11.54 A reactor pressure vessel is usually clad in stainless steel to prevent corrosion and radiation embrittlement. Thus, the occurrence of subclad cracks is higher than that of surface cracks. Kim et al. (Transactions of the ASME, 2003) performed 3-D elastic-plastic finite element analysis to investigate the validity of present ASME code in evaluating the integrity of a vessel under pressurized thermal shock conditions. The hoop stress (in MPa) data recorded for different values of are given in the following table.

a Plot the hoop stress versus values.
Describe the relation between the two variables.
b Estimate the relation between the hoop stress and values, using the leastsquares method.
c Does it appear that the hoop stress changes significantly with values. Use .

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x/a Hoop Stress 0 425 0.05 400 0.08 380 0.175 280 0.25 270 0.35 250 0.45 240 0.725 200 1.00 160