1. AERSP 301 Torsion of Multi-Cell Cross-Sections
Jose Palacios
July 2008

2. Torsion of Multi-Cell sections Ch. 23.3
Mid-term Exam
Evening Exam
July 29, 2:00 pm VLRCOE
HW Policy
Due in my mail box by end of day on due date
Late policy
-10 % per day starting with HW 4
Torsion of Multi-Cell sections Ch. 23.3

3. Pure torsion of multi-cell c/s
Pure torsion case, no axial restraint ( no direct stresses, only shear stresses present).
Wing booms have no effect in the pure torsion case.
Wing section comprises N cells, carries torque T.
All cells experience the same rate of twist.

4. Pure torsion of multi-cell c/s
Individual torques (unknown) are generated in each cell
Each cell develops constant shear flow:

5. Pure torsion of multi-cell c/s
Also use compatibility of rate of twist between the cells.
For the Rth cell the rate of twist is:
Note:
for each wall

6. Pure torsion of multi-cell c/s
Rearranging terms: or

7. Pure torsion of multi-cell c/s
In general terms:
R-1,R is for wall common to cells R-1 & R
R is for all the walls enclosing the Rth cell
R+1,R is for wall common to cells R & R+1

8. Pure torsion of multi-cell c/s
Skin panels and spar webs are frequently made from different materials, so instead of:
We use:
From which:
If ,
the modulus weighted thickness
Then:

9. Multi-Cell Torsion Sample Problem
Calculate shear stress distribution in the walls of the 3-cell wing section shown when it is subjected to 11.3 kNm anti-clockwise torque. Use GREF = N/mm2

10. Multi-Cell Torsion Sample Problem
Choosing GREF = 27,600 N/mm then,
Similarly:
Similarly:

11. Multi-Cell Torsion Sample Problem
For Cell I: 1
For Cell II: 2
For Cell III: 3

12. Multi-Cell Torsion Sample Problem
In addition: (Looking at the torque) 4
Solving equations 1 – 4 simultaneously:
5.8 Pa
7.3 Pa
qI = 7.1 N/mm
4.6 Pa
0.89 Pa
qII = 8.9 N/mm
2.9 Pa
4.6 Pa
qIII = 4.2 N/mm
7.3 Pa
4.6 Pa