Determination of the minimum thickness of end caps and influencing factors

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1. Introduction GB150.1–150.4–2011 \"Pressure Vessels\" is the authoritative design standard for pressure vessel design in China. Determining the appropriate thickness in accordance with this standard is of great significance for meeting the strength requirements of such vessels and ensuring their safe operation. Since pressurized components such as end caps experience a certain amount of thickness reduction during the forming process, it is specified in the literature that the nominal thickness and minimum formable thickness of container components should generally be indicated on the design drawings. 2. Conventional method for determining the minimum thickness of heads Generally, the conventional method for determining the minimum thickness of heads is to set it equal to the design thickness, that is, the calculated thickness plus the corrosion allowance. This approach takes into account only the effect of pressure loads on the heads, without considering the influence of other loads and constraints; as a result, the minimum thickness of the heads may not meet the requirements under design conditions, posing safety risks in the operation of the pressure vessel. 3. Factors affecting the determination of the minimum thickness of the head ① Influence of stiffness: The head must possess a certain degree of stiffness while under pressure, in order to avoid deformation and failure. Therefore, the literature specifies that the minimum thickness of carbon steel and low-alloy steel vessels, without including a corrosion margin, shall be not less than 3 mm ； The minimum thickness of high-alloy steel containers, excluding the corrosion allowance, shall be not less than 2 mm. ②Effect of pressure loads: A head is a compressed component that is subjected to certain pressures. The primary consideration is the pressure load; whether it is subjected to internal or external pressure, the calculated thickness of the head can be determined using the formulas provided in Chapter 3 of the relevant literature. The calculated thickness, plus the corrosion allowance, equals the design thickness – which represents the minimum thickness required for the head based solely on pressure load considerations. ③Effect of internal pressure instability: The stress distribution in a standard elliptical head under internal pressure is shown in Figure 1. As can be seen from this stress distribution diagram, circumferential compressive stresses occur at the bottom edge of the head, and this area is prone to circumferential instability. To prevent buckling under internal pressure in elliptical heads, literature specifies 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, while 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 restricts the effective thickness, it actually indirectly limits the minimum thickness for head forming as well. Figure 1: Stress distribution diagram of a standard elliptical head. Where: Di – inner diameter of the head; hi – depth of the inner curved surface of the convex head; ④ Effect of hole reinforcement. Common methods for hole reinforcement in pressure vessels include reinforcement using forged pipes, reinforcement rings, and integral reinforcement. The so-called overall reinforcement involves increasing the thickness of the shell to compensate for the weakening of the shell resulting from the openings. 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. ⑤The influence of local stresses generated by the loads on the connections: In the design of pressure vessels, certain important process connections on the head require that the local stresses in the vessel shell resulting from the external loads on these connections be evaluated. When these external loads are severe, the thickness of the head is increased to reduce the impact of the stresses caused by those connections, thereby ensuring that the requirements are met. In this case, the minimum thickness of the head is the one that satisfies the criteria for acceptable local stress levels. ⑥The effect 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 buckling at this point; meanwhile, the tangential shear forces at the cylinder 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 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; ⑦ Influence during stress verification for pressure tests. According to the literature, if a pressure test is carried out using a pressure higher than that specified in 4.6.2.2.4.6.2.3, it is necessary to verify the stress levels of all stressed components under the test conditions prior to the pressure test, to ensure that the verification requirements 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 of the stress verification. The minimum thickness of the head at this point is the one that ensures successful compliance with the stress requirements for the pressure test. ⑧The effect at the critical material thickness: The literature specifies that the calculated thickness refers to the thickness obtained using the formulas provided in various chapters ； The design thickness refers to 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 thickness of the steel material, that is, the thickness indicated on the drawing ； 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 equals the design thickness plus the thinning due to forming plus the amount needed to round it to the thickness specified by the material standards; the minimum thickness after forming must not be less than the design thickness, where the design thickness = calculated thickness + corrosion allowance. When the thickness of the head blank after rounding to the standard material specification does not fall within the same stress allowance range as that selected for calculating the thickness of the head, as indicated in the material stress allowance tables in the literature (a shift in range occurs), calculating the head thickness using the stress allowance for the range corresponding to the head blank thickness will result in a higher value. This is because, according to the tables of stress allowances for various materials provided in the literature, the stress allowance varies for different thicknesses of the same material, and it decreases as the plate 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. 4. Conclusion: The minimum thickness of the head cannot be simply determined based on the design thickness; instead, it should be determined according to the specific design conditions, taking into account all the factors mentioned in this paper. 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. References: GB150.1～150.4－2011, Pressure Vessels.