A young engineer has come up with a 'brilliant idea': an aircraft with a square fuselage for more space. Since all aircraft have a circular fuselage cross section you suspect there must be a downside to this plan and you suspect it has to do with stress in the fuselage skin due to the cabin pressure.
To convince the young engineer, you have to determine the 'circular' stress in the fuselage due to the cabin pressure as a function of R,P(in) , P(out) and t . To do so, make use of the figure below.
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I'm sorry, but I cannot see any figure attached to your question. Could you please provide more information or describe the figure in detail?
young engineer has come up with a 'brilliant idea': an aircraft with a square fuselage for more space. Since all aircraft have a circular fuselage cross section you suspect there must be a downside to this plan and you suspect it has to do with stress in the fuselage skin due to the cabin pressure.
To convince the young engineer, you have to determine the 'circular' stress in the fuselage due to the cabin pressure as a function of R,P(in) , P(out) and t . Give an equation for the 'circular' skin stress phi
To convince the young engineer, you have to determine the 'circular' stress in the fuselage due to the cabin pressure as a function of R,P(in) , P(out) and t . Give an equation for the 'circular' skin stress phi
To determine the circular stress in the fuselage due to cabin pressure, we can consider the hoop stress on the fuselage skin. Hoop stress is the stress that acts circumferentially around a structure.
The equation for hoop stress (σ) is given by:
σ = (P(in) - P(out)) * R / t
Where:
- P(in) is the pressure inside the cabin
- P(out) is the pressure outside the cabin
- R is the radius of the circular fuselage
- t is the thickness of the fuselage skin
The difference between the inside and outside pressure is multiplied by the radius and divided by the thickness of the skin. This will give us the circular stress in the fuselage due to the cabin pressure.
It is important to note that this equation assumes that the fuselage is perfectly circular and that the pressure difference is evenly distributed throughout the circumference. In the case of a square fuselage, the stress distribution will be different, and the equation for determining the stress would need to be modified accordingly.
The equation for hoop stress (σ) is given by:
σ = (P(in) - P(out)) * R / t
Where:
- P(in) is the pressure inside the cabin
- P(out) is the pressure outside the cabin
- R is the radius of the circular fuselage
- t is the thickness of the fuselage skin
The difference between the inside and outside pressure is multiplied by the radius and divided by the thickness of the skin. This will give us the circular stress in the fuselage due to the cabin pressure.
It is important to note that this equation assumes that the fuselage is perfectly circular and that the pressure difference is evenly distributed throughout the circumference. In the case of a square fuselage, the stress distribution will be different, and the equation for determining the stress would need to be modified accordingly.
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