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Airframe Design and Construction
Maximum stresses due to applied loadsSymmetric Fuselage
Instructor: Mohamed Abdou Mahran Kasem, Ph.D.
Aerospace Engineering Department
Cairo University
Fuselage Structure
➢Given fuselage structure and determinethe ultimate bending strength.
➢ Given loads and determine themaximum stresses applied to thefuselage structure.
➢ Given loads and determine the shearflow distribution.
Ultimate bending strength - Example
The figure shows a fuselage cross-section. The stringers are arrangedsymmetrically w.r.t. the fuselage z-axis.
The skin and stringer were made fromaluminum 2024. The stringer Hight is 1in. while there area is 0.12 𝑖𝑛2.
Calculate the maximum stresses due to adesign bending moment 1.6 E6 Ib.in.?
Determine the fuselage Margin of safetyif the Stringer-skin allowable strength is32000 psi?
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 = 1.9𝑡𝐸
𝜎𝑙𝑖𝑛𝑒𝑎𝑟
• Due to the fuselage symmetry about the z-axis only one-half
of the fuselage will be considered in the present analyses.
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:
Ultimate bending strength - Example
Solution Procedure – Trial-1
• Stringer and skin initial position
Skin centroid position
Ultimate bending strength - Example
Solution Procedure – Trial-1 Buckled skin contribution
Ultimate bending strength - Example
Solution Procedure – Trial-1
Buckling stress
Buckled skin contribution
ZBuckling
coefficient
r/t 𝐾𝑐343.75 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 ∗ 𝒕1 − 𝒗2 ,
𝝈𝒄𝒓 =𝒌𝒄𝝅
2𝑬
ሻ12(1 − 𝒗2𝒕
𝒃
2
Z can be obtained
from Figure C9.1
This formula
can be used
for Poisson’s
ration 0.3
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.
Ultimate bending strength - ExampleSolution Procedure – Trial-1 All together
Ultimate bending strength - ExampleSolution Procedure –Trial-1
Skin without buckling
Buckled skin
Ultimate bending strength - ExampleSolution 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.
Ultimate bending strength - ExampleSolution Procedure –Trial-2 Skin without buckling
Buckled skin
Ultimate bending strength - Example
Solution Procedure –Trial-2 All together
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
𝑍2𝑥100 =
27.6−24.2
24.2𝑥100 = 14%
Ultimate bending strength - Example
Solution Procedure –Trial-2 All together