Can somebody please explain this solution to me or at least the beginning to get me going. I am studying for an exam and struggling to understand this problem.

I am aware of the Gerber relation and what everything represents (I think). I have put the parts im confused about/where they come from in bold.

Thank you

Problem

The member is made of steel (Y = 345 Mpa and 0u = 586 ma), has a diameter d =20 mm, lies in the plane of the paper, and has a radius of curvature R = 800 mm. The member is simplysupported at A and B and is subjected to a cyclic load P at C normal to the plane of the member.

(a) The load varies from Pmax to Pmin = -5Pmax/6. The endurance limit for N = 10^7 for the steel is 0am = 290 MPa. Determine the magnitude of Pmax based on a factor of safety SF = 1.8 against failureat N = 10^7 cycles. Use the octahedral shear-stress criterion of failure. Assume that the Gerber relation is valid.

(b) Obtain the solution for Pmin = -Pmax/2. 574

Solution

(a) The magnitude of the alternating component of stress 0a, is obtained by Gerber relation. For linearly elasticbehavior, 0min = -5*0max/6. However, 0max - 0min = 2*0a, and 0max = 0m + 0a Hence, 0m = 0a/11.Substituting this value of0m and values of 0am and 0u in Gerber relation, we obtain 0a = 289 MPa. Thus,0max = 12/11*0a = 315 MPa and 0min = -263 MPa. This result indicates that a smooth fatigue specimencycled between these stress levels would not fracture before 10^7 cycles. Since 0max is less than Y, failurewould be by fatigue and not general yielding.

The load P on member ACB can be cycled from Pmax(SF) to Pmin(SF) through 10^7cycles before fracture by fatigue. The reactions at A and B when Pmax(SF) is applied are equal toPmax(SF)/2 = 0.90Pmax. The reaction 0.90Pmax produces a moment and torque of equal magnitude atthe critical section at C. Thus,M = T = 0.90PmaxR = 720Pmax. The bending stress 0 resulting from M and shear stress z resulting from T at C....

I understand the majority of the rest of the solution for part a so I will leave it out however C is the only value im not sure about?

(b) From following the solution I think I can work this out if I can understand part a.