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

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

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.

Pure 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/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/s Rearranging terms: or

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

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:

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 = 27600 N/mm2

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

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

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