Alternating Stress parameter table
Maximum stress
\[{{s}_{\max}}\]
Minimum stress
\[{{s}_{\min}}\]
Average stress
\[{{s}_{\text{m}}}=\frac{1}{2}\left ({{S}_{\max}}+{{s}_{\min}} \right) \]
Stress ratio (stress characteristics)
\[r=\frac{{{s}_{\min}}}{{{s}_{\max}}}\]
Stress amplitude
\[{{s}_{a}}=\frac{1}{2}\left ({{S}_{\max}}-{{s}_{\min}} \right) ={{s}_{\text{m}}}\left (\frac{1-R}{1+R} \right) \]
Equal Life curve
\[{{s}_{\max}}=\frac{2{{s}_{m}}}{1+r}\]
\[{{s}_{\min}}=\frac{2{{s}_{m}}}{1+\frac{1}{r}}\]
Partial calculation
Stress ratio |
Average Stress |
Maximum Stress |
Minimum Stress |
stress Amplitude |
|
\ (r\) |
\ ({{s}_{m}}\) |
\ ({{S}_{\max}}\) |
\ ({{s}_{\min}}\) |
\ ({{s}_{a}}\) |
|
-1 |
0 |
\ ({{S}_{\max}}\) |
-\ ({{S}_{\max}}\) |
\ ({{S}_{\max}}\) |
Symmetrical cyclic stress |
0 |
\ ({{s}_{m}}\) |
2\ ({{s}_{m}}\) |
0 |
\ ({{s}_{m}}\) |
|
0.1 |
\ ({{s}_{m}}\) |
1.81818\ ({{s}_{m}}\) |
0.18181\ ({{s}_{m}}\) |
0.81818\ ({{s}_{m}}\) |
|
0.2 |
\ ({{s}_{m}}\) |
1.66667\ ({{s}_{m}}\) |
0.33333\ ({{s}_{m}}\) |
0.66666\ ({{s}_{m}}\) |
|
0.3 |
\ ({{s}_{m}}\) |
1.53846\ ({{s}_{m}}\) |
0.46154\ ({{s}_{m}}\) |
0.53846\ ({{s}_{m}}\) |
|
0.4 |
\ ({{s}_{m}}\) |
1.42857\ ({{s}_{m}}\) |
0.57143\ ({{s}_{m}}\) |
0.42857\ ({{s}_{m}}\) |
|
0.5 |
\ ({{s}_{m}}\) |
1.33333\ ({{s}_{m}}\) |
0.66667\ ({{s}_{m}}\) |
0.33333\ ({{s}_{m}}\) |
|
1 |
\ ({{s}_{m}}\) |
\ ({{s}_{m}}\) |
\ ({{s}_{m}}\) |
0 |
Static |
Python code
from sympy import *Sm = symbols('Sm')Smax = []Smin = []Sa = []Range = [0.1, 0.2, 0.3, 0.4, 0.5]for R in Range: Smax.append(2*Sm/(1+R)) Smin.append(2*Sm/(1+1/R)) Sa.append(Sm*((1-R)/(1+R)))
Alternating Stress parameter table