Structural assessment of 40 ft mini LNG ISO tank: Effect of structural frame design on the strength performance
-
Dian Purnamasari
,
Teguh Muttaqie
Abstract
Due to the escalating demand for liquefied natural gas (LNG) as a low-emission and environmentally friendly energy source, ISO tank containers have emerged as an innovative solution to facilitate efficient and cost-effective mass transportation. The 40 ft ISO tank container, which encompasses a pressure vessel structure, is a versatile intermodal unit that seamlessly integrates into sea and land transportation networks. The main objective of this study is to present a comprehensive analysis for assessing the various frame design scenarios of the 40 ft ISO tank container for mini LNG carrier operation. The assessment is conducted under the provisions outlined in ASME Section VIII Division I code, which governs the design standards for boilers and pressure vessels. The finite-element analysis (FEA) scrutinizes three different structural design alternatives: frame thickness, the addition of support plates, and the addition of saddle supports, which are subjected to various loading conditions: stacking, lifting, and racking load tests. The analysis offers a comparative assessment of the safety level provided by the ASME design guidance in contrast to the FEA judgments based on ISO standards. It can be found that stacking and longitudinal load tests are more critical operational load scenarios. Increasing the frame thickness of the LNG ISO tank is more practical in increasing structural weight savings than adding more saddle supports and support plates.
1 Introduction
Indonesia aims to reduce greenhouse gas (GHG) emissions by 29–40% by 2030 by strengthening the use of alternative energy sources [1]. Liquefied natural gas (LNG) as a fuel is one method for minimizing GHG emissions from maritime transportation [2]. Meanwhile, Indonesia, having served as a prominent exporter of LNG for over three and a half decades, has witnessed a notable proliferation of LNG facilities, numbering in the dozens [3]. To facilitate the efficient conveyance of gas, both presently and in anticipation of future demands, mini LNG carriers have emerged as a highly convenient mode of transportation across terrestrial and maritime domains. Mini LNG carriers are an alternate approach for delivering liquid natural gas to archipelago areas with low operational costs.
The interest in advancing the technology of mini LNG ISO tanks in Indonesia stems from the fact that these products are currently imported entirely, lacking standardized guidelines for domestic ISO tank design. Consequently, there is a need to conduct a design study on LNG ISO tanks to ensure structural safety and integrity by applying the proposed procedure. A series of studies on structural integrity assessment by numerical analysis using international guidance of various independent LNG tank designs (types B and C) applied for LNG carriers [4,5,6] and apple-shaped LNG cargo tanks for LNG carriers was conducted [7]. Although numerous studies were conducted for the optimum design and structural integrity assessment of the independent type tank, analytical studies on LNG ISO tank containers according to codes are inadequate and difficult to find. This results from the challenge of establishing a proven procedure for the structural integrity assessments for ISO tank designs.
The basic structural component of an LNG ISO tank is a pressure vessel with a working pressure that differs from atmospheric pressure. Pressure vessel design parameters are designed under ASME standards, while the specification and testing requirements of freight containers under operational loading conditions follow the ISO 1496 standard. The design purpose is to develop the tank containers to have sufficient safety level and weight management [8]. However, the design of ISO tank containers has evolved through trial and error. It is partly owing to a lack of definitive methods for analyzing the strength and stiffness of the tank and frame. It has resulted in several patents for various designs, which are then statically tested to agreed general criteria [9].
Several previous investigations on the design and analysis of freight containers were reviewed. The finite-element analysis approach was used by Wang and Qian [10] and Xuemei and Caifu [11] to investigate the effect of liquid inertial force on stress distribution at the frame and shell of tank containers under various loading conditions [10,11]. Further, Zhaochun et al. [12] calculated the stress distribution and displacement of LNG tank containers subjected to inertial force and determined the strength requirements. Xiaodong and Hu [13] used numerical analysis to simulate an LNG tank container subjected to inertial force and evaluated the safety level performance. Moreover, static structural and buckling estimations of a 40 ft ISO container were utilized to test and validate the proposed design for replacing typical steel containers with E-glass/S-glass composites. According to the findings, corner fittings should be reinforced further to withstand the harsh conditions that occur when containers are lifted and stacked on top of each other [14]. In addition, the complete procedure for evaluating the scantling size of the 20 ft ISO tank LNG type was proposed by Muttaqie et al. [15]. To enhance the safety allowance, the design must be improved by adding brackets or support plates at both the horizontal and vertical parts. Besides that, static numerical analysis was conducted to analyze various pressure vessel head designs. Moreover, De Souza et al. [16] investigated container stack dynamics of 20 ft ISO tank, both numerically and experimentally, to predict conditions similar to those encountered by container stacks while stored on a ship’s deck. Several pressure vessel heads were investigated, including flat, hemispherical, ellipsoidal, torispherical, and conical heads [17]. The numerical approach is used to predict the fatigue life [18] and boil-off rate [19], and static and dynamic strength [20] of various container tank models can be found in a series of literature.
Although numerous previous studies were conducted for the structural assessment of freight container design, there are limited studies in evaluating the structural performance of LNG ISO tanks developed by local manufacturers. It can be noted that specific LNG ISO frame design requirements may vary based on local regulations, transport facilities, operational areas, and manufacturer specifications. Due to these factors, national manufacturers under the National Research and Innovation Agency (BRIN) chose to develop LNG ISO tanks for mini LNG carriers to support the energy logistics of eastern Indonesia. Therefore, a procedure for structural integrity and safety assessment considering ASME standards and specification and testing based on ISO 1496 was proposed to develop a domestically LNG ISO tank design. Structural safety and weight savings are the most essential aspects in the design of the LNG ISO tank and will be considered as design parameters. Several proposed design criteria will be studied in this study, including variations in frame thickness and the addition of saddle support and support plates. As a result, a systematic FEA was carried out to evaluate structural safety and to develop a technique for analyzing the safety levels and weight savings of various frame designs.
2 Overall assessment procedure of LNG ISO tank
A tank container is a freight container with two basic structures: the tank and the framework. The framework consists of the tank mountings, end structure, and all load-bearing components, which transmit static and dynamic forces from the lifting and handling of the tank container. In this present study, the structural assessment procedure of 40 ft LNG ISO tank consists of two main sectional procedures: the pressure vessel tank analysis and the ISO container frame analysis. Each section undergoes steps to ensure the structural integrity and operational safety of the LNG ISO tank. In the first stage, the material selection and initial thickness calculation of the LNG ISO tank are performed based on the required design requirements. The material selection for the pressure vessel is defined in ASME Section II Part D Properties [21], which provides guidelines for selecting materials with suitable mechanical properties and corrosion resistance.
Additionally, the initial thickness calculation of the pressure vessel is determined by ASME Section VIII Division I Boiler and Pressure Vessel Codes [22]. The code ensures the developed pressure vessel meets the necessary strength, durability, and safety standards. After that, the material choice, thickness, and total weight of the pressure vessel are included in the numerical analysis for ISO container frame strength calculation. The dimensions of each container frame type are specified in the relevant section of the ISO 1496 Series 1 freight containers [23]. The standard specifies freight container dimensions and structural criteria. The analysis then focuses on operational safety standards utilizing the ISO 1496 standard, which restricts the load and pressures exerted on the frame container constructions. It assures that the ISO tank can endure the predicted stresses and loads during shipping and handling. Using these safety standards, the structural reaction of the ISO tank, including stress, displacement, safety factor value, and performance threshold, can be correctly determined. The procedure of structural strength of a 40 ft ISO tank container is depicted in Figure 1.
The procedure of the ISO tank container strength assessment.
3 LNG ISO tank design requirement
This section introduces a design requirement to support a substantive framework of 40 ft LNG ISO tank design requirement. The contents cover the ISO tank pressure vessel design parameter based on ASME Sections II and VIII and calculate the LNG ISO tank loading parameter based on the ISO 1496 standard.
3.1 Design parameter of ISO tank pressure vessel
Designed to store and transport LNG in its liquid condition, the 40 ft LNG ISO tank is an example of a standardized container. These tanks are essential to the world’s LNG supply chain since they are built using high-quality materials and are designed to resist the harsh conditions associated with LNG. The outer shell and inner shell geometries of the ISO tank are depicted in Figure 2. The selection of suitable materials and determination of the necessary thickness for the pressure vessel of the 40 ft LNG ISO tank are both covered in detail in this section. It starts by exploring important elements and standards defined in ASME Sections II and VIII [21,22], including material choice, allowed material stress, and the specific methods used to calculate pressure vessel thickness.
ISO tank cylindrical shell geometry.
For this calculation, the selected material is SUS 304L alloy steel, which possesses an ASME Section II specification conversion known as SA 240 Gr 304L-S 30403. SA 240 Gr 304L-S 30403 is based on ASME. It refers to a stainless-steel material that complies with the ASME SA 240 specification, specifically using grade 304L stainless steel (low-carbon variant) with the UNS designation of S30403. Within ASME Section II [21], the material properties are meticulously regulated and categorized based on distinct types of nominal material composition. By adhering to these stringent guidelines and rules established by ASME, the procedure ensures that the material selection and thickness calculation for the pressure vessel meet the required standards for safety and functionality in LNG transportation. These systematic methodologies are essential in guaranteeing the structural integrity and operational reliability of the LNG ISO tank, thereby minimizing potential risks and ensuring the secure transport of LNG cargo.
The minimum thickness calculation is provided in UG-27 of ASME VIII-1 [22]. The description of the input parameters is shown in Figure 2. The thickness required by the code is greater than the result by
where P is the internal design pressure, R is the inner radius, S is the allowed stress for steel stainless (SUS 304L), and E is the butt joint efficiency. For further information, see Table UW-12 ASME [22]. Further, as demonstrated by Eqs (2) and (3), the computation of the toruspherical shell’s concave side for the cylinder’s two ends refers to paragraph UG-32
where r denotes the inside knuckle radius and L denotes the inside crown radius in mm. Figure 2 describes the geometry of the torispherical head.
Meanwhile, Section VIII UG-28 [22] paragraph has resorted to estimating the maximum allowed external pressure (MAEP) for the planned cylindrical shell. To utilize the following formula, the geometry D 0/t ≥ 10 must be verified in the first stage. Following verification, the external load graph reference of Figure G in ASME Section II, Part D Subpart 3 [21], is used to obtain A utilizing L/D 0 and D 0/t. After obtaining the A value, the B value in Figure HA-3, which is appropriate for the 304L material specification, is calculated using this value. Finally, the maximum is determined using the B value using Eq. (4). The process is comparable to determining the convex side of the cylindrical end’s maximum pressure based on UG-33. B is used in the following equation:
The calculation relates to paragraph UG-29 ASME Section VIII [22] to determine the ring stiffener’s compressive pressure on the pressure vessel. The techniques needed for this phase presume the original size and shape of the ring stiffener.
where A s is the ring stiffener’s anticipated cross-sectional area, L s is the space between stiffeners, and t is the predicted shell thickness from the previous step. After that, the B value is calculated using Eq. (6). Utilizing the resulting B value, find the A value that equals the calculated B value using the external pressure table in ASME Section II, Part D [21]
The moment of inertia necessary for the stiffening ring alone is then calculated using Eq. (7). Next, depending on the initial assumptions made by Eq. (8), determine the actual moment of inertia of the ring stiffener. Additionally, the needed moment of inertia must be equal to or greater than the findings of the actual moment of inertia. The result of pressure vessel thickness according to ASME Section VIII [22] is stated in Table 1.
Design parameters of inner and outer tank of LNG ISO tank using ASME Section VIII [22]
| Design parameter | Value | Unit |
|---|---|---|
| Internal design pressure (P int) | 1 | MPa |
| External design pressure (P ext) | 0.8 | MPa |
| Inner Tank | ||
| Inner shell thickness (t) | 7.1 | mm |
| Inner head thickness (t) | 11.22 | mm |
| Inside diameter (D) | 2,218 | mm |
| Cylindrical length (L cyl) | 11,018 | mm |
| Inside crown radius (L) | 2,218 | mm |
| Knuckle corner radius (r) | 221.8 | mm |
| Outer Tank | ||
| Outer shell thickness (t) | 3.95 | mm |
| Outer shell thickness (t) | 6.28 | mm |
| Inside diameter (D) | 2,438 | mm |
| Cylindrical length (L cyl) | 11,018 | mm |
| Inside crown radius (L) | 1,950.4 | mm |
| Knuckle corner radius (r) | 243.8 | mm |
| Material: steel stainless (SUS 304L) | ||
3.2 ISO tank loading parameter
FEA involves the utilization of scenarios outlined in ISO 1496 to perform calculations. To receive certification and approval, new or modified designs must undergo testing per ISO 1496 standards [23]. The loading scenario for the ISO tank structure is described in detail based on the ISO 1496 standard data provided in Table 2. According to the aforementioned standard, a 40 ft ISO tank is classified under class A, which entails a stacking load of 942 kN at each shoe/corner fitting location. For example, a 40 ft ISO tank container with a gross weight of approximately 32 tons is assumed, divided equally at each corner, resulting in a minimum load of 8 tons or 73 kN. Thus, ISO 1496 specifies exceptionally high strength requirements, estimated to accommodate up to three tiers (excluding the dynamic safety factor of 1.8). However, the intended transportation method for the ISO tanks is via mini-LNG carriers. These carriers have a capacity of 36 TEUs. The ISO tanks will be stacked in a maximum of two tiers during the voyage, as illustrated in Figure 3. A summary of the loading scenarios is given in Table 2.
Loading scenario and layout
| Load scenario | Loading layouts |
|---|---|
| Stacking strength |
|
| Lifting strength |
|
| Racking (transverse) |
|
| Racking (longitudinal) |
|
Configuration design of mini LNG ISO tank container 40 ft.
The stacking loading test assesses the weight capacity of a 40 ft container. This test is designed to determine whether any fully loaded container can withstand the whole weight stacked on top. Based on ISO 1496 standards, the container is subjected to vertical forces of about 942 kN (approximately 384 tons) applied to all four corner fittings simultaneously or at each pair of end fittings. The capacity of the LNG tank also contributes about 189.3 kN distributed load, equivalent to 19.3 tons of cargo. The load is precisely applied at the midpoint of the upper surface of the corner fitting. This test demonstrates the ISO tank’s structural ability to support stacked containers while considering sea conditions.
Moreover, the lifting test demonstrates a container’s capabilities to withstand being lifted vertically from an appropriate set of four corner fittings. This test is also intended to determine whether the floor’s loading capability is sufficient to withstand the acceleration forces experienced by laden containers when handled by cranes. The load on the container under test must be spread uniformly on the floor so that the combined weight of the container and test load equals 2R. The container must be hoisted at the four top corners so that no significant acceleration or deceleration forces occur. The R (gross weight) and T (tare weight) components are required for this test.
Further, the racking test is conducted to verify the structural integrity of the container when subjected to racking loads during transportation via various intermodal routes such as ships and trains. The ISO procedure outlines two types of racking loads: transverse and longitudinal. In the transverse racking test, the container tank is assumed to be empty, and a load of 150 kN is applied. This test is intended to prove the ability of containers to withstand the transverse racking forces in the end frames resulting from ship movements. The container under test will be placed in unladen (tare) condition on four level pads, one under each bottom corner fitting. It shall be restrained against lateral and vertical movement using anchor devices acting through the bottom apertures of the bottom corner fittings. The concentrated load is applied simultaneously on the top corners, parallelly, or diagonally. The bottom area is securely fixed to prevent any vertical or lateral movement.
Further, the longitudinal racking test is designed to demonstrate the ability of containers to withstand longitudinal racking forces in side frames caused by ship movements. The container under test is to be placed unladen (tare) on four level pads, one beneath each bottom corner fitting, and fastened through the bottom apertures such that no vertical movement is permitted. Forces of 75 kN must be applied simultaneously to each top corner fitting at one end of the container parallel to both the side wall and the base plane.
4 FEA set up
In this section, a numerical setup for FEA by using ABAQUS software was presented. The contents cover several important steps in finite-element discretization, such as computational domain and material selection, boundary condition and applied load scenarios, mesh convergence test, and design variable of ISO tank frame. The detailed explanation of the design variable covers the load and weight calculations.
4.1 Computational domain and material selection
This investigation utilized numerical simulations through the implementation of a finite-element software package. The finite-element method, a numerical technique well-suited for digital computers, discretizes a continuous elastic structure (continuum) into smaller, finite substructures (elements). Comprehensive equations can represent these substructures. This study chose ABAQUS as the FEA tool for modelling and simulation. The process consisted of three steps: (i) The ISO tank model is discretized using SolidWorks. (ii) The material type, loading scenario, and constraints are applied to the model. (iii) A static linear analysis examines the physical effects of the aforementioned parameters.
The ISO tank’s geometry encompasses several components: the inner shell, inner baffle, outer shell, ring stiffener, and frame structure. These components are precisely modeled to replicate the dimensions of the actual tank. The material modeling of the tank assumes a linear elastic behavior that transitions into perfect plasticity. The material’s yield strength is a reference point for determining the ultimate strength, which signifies the point at which the material enters the plasticity regime. Material selection is carried out according to the requirements listed in ASME Section II [21]. The material properties of the LNG ISO tank are presented in Table 3. In this particular scenario, the SA240Gr304L-PV material is utilized for the inner tank, while carbon steel ASTM A516 is employed for the ring stiffener and outer shell. The structural frame, inclusive of the saddle supports, is constructed using a steel frame material.
Material properties of LNG ISO tank
| Materials | Elasticity properties | Plasticity properties | |||
|---|---|---|---|---|---|
| Density | Young modulus | Poisson’s ratio | Yield strength | Plastic strain | |
| ton/mm3 | N/mm2 | – | N/mm2 | – | |
| Steel frame [24] | 7.85 × 10−9 | 210,000 | 0.3 | 340 | 0 |
| SA240Gr304L-PV [21] | 7.85 × 10−9 | 193,000 | 0.3 | 175 | 0 |
| ISO corner casting [25] | 7.85 × 10−9 | 215,800 | 0.3 | 275 | 0 |
| Carbon steel ASTM A516 [9] | 7.75 × 10−9 | 200,000 | 0.3 | 248 | 0 |
4.2 Applied boundary condition and contact interaction
To decrease computational time, kinematic coupling with movement locking is implemented in the upper and lower regions. This technique involves constraining a group of nodes to follow the rigid body motion of a specific reference point. The nodes within the coupled group are effectively locked together. The kinematic coupling constraints are particularly useful in load application scenarios as they enable the coupling of continuum and structural elements. It ensures a cohesive interaction between different parts of the models, facilitating accurate load distribution. For more detailed information on the applied boundary setting is depicted in Figure 4. In the case of the bottom corner fitting, a fixed assumption is utilized as the boundary condition. It implies that the movement of the nodes in this area is completely restricted, providing a stable foundation for analysis purposes.
Applied fixed boundary conditions at the bottom corner and concentrated load scheme at the top corner casting.
As shown in Figure 5, a tie constraint is used in FEA to create a non-linear contact interaction between a cylindrical tank and an ISO tank frame structure. The forward structure and the support plate are connected by node-to-node tie constraint in the first area, which involves the front and back spherical tanks. This tie constraint guarantees a solid and dependable connection between these parts, allowing them to operate together efficiently in various situations. In the second section, a surface-to-surface tie constraint joins the bottom cylindrical tank with the saddle supports. This restriction enables a dependable and consistent connection between the tank and the supports, enabling structural integrity and reliable load transfer. These tie constraints allow the FEA study to realistically represent the contact interaction between the cylindrical tank and the ISO tank structure while accounting for each location’s particular characteristics and connectivity requirements.
Contact interaction between structural frame and cylindrical tank.
4.3 Computational mesh convergence test
The mesh convergence study aims to find the optimum mesh size that balances computation efficiency and accuracy [26,27]. This analytical method entails running FEA simulations with increasingly refined meshes. The mesh refinement can be accomplished by reducing the mesh sizes or increasing the node density within the mesh. The analysis is iterated until the results converge, exhibiting minimal changes upon further mesh refinement. The present study focused on quantifying the structural displacements to ascertain the most suitable mesh size. The finite-element simulations are conducted within a range of 40–80 mm, as depicted in Figure 6, and these are examined under various loading scenarios, including stacking, lifting, transverse, and longitudinal racking tests. The structural representation of the ISO tank utilized shell elements (S4R) for the model discretization. The convergence test is achieved with a mesh size of 50 mm, utilizing 74,890 elements, as seen in Figure 7.
Various finite-element meshing on the ISO tank structure.
Convergence assessment under different loading tests.
4.4 Design variables
This study aims to analyze the impact of different structural frame designs of the LNG ISO tank on its overall structural performance. Three specific scenarios will be examined: increasing the thickness of the frame, incorporating a support plate, and introducing saddle support. The initial design variant involves a gradual increase in frame thickness, check plate thickness, and saddle support thickness, ranging from 6 to 14 mm, as illustrated in Figure 8. A total of nine variations in frame thickness will be investigated. The loading conditions for each frame thickness model variant are outlined in Table 4.
Design variation by increasing the thickness of the frame, saddle support, and check plate.
Load scenario of frame thickness model variations
| Frame thickness (mm) | Load scenario (kN) | ||||||
|---|---|---|---|---|---|---|---|
| Stacking | Lifting | Racking (transverse) | Racking (longitudinal) | ||||
| F | 1.8R − T | 942 + ((1.8 Rg)/4) | Rg/2 | 2R − T | F | F | |
| 6 | 942 | 434 | 1,080 | 153 | 496 | 150 | 75 |
| 7 | 942 | 437 | 1,081 | 155 | 499 | 150 | 75 |
| 8 | 942 | 439 | 1,083 | 156 | 502 | 150 | 75 |
| 9 | 942 | 442 | 1,084 | 158 | 505 | 150 | 75 |
| 10 | 942 | 444 | 1,085 | 159 | 508 | 150 | 75 |
| 11 | 942 | 447 | 1,087 | 161 | 511 | 150 | 75 |
| 12 | 942 | 449 | 1,088 | 162 | 514 | 150 | 75 |
| 13 | 942 | 452 | 1,090 | 164 | 517 | 150 | 75 |
| 14 | 942 | 454 | 1,091 | 165 | 520 | 150 | 75 |
The comparison of the total weight of a 40 ft LNG ISO tank, considering the variation of frame thickness, is presented in Figure 9. Such containers are ISO containers if their maximum gross weight (R) does not exceed 36 tons based on ISO 668:2020 Series 1 freight container classification, dimensions, and ratings [28]. It is important to note that all models in this comparison have the same cargo payload of approximately 19.3 tons. The results indicate that increasing the frame thickness leads to a corresponding increase in the gross weight (R) within a range of 0.99–8.03%. While this weight increase may seem marginal, it is an important factor to consider in designing and operating LNG ISO tanks. The total weight of the tank affects various aspects, such as transportation costs, load capacity, and overall structural integrity.
Comparison of weight due to frame thickness variations.
Various model variations are considered when investigating the effects of support plates on ISO tank containers. The effect of adding support plates, with the number of plates ranging from 8 to 32, on the structural performance will be assessed. Figure 10 illustrates the six different model variations that are developed for the model with a frame thickness of 10 mm. These variations are created to evaluate how adding support plates influences structural behaviour. To assess the effect of the support plates, loading conditions are defined for each model variant, as outlined in Table 5. It is observed that the magnitude of the applied load increased with the addition of more support plates. The increase in loading magnitude can be attributed to the corresponding increase in the container’s tare weight and gross weight, which accompanies the addition of support plates.
Design variations by adding support plates.
Load scenario of various total support plates
| Total of support plate | Load scenario (kN) | ||||||
|---|---|---|---|---|---|---|---|
| Stacking | Lifting | Racking (transverse) | Racking (longitudinal) | ||||
| F | 1.8R − T | 942 + ((1.8 Rg)/4) | Rg/2 | 2R − T | F | F | |
| 8 | 942 | 444.2 | 1085.4 | 159.3 | 508.0 | 150 | 75 |
| 12 | 942 | 444.9 | 1085.8 | 159.8 | 508.8 | 150 | 75 |
| 16 | 942 | 445.7 | 1086.2 | 160.2 | 509.8 | 150 | 75 |
| 20 | 942 | 446.5 | 1086.7 | 160.7 | 510.8 | 150 | 75 |
| 26 | 942 | 447.7 | 1087.3 | 161.5 | 512.3 | 150 | 75 |
| 32 | 942 | 448.5 | 1087.8 | 162.0 | 513.3 | 150 | 75 |
The calculation of the overall weight of a 40 ft LNG ISO tank, considering the addition of support plates, is illustrated in Figure 11. It is noteworthy to emphasize that all the models included in this comparison possess an equivalent cargo payload of approximately 19.3 tons. The findings reveal that adding support plates results in a marginal increment in the gross weight (R), ranging from 0.27 to 1.66%. It is evident that the weight increase resulting from the addition of support plates is negligible compared to the increasing frame thickness.
Comparison of weight due to total support plate variations.
The saddle support system is designed to cradle and stabilize the tank, especially during transportation or storage. The saddle support is a crucial component of this frame and is located underneath the tank at specific support points. The saddle support structure is designed to distribute the weight of the tank and its contents evenly across its base. The saddle support system is connected to the tank frame or chassis, ensuring a secure and stable attachment. In the third variation, the LNG ISO tank model is varied between 1 and 4 saddle supports at the model with a frame thickness of 10 mm, as depicted in Figure 12. To assess the effects of the saddle supports, loading conditions are defined for each model variant, as outlined in Table 6. It is observed that the magnitude of the applied load increased with the addition of saddle supports. Figure 13 shows the comparison of weight components due to saddle support variations. It can be found that adding more saddle support can increase the gross weight (R) by about 1.4–4.4%.
Design variations by adding saddle supports.
Load scenario between various total of saddle support
| Total of saddle support | Load scenario (kN) | ||||||
|---|---|---|---|---|---|---|---|
| Stacking | Lifting | Racking (transverse) | Racking (longitudinal) | ||||
| F | 1.8R − T | 942 + ((1.8Rg)/4) | Rg/2 | 2R − T | F | F | |
| 1 | 942 | 437.0 | 1081.3 | 154.8 | 498.9 | 150 | 75 |
| 2 | 942 | 440.7 | 1085.8 | 159.8 | 503.5 | 150 | 75 |
| 3 | 942 | 444.2 | 1086.2 | 160.2 | 509.8 | 150 | 75 |
| 4 | 942 | 447.9 | 1087.5 | 161.6 | 512.6 | 150 | 75 |
Comparison of weight due to total saddle support variations.
5 Result and discussion
5.1 Effect of frame thickness on structural strength
The structural evaluation of an LNG ISO tank is critical to guaranteeing its safe and dependable operation. Understanding the relationship between frame thickness and stress levels is critical for designing and constructing LNG ISO tanks capable of withstanding harsh transportation and storage conditions. Manufacturers can balance structural strength and weight issues by optimizing frame thickness, assuring the tank’s safe functioning while avoiding unnecessary material. This study focused on how increasing frame thickness affected the structural strength of the ISO tank structure. The results, shown in Figure 14, indicated an intriguing relationship between frame thickness and stress levels. The stress value reduced dramatically as frame thickness increased, particularly in structural frames. This study implies that stronger frames improve structural integrity and load-bearing capacities. The stress reduction is caused by the greater stiffness and stability of the frame, which effectively distributes the applied loads more uniformly over the tank structure.
Comparison of maximum stress of different frame thicknesses under different loading scenarios: (a) stacking, (b) lifting, (c) racking (transverse), and (d) racking (longitudinal).
Among the various structural parts, the structural frame experienced the highest stress levels among all the loading scenarios because it is primarily responsible for bearing the weight of the tank and supporting its contents. The higher stress values in the structural frame highlight its critical role in maintaining the tank’s overall integrity and safety during transportation and storage. In contrast, the pressure vessel experienced the lowest stress levels. This observation can be attributed to the design and engineering considerations prioritizing the vessel’s strength and resistance to internal pressure. The pressure vessel is designed to withstand the high internal loads generated by the LNG cargo, ensuring its containment without compromising the tank’s structural integrity. Additionally, it is worth mentioning that the stress levels in the ISO corner casting, which provides connection points for the tank during transportation, fall within an acceptable range, as it is not highlighted as the component with the highest or lowest stress levels.
Compared with all loading scenarios, it can be found that stacking and longitudinal racking tests are critical load scenarios. The stacking load for the LNG ISO tank appears to be excessive. It is mostly due to the fact that under operational conditions, ISO tanks are considered differently from regular solid goods containers and, in this case, are only stacked up to a maximum of two tiers. Moreover, the largest stress reduction at the structural frame is discovered due to the longitudinal racking test in the 13.9–54.3% range compared to all examined loading scenarios in Figure 14. The longitudinal racking test results show that the ISO corner has the largest stress reduction, ranging from 9.9%. In contrast, the pressure vessel generally suffers stress increases due to stacking, lifting, and racking load. The stress increase, ranging from 9.7 to 65.4%, is subject to the largest trend due to longitudinal racking load.
Figure 15 compares all models’ safety factors in different structural locations. It is a measure that quantifies the level of safety margin or reserve strength within a structure, indicating how much it can safely handle loads beyond its design limits. In the LNG ISO tank context, the safety factor considers various factors such as material properties, design specifications, load conditions, and anticipated operational scenarios. It this case, safety factor is calculated by the ratio between occurred stress with the permissible stress of each material. The analysis demonstrates that the longitudinal racking and stacking strength tests result in a higher safety factor value for the structural frame and ISO corner casting than other load scenarios. The results of the longitudinal racking simulation are carried out using a load with a frontway direction of 75 kN at two concentration points on the top of the fitting corner.
Comparison of safety factors under different structural locations: (a) structural frame, (b) pressure vessel, and (c) ISO corner casting.
Conversely, the lifting and stacking load contribute to a higher safety factor value for the pressure vessel. Notably, structural frames featuring frame thicknesses ranging from 6 to 9 mm exhibit significantly high safety factors above 1 due to stacking and longitudinal racking tests indicating the occurred stress is higher than the yield strength of the material. It indicates that the structure possesses a substantial safety margin and is engineered to withstand loads well beyond its projected maximum capacity. The safety factor value reflects the structural robustness and substantial reserve strength of the system, installing confidence in its ability to endure applied loads and external loads without failure or compromising its integrity. In addition, the results of all load scenarios in pressure vessels and ISO corner casting are still within the safety limits in accordance with ISO regulations. In general, it is evident that an increase in frame thickness leads to a noticeable decrease in the safety factor value, particularly in the structural frame and ISO corner casting. Conversely, adding frame thickness tends to increase the safety factor for the pressure vessel.
Figure 16 comprehensively depicts the stress contour response at various structural locations resulting from the longitudinal racking test. Notably, the joint connecting the vertical frame and top support plate exhibits the most significant stress concentration within the entire structural frame. This location consistently experiences the highest stress levels across all loading scenarios, as illustrated in Figure 17. Consequently, it is advisable to reinforce the vertical and horizontal frames by incorporating supplementary supporting plates, as recommended by Muttaqie et al. [15]. Furthermore, the inner head demonstrates localized stress due to the longitudinal racking test because there is no supporting stiffener between the inner and outer head.
Comparison of stress contour due to longitudinal racking test at different structural parts with 14 mm frame thickness: (a) structural frame, (b) pressure vessel, and (c) iso corner casting.
Comparison of stress contour due to different loading scenarios at the model with 14 mm frame thickness: (a) stacking, (b) lifting, (c) racking (transverse), and (d) racking (longitudinal).
Figure 18 compares displacement values for different frame thicknesses under various loading scenarios. Generally, it can be observed that an increase in frame thickness results in a decrease in displacement values for all loading scenarios. The results indicate that increasing the frame thickness leads to a notable reduction in displacement, particularly in the structural frame and ISO corner casting. The highest displacement reduction in the structural frame can be found in the longitudinal racking test in the range of 23.3–76.6%. The highest displacement reduction in the ISO corner casting can be found in the same loading scenario with the 23.9–77.7% range. Notably, the longitudinal racking test emerges as a critical loading scenario, producing the highest displacement response among all the scenarios examined. This finding suggests that the ISO tank structure is particularly vulnerable to longitudinal forces, emphasizing the need for robust reinforcement measures to counteract these forces effectively. In contrast, the lifting strength scenario exhibits the lowest displacement response.
Comparison of displacement value of different frame thicknesses under different loading scenarios: (a) stacking, (b) lifting, (c) racking (transverse), and (d) racking (longitudinal).
The analysis of displacement contours holds paramount importance as it visually represents the magnitude and distribution of displacements across the ISO tank structure. This information identifies regions susceptible to excessive displacement or deformation, posing a risk of structural failure or compromising the overall safety of the tank. Figure 19 compares displacement contours from critical longitudinal racking tests conducted on various structural components. It is evident that the greatest displacement occurs in the structural section situated at the midpoint of the top longitudinal frame. Additionally, the inner head exhibits the highest displacement within the inner tank due to its lack of support from stiffeners. Furthermore, Figure 20 compares displacement contours resulting from different loading scenarios. The highest displacement attributable to stacking and lifting tests is observed in the upper corner of the frame. In contrast, the top portion of the structural frame displays the highest displacement overall.
Comparison of displacement contour due to longitudinal racking test at different structural parts with 14 mm frame thickness: (a) structural frame, (b) pressure vessel, and (c) iso corner casting.
Comparison of displacement contour due to different loading scenarios at the model with 14 mm frame thickness: (a) stacking, (b) lifting, (c) racking (transverse), and (d) racking (longitudinal).
5.2 Effect of support plate addition on structural atrength
The effect of the addition of support plates on structural strength is investigated. Support plates are strategically placed at critical locations within the structural frame, such as the corners or areas prone to higher stress concentrations. These components are suggested to play a crucial role in providing additional reinforcement and stability to the overall structure. Figure 21 compares maximum stress levels for different total support plate configurations under various loading scenarios. The findings indicate that adding support plates does not significantly influence the structural strength of LNG ISO tank containers. However, the presence of support plates effectively enhances the structural integrity of the framework by mitigating longitudinal racking, as depicted by the decrease in obtained stress. Adding support plates due to longitudinal racking can decrease the stress to 20.4% in the structural frame and 19.7% in the pressure vessel. In contrast, ISO corner casting experiences a stress increase of up to 23.2% due to longitudinal racking.
Comparison of maximum stress of various total support plates under different loading scenarios: (a) stacking, (b) lifting, (c) racking (transverse), and (d) racking (longitudinal).
Moreover, the structural frame experiences a slight reduction in stress when subjected to stacking, lifting, and transverse racking loads. Conversely, the addition of support plates can increase the safety factor in the pressure vessel and ISO corner casting, particularly during lifting and stacking strength tests, as seen in Figure 22. The load distribution becomes more balanced throughout the structural frame by incorporating support plates. This balanced load distribution helps minimize localized stress concentrations and ensures the container can withstand operational loads.
Comparison of the safety factors of various total support plates under different structural locations: (a) structural frame, (b) pressure vessel, and (c) iso corner casting.
Figure 23 presents a comprehensive illustration of the stress contour response at various structural locations resulting from the longitudinal racking test at the model with 32 total support plates. Notably, the joint connecting the vertical frame and top support plate exhibits the most significant stress concentration within the entire structural frame. This location consistently experiences the highest stress levels in stacking, lifting, and transverse racking tests, illustrated in Figure 24. In addition, the highest stress in the frame due to longitudinal racking is experienced in the check plate. Furthermore, the inner head demonstrates localized stress due to the longitudinal racking test because there is no supporting stiffener between the inner and outer head.
Comparison of stress contour due to longitudinal racking test at different structural parts of the model with 32 total support plates: (a) structural frame, (b) pressure vessel, and (c) ISO corner casting.
Comparison of stress contour due to different loading scenarios at the model with 32 total support plates: (a) stacking, (b) lifting, (c) racking (transverse), and (d) racking (longitudinal).
Figure 25 presents a comparative analysis of displacement values for different total support plate configurations under various loading scenarios. Notably, the longitudinal racking test emerges as a critical loading scenario, exhibiting the highest displacement response in the structural frame compared to other scenarios. It is evident that an increase in the number of support plates generally corresponds to a decrease in displacement values. The results clearly indicate that adding the support plate configuration significantly reduces displacement, particularly in the transverse and longitudinal racking tests. It can be found that the highest displacement reduction due to transverse racking load can be found in the structural frame between 7.5 and 27.8%. In addition, the highest displacement reduction due to longitudinal racking can be found in the structural frame in the range of 7.2–23.9%. Further, this reduction in displacement is consistently observed in the ISO corner casting and pressure vessel across all evaluated loads. However, it should be noted that adding support plates can result in increased displacement in structural frames during stacking and lifting loads. It is projected to increase displacement in the structural frame by about 12.5–32.4% in stacking load and about 16.3–35.4% in lifting load. This displacement shift occurs due to the redistribution of stresses, causing the highest displacement to transition from the top corner area to the middle of the top structural frame.
Comparison of displacement value of different total support plates under different loading scenarios: (a) stacking, (b) lifting, (c) racking (transverse), and (d) racking (longitudinal).
Figure 26 compares displacement contours from critical longitudinal racking tests conducted on three structural components. The greatest displacement occurs in the structural frame situated at the midpoint of the top longitudinal frame. Additionally, the bottom of the inner tank exhibits the highest displacement. Furthermore, Figure 27 compares displacement contours resulting from different loading scenarios in the model with 32 total support plates. Adding a support plate in the structural frame due to stacking and lifting loads causes the highest displacement shifting from the upper corner area to the middle point of the structural frame.
Comparison of displacement contour due to longitudinal racking test at different structural parts at the model with 32 total support plates: (a) structural frame, (b) pressure vessel, and (c) ISO corner casting.
Comparison of displacement contour due to different loading scenarios at the model with 32 total support plates: (a) stacking, (b) lifting, (c) racking (transverse), and (d) racking (longitudinal).
5.3 Effect of saddle support on structural strength
In the third variation, the effect of saddle support on the structural strength is investigated. Figure 28 compares the maximum stress of various total saddle supports under different loading scenarios. The results show that adding saddle support does not significantly affect the structural strength of LNG ISO tank containers. The stress reduction displayed in Figure 28 illustrates how the implementation of saddle support substantially improves the structural integrity due to longitudinal racking load tests. It is discovered that the structural frame experiences a stress reduction of between 4.9 and 5.4% as a result of the installation of saddle support, the pressure vessel experiences a stress decrease between 13.9 and 31.8%, and the ISO corner casting experiences a stress reduction between 4.6 and 5.5%. The addition of saddle support significantly affects the pressure vessel stress because the saddle support structure is designed to distribute the weight of the pressure vessel tank. Moreover, when stacked loads are applied, the stress in structural frame stress slightly decreases, notably in ISO corner casting. In contrast, the model has no stress reduction due to lifting and transverse racking tests. Moreover, the highest stress in the structural frame in all evaluated loading tests is experienced in the check plate, as seen in Figure 29.
Comparison of maximum stress of various total saddle supports under different loading scenarios: (a) stacking, (b) lifting, (c) racking (transverse), and (d) racking (longitudinal).
Comparison of maximum stress due to different loading scenarios at the model with four saddle supports: (a) one saddle support, (b) two saddle support, (c) three saddle support, and (d) four saddle support.
A comparison of displacement values for various saddle support systems under various loading conditions is shown in Figure 30. Notably, the longitudinal racking test exhibits the largest structural frame displacement response compared to other loading scenarios, making it a crucial loading scenario. It is evident that a decrease in displacement values often follows an increase in the number of saddle supports. The findings show that adding the saddle support causes a significant decrease in displacement, particularly in the longitudinal racking test. The pressure vessel exhibits the greatest displacement decrease caused by longitudinal racking load, with values between 53 and 71%. Furthermore, the displacement reduction carried on by longitudinal racking is 4.9–55 and 7.7–10.7%, respectively, in the structural frame and ISO corner casting. It is important to note that the installation of saddle supports may cause a slight increase in displacement in structural frames, pressure vessels, and ISO corner castings subject to stacking and lifting loading scenarios (Figure 31).
Comparison of displacement of various total saddle supports under different loading scenarios: (a) stacking, (b) lifting, (c) racking (transverse), and (d) racking (longitudinal).
Comparison of displacement of various total saddle supports under different loading scenarios: (a) one saddle support, (b) two saddle supports, (c) three saddle supports, and (d) four saddle supports.
5.4 Relationship between structural strength and gross weight
Figure 32 depicts the relationship between structural strength and total gross weight in the longitudinal racking test, exhibiting three different techniques. Following the study, it is clear that increasing the frame thickness of the LNG ISO tank is a more practical choice than installing saddle supports and support plates. Increased frame thickness substantially reduces stress and displacement, outperforming the benefits of saddle support. Furthermore, the addition of support plates significantly reduces stress and displacement, albeit it is important to note that model modifications are limited.
Relationship between obtained stress and displacement with total gross weight: (a) stress and (b) displacement.
This finding highlights the significance of evaluating frame thickness as a viable solution for improving the structural strength of LNG ISO tanks. By taking this method, the tank’s overall performance can be improved, resulting in lower stress and displacement levels. This outcome offers various advantages, including lowering the danger of structural failure and assuring safe LNG delivery.
It is essential to recognize that the decision-making process should take into account aspects other than stress and displacement reduction. Other considerations include cost-effectiveness, manufacturing ability, and the overall structural integrity of the tank. Nonetheless, based on the findings in Figure 32, increasing the frame thickness appears to be a promising option for improving the structural strength of LNG ISO tanks and needs additional investigation and evaluation.
6 Concluding remarks
A series of numerical analyses are conducted to evaluate the effect of frame design on the weight-saving and structural strength of 40 ft LNG ISO tank. The effect of frame thickness, saddle support variations, and support plate variations of LNG ISO tanks are evaluated. Compared to all evaluated loading conditions, it can be found that the stacking and longitudinal load tests are critical load scenarios. Several frame designs have a larger stress than yield stress. As a result, it is required to enhance the design to increase the safety level. Higher frame thickness can increase the structural performances of the structural frame and ISO corner casting. In contrast, the pressure vessel typically suffers stress increases. It can be found that the ISO tank model with a frame thickness ranging from 6 to 9 mm exhibits safety factors above 1, indicating the recommended frame thickness is above 9 mm.
Moreover, the structural integrity of the LNG ISO tank is normally not significantly affected by the addition of support plates. There is a small stress decrease when the structural frame is subjected to operational loads. Support plates added under longitudinal racking can reduce stress in the structural frame and pressure vessel by up to 20.4 and 19.7%, respectively, but can increase stress in ISO corner casting by up to 23.2%. Support plates impose greater stress on the pressure vessel and ISO corner casting, especially when lifting and stacking strength tests. The ISO corner casting and pressure vessel displacement are also consistently reduced across all investigated loads. The addition of saddle supports significantly reduces the stress and displacement on the pressure vessel, particularly in the longitudinal racking test. The pressure vessel experiences the highest stress and displacement reduction at 13.9–31.8 and 53–71%, respectively.
The design optimization of frame design by numerical simulations by using several optimization methods, such as shape, size, and topology optimization, is one of the important aspects for future studies. Design optimization is an important parameter in developing the frame design of an LNG ISO tank to produce lighter structural designs while maintaining structural performance.
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Funding information: All authors would like to thank the RISPRO-LPDP Ministry of Finance of the Republic of Indonesia for funding this research through the Research and Innovation for Advanced Indonesia (RIIM) batch 3 scheme with contract number B-839/II.7.5/FR.06/5/2023. The corresponding author would like to thank the Postdoctoral Fellowship Program at the Hydrodynamic Technology Research Center of the National Research and Innovation Agency (BRIN) with contract No.64/II/HK/2022.
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Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.
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Conflict of interest: The authors state no conflict of interest.
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