LECTURE+13+COE-3001-A

Linear speed at the rim is the

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Unformatted text preview: ARD TA Driving Torque (from motor) 2/1/13 M. Mello/Georgia Tech Aerospace TB TC ResisZng Torques (from external machines) 10 STATICALLY INDETERMINATE TORSIONAL MEMBERS EXAMPLE: COMPOSITE BAR LOADED IN TORSION (from Gere and Goodno sec. 3.8 (Brief EdiZon)) GIVEN: •  solid (interior) bar: (G1 , d1 , Ip1 ) i o •  hollow (exterior) bar: (G2 , d2 , d2 , Ip2 ) DETERMINE: SMALL CLEARANCE BETWEEN SOLID AND HOLLOW TUBES 2/1/13 d1 RIGID END CAP BINDS INTERIOR BAR WITH EXTERNAL SLEEVE C O MP OSITE BAR RIGID END CAP ROTATES BY ANGLE φ do di 2 2 M. Mello/Georgia Tech Aerospace 11 EQUILIBRIUM: TORQUE DEVELOPED WITHIN HOLLOW BAR APPLIED T = T1 + T2 (STATICALLY INDETERMINATE PROBLEM) TORQUE TORQUE DEVELOPED WITHIN SOLID BAR COMPATIBILITY: = 1 = 2 twist of outer (hollow) bar twist of inner (solid) bar total twist 2/1/13 M. Mello/Georgia Tech Aerospace 12 GIVEN: •  Bar ACB fixed at both ends and loaded by torque (T0) T point C. •  Each segment AC and CB made of same material •  dA = diameter of AC ; LA = length of AC •  dB = diameter of CB ; LB = length of AB •  IPA = polar moment of inerZa of segment AC •  IPB = polar moment of inerZa of segment CB DETERMINE: (A)  ReacZve torques TA and TB at each end (B)  Max shear stress (τmax) in each segment (C)  Angle of rotaZon (twist) at cross secZon at C (where T0 is applied) SOLUTION: WORKED OUT ON BOARD Figure (c) : Consider the twist angle of T0 acZng alone Figure (d): Consider the twist angle of reacZon torque TB acZng alone 2/1/13 M. Mello/Georgia Tech Aerospace 13...
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