Engineering core problem solutions

Solution to Problem 1 – Structural resonance load#

The load is

$$ L = \frac{D_6}{τ_r}. $$

If $$τ_r$$ doubles:

$$ τ_r' = 2τ_r, \quad L' = \frac{D_6}{2τ_r} = \frac{L}{2}. $$

Answer: The load is cut in half.

Solution to Problem 2 – Thermal expansion#

We have

$$ E = ΛΘ T_f. $$

• $$Θ$$ increases by 15% → becomes $$1.15Θ$$
• $$T_f$$ decreases by 5% → becomes $$0.95T_f$$

Thus,

$$ E' = Λ(1.15Θ)(0.95T_f) = 1.0925 E. $$

Answer: Expansion increases by 9.25%.

Solution to Problem 3 – Fluid flow resonance#

Flow rate is

$$ Q = F_3 τ_r^2. $$

If $$τ_r$$ increases by 10%:

$$ τ_r' = 1.1τ_r, \quad Q' = F_3 (1.1τ_r)^2 = 1.21Q. $$

Answer: Flow increases by 21%.