Static Equivalent force for cyclic load (fatigue related)

[Nikstykal]

Homework Statement

I have a suspension mount (square tube with unknown thickness) with a bolt going through it that undergoes an 800 lb load laterally into the bracket in an on/off fashion (NOT fully reversed) at a rate of 50 Hz. Ultimately we are trying to calculate the dimensions of the bolt and bracket given minimum and maximum safety factors. The cycle life till failure is 5x10⁵ cycles. I want to know how to solve for the equivalent static force.

Also relevant:
Ultimate strength (S_u) ~~ 125 ksi
C_g = 1.0, C_s = 0.74, C_r = 0.814, C_t = 1.0, C_L = 1.0
N = 5x10⁵

Homework Equations

Stress = Load / Area
S_f (endurance limit at 10³ cycles) = 0.9*Su
S_N' (RR Moore endurance limit) = 0.5*Su
S_N (endurance limit) = S_N' * C_L * C_g * C_s * C_t * C_r
Basquin's Equation: S_alternating = A*N^m where m = -log(S_f/S_N) / 3 and A=S_N / 10^6m
P_mean = (P_max + P_min) / 2, P_varying = (P_max - P_min) / 2

The Attempt at a Solution

I know that P_max = 800 lb, and P_min = 0, so P_mean = 400lb and P_varying = 400lb. Also, solving for the endurance limit (S_N), given the environment factors, I got 37647.5 psi. The Basquin's Equations gave me the applied alternating stress for finite life of 42,018.5 psi. From here I want to solve for the equivalent load so I can then solve for the dimensions of my bolt by doing S_alternating = P_equivalent / [ 2 * (pi/4) diameter²]. I do not know how to find the equivalent load. One suggestion was

P_equivalent = P_mean + P_varying*(ultimate stress / endurance stress)

but I have no idea how they even got that. Any insight would be helpful!