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!

 

[KataKoniK]

Hi there,

Thank you for sharing your problem with us. Solving for the equivalent static force can be done by using the Goodman diagram, which takes into account both the alternating and mean stresses. The equation you mentioned, Pequivalent = Pmean + Pvarying*(ultimate stress / endurance stress), is derived from the Goodman diagram.

To solve for the equivalent static force, you can use the following steps:

1. Calculate the alternating stress (Sa) using Basquin's equation: Sa = A*Nm, where m = -log(Sf/SN) / 3 and A = SN / 106m. In this case, Sa = 42,018.5 psi.

2. Calculate the mean stress (Sm) using the equation Sm = Pmean / (pi/4 * diameter^2). In this case, Sm = 400 lb / (pi/4 * diameter^2).

3. Plot the alternating stress (Sa) and mean stress (Sm) on the Goodman diagram. The intersection of these two points will give you the equivalent static force (Pequivalent).

4. Once you have Pequivalent, you can use it to calculate the dimensions of your bolt using the equation Salternating = Pequivalent / [ 2 * (pi/4) diameter^2].

I hope this helps. Good luck with your calculations!