Determination of the minimum thickness of pressure vessel heads and influencing factors

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GB150.1~150.4-2011 \"Pressure Vessels\" is the authoritative design standard for pressure vessel design in China. Knowing how to appropriately select the thickness of pressure vessels in accordance with this standard to meet the strength requirements of the equipment is of great significance for the safe operation of such vessels. Since pressurized components such as end caps experience a certain amount of thickness reduction during the forming process, GB150 stipulates that the nominal thickness and minimum formable thickness of container components should generally be indicated on the design drawings. 1. Conventional method for determining the minimum thickness of end caps: Typically, the conventional method for determining the minimum thickness of end caps is to set it equal to the design thickness; in other words, the calculated thickness is equal to the design thickness plus the corrosion allowance. However, this method takes into account only the effect of pressure loads on the end caps, ignoring the influence of other loads and constraints. As a result, the minimum thickness of the end caps may not meet the requirements under design conditions, posing safety risks during the operation of the pressure vessel. 2. Factors affecting the determination of the minimum thickness of the head 2.1 Influence of stiffness The head must possess a certain degree of stiffness while under pressure, in order to avoid deformation and failure. Therefore, GB150 stipulates that the minimum thickness of carbon steel and low-alloy steel vessels, excluding the corrosion allowance, shall not be less than 3 mm ； The minimum thickness of high-alloy steel containers, excluding the corrosion allowance, shall be not less than 2 mm. 2.2 Influence of pressure loads: The head is a compressive component that is subjected to certain pressures. The primary condition that must be met is related to pressure loads; whether subjected to internal or external pressure, the calculated thickness of the head can be determined using the formulas provided in Chapter 3 of GB150. Here, the calculated thickness equals the design thickness plus the corrosion allowance, with the design thickness representing the minimum thickness required for the head based solely on pressure loads. 2.3 Effect of internal pressure instability: Under the action of internal pressure, the stress distribution in a standard elliptical head is shown in Figure 1. As can be seen from the stress distribution diagram, circumferential compressive stress is generated at the bottom edge of the head, where circumferential instability is likely to occur. To prevent elliptical heads from becoming unstable under internal pressure, GB150 stipulates that for elliptical heads with Di/2hi ≤ 2, the effective thickness shall be no less than 0.15% of the inner diameter of the head; for those with Di/2hi > 2, the effective thickness shall be no less than 0.30% of the inner diameter of the head. Although the above restricts the effective thickness, it actually indirectly limits the minimum thickness for head forming as well. 2.4 Effects of hole reinforcement Common methods for hole reinforcement in pressure vessels include: forged pipe reinforcement, ring reinforcement, and integral reinforcement. The so-called overall reinforcement involves increasing the thickness of the shell in order to strengthen the strength of the shell, which is weakened after openings are made in the container. When the opening in the head uses an integral reinforcement structure, the minimum thickness of the head is the thickness required to meet the reinforcement needs of the opening. 2.5 Influence of local stresses induced by connection loads In pressure vessel design, it is necessary to evaluate the local stresses in the vessel shell resulting from external loads applied to the connections on the head. When these external loads are severe, the thickness of the head must be increased to reduce the impact of these connection loads, thereby ensuring that the stress requirements are met. The minimum thickness of the head in such cases is the one that satisfies the criteria for acceptable local stress levels. 2.6 Influence of the reinforcing effect of horizontal vessel heads In the design of horizontal vessels, the reaction forces at the vessel supports generate circumferential compressive stresses in the cylinder in contact with the saddles. The circumferential compressive stress is greatest at the lowest point of the cylinder cross-section at the support location; in the absence of reinforcing rings, the cylinder is prone to instability at this point. Meanwhile, the tangential shear forces at the cylinder cross-section induce circumferential bending moments in the radial sections of the cylinder. In the design of the saddle, the distance A between the centers of the saddle bottom plates and the tangent to the head should be kept at or less than 0.5Ra, so that the head can reinforce the cylinder and help balance the circumferential compressive forces and bending moments acting on it. The minimum thickness of the head is then the thickness required to ensure that the stresses in the saddle are within acceptable limits. Wherein: Ra – the average radius of the cylinder body. Impact on stress verification during pressure testing: According to GB150, if a pressure test is carried out using a pressure higher than that specified in 4.6.2.2 and 4.6.2.3, it is necessary to verify the stress levels of all stressed components under the test conditions prior to the pressure test, to ensure that these conditions are met. When a pressure vessel requires an increased test pressure for stress verification purposes, the stress under the testing conditions on the head may exceed the allowable value. In such cases, the effective thickness of the head is increased to meet the requirements for stress verification; the minimum thickness of the head at this point is the one that ensures successful compliance with the stress verification criteria for the pressure test. 2.8 Effects when at the critical value of material thickness: GB150 stipulates that the calculated thickness refers to the thickness obtained by using the formulas provided in various chapters ； The design thickness refers to the thickness that is the sum of the calculated thickness and the corrosion margin ； The nominal thickness refers to the design thickness plus the negative deviation of the steel plate thickness, rounded up to the standard specification for the steel material – that is, the thickness indicated on the drawings ； Effective thickness refers to the nominal thickness minus the corrosion allowance and the negative deviation of the steel plate thickness. For the head, the thickness of the raw material is equal to the design thickness minus the amount of thinning that occurs during shaping, with the result being rounded to the thickness specified by the material standards; the minimum thickness after shaping must not be less than the design thickness. Among them, design thickness = calculated thickness + corrosion allowance. When, after rounding to the standard material specifications, the thickness of the head blank differs from the calculated thickness for that head, and the allowable stress corresponding to that thickness is not in the same range as specified in GB150’s table of allowable stresses for materials (i.e., there is a shift to another range), then calculating the head thickness using the allowable stress for the thickness range of the head blank will result in a higher value. This is because, according to GB150’s tables of allowable stresses for various materials, the allowable stress varies depending on the thickness of the material, and it decreases as the thickness increases. At this point, the minimum thickness of the head is the design thickness calculated based on the allowable stress value for the thickness grade to which the head blank belongs after the gear shift. 3. Conclusion: The minimum thickness of the head cannot be simply determined based on the design thickness. It is necessary to consider the specific design conditions as well as various influencing factors outlined in this paper, and to adopt the maximum value among these factors as the minimum thickness of the head, in order to ensure the safe operation of pressure vessels.