Fuselage Design

2. Fuselage Structure
➢Given fuselage structure and determine
the ultimate bending strength.
➢ Given loads and determine the
maximum stresses applied to the
fuselage structure.
➢ Given loads and determine the shear
flow distribution.
ACE - Dr Mohamed Elfarran

3. Ultimate bending strength - Example
The figure shows a fuselage cross-
section. The stringers are arranged
symmetrically w.r.t. the fuselage z-axis.
The skin and stringer were made from
aluminum 2024. The stringer Hight is 1
in. while there area is 0.12 𝑖𝑛2.
Calculate the maximum stresses due to a
design bending moment 1.6 E6 Ib.in.?
Determine the fuselage Margin of safety
if the Stringer-skin allowable strength is
32000 psi?
ACE - Dr Mohamed Elfarran

4. Ultimate bending strength - Example
Solution strategy
• The given problem is a trail and error problem, because the
neutral axis position depends on the applied compressive
stresses (unknown), and the applied stresses depends on the
fuselage effective area (unknown) which is also depends on
the stringer-skin stresses.
• Initially, an effective width should be assumed either as a
factor of the skin thickness 𝑊𝑒𝑓𝑓 = 30 ∗ 𝑡𝑠𝑘𝑖𝑛 or by
assuming linear stress distribution 𝑤𝑒𝑓𝑓 = 1.9𝑡
𝐸
𝜎𝑙𝑖𝑛𝑒𝑎𝑟
• Due to the fuselage symmetry about the z-axis only one-half
of the fuselage will be considered in the present analyses.
ACE - Dr Mohamed Elfarran

5. Ultimate bending strength - Example
Solution Procedure – Trial-1
• Calculate total areas of stringer and
effective skin. All sheets in tension
side are assumed to be effective.
𝐴 = 𝐴𝑠𝑡 + 30 ∗ 𝑡𝑠𝑘𝑖𝑛 ∗ 𝑡𝑠𝑘𝑖𝑛
Area under compression:
ACE - Dr Mohamed Elfarran

6. Ultimate bending strength - Example
Solution Procedure – Trial-1
• Stringer and skin initial position
Skin centroid position
ACE - Dr Mohamed Elfarran

7. Ultimate bending strength - Example
Solution Procedure – Trial-1 Buckled skin contribution
ACE - Dr Mohamed Elfarran

8. Ultimate bending strength - Example
Solution Procedure – Trial-1
Buckling stress
Buckled skin contribution
Z
Buckling
coefficient
r/t 𝐾𝑐
343.75 55.86 19.6
343.75 44.23 16
750 20.27 9
1187.5 12.80 6
1187.5 28.62 12
1187.5 33.35 14
𝒓 =
𝒓𝒔𝒕𝒂𝒕𝒊𝒐𝒏1 + 𝒓𝒔𝒕𝒂𝒕𝒊𝒐𝒏2
2
, 𝒁 =
𝒃2
𝒓 ∗ 𝒕
1 − 𝒗2 ,
𝝈𝒄𝒓 =
𝒌𝒄𝝅2
𝑬
ሻ
12(1 − 𝒗2
𝒕
𝒃
2
Z can be obtained
from Figure C9.1
This formula
can be used
for Poisson’s
ration 0.3
ACE - Dr Mohamed Elfarran

9. ACE - Dr Mohamed Elfarran

10. Ultimate bending strength - Example
Solution Procedure –Trial-1
Effective area
Buckled skin contribution
• Calculate the effective factor
based on assumed stresses.
• Then calculate the effective area
for the buckled skin.
In our analysis, we will not assume any
stresses, instead in the initial trail we will
assume all the skins as in tension.
ACE - Dr Mohamed Elfarran

11. Ultimate bending strength - Example
Solution Procedure – Trial-1 All together
ACE - Dr Mohamed Elfarran

12. Ultimate bending strength - Example
Solution Procedure –
Trial-1
Skin without buckling
Buckled skin
ACE - Dr Mohamed Elfarran

13. Ultimate bending strength - Example
Solution Procedure –
Comments
• The importance of trial – 1 is to determine the skin in
tension and compression which depends on the neutral
axis position which also depends on the skin effective
width.
• In the initial trail we will assume all the stringers and
skins are effective.
ACE - Dr Mohamed Elfarran

14. Ultimate bending strength - Example
Solution Procedure –
Trial-2 Skin without buckling
Buckled skin
ACE - Dr Mohamed Elfarran

15. Ultimate bending strength - Example
Solution Procedure –Trial-2 All together
ACE - Dr Mohamed Elfarran

16. Ultimate bending strength - Example
Solution Procedure –Comments
• The results of trail – 1, give the neutral axis position 3.38” below the fuselage
center line, and a second moment of area 1470 𝑖𝑛4
.
• The results of trail – 2, give the neutral axis position 0.135” above the location
from the first trail, and a second moment of area 1489 𝑖𝑛4
.
• The error between trail – 1 and trail – 2 can be calculated to be
• Error based on the centroid position 𝜖% =
𝑍2 − 𝑍1
𝑍2
𝑥100 =
27.6−24.2
24.2
𝑥100 = 14%
ACE - Dr Mohamed Elfarran

17. Ultimate bending strength - Example
Solution Procedure –Trial-2 All together
ACE - Dr Mohamed Elfarran