SME
Aerospace Structures · Problem type
Miner’s rule: damage from two load blocks
Use this for “A spar takes 10,000 cycles at a stress with a life of 100,000, then 2000 cycles where the life is 10,000. What damage is used, and how many repeats fail it?”
Diagram
D
=
Σnᵢ
Nᵢ
=
10,000
100,000
+
2,000
10,000
=
0.3.
30 % of the life is used; the bar fills at D = 1.
Repeating
the
whole
set:
1
D
=
3.33
times
to
failure.
This is an example. Type your own values to start a new problem.
D
=
n₁
N₁
+
n₂
N₂
R
=
1
D
Formulas
D
=
n₁
N₁
+
n₂
N₂
0.3
=
10,000
100,000
+
2,000
10,000
R
=
1
D
3.333
=
1
0.3
Assumptions
•
Each block uses n ÷ N of the life, N read off the S–N curve at its stress.
•
Damage adds in any order (Miner’s rule); the part fails when D reaches 1.
Step-by-step
WE KNOW
n₁ = 10,000, N₁ = 100,000, n₂ = 2,000, N₂ = 10,000
FIND
damage used (D), repeats to failure (R)
Step 1 · Find damage used (D)
Use D = n₁ ÷ N₁ + n₂ ÷ N₂
Each block uses its cycles’ share of the life at its stress; the shares add.
D
=
10,000
100,000
+
2,000
10,000
D
=
0.1
+
0.2
D
=
0.3
Step 2 · Find repeats to failure (R)
Use R = 1 ÷ D
The
part
fails
when
the
damage
reaches
1,
so
the
set
repeats
1
D
times.
R
=
1
0.3
R
=
3.333
Check
Put the numbers back in. Both sides should match.
0.3
=
10,000
100,000
+
2,000
10,000
✓
3.333
=
1
0.3
✓
Topic check
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