M anwar hossain phd peng ryerson university shearing

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Unformatted text preview: hD, PEng; Ryerson University Shearing stress is maximum at the midpoint of the cross-section and zero at the corner K.M. Anwar Hossain, PhD, PEng; Ryerson University K.M. Anwar Hossain, PhD, PEng; Ryerson University 7 Equations for maximum shearing stress and angle of twist a and b are the lengths of the short and long sides of the rectangular cross-section, respectively α,β : numerical factors Torsional stress Angle of twist K.M. Anwar Hossain, PhD, PEng; Ryerson University Torsion of Thin-walled tubes-Shear Flow non-circular section with a wall of variable thickness, t nonShear flow (q) - internal shear force per unit length (N/m) and in terms of average shearing stress: Shear flow on a cross-section (q) is constant even though the thickness of section (t) varies K.M. Anwar Hossain, PhD, PEng; Ryerson University K.M. Anwar Hossain, PhD, PEng; Ryerson University 8 State of stress in a block cut between A and B • Member in pure torsion, no normal forces and only shear forces (V1…V4) are necessary for equilibrium; Summing forces in x-direction: K.M. Anwar Hossain, PhD, PEng; Ryerson University Torsion of Thin-walled tubes-Shear Flow (a) The shearing stress at point A on the longitudinal and transverse planes have the same magnitude; likewise; the shearing stresses at point B have the same magnitude on the two orthogonal planes; hence, Eq (a) my be written as τΑtΑ = τΒtΒ Shear flow at A and B are same K.M. Anwar Hossain, PhD, PEng; Ryerson University K.M. Anwar Hossain, PhD, PEng; Ryerson University 9 Torsion and shear stress of Thin-walled non-circular section with a wall of variable thickness, t non- = t(2A) = ττt(2A) Resisting Torque (Tr) (Tr) A = Area enclosed by the median line of the section Applies to closed K.M. Anwar Hossain, PhD, PEng; t = thickness of the section section Ryerson University Torsional resistance of longitudinally slotted thin member Significantly lower than closed section due to the discontinuity of shear flow K.M. Anwar Hossain,...
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This document was uploaded on 03/31/2014.

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