AERSP 301Torsion of Multi-Cell Cross-Sections

Jose Palacios

July 2008

• 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

Pure torsion of multi-cell c/sPure 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.

Pure torsion of multi-cell c/sPure torsion of multi-cell c/s

• Individual torques (unknown) are generated in each cell

• Each cell develops constant shear flow:

Pure torsion of multi-cell c/sPure 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

Pure torsion of multi-cell c/sPure torsion of multi-cell c/s

Rearranging terms:

or

Pure torsion of multi-cell c/sPure 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

Pure torsion of multi-cell c/sPure 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:

Multi-Cell Torsion Sample ProblemMulti-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 = 27600 N/mm2

Multi-Cell Torsion Sample ProblemMulti-Cell Torsion Sample Problem

Choosing GREF = 27,600 N/mm then,

mm 07.122.1600,27

200,24*

120 t

Similarly:

mm 07.1*24

*13 tt mm 69.0*

56*46

*35 ttt

12

*12

121542

07.1

1650

t

dso

Similarly:

368 ,736

,233 ,725 ,250

564635

34241312

i

Multi-Cell Torsion Sample ProblemMulti-Cell Torsion Sample Problem

For Cell I:

For Cell II:

For Cell III:

IIIREF

qqGz

2502501542000,2582

1

IIIIIIREF

qqqGz

233725233725250250000,3552

1

368736233736233000,1612

1

IIIIREF

qqGz

1

2

3

Multi-Cell Torsion Sample ProblemMulti-Cell Torsion Sample Problem

In addition: (Looking at the torque)

IIIIII qqq 000,161000,355000,2582103.11 6 4

Solving equations 1 – 4 simultaneously:

qI = 7.1 N/mm

qII = 8.9 N/mm

qIII = 4.2 N/mm

t

q

7.3 Pa5.8 Pa

7.3 Pa 4.6 Pa

4.6 Pa

4.6 Pa2.9 Pa

0.89 Pa