Calculations on the buckling of disc-shaped heads

Of course there are. One of the main failure modes of dish heads (especially spherical heads with flanges) when subjected to external pressure is **elastic instability buckling**. Its calculation method is basically the same as that of a **pressurized spherical shell**, with the core being the calculation of its **critical instability pressure**. In simple terms, the most commonly used and authoritative method in engineering is to follow the **graphical method** specified in **GB/T 150.3 \"Pressure Vessels – Part 3: Design\"** (or ASME VIII-1). However, there are also theoretical formulas for preliminary estimation and understanding the principles. Below is a summary of the methods and key formulas for you: ### 1. Core calculation approach (GB/T 150 method) For the buckling calculation of disc-shaped end caps, their **spherical cap portion** (i.e., the section with high curvature in the middle) is essentially treated as an \"equivalent spherical shell\". 1. **Determine the equivalent shell radius**: The inner radius `Ri` of the spherical cap portion of the dish head is the shell radius used in the calculations. For standard disc-shaped heads, this `Ri` is usually equal to a multiple of the head diameter (for example, `Ri = 0.9Di` is commonly used, where `Di` is the inner diameter of the head). 2. **Calculate geometric parameters**: * `Ro`: The outer radius of the spherical shell, `Ro = Ri + δn` (where δn is the nominal thickness of the head). * `A` value (strain coefficient): This is a key intermediate parameter. * Formula: **`A = 0.125 / (Ro / δe)`** * where `δe` is the **effective thickness** of the head (nominal thickness minus corrosion allowance and material negative deviation). * The physical meaning of this formula is: assume that the spherical shell experiences a circumferential strain of 0.125% at the critical pressure. 3. **Consult the material curve chart**: Based on the head material (such as carbon steel, stainless steel, etc.) and design temperature, use the calculated value of `A` to find the corresponding **`B` value** (stress coefficient, in MPa) in the standard external pressure stress coefficient curve chart (Chart B) specified in GB/T 150.3. 4. **Calculation of the allowable external pressure ``**: * Formula: **` = B / (Ro / δe)`** * This `` represents the **maximum external pressure** that the dish head can safely withstand. 5. **Compliance judgment**: Compare the design external pressure `P` (which must be less than or equal to ``). If `P