Problem 1 (20 points)-A 4 in-16 UNF SAE grade 5 bolt is used in a joint loaded by a tensile cyclic force F. The cyclic force varies between 2,500 lbf

and 3,500 lbf. The bolt is tightened with to a recommended preload for non permanent assembly. The length of the grip is l = 1.5 in. The threaded and unthreaded portions in the grip have the same length, l = la = 0.75 in. The members are of equal thickness (0.75 in) and made of cold-drawn SAE 1040 steel (E = 29,000kpsi, Sy= 75 kpsi, Sut= 85 kpsi). (a) Determine the fastener stiffness kp, the member stiffness km, and the stiffness constant of the joint C. Reference the tables in the book that you used to find the required properties of the bolt. (b) Using the maximum load, determine the proof strength safety factor np, the load factor ng and the joint separation safety factor no. (c) Using the maximum and minimum loads, determine the fatigue safety factor nf.