Answer:
long duct: 1.0 and 0.424
Hemisphere 1.0 ; 0.125; 0.5
Explanation:
For a long duct:
By inspection,
Calculating by reciprocity,
Hemisphere:
By reciprocity gives = 0.125
using the summation rule:
However, because this is a hemisphere, the value will be= 0.5 * 1
= 0.5
Answer:
Explanation:
Given f(x, y) = 5x + y + 2 and g(x, y) = xy = 1
The step by step calculation and appropriate substitution is clearly shown in the attached file.
Answer:
i) S–N plot is attached
ii) fatigue strength = 100 MPa
iii) fatigue life = 5.62 x 10^(5) cycles
Explanation:
i) I have attached the S–N plot (stress amplitude versus logarithm of cycles to failure)
ii) The question says we should find the fatigue strength at 4 × 10^(6) cycles.
So let's find the log of this and trace it on the graph attached.
Log(4 × 10^(6)) = 6.6
From the graph attached, at log of cycle value of 6.6, the fatigue strength is approximately 100 MPa
iii) The question says we should find the fatigue life for 120 MPa.
Thus, from the graph, at stress amplitude of 120 MPa, the log of cycles is approximately 5.75.
Thus,the fatigue life will be the inverse log of 5.75.
Thus, fatigue life = 10^(5.75)
Fatigue life = 5.62 x 10^(5)
