HYDROSTATIC PRESSURE
This dataset and calculations are for educational purposes only.
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PROBLEM STATEMENT:
The design and structural integrity of above-ground cylindrical storage tanks are critical in many industrial applications, particularly when subjected to hydrostatic pressure from stored liquids. In this study, we aim to determine the maximum hydrostatic pressure that a cylindrical storage tank, with a diameter of 10 meters and a height of 5 meters, can withstand when constructed using structural steel. The structural steel has a density of 7.85×10E6 kg/mm3, Poisson’s ratio of 0.3, compressive/tensile stress limits of 0.25 GPa, and a tensile ultimate strength of 0.46 GPa. The tank is made using 6 mm thick steel plates for shell and flat bottom plates. Use heavy crude oil with density of 1200 kg/m3 as a fluid with a maximum filled capacity of 4.7m.
Determine Maximum Hydrostatic Pressure: Calculate the maximum hydrostatic pressure that the steel tank can safely sustain, ensuring the structural steel material does not fail under the compressive, tensile, or ultimate stress limits.
Material and Thickness Optimization: In the event that the design fails under the given hydrostatic pressure, identify alternative materials and optimal plate thicknesses that would maintain the structural integrity of the tank under the same operating conditions. The alternative materials must provide improved performance while meeting safety and cost-effectiveness considerations.
first iteration:
Free Modal Analysis:
Based on the illustrations and computations, it is evident that both the bottom plate and shell plate of the storage tank will fail under the given conditions. The calculated values demonstrate that the current design does not meet the required structural limits. The determination of the factor of safety further confirms the inadequacy of the design, revealing a safety factor of zero for both the bottom and shell plates. This indicates that the tank, as currently designed, will not withstand the applied hydrostatic pressure and is highly prone to structural failure. These results are computed without the support of concrete foundation, hence this size of tank cannot be elevated from the ground without proper support.
fOUNDATION SUPPORT:
With the concrete foundation support, fixing support at the bottom plate, we can now analyze the total forces acting on the tank due to hydrostatic pressure.
INVESTIGATING THE BOTTOM PLATE:
The staggered arrangement of steel plates along the shell enhances the overall structural strength of the tank. This layout helps distribute stress more evenly across the tank's surface, reducing the likelihood of failure by mitigating weak points along the joints. As a result, the staggered configuration contributes to improved resistance against external pressures, providing added strength and stability to the shell.
However, upon examining the junction between the shell and the bottom plate, certain areas exhibit high concentrations of stress. These localized stress points indicate potential vulnerabilities in the tank's design, particularly at the shell-to-bottom plate connections, which may compromise the overall structural integrity.
welding profile shell-bottom plate
According to API 650, the code provides specific guidelines for the fundamental design connections between the shell material and the annular plate, with requirements based on the height of the tank and the design thickness of the bottom plate. However, the appropriate weld size for these connections must still be determined to ensure the integrity and safety of the tank structure. In our case, we will not include the annular plate for simplicity.
We will modify the geometry to incorporate the weld bead size and evaluate the impact of the heat-affected zone (HAZ) on residual stresses induced by cooling from high welding temperatures during fusion. It is important to note that the geometry has a thickness-to-nominal-diameter ratio of 0.00012.
Adding the hydrostatic load on the tank with the weld in place between shell and bottom plate.
The interaction between welded components, such as the bonding between fillet welds and the adjoining plates, as well as frictionless contacts between surfaces, plays a critical role in the structural integrity of welded joints. Bonded contacts ensure that welded areas, such as between the bottom of fillet welds and the face of a horizontal plate, remain securely joined, preventing separation under load. Frictionless contacts, like those between the bottom of a vertical plate and the top of a horizontal plate, are used to model idealized, low-friction interfaces that hold components together without transmitting shear forces.
Sharp corners and notches in the welded geometry create areas of stress concentration, where localized stresses are significantly higher than in smoother regions. These geometric discontinuities amplify the stress levels, potentially leading to premature failure or crack initiation, particularly in cyclic loading scenarios. The presence of such notches, often inherent in weld profiles, must be carefully analyzed and mitigated to improve the structural performance and fatigue life of the welded assembly.
Understanding the influence of both bonded and frictionless contacts, as well as the stress concentrations arising from geometric irregularities, is essential for accurately predicting the behavior of welded joints under load. This knowledge can guide design improvements and enhance the durability and reliability of welded structures.
Stress propagation due to heat of welding fusion (HAZ) based on weld size on 10mm base plate and 8mm shell plate. The heat affected zone (HAZ) is the area of metal that has not melted but has changed properties due to exposure to high temperatures during welding. The HAZ is located between the weld and the base metal ramped from 22 C ambient temperature to 1300 C which is the melting temperature of inconel welding rod. However, this is just a approximation of the material behavior.
Weld profiles and geometries have significant effects on the structural behavior and fatigue life of welded joints. Different welding techniques and joint configurations, such as butt joints, corner joints, T-joints, lap joints, and edge joints, exhibit varied mechanical properties under load due to their design and the type of weld used. These welds can be broadly categorized into fillet welds, which primarily connect the outer surfaces, and penetration welds, where the weld material penetrates into the plates, resulting in a stronger bond.
Full penetration welds, such as double-sided butt welds, are generally considered the most durable due to the complete fusion of the materials and the absence of initial cracks common in partial penetration welds. To enhance fatigue resistance further, techniques such as grinding out the weld toes—where cracks often initiate—can be applied. This refinement increases the lifespan of the welded structure by reducing localized stress concentrations.
In fatigue life calculations, factors like weld profile (including the face, toes, throat, and root of the weld), stress levels, and potential imperfections must be accounted for. These variables are essential when determining the load-bearing capacity and fatigue resistance of welded connections. The thickness of the weld, particularly the weld throat, is a critical factor in defining the structural strength of the joint. Understanding these profiles allows for more accurate predictions of structural behavior and lifespan under various loading conditions. Q.E.D.
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