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Unformatted text preview: Department of Aerospace Engineering AERSP 301 Torsion of closed and open section beams Jose L. Palacios July 2008 Department of Aerospace Engineering REMINDERS • IF YOU HAVE NOT TURN IN HW# 4 PLEASE DO SO ASAP TO AVOID FURTHER POINT PENALTIES. • HW #5 DUE FRIDAY, OCTOBER 3 • HW #6 (FINAL HW from me) DUE FRIDAY OCTOBER 10 • EXAM: OCTOBER 20 – 26 HOSLER – 8:15 – 10:15 PM • REVIEW SESSION: OCTOBER 19 – 220 HAMMOND – 6 – 9 PM Department of Aerospace Engineering Torsion of closed section beams Torsion of closed section beams • To simultaneously satisfy these, q = constant • Thus, pure torque const. shear flow in beam wall • A closed section beam subjected to a pure torque T does not in the absence of axial constraint, develop any direct stress, σ z • Now look at pure torsion of closed c/s Department of Aerospace Engineering Torsion of closed section beams Torsion of closed section beams • Torque produced by shear flow acting on element δ s is pq δ s [BredtBatho formula] • Since q = const. & Hw # 3, problem 3 Department of Aerospace Engineering Torsion of closed section beams Torsion of closed section beams • Already derived warping distribution for a shear loaded closed c/s (combined shear and torsion) • Now determine warping distribution from pure torsion load • Displacements associated with BredtBatho shear flow (w & v t ): 0 = Normal Strain Department of Aerospace Engineering Torsion of closed section beams Torsion of closed section beams • In absence of direct stress, • Recall No axial restraint Department of Aerospace Engineering Torsion of closed section beams Torsion of closed section beams • To hold for all points around the c/s (all values of ψ ) c/s displacements have a linear relationship with distance along the beam, z Department of Aerospace Engineering Torsion of closed section beams Torsion of closed section beams • Earlier, • For const. q Twist and Warping of closed section beams Lecture Also Needed for HW #5 problem 3 Department of Aerospace Engineering Torsion of closed section beams Torsion of closed section beams • Starting with warping expression: • For const. q • Using Department of Aerospace Engineering Twisting / Warping sample problem Twisting / Warping sample problem • Determine warping distribution in doubly symmetrical, closed section beam shown subjected to anticlockwise torque, T. • From symmetry, center of twist R coincides with midpoint of the c/s. • When an axis of symmetry crosses a wall, that wall will be a point of zero warping. • Take that point as the origin of S. Department of Aerospace Engineering Sample Problem Sample Problem • Assume G is constant ab A t a t b w t ds t ds A A AG T w w a b s s s o s = + = = = =  = ∫ ∫ and , 2 , and 2 0s δ δ δ δ δ δ From 0 to 1, 0 ≤ S 1 ≤ b/2 and 4 and , 1 1 1 1 as A t s t ds s b s s = = = ∫ δ Find Warping Distribution Department of Aerospace Engineering...
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 '09
 GANDHI,FARHANLESIEUTRE,GEORGE
 Aerospace Engineering, Shear Stress, Department of Aerospace Engineering

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