Two parts are to be assembled in a way that if one part fails, the entire assembly fails. Each of the parts have undergone exten
sive individual analysis and you are provided with statistics on the stresses that are expected. Specifically, you are provided with the mean and standard deviation of the stress, and the yield stress of the material for each part. Failure of a part will be defined as a part experiencing stress exceeding the yield stress. What is the probability that the assembly fails? (Hint: Use Table A-10 in the textbook to find the probability of failure for each part.)
Part #1: σnom = 260 MP a, U (σ) = 25 MP a, σyield = 310 MPa
Part #2: σnom = 475 MP a, U (σ) = 5 MP a, σyield = 490 MPa
Part #1: σnom = 260 MP a, U (σ) = 25 MP a, σyield = 310 MPa
Part #2: σnom = 475 MP a, U (σ) = 5 MP a, σyield = 490 MPa
1 answer:
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Answer:
T = 167 ° C
Explanation:
To solve the question we have the following known variables
Type of surface = plane wall ,
Thermal conductivity k = 25.0 W/m·K,
Thickness L = 0.1 m,
Heat generation rate q' = 0.300 MW/m³,
Heat transfer coefficient hc = 400 W/m² ·K,
Ambient temperature T∞ = 32.0 °C
We are to determine the maximum temperature in the wall
Assumptions for the calculation are as follows
- Negligible heat loss through the insulation
- Steady state system
- One dimensional conduction across the wall
Therefore by the one dimensional conduction equation we have
During steady state
= 0 which gives
From which we have
Considering the boundary condition at x =0 where there is no heat loss
= 0 also at the other end of the plane wall we have
hc (T - T∞) at point x = L
Integrating the equation we have
from which C₁ is evaluated from the first boundary condition thus
0 = from which C₁ = 0
From the second integration we have
From which we can solve for C₂ by substituting the T and the first derivative into the second boundary condition s follows
→ C₂ =
T(x) = and T(x) = T∞ +
∴ Tmax → when x = 0 = T∞ +
Substituting the values we get
T = 167 ° C