6._Torsion_of_Closed_Section_Beams_-_Hw_

6._Torsion_of_Closed_Section_Beams_-_Hw_ - Department of...

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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, 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 s is pq s [Bredt-Batho 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 Bredt-Batho 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 ) 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 mid-point 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 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 = = = Find Warping Distribution Department of Aerospace Engineering...
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6._Torsion_of_Closed_Section_Beams_-_Hw_ - Department of...

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