The stress concentration factor for a stepped circular shaft ia approximated by

K_t = c(D/2d - 1/2)^-a

where c and a are given in Table1. Obtain two expressions one for c and the other for a, as a function of D/d in two ways:

1)with a fifth-order polynomial and (2) with a spline. For both methods, compare the values of K_t obtained with the two sets of fitted values to those obtained with the original values given in Table 1. Which is a better method to use in this case? State your justification.

Table 1:Stress concentration Factor constants

D/d	c	a
6.00	0.88	0.33
3.00	0.89	0.31
2.00	0.91	0.29
1.50	0.94	0.26
1.20	0.97	0.22
1.10	0.95	0.24
1.07	0.98	0.21
1.05	0.98	0.20
1.03	0.98	0.18
1.01	0.92	0.17

Pls use mathlab software to solve the question and show all mathlab working steps and ans