Airframe Design and Construction Fuselage Ultimate bending ......Airframe Design and Construction...

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