von Mises stress of 485.4 MPa was recorded
(surpassing the tank material's yield strength), with a maximum principal strain of
2.095 × 10−3 . These elevated stress and strain levels suggest a high possibility of plastic
deformation under the specified operational parameters. Since the tank is subject to an
internal pressure of 0.5 MPa and a relatively low external wind pressure of 250 Pa, it
experiences considerable mechanical strain which was primarily induced by the internal
pressure. The contour plot indicates stress concentration on the wind-facing side of the tank,
where the combined effect of internal and wind pressures is most pronounced, thus, resulting
in the observed high stress and strain levels. Additionally, the stress and strain distribution
pattern across the tank highlights that the side opposite the windward direction experiences
the least stress, thus, illustrating the contribution of wind pressure to the overall stress and
strain on the filled tank [22, 23].
(a) (b)
Figure 2: (a) Stress and (b) strain developed in the oil storage tank
In the analyzed scenario of the filled oil storage tank, as depicted in Figure 3, the finite
element analysis results indicate that the tank's deformation is predominantly attributed to
the internal pressure rather than the external wind load. The highest displacement (0.00818
m) was observed in the windward direction, and this is primarily due to the substantial
internal pressure. Conversely, minimal displacement was recorded on the leeward side of the
tank, and this can be attributed to the comparatively lower external pressure experienced on
that side of the tank. The notable contrast between internal and external pressures emphasizes
the predominant influence of internal pressure on the tank's deformation [22].
Figure 3: Displacement in the oil storage tank under the loading condition
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MATEC Web of Conferences 406, 06011 (2024) https://doi.org/10.1051/matecconf/202440606011
2024 RAPDASA-RobMech-PRASA-AMI Conference
Figure 4 displays the finite element analysis (FEA) results that showcase the buckling
contour plots of the first 10 eigenvalue buckling mode shapes for the filled oil storage tanks
under combined high internal pressure and wind-induced external pressure. The analysis
offers vital insights into the buckling behaviour of the storage tank under the specified
loading conditions. It reveals that the tank is prone to buckling under these conditions, with
the initiation of buckling predominantly observed in the windward direction. The first 10
modes of both tanks illustrate deformation patterns, particularly noticeable in the outward
bulging on the windward side. This bulging results from the pressure gradient between high
internal pressure and low external pressure induced by wind velocity [23]. The combination
of these pressures causes the tank to deform outward on the windward side, relieving the
pressure differential between its interior and exterior surfaces. Subsequent modes exhibit
more complex buckling patterns, initiated by stress concentrations resulting from the initial
deformation.
Figure 4: First 10 buckling mode shapes for filed oil storage tank
Accurately assessing the useful life of oil storage tanks under varying oil levels and
operational circumstances is essential for ensuring industrial safety, reliability, and cost-
efficiency. In this context, the stress and strain data obtained from the analysis were utilized
in fe-safe postprocessing software to determine the tank's useful life under specified
conditions. During the analysis, the Brown-Miller method with Morrow correction which
combines strain and stress to predict fatigue under varying load conditions was applied and
Miner’s rule was used for predicting the cumulative damage. The analysis indicates that the
filled storage tank is expected to remain operational for approximately 1 429 hours before
experiencing failure, as depicted in Figure 5. The contour plot of the tanks' useful life shows
that the lowest life is expected to occur towards the bottom of the tank in the windward
direction.
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MATEC Web of Conferences 406, 06011 (2024) https://doi.org/10.1051/matecconf/202440606011
2024 RAPDASA-RobMech-PRASA-AMI Conference
Figure 5: fe-safe computed useful life of filled oil storage tank
Given the intricate nature of the tank model under varied loading conditions beyond the
hydrostatic pressure from its contained liquid, validating the model becomes practically
challenging. However, in this study, the validation was done by using the stress developed
by the tank solely under hydrostatic pressure. By employing analytical techniques and
utilizing expressions provided in Equations (1 and 4), the finite element analysis (FEA)
results for the hydrostatic pressure within the oil storage tank, illustrated in Figure 6, were
effectively validated; and the analytical findings closely aligned with FEA results, as
demonstrated in Table 3.
Figure 6: Hydrostatic stress developed due to hydrostatic pressure of the oil
Table 3: FEA result validation
Analytical Computed Hydrostatic Numerically Computed Hydrostatic % Deviation
Stress (MPa) Stress (MPa)
50.1 52.1 3.8
5 Conclusion
The study investigated the structural integrity of a filled oil storage tank under combined
internal and external pressures, by employing Finite Element Analysis (FEA). Various
parameters such as stress, strain, displacement, buckling behaviour, and useful life were
assessed for specified operating conditions. Findings highlighted significant stress
concentrations and deformation patterns, particularly on the windward side of the tank,
indicating susceptibility to buckling. Internal pressure emerged as the primary factor
contributing to mechanical strain and deformation, while wind load played a secondary but
significant role. The outcome of the analysis shows the influence of the operating conditions
on structural assessments, with fluid distribution and stress levels significantly impacting
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MATEC Web of Conferences 406, 06011 (2024) https://doi.org/10.1051/matecconf/202440606011
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useful life. Additionally, the validation of hydrostatic stress through analytical methods
confirmed the reliability of the FEA technique and the developed model.
This research is supported by the National Research Foundation (NRF) of South Africa under the
Unique Grant No: PMDS22070431246, and the University of Johannesburg, South Africa. The authors
also appreciate the support of the Sound and Vibration Laboratory, at the Tshwane University of
Technology, South Africa and Eskom Power Plant Engineering Institute (Republic of South Africa).
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