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AERSP 301 Torsion of Multi-Cell Cross-Sections

AERSP 301 Torsion 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.

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AERSP 301 Torsion of Multi-Cell Cross-Sections

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

  2. 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,Ris for wall common to cells R-1 & R Ris for all the walls enclosing the Rth cell R+1,R is for wall common to cells R & R+1

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

  9. 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

  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: 7.3 Pa 5.8 Pa 4.6 Pa qI = 7.1 N/mm 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

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