Evaluation of the Structural Suitability of Lifting Trunnions in Large Pressure Vessels

Pressure vessels comprise most of the equipment used in the petroleum, chemical, nuclear, and energy industries and many others. Pressure vessels are usually spherical or cylindrical in shape and have curved ends. They are equipped with openings or nozzles with means of flange connections and various means for supporting and lifting the pressure vessel. Weighing up to 1000 metric tons, large pressure vessels are much heavier than typical pressure vessels.

To predict the failure of the lifting components, several analyses must be performed. The design and analysis of lifting trunnions are not explicitly covered in ASME’s Boiler and Pressure Vessel Code (BPVC) Section VIII, Division 1 [1]. Welding Research Council Bulletin 107 (WRC 107) was originally developed to address the need for accurate, simplified methods to evaluate the localized stresses induced in pressure vessel shells by attachments such as lifting lugs, trunnions, and piping nozzles. This work serves as a critical validation of the WRC 107 methodology by comparing its results with those obtained from advanced finite element analysis (FEA). The strong correlation between the WRC 107 and FEA results, particularly in the context of heavy lifting scenarios involving trunnions, underscores the accuracy and reliability of WRC 107, reinforcing its continued use in industry practices where ASME’s BPVC Section VIII, Division 1 guidelines may not provide explicit coverage.

The analysis of stress distribution in cylindrical shells has been a fundamental aspect of pressure vessel design, particularly under symmetrical loading conditions. Bijlaard’s [2] pioneering work provided a deep understanding of stress distribution in cylindrical and spherical shells, which has been foundational in developing design standards. Another significant contribution in this field was made by Wichman et al. [3], whose work on local stresses in spherical and cylindrical shells resulting from external loadings, as documented in WRC 107, remains a critical reference. This bulletin provides detailed methods for calculating local stresses induced by external loadings, such as those from attachments such as lifting lugs and trunnions, which are crucial for ensuring the structural integrity of pressure vessels under operational and other extreme conditions. Wichman et al. [3] further contributed to this field by providing detailed guidance on evaluating these local stresses in WRC 107.

Membrane theory simplifies stress analysis in thin-walled pressure vessels by assuming uniform stress distribution across the vessel wall. However, real-world complexities, such as nonuniform loading and geometric imperfections, often require the use of more advanced analytical methods. Sanders and Simmonds [4], in his 1970 study, “Concentrated Forces on Cylindrical Shells,” highlighted the significant stress concentrations that occur when concentrated forces are applied to cylindrical shells. This work demonstrated that while membrane theory provides a good baseline, the presence of concentrated forces necessitates more detailed analysis to account for localized stress concentrations. Xue et al. [5] extended this understanding by integrating thin-shell theory with FEA to analyze stress distributions in cylindrical shells, particularly at intersections with nozzles under various loading conditions. Their findings showed that while membrane theory provides a solid foundation, it must be supplemented with FEA to accurately capture complex stress distributions in practical applications.

Local stress analysis in pressure vessels, especially of stresses caused by external loadings, has been a significant focus of research. The studies by Brooks [6,7] and Williams [8] have been particularly influential in developing boundary integral analysis methods to model stress concentrations around attachments such as lugs and trunnions. These methods are crucial for understanding how stress concentrations develop during lifting and transportation and indicate where the interface between the vessel shell and the attachments is particularly vulnerable to failure. Sanders and Simmonds [4] also provided critical insights into how concentrated forces impact cylindrical shells, contributing to a more refined understanding of local stress analysis. This work emphasized the importance of considering these concentrated forces in design calculations to prevent structural failures in pressure vessels.

Finite element analysis has become a cornerstone in modern stress analysis for pressure vessels. Researchers such as Skopinsky [9] and Porter et al. [10] used FEA to model the complex interactions between vessel shells and lifting components. Their work demonstrated the effectiveness of FEA in predicting potential failure points, especially in large, heavy pressure vessels where traditional analytical methods may fall short. These studies, in addition to validation against experimental data, highlighted FEA’s critical role in enhancing the accuracy and reliability of pressure vessel design, particularly when assessing the risks associated with external loadings. Kalnins and Updike [11] studied the analysis of stress in pressure vessels by focusing on stress evaluation in the vicinity of nozzle connections. Their study provided critical insights into the stress concentrations that occur at these critical junctions, particularly when subjected to combined loading conditions.

The application of external loads, such as those encountered during lifting operations, introduces significant stress concentrations in pressure vessels, particularly at attachment points. The present work builds on the foundational work of Bijlaard, Wichman et al., Sanders, Brooks, Williams, and others by using FEA to simulate the stresses encountered during lifting. Vertical load cases are particularly critical because of the high stress concentrations they generate at attachment points such as lifting lugs and trunnions. The simulation results aligned closely with those from the theoretical models provided by WRC 107, particularly for circumferential, longitudinal, and shear stresses, confirming the reliability of WRC 107 as a tool for predicting and mitigating lifting-related risks.

Stress analysis is the determination of the relationship between external forces applied to a vessel and the resulting stress. Pressure vessels are commonly shaped as spheres, cylinders, cones, ellipsoids, or combinations of these. When the thickness is small in comparison with other dimensions (R_m/T > 10), vessels are referred to as membranes, and the associated stresses resulting from the contained pressure are called membrane stresses. These membrane stresses are average tension or compression stresses. They are assumed to be uniform across the vessel wall and act tangentially to its surface. The membrane or wall is assumed to offer no resistance to bending. When the wall offers resistance to bending, bending stresses occur in addition to membrane stresses. In any pressure vessel subjected to internal or external pressure, stresses are set up in the shell wall. The state of stress is triaxial, and the three principal stresses are longitudinal/meridional stress, circumferential/hoop stress, and radial stress. In certain cases, the contact stresses are created when the surfaces of two bodies are pressed together by external loads.

The principal stresses at or on the contact area between the two curved surfaces that are pressed together are greater than at a point located beneath the contact area. The problem considered here initially was to determine the maximum principal and shear contact stresses beneath the contact area between two ideal elastic bodies having curved surfaces that are pressed together by external loads. However, the effect of complex lifting scenarios as a result of heavy lifting introduces additional challenges that extend beyond basic membrane stress analysis. During the lifting of large pressure vessels, particularly those with irregular shapes or multiple lifting points, nonuniform load distribution can result in significant deviations from the idealized membrane stress state. These deviations can lead to localized bending, shear stresses, and stress concentrations at critical points, such as at lifting lugs and trunnions. Additionally, dynamic effects such as acceleration, deceleration, and the angle of lift further complicate the stress analysis. Understanding and predicting these complex stress interactions require advanced simulation techniques such as elastoplastic FEA, which can model the behavior of the vessel under these multifaceted loading conditions. Addressing these complexities is essential to prevent failures during lifting operations and ensure the structural integrity of the vessel throughout its handling and transportation.

Stresses caused by external local loads are a significant concern to designers of pressure vessels. The techniques for analyzing local stresses and the methods of handling these loads to keep these stresses within prescribed limits have been the focus of much research. Various theories and techniques have been proposed, and experimental testing has been used to investigate and verify the accuracy of the solutions. Stresses should be considered in the shell at the attachment points to the shell junctures in both the circumferential and longitudinal directions, as shown in Fig. 1.

The present work assesses the determination of the critical regions in the lifting trunnion at different load cases. The lifting device was analyzed using FEA and the ASME’s BPVC Section VIII, Division 1 methodology for stress evaluation under the prescribed lifting load conditions. The FEA results were verified using theoretical results, and the results were in good agreement with WRC 107. The analysis centered on the vessel itself and the attachment points, where stress concentrations are most critical. Nevertheless, the associated lifting gears, for instance, the crane hook, being part of a standardized and certified lifting system are assumed to meet all relevant safety and operational standards.

Static stress analysis was used to solve the displacement and stress under the action of the applied loads. The primary objective of this static analysis was to determine the critical regions in the lifting trunnion in the vertical load case. The vertical load is considered to be the governing load case. Other loading cases such as horizontal and inclined position lifting have been considered appropriately for the purposes of this analysis. Usually for large vertical vessels, the forces on 10 deg incremental would have to be checked; however, for the purpose of this analysis, only three conditions have been evaluated. To consider the effect of the critical load condition for a lifting trunnion mounted on the primary lifting device, the material properties and loadings provided in Table 1 have been assumed.

Static FEA was conducted using ansys on a half-symmetric model of the trunnion to assess its structural integrity. The choice of a half-symmetric model enables a more efficient analysis to be performed while maintaining the accuracy of the results. The dimensions of the half model used in the analysis are detailed in Fig. 2. For the modeling of the components, eight-node solid elements were used, which provided a high degree of accuracy in capturing the stress distribution and deformation characteristics of the trunnion under the applied loads. This approach ensured that the analysis results would be both reliable and reflective of real-world conditions.

Given the significance of the Bijlaard methodology [2] in assessing the local stresses in cylindrical and spherical pressure vessels, this section introduces the Bijlaard parameters and details the process for calculating circumferential and longitudinal stresses. These calculations are crucial for understanding the structural integrity of vessels subjected to localized loadings, particularly around nozzles or other attachments. The Bijlaard parameters are dimensionless quantities that relate the geometry of the pressure vessel and its attachments to the stress distribution within the vessel wall. These parameters simplify the complex stress equations by normalizing the dimensions of the vessel and attachments, making it easier to apply standard curves and formulas.

where N_p is the circumferential force per unit length, representing the internal force acting along the circumference as a result of internal pressure, and P is the internal pressure exerted within the vessel.

While generally lower than hoop stress, longitudinal stress is still important for the overall structural integrity of the vessel, especially in regions near nozzles and other attachments where stress concentrations can occur.

where N_x is the longitudinal force per unit length, representing the internal force acting along the vessel’s length as a result of internal pressure.

Figures 3C and 4C in WRC 107 are essential tools in applying the Bijlaard methodology to real-world scenarios involving pressure vessels:

• Figure 3C provides a nondimensional curve that represents the circumferential membrane force N_θ for different configurations of radial loads. By using the Bijlaard parameters γ and β, Fig. 3C enables the precise calculation of hoop stress in the vessel wall.

• Figure 4C offers a similar curve for the longitudinal membrane force N_x, which is essential for calculating longitudinal stress in the vessel. The application of Fig. 4C, in conjunction with the parameters γ and β, facilitates accurate stress analysis around nozzles and attachments where stress concentrations are likely. The integration of Bijlaard parameters γ and β into the stress analysis process provides a robust framework for assessing the structural integrity of pressure vessels subjected to localized loadings.

Heavy pressure vessels are typically fitted with two lifting trunnions, and the vertical lifting of the vessel represents the most critical loading condition, with each trunnion bearing exactly half of the vessel’s total weight. Along the side faces of the trunnion pad, the translational displacements around all axes were restrained. Symmetric boundary conditions, as applicable, were imposed along the model edges, which lie on the vertical plane. Because of the symmetry, a load of 1086.397 kN—which is the half load of 2172.794 kN—was applied at the center node of the trunnion. This center node is connected to the remaining nodes at the circumference of the trunnion by multipoint constraint elements. Figure 3 shows the meshed model of the lifting trunnion with the applied boundary conditions.

In this section, the results obtained from the WRC 107 analysis and those derived from FEA for the structural evaluation of lifting trunnions in large pressure vessels are provided and compared in Table 2. The purpose of this comparison is to validate the accuracy and reliability of WRC 107 in predicting stress concentrations and to identify any discrepancies that could arise when using FEA, which is known for its detailed and comprehensive analysis capabilities.

Figure 4 shows the stress distribution resulting from the 2172.794 kN load at the free end of the trunnion. Because of symmetry, a load of 1086.397 kN, which is half of the full load of 2172.794 kN, was applied at the center node of the trunnion. The maximum longitudinal stress of 24.78 MPa was observed in the middle portion of the trunnion. There was an equal and opposite stress at the diametrically opposite corner. Figure 4 shows the circumferential stress variation at the 0 deg lifting position. The maximum circumferential stress of 21.956 MPa was observed in shell trunnion junction, and there was an equal and opposite stress at the diametrically opposite corner. At the location of peak circumferential stresses (i.e., at the top and bottom sides), a difference of 2.855 MPa was observed at the trunnion and 3.883 MPa at the trunnion pad, further highlighting the close alignment between the theoretical predictions and FEA results. The longitudinal stress measurements at the peak stress locations revealed a difference of 5.182 MPa at the trunnion and 5.924 MPa at the trunnion pad. These findings further substantiate the strong correlation between the theoretical predictions and the results obtained from FEA. For shear stresses, the values obtained from FEA were significantly less than the theoretical values. This is because the force and moment values taken from the graph in WRC 107 may not be exact because of the constraints of the scale used.

Critical regions in the lifting trunnion are identified for the vertical load case. The lifting attachments are assumed to be welded to the cylindrical shells with full penetration weld. The effect of welding was not included in the analysis. The exact locations of the peak stress in the trunnion pads have been determined. The theoretical and FEA results of circumferential, longitudinal, and shear stresses on the shell for various lifting positions of the lifting trunnion have been compared. The results align well with WRC 107 and show a strong correlation between the theoretical predictions and FEA outcomes. This evaluation helps to identify the proper geometry of lifting trunnions to avoid any failures in pressure vessel lifting trunnions. The strong correlation between the WRC 107 and FEA results demonstrates the accuracy and reliability of WRC 107, reinforcing its continued use in industry practices in heavy lifting scenarios.

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.