It's important to note that the design of a nuclear containment vessel is a complex and highly regulated process, and hand calculations are only the preliminary step in the design process. The final design must meet all applicable codes, standards, and regulatory requirements to ensure the safety of the nuclear facility.

The design of a pre-stressed nuclear containment involves several steps, including the calculation of the internal pressure and external loads, the selection of the material, and the determination of the prestressing force. Here is a general overview of the hand calculation process:

Dear Jassim,

Thanks for your detailed reply. Let us center our discussion around a prestressed concrete containment for which materials and internal pressure due to LOCA (Loss Of Coolant Accident) have been already selected as follows:

concrete compressive strength fc = 37.5 MPa

Modulus of elasticity of concrete = 29 000 MPa

Poisson's ratio of concrete =0.2

Coefficient of thermal expansion =1.0×10-5 /°C

prestressing tendons yield strength = fy = 1630 MPa

prestressing tendons tensile strength = fy = 1860 MPa

Modulus of elasticity of tendons= 199 000 MPa

x-sectional area of stand = 1825 mm2

LOCA internal pressure, pi = 260 kPa

Containment internal diameter = 18 m

Containment dome radius= 22 m

Containment cylinder height = 47 m

Containment dome height = 10 m

Now, how to calculate the number of hoop and vertical prestressing strands and the containment wall thickness with these initial information?