The geometric and material properties of a bolt (made of A36 steel) are given in the table. Value Propert Yield strength Thread area Endurance limit 0.25"n"d2 mlm? 50 MPa 450 MPa 1000 N 200 MPa 100 MPa Ultimate stren Preload (F Bolt stiffness Resultant member stiffness where d is the diameter (2mm Sd s 6mm) of the thread cross-sectional area (A The time-dependent external force, P(t) (in N), is acting on the bolt and members, and it can be approximated with the following function: P(t)2000t 50dt3 and 0st s 1.5 1) Find the optimum diameter value, dopt, which maximizes the factor of safety according to Modified Goodman Failure Criterion. (70 points) The geometric and material properties of a bolt (made of A36 steel) are given in the table. Value Propert Yield strength Thread area Endurance limit 0.25"n"d2 mlm? 50 MPa 450 MPa 1000 N 200 MPa 100 MPa Ultimate stren Preload (F Bolt stiffness Resultant member stiffness where d is the diameter (2mm Sd s 6mm) of the thread cross-sectional area (A The time-dependent external force, P(t) (in N), is acting on the bolt and members, and it can be approximated with the following function: P(t)2000t 50dt3 and 0st s 1.5 1) Find the optimum diameter value, dopt, which maximizes the factor of safety according to Modified Goodman Failure Criterion. (70 points)