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CE 203- structural Mechanics I

CE 203- structural Mechanics I. Lecture # 22-24 Torsion-noncircular sections. Torsion of Solid Noncircular Shafts. Solid Noncircular shafts.

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CE 203- structural Mechanics I

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  1. CE 203- structural Mechanics I Lecture # 22-24 Torsion-noncircular sections

  2. Torsion of Solid Noncircular Shafts

  3. Solid Noncircular shafts Unlike deformation in shafts with circular cross-sections, other cross sections will bulge or warp when the shafts is twisted resulting in complex distribution of stress

  4. Shear stress distribution along two radial lines

  5. Max shear stress and stress at corner

  6. Helpful expressions for max shear and angle of twist

  7. See handout for other sections • Rectangle • Thin rectangle • Sections composed of narrow rectangles

  8. Compare the values of max shear stress and angle of twist Developed in the shaft having circular and square x-section. Each shaft has an area of 9 sq. in., length = 36 in. Take T = 4000 lb.in, G =11x106 psi

  9. Torsion of thin walled closed sections

  10. Assumptions Small thickness End torque only Cross-section does not vary with length No slit Result constant shear flow q =t shear stress It can be shown using statics ie Σ T = 0 That :

  11. Average shear and twist q = T/2 Am Hence τavg = T/2 Am t And φ = T L/(4 Am2 G) ∫ ds/t Where Am is the mean area enclosed by centerline of thickness

  12. Shaft design (sec. 11.4 partly) • If we know the allowable shear stress and the internal torque diagram, we must be able to determine the minimum diameter required • Use basic torsion formula

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