TORSION OF THIN-WALLED BARS

Mechanics of Structures, 2 nd year, Mechanical Engineering, Cairo University TORSION OF THIN-WALLED BARS.......................................................................................2 Review of Circular Shafts........................................................................................................................2 An Approximate Formula for Thin-walled Circular Tubes................................................................2 Example 1..............................................................................................................................................3 Types of Thin-Walled Bars.....................................................................................................................4 Non-Circular Tubes of Variable wall thickness....................................................................................5 Example 2..............................................................................................................................................7 Example 3..............................................................................................................................................8 Example 4..............................................................................................................................................9 Rectangular Cross Sections...................................................................................................................10 Example 5............................................................................................................................................11 Open Thin-Walled bars with Uniform Thickness...............................................................................12 Example 6............................................................................................................................................12 Example 7............................................................................................................................................13 Branched and Tapered Open Cross Sections......................................................................................14 Proof....................................................................................................................................................14 Tapered Cross Sections.......................................................................................................................16 Example 8............................................................................................................................................17 Example 9............................................................................................................................................18 Rolled Steel Cross Sections....................................................................................................................20 Stress Concentration..............................................................................................................................20 The Displacements of Open Cross Sections.........................................................................................21 Displacements in the Plane y-z of the Cross Section..........................................................................21 The Axial Displacement u .................................................................................................................22 Field of Application................................................................................................................................22 Conclusion...............................................................................................................................................22 References...............................................................................................................................................22 Appendix I Shear Flow for Tubular Cross Sections..........................................................................23 Appendix II Shear Stress Bredt’s Formula.........................................................................................24 Torsion of Thin-Walled Bars 1/24

TORSION OF THIN-WALLED BARS

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