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

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 vessels, excluding the corrosion allowance, shall be not less than 2 mm. 2.2 Influence of pressure loads: The head is a compressed 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, which represents 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 should be no less than 0.15% of the inner diameter of the head; for those with Di/2hi > 2, the effective thickness should be no less than 0.30% of the inner diameter of the head. Although the above limits the effective thickness, it actually indirectly limits the minimum thickness for head forming as well. 2.4 Effects of opening reinforcement Common methods for reinforcing pressure vessels through openings include: forging tube reinforcement, 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 generated 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 in order to reduce the impact of these loads and ensure that the requirements are met; the minimum thickness of the head in such cases is the one that allows the local stress requirements to be satisfied. 2.6 Influence of the head of a horizontal vessel serving as a reinforcement element: In the design of horizontal vessels, the reaction forces at the vessel supports generate circumferential compressive stresses in the cylinder section in contact with those supports. The circumferential compressive stress is greatest at the lowest point of the cylinder 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 section induce circumferential bending moments in the radial cross-section 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 as small as possible, such that A ≤ 0.5Ra; this allows the head to act as a reinforcement for the cylinder, helping to balance the circumferential compressive forces and bending moments on the cylinder. 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. Influence during stress verification for pressure tests: 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 needs to have its test pressure increased for stress verification purposes, the stress under the testing conditions applied to the head may exceed the allowable values. 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 specifies 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; in other words, it 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, plus any adjustments made to bring it 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 margin. 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 simply be taken as the design thickness. It should be determined based on specific design conditions, taking into account all the factors mentioned in this article; the maximum value among these factors should be used as the minimum thickness of the head in order to ensure the safe operation of pressure vessels.

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