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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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