CIV E 270 Lab #5

# CIV E 270 Lab #5 - University of Alberta Department of...

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University of Alberta Department of Civil and Environmental Engineering Civ E 270 Laboratory 5 Name: I.D.: Date: Mark: Lab Section: TORSION 5.1 GENERAL BACKGROUND When a straight prismatic bar is subjected solely to moment about its longitudinal axis, it twists about that axis, shearing stresses are developed, and a single stress resultant, the twisting moment T, is developed on each transverse cross section. The straight prismatic bar of circular cross section is the most common structural element subjected primarily to torsion. (Consider, for example, the transmission shaft used in conjunction with most engines.) Because of symmetry, planes normal to the axis of the bar remain plane during deformation, and the shearing stress τ varies linearly with ρ , the radial distance from the axis of the shaft. Using equilibrium and compatibility relationships, the elementary theory of torsion can be described as: τ ρ τ = = T J or Tc J max and GJ TL = φ where J = the polar moment of inertia = 1 2 32 4 4 π π c d = for a solid circular shaft = ( ) ( ) 4 1 4 2 4 1 4 2 d d 32 c c 2 1 π = π for a hollow circular shaft c = the radius of a solid circular shaft c 2 = the outside radius of a hollow circular shaft c 1 = the inside radius of a hollow circular shaft and d, d 1 , and d 2 are the corresponding diameters

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