# Homework Help: Static Equivalent force for cyclic load (fatigue related)

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1. Dec 4, 2016

### Nikstykal

1. The problem statement, all variables and given/known data
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 (Su) ~~ 125 ksi
Cg = 1.0, Cs = 0.74, Cr = 0.814, Ct = 1.0, CL = 1.0
N = 5x105

2. Relevant equations
Sf (endurance limit at 103 cycles) = 0.9*Su
SN' (RR Moore endurance limit) = 0.5*Su
SN (endurance limit) = SN' * CL * Cg * Cs * Ct * Cr
Basquin's Equation: Salternating = A*Nm where m = -log(Sf/SN) / 3 and A=SN / 106m
Pmean = (Pmax + Pmin) / 2, Pvarying = (Pmax - Pmin) / 2

3. The attempt at a solution
I know that Pmax = 800 lb, and Pmin = 0, so Pmean = 400lb and Pvarying = 400lb. Also, solving for the endurance limit (SN), 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 Salternating = Pequivalent / [ 2 * (pi/4) diameter2]. I do not know how to find the equivalent load. One suggestion was

Pequivalent = Pmean + Pvarying*(ultimate stress / endurance stress)

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

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2. Dec 9, 2016