# How do the calculation formulas of various heads come from?

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There are many types of pressure vessel heads, and the commonly used forms include a hemispherical head, an elliptical head, a dish head, a spherical cap, a conical head, a flat cover, a flanged convex head, and the like. There are two types of internal pressure and external pressure from the load condition. The calculation formula is derived from the film theory, and the wall thickness can be calculated based on the inner or outer diameter of the container. See the contents of the spherical shell in Section 3.4 of GB150.3 for details.
The medium diameter formula of the cylinder is based on the equivalent strength and failure criteria: Among them, D=Di+δ, after finishing, get the formula that everyone often uses: The medium diameter formula of the hemispherical head is based on the equivalent strength and the failure criterion (ie, the same axial direction as above): Among them, D=Di+δ, after finishing, get the formula that everyone often uses: 1. The calculation formula is based on the cylinder formula, and the boundary effect of the joint between the head and the cylinder is reflected by the shape factor K. The larger the ratio of the long and short axes α/b, the larger the K value; when the ratio of the long and short axes is greater than 2.5, the head is prone to circumferential instability, so α/b is controlled at 2.6. The standard elliptical head has a ratio of length to length of 2, which is most commonly used, with K=1.
2. The head can be calculated based on the inner or outer diameter of the container.
3. In addition to meeting the strength, the thickness calculation of the head should also meet the stability requirements. For an elliptical head with α/b less than or equal to 2, the effective thickness shall not be less than 0.15% Di, and the effective thickness of the elliptical head with α/b>2 shall not be less than 0.30% Di.

1. The calculation formula is calculated by multiplying the spherical shell calculation formula of the spherical portion by the shape factor M. The larger Ri/r is, the more prominent the local stress is at the discontinuity of the surface of the head, and the larger the shape factor M is. Therefore, the inner diameter of the transition section should be limited to the range of r >= 10% Di.
2. Heads can be used to calculate the wall thickness based on the inner or outer diameter of the container.
3. In addition to meeting the strength, the thickness calculation of the 3 heads should also meet the stability requirements. For a dish-shaped head with M<=1.34, the effective thickness shall not be less than 0.15% di, and for a dish-shaped head with m> 1.34, the effective thickness shall not be less than 0.30% Di.

## Ball crown

1. The calculation formula is based on the cylinder formula. For the joint between the spherical crown and the barrel, the influence of local film stress and bending stress caused by the boundary effect is corrected by the coefficient Q. For different pressure conditions, the Q values are taken from different maps.
2. For the large-diameter spherical crown head, it can be considered that the middle spherical area of the head and the reinforcing section of the end take different thicknesses, wherein the length of the head reinforcing section should not be less than . The T-joint of the joint between the crown and the cylinder must be a full penetration structure of the section.

1. Due to the discontinuity of the structure, large local stresses are generated at the joint. When the half angle apex α of the cone shell is less than or equal to 30 degrees, the bending stress is small. At this time, a non-folded cone head can be used. When α > 30 degrees, the large end of the cone shell should adopt a hemmed structure, when α> At 45 degrees, the small end of the cone shell should also adopt a transition structure with a hem.
2. The formula for calculating the thickness of the cone shell is calculated by the equivalent cylinder. For the large and small end reinforcement section, the cylinder calculation formula is also adopted, and the stress increase coefficient Q is corrected. For the tapered head with the hemming, the big end can be calculated by the equivalent disc shape head.

## Eccentric cone

The eccentric cone shell can be treated as a cone shell. When the cone apex angle α is less than or equal to 30 degrees under internal pressure, the thickness of the eccentric cone shell is calculated according to the plated head. The half apex angle α of the cone shell is larger than the angle between the eccentric cone shell and the simplified body. Value selection. Under the action of external pressure, when the half apex angle α of the cone shell is less than or equal to 60 degrees, the thickness of the cone shell is stably checked according to the outer pressure cone shell, and the check should be carried out according to the two half angles.

## Flat cover

The coefficient K is used to represent the support around the flat cover. The smaller the K value, the closer the periphery of the flat cover is to the solid support, and the closer it is to the simple support.