Determination of δ in the calculation of the reinforcement area required for openings in the elliptical heads of pressure vessels
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While working on the design, I accidentally noticed that the calculated thickness used for reinforcing the nozzles of the elliptical head was different from the calculated thickness for the head itself. After referring to clause 8.5.1 of GB150, I encountered an issue whose explanation I’m not sure about: First, formula 8-2 uses a coefficient K1, and this coefficient is determined by the ratio of the long and short axes of the ellipse. As can be seen from table 7-2, this coefficient corresponds to conditions where the head is under external pressure; however, clause 8.5.1 deals with containers under internal pressure. Is there any contradiction here? 2. As can be seen in Table 7-2, K1 is determined using the formula 【Outer diameter of the head / 2 × (Depth of the head’s curved surface + Thickness of the head)】. It is indicated in the table that for a standard elliptical head, this value should be 0.9; in this case, the value of 【Outer diameter of the head / 2 × (Depth of the head’s curved surface + Thickness of the head)】 is 2.0. Clearly, for a standard elliptical head, the value of 【Inner diameter of the head / 2 × Depth of the head’s curved surface】 is also 2.0, so it should not be possible for 【Outer diameter of the head / 2 × (Depth of the head’s curved surface + Thickness of the head)】 to equal 2.0. How can this be explained?
Whether it is internal or external pressure, it is related to the shape of the head.
The problem is that the calculation formulas for internal and external pressures are different, and the value of the coefficient K1 also varies. 2# Ningxue
This is because the stress in the central part of the head is lower than that in the transition zone; therefore, the principle of the equivalent radius for pressure heads under external pressure was applied, and from the formula for calculating the thickness of hemispherical heads, a formula for calculating the thickness of elliptical heads was derived. It is precisely because of the distinction between internal and external pressure that the coefficients are different.
This post was last edited by watermind on 2010-1-1 20:53. 1. K refers to the ratio of the stress in the cylinder section to the maximum total stress in the head; an approximate formula is derived from this definition: K = (2 + (a/b)^2)/6. When a/b = 2, K = 1. 2. When Ri = 0.9Di and r = 0.17Di, it is considered an approximately standard elliptical head. Thus, the larger arc portion of the elliptical head can be regarded as a spherical cap. 3. As mentioned above, the external pressure calculation for an elliptical head is carried out using the methods applicable to spherical shells. Since external pressure calculations are based on the outer diameter, K1 = RO/2h0 is introduced. 4. K and K1 are two different concepts; the apparent contradiction arises from treating the ellipse as a spherical shell.