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20_Torsional_Loading

20_Torsional_Loading - EM 324 Mechanics of Materials...

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1 © 2002-2003, L.D. Sturges EM 324 Mechanics of Materials Torsional Loading Torsion – the twisting of a straight bar when it is loaded by moments (torques) that tend to produce rotation about the longitudinal axis . Synonyms : Torques, twisting moments. © 2002-2003, L.D. Sturges EM 324 Mechanics of Materials Torsional Loading (cont) Definition : Positive torque – the torque vector points outward from the “cut” surface. According to the right-hand-rule , this is a counter-clockwise torque when viewed from the “part discarded.” © 2002-2003, L.D. Sturges EM 324 Mechanics of Materials Torsional Loading (cont) Approximations/Assumptions : Circular shaft (solid or hollow). Straight; constant diameter. Shearing strains are small. Plane section before twisting – remains plane. A diameter before twisting – remains straight.
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2 © 2002-2003, L.D. Sturges EM 324 Mechanics of Materials Torsional Shearing Strain Take a short segment of a shaft rotated by a negative torque T (not shown). The right end of the shaft will rotate through an angle θ as shown. © 2002-2003, L.D. Sturges EM 324 Mechanics of Materials Torsional Shearing Strain (cont) Inscribe a line AB down the side of the shaft. The right end of the line will rotate taking B to B' and making an angle of φ between the lines AB and AB' . © 2002-2003, L.D. Sturges EM 324 Mechanics of Materials Torsional Shearing Strain (cont) The length of the line/arc BB' is A square element of material at B will deform into a parallelogram. ' BB L c φ θ = =
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