A modern jet flies at an altitude of 6,200 metres, during its climb to cruise altitude. For additional passenger comfort, the cabin pressure is maintained at 80% of the sea level value.

Question

Given that the fuselage radius is 3.2 metres and that the skin thickness is 2.4 mm, compute the circumferential stress in the fuselage skin (in MPa or MegaPascal): (Assume ISA conditions)

Additionally, compute the longitudinal stress in the fuselage skin (in MPa or MegaPascal):

Answer 1

To calculate the circumferential stress, we can use the formula:

σ = (p * r) / t

where σ is the circumferential stress, p is the pressure difference between the inside and outside of the fuselage, r is the radius of the fuselage, and t is the thickness of the skin.

First, we need to calculate the pressure difference. At an altitude of 6,200 metres, the atmospheric pressure is approximately 43 kPa. To maintain the cabin pressure at 80% of sea level, we need to add an additional pressure of:

0.8 * (101.3 kPa - 43 kPa) = 45.04 kPa

Therefore, the total pressure difference is:

45.04 kPa + 43 kPa = 88.04 kPa

Next, we can substitute the values into the formula:

σ = (88.04 kPa * 3.2 m) / (2.4 mm * 10^-3) = 117.39 MPa

Therefore, the circumferential stress in the fuselage skin is 117.39 MPa.

To calculate the longitudinal stress, we can use the formula:

σ = (p * r^2) / (2t)

where σ is the longitudinal stress, p is the pressure difference, r is the radius of the fuselage and t is the thickness of the skin.

Substituting the values we get:

σ = (88.04 kPa * (3.2 m)^2) / (2*2.4 mm*10^-3) = 309.27 MPa

Therefore, the longitudinal stress in the fuselage skin is 309.27 MPa.

Answer 2

the circumferential stress in the fuselage skin 46.9 Megapascals
the longitudinal stress in the fuselage skin is 23.45 Megapascals