Fig. 3.4 Normalized dimensionless thicknesses T40 in the VTD class, generating a flexure z40 = A4or4 i.e. the Sphe3 mode. p = r/a G [ 0,1

1. Uniform loading and reaction at edge T40 = [p 8/(3+v) - 1 ]1/3

2. Axial force at center and edge reaction T40 = [^p-8/(3+v) - ^p-2]1/3

3. Uniform loading and reaction at center T40 = [3+vP-8/(3+v) - ^P-2 + 1 ]1/3

The radial and tangential maximum stresses must be lower than the ultimate stress oult of the material. The maximum stresses are represented by

Considering the case of Sphe 3, the bending moment Mr and Mt are derived from (3.1a) to (3.1b). For the radial bending moment, we obtain

With the three previous rigidities and after calculation and simplifications, the radial maximum stress is

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