- An axial load Faxial as described in RCB-8.42 shall be applied at the smaller end of end FSE. Faxial will be calculated as per (p/4) x G2 x 100 lbf/in2. We need to model dummy flange at the smaller end by considering the shell up to the minimum length of 2.5SQRT(RT) of the FSE to reduce the stress concentration factor in the stresses induced.
- Finite Element Analysis will be performed and displacement in the axial direction (d) shall be noted for the applied force (Faxial).
- The spring rate of the axisymmetric FSE, KAS will be computed as the force applied (Faxial) / displacement induced (d).
- The Spring rate of the entire FSE is KFSE = KAS/2
- When only one FSE is present then the spring rate is given by K FSE above. When multiple FSE’s are present, the spring rate is given by KE = 1/ ((1/KFSE1) + (1/KFSE2) + …. (1/KFSEn)) Where KE is the equivalent spring rate of the entire system.
Spring Rate Calculation for Expansion Bellow Expansion bellows are applicable to fixed tube sheet heat exchanger which help in reducing the longitudinal stresses or tube to tube sheet joint loads by allowing the axial displacement between shell and tubes. RCB-8 flexible Shell Elements (FSE) of TEMA standards deals with the calculation of spring rate and stresses induced in the FSE by using Finite Element Analysis method. Historically engineers used to calculate the stresses and spring rate using the plate and beam theory nut due to limitations in the plate and beam theory Finite Element Analysis method is the most widely used method for calculating the spring rate and stress induced in the FSE. Now let us take practical example of FSE for calculation of the spring rate – Fig – Expansion Bellow Spring rate calculation as per TEMA RCB-8.5 will be carried out as per following steps – The flexible shell element (FSE) will be modeled as per section RCB-8.2 & RCB-8.3 i.e. Axisymmetric model will be created for Finite Element Analysis. Meshing is done in such a way that there much be at least 8 elements across the length of the flexible shell element.