A section of eylindrical pipe shown in Figure Q2(a) below has flange with a hole diameter of " 3 in" that attached to a pipe. The flange is made from gray cast iron and weld to the pipe. The flange is then being closed by a flange cover that made from steel. Six (6) steel bolts which the size are 1/4 in-20 UNC SAE grade 7 with hardened- steel washer are used to secure the joint. All bolts are use for reused condition when the joint is taken apart. Then the pipe will be pressurized up to 1000psi as illustrated in a) Evaluate this joining by determine the, yielding factor of safety, nr, load factor, nl and factor of safety again joint separation, n, (22 marks) b) If the joint is subjected to a fluctuating pressure whose maximum value is 1000psi, i. Calculate the fatigue factor of safety using modified Goodman criteria, nf. (3 marks) ii. Draw proper modified Goodman fatigue diagram and proof strength line. List and calculate all intersection points at X and Y axis. Give conclusion to the graph