Effect of Pad Thickness and Width Variations on Plastic Limit Moment in Cylindrical Pressure Vessels Due to Nozzle In-Plane Load

This study investigates how different pad thicknesses and diameters affect the maximum stress a cylindrical pressure vessel can handle without failing, particularly around the areas where nozzles are attached. Nozzles on these vessels often face directional stress from loads applied in a specific plane, and these stresses mustn’t push the nozzle material beyond its breaking point. The research used computer simulations to see how these vessels, with various pad sizes and a set shell and nozzle size, behave under increasing stress until they reach their breaking point. Findings indicate that making the pad thicker or wider increases the vessel’s resistance to breaking up to a certain point; beyond this optimal size, making the pad larger doesn’t provide any additional benefit. This information helps design better and safer pressure vessels by identifying the best pad size to prevent failure. The study contributes to understanding how to avoid design issues and optimize the construction of these vessels, adhering to specific industry standards.


Introduction
Pressure vessels are commonly used in process industries such as oil and gas exploitation and production, petrochemicals, power plants, and food and beverages.A pressure vessel is a closed container that holds fluid pressure from the inside (internally) and from the outside (externally).Pressure vessels will experience various load variations in their operation.The loads consist of internal loads from the working fluid and external loads from outside the pressure vessel.These loads will cause stress on the parts of the pressure vessel.The external loads of pressure vessels include wind, earthquake, nozzle loads, lifting lugs, supports, etc.The pressure vessels are designed to withstand combined loads during their operation.In addition to that, the design factor is added to the stress limit, so the pressure vessel always works below its maximum load.When the pressure vessel is overloaded, the stress in its critical section will exceed the maximum limit then the pressure vessel will fail.The failure of the pressure vessel will cause leakage and further structural damage, which can result in worker safety incidents, environmental pollution, and equipment damage.
The design of pressure vessels referring to the ASME Code Section VIII Div 2 [1] can use two methods: design by rules and design by analysis.The design method with rules provides design rules for pressure vessels with commonly used shapes under simple pressure loading within certain limits, regulations, or guidelines for other loading treatments.In comparison, the analytical design provides a detailed design procedure that utilizes the results of the stress analysis for the design of special cases such as pressure vessels with large nozzles, pressure vessels with a large number of nozzles, etc.An analytical design procedure is provided to evaluate components for anticipating plastic collapse, local failure, buckling loads, and cyclic loading.
A failure in pressure vessels occurs when the stress in the critical region exceeds the yield limit (plastic), resulting in plastic deformation of the critical part.And furthermore, it causes failure in the form of cracks and leaks.To avoid failure during operation, ASME Section VIII requires the design load to be at least two-thirds of the plastic limit load.This underlies the importance of determining the plastic limit load in the pressure vessel design process [2] [3].
ASME Section VIII describes the determination of the experimental plastic limit load.Mackenzie [4], in his paper, mentions that the determination of the plastic limit load is known as the Twice-Elastic-Slope (TES) method or the Double Elastic Slope Method.In order to confirm the effectiveness of determining the plastic limit load using the finite element method, Sang et al. [5] conducted a comparative study to compare the results of the plastic limit load with the ASME experimental method and the finite element simulation method.It was concluded that the results of determining the plastic limit load with the experimental method and the finite element method were in agreement.ASME Section VIII recommends the installation of pads in critical areas such as nozzle and cylinder junctions to reduce stress.A pad is a sheet of metal affixed around the junction of the nozzle and cylinder to strengthen the part.The pads that ASME recommends have a volume proportional to the volume of metal removed in the cylinder perforation process to attach the nozzle.In addition to pad size, Sang et al. [5] also showed that variations in cylinder size, nozzle, and thickness have an effect on the plastic limit load.In order to find out the optimum size and thickness of cylinders, nozzles, and pads, Ginting [2] conducted a study to determine the plastic limit load on pressure vessels with various sizes and thicknesses of cylinders, nozzles, and pads.The applied load is the out-of-plane bending moment load at the nozzle, as conducted by Sang et al. [5].Based on the information provided, it appears that Ginting [2] has concluded that the plastic limit moment of a cylindrical pressure vessel increases as the thickness of the pad increases.The plastic limit moment will reach the maximum plastic limit at the optimal pad thickness, where the increase in pad thickness no longer affects the change in the plastic limit moment.Likewise, for the optimal pad diameter, increasing the pad diameter beyond the optimal pad diameter does not affect the change in the plastic limit moment.The final conclusion is that the larger the shell thickness (T) and/or nozzle diameter (di) in the cylindrical pressure vessel, the greater the plastic limit moment.
Under operational conditions, the load on the nozzle is not always an out-of-plane bending moment.There are times when the loading that occurs is an in-plane bending moment.Mackenzie [4], in his research, showed that the out-of-plane bending moment provides a lower plastic limit load than the inplane bending moment.However, in his study, Mackenzie [4] only used the finite element method on cantilever rods with bending moment loads.To confirm the suitability of the calculation of the plastic limit load on the pressure vessel with the in-plane bending moment load on the nozzle, Sang et al. [6] conducted experimental research and the finite element method on pressure vessels with a nozzle.The findings indicated that the finite element method for calculating the plastic limit load on a pressure vessel was consistent with the experimental approach.Based on these studies, the magnitude of the different plastic limit moments at different loading directions is suspected to affect the optimum size and thickness of the shell, nozzle, and pad.
Therefore, research is needed to prove the effect of loading direction on the dimensions and thickness of the optimal shell, nozzle, and pad on pressure vessel design.
A finite element analysis (FEA) was used to examine the effect of the bending moment direction on the optimal pad geometry.An investigation is carried out on various models with certain geometric variations to observe the effect of geometry on the plastic limit moment.Geometric variations that will be carried out in this study include the thickness and diameter of the pad.
Simulations are carried out to determine the plastic limit load of pressure vessels due to external loads received on various variations of models.It is expected that at a certain geometry, the plastic limit load is no longer affected by changes in geometry.Under these conditions, the shell, nozzle, and pad geometry are considered the optimum.The optimum geometry will then be compared with the optimum geometry in the previous study, which was subjected to non-plane bending moment loading on the nozzle.
The scope of the problem to be studied and the assumptions to be used are as follows.The shape of the pressure vessel model is in accordance with the experimental construction of Sang et al. [6].The plastic limit load is determined using the double elastic slope method according to ASME Section VIII Div 2 [1].Only the loading due to the bending moment on the cylindrical pressure vessel nozzle is considered in this study.The effects of earthquake loads and internal loads due to fluids are not considered in this study.This study does not use analytical analysis with a mathematical formula to determine the amount of plastic limit load (moment) on a cylindrical pressure vessel.In determining the load (moment) of the plastic limit, this study did not consider the influence of other cylindrical pressure vessel parts such as the head, lug, skirt, and saddle.
This study aimed to assess how modifications to the geometry of the pad impact the plastic limit of the in-plane moment.Furthermore, it is expected to evaluate the loading direction to optimum pad geometry.

Research Method
This study aims to analyze how the pad geometry of the pressure vessel nozzle influences the plastic limit load resulting from external forces.This study uses a finite element analysis method using Autodesk Inventor software to create a pressure vessel 3D model and ANSYS software to perform simulations.The simulation result is a load-deformation curve.According to Skopinskii [7] [8], one way to determine the plastic limit load is by using a twice-elastic slope, as illustrated in Figure 1.To obtain the load (q) limit, the point at which the load-deformation curve intersects with a line having a gradient twice that of an elastic line is identified.If the gradient of elastic limit is considered as θ, the plastic load limit will be determined by a double-elastic line with a gradient of ϕ.Which tan ϕ = 2 tan θ.The gradient of the elastic line is determined by linear regression.The plastic limit load is the ordinate of the point of intersection of the double elastic slope straight line with the load-deformation curve in the plastic region.Three sets of pressure vessels were analyzed, as shown in the model Figure 2 and Table 1.The variation of pad thickness (Tp) on pressure vessel #1 with shell thickness (T) of 8 mm is shown in Table 2. Variations of pad diameter (dp) on pressure vessel set #2 with the nozzle inside diameter (di) 86mm, shell thickness (T) 8 mm, and pad thickness (Tp) 10 mm are shown in Table 3.The material of the pressure vessel and pad is steel Q235 (low carbon steel, equivalent to ASTM A36), and the nozzle is steel 20 (low carbon steel, equal to ASTM A106 Gr.A), as shown in Table 4. Furthermore, Table 5 displays the proportions of chemical composition and mechanical properties.
The weld type in the longitudinal shell is a single V-groove butt joint, as illustrated in Figure 3. Single bevel between nozzle and shell, fillet weld between shell and pad.
An investigation was conducted to analyze how the thickness or width of the pad influences the plastic limit moment resulting from the load on the nozzle, using elastic and plastic non-linear finite element analysis.The pressure vessel 3D model was made with Autodesk Inventor, and the simulation of the finite element analysis method was carried out using ANSYS software.Material engineering data is input into the ANSYS software, and models are imported from Autodesk Inventor.After importing the geometry model, meshing is conducted on the pressure vessel, pad, and nozzle, as illustrated in Figure 4.
The boundary conditions on the pressure vessel model in this finite element analysis simulation are that the lower side of the pressure vessel is in a fixed condition, and the upper side is in a free condition.In addition, the chemical composition and mechanical properties are presented in Table 5. External loading is carried out at the tip of the nozzle by adding moments gradually (incrementally) with the initial load (to) being M0 = 0 kN.m, at 1 second (t1), M1 = 1 kN.m, 2 seconds (t2), M2 = 2 kN.m and so on as shown in Table 6.The ANSYS software will adjust the loading in a way that the initial load occurs at time t0 or the beginning of the loading, and the next step occurs at t1 or the 1st second with a load of 1 kN.m and so on.

Result and Discussion
The finite element simulation results will provide stress (σ) and deformation (δ) at the location of the points shown in Figure 6 for the distribution of the plastic area in the pressure vessel, the plastic moment (load) (Mp) due to variations in pad thickness (Tp) and pad width (dp) due to the loading in the nozzle towards the top of the image plane (Y axis).It should be noted that moments like this usually occur during the installation of the spool pipe, which is forced into the pressure vessel nozzle during the installation of the piping system with the pressure vessel.This section will cover the discussion of stress (σ), deformation (δ), distribution of plastic area, the moment at the limit (Mp), moment of plastic limit (MpL), thickness, and width resulting from loading at the nozzle.These findings are obtained through finite element analysis simulations using ANSYS software.For model validation purposes, a pressure vessel simulation is developed with a shell thickness (T) of 500 mm, pad thickness (Tp) of 0 mm, pad width (dp) of 0 mm, nozzle thickness (t) of 3 mm, and inner nozzle diameter (di) of 86 mm.Then the yield stress is obtained in the nozzle area and around the nozzle and shell branches, as shown in Figure 7, which represents the stress contour due to loading of 8 kN.m. Figure 7 shows that the maximum stress is 354.22 MPa and indicates that the plastic deformation starts from the nozzle and moves to the pad and shell around the junction between the nozzle and the shell.While the deformation due to loading is shown in Figure 8, the maximum elastic strain occurs at the same location of 0.00382 mm/mm.
In order to determine the moment (load) of the plastic limit (MpL), the double elastic slope method is used, as described above.The simulation results get a moment and deformation curves, and then a regression line is drawn from the original point following the elastic line at the moment-deformation curve, and the double elastic slope line from the original point intersects the moment-deformation curve in the plastic region, then Figure 9 is obtained as shown below.
The plastic limit moment (MpL) is 5.9 kN.m from the double elastic slope method above.Referring to the experimental method of Sang et al. [6], the plastic limit moment is 5.5 kN.m.The deviation between the model and the experimental result is about 7%.It is considered acceptable since the reference paper uses using acceptable deviation below 10%.Furthermore, considering the acceptable design limit of ASME Section VIII, such as two-thirds of the plastic load limit, such deviation below 10% is considered sufficient.In addition to that, comparing the plastic limit moment on an un-padded nozzle with the one that is simulated by Ginting [2], it is shown that the plastic limit of the out-of-plane moment is lower such as 4.48 kN.m.Based on the plastic moment limit curve with pad thickness variation that is shown in Figure 10, it is shown that the plastic moment limit increases with a thicker pad.However, at specific points, such as the thickness of 8 mm, the addition to pad thickness is no longer increasing the plastic moment limit.The plastic moment limit seems to be unchanged with pad diameter variation, as illustrated in Figure 11.Comparing the result with Ginting [2], it is observed that the optimal pad geometry for the in-plane moment is similar with out of the plane moment.

Conclusion
The conclusions drawn from the research are as follows: Firstly, the plastic limit moment (MpL) of a cylindrical pressure vessel increases as the pad thickness (Tp) increases.However, there is an optimal thickness at which the MpL does not increase further.This occurs when the maximum plastic stress is reached on the pad due to external loads at the nozzle tip.Secondly, the pad diameter (dp) does not significantly impact the MpL of a cylindrical pressure vessel.Thirdly, the plastic limit moment (MpL) for in-plane moment loading is higher than out-of-plane moment loading in un-padded nozzles.Finally, the plastic limit moment (MpL) significantly improves with nozzle pads, making the MpL for in-plane and out-of-plane moments similar.

Figure 2
Figure 2 Pressure Vessel Illustration [2] Table 1.Pressure Vessel Dimension Parameter Dimension Vessel inside diameter (Di) 500 mm Vessel Length (L) 1000 mm Vessel thickness (T) variation Pad thickness (Tp) variation Pad diameter (DP) variation Nozzle Length (l) 1000 mm Nozzle inside diameter (di) 86 mm Nozzle thickness (t) 3 mm Distance nozzle center line to end of the vessel (Li = 0.5L) 500 mm

Figure 6 .
Figure 6.Location of the measurement point on the pressure vessel

Table 2 .
The model with Pad Thickness Variation (mm)

Table 3 .
The model with Pad Diameter Variation (mm)