notes_14_twist_closed

Notes_14_twist_close - Lecture 5 2003 Twist closed sections As this development would be almost identical to that of the open section some of the

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Lecture 5 - 2003 Twist closed sections As this development would be almost identical to that of the open section, some of the development is simply repeated (copied) from the open section development. pure twist around center of rotation D => neither axial ( σ ) nor bending forces (Mx, My) act on section ----------------------------- from equilibrium -------------------------------- pure twist σ dA = N x τ⋅ h p dA = qh p ds = T p σ dA = 0 σ⋅ y dA = -M.z () dA = q cos α cos α ds = V y y dA = 0 sin α ds = V z z dA = 0 z dA = M y dA = q sin α a) equilibrium of wall element: pure twist => . ξ = η = 0 => δ v δψ + δη sin α = δ x cos α δ x + h p δφ becomes δ v = h D δφ δ x δ x δ x δ x b) compatibility (shear strain) d u + d v = γ ds dx here is first change. we cannot set γ = 0 as we did in the open problem => d u = γ d v => d u = τ ⋅ − h D δφ s τ δφ ds dx ds G δ x u = ds h D ds + u 0 x and integration along s => G δ x 0 δ x as γ is small => = 0 for open sections u = δφ h D ds + u 0 x other assumptions: section shape remains etc. same 1 notes_14_twist_closed.mcd
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
δ x δ x M x s τ ds See: Torsion of Thin-Walled, Noncircular Closed Shafts; Shames Section G 14.5 particularly; equations 14.17, 14.18 and 14.21 (Bredt's formula) 0 also: Hughes 6.1.19, 6.1.21, 6.1.22 and section 6.1 δφ GJ δφ M x = 2q A q := 2A and . .....
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/24/2012 for the course MECHANICAL 2.082 taught by Professor Davidburke during the Spring '03 term at MIT.

Page1 / 5

Notes_14_twist_close - Lecture 5 2003 Twist closed sections As this development would be almost identical to that of the open section some of the

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online