{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

notes_14_twist_closed

# notes_14_twist_closed - Lecture 5 2003 Twist closed...

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

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 = q h p ds = T p σ dA = 0 σ⋅ y dA = -M.z ( ) dA = q cos α τ⋅ cos α ( ) ds = V y σ⋅ y dA = 0 τ⋅ sin α ( ) ds = V z σ⋅ z dA = 0 σ⋅ 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

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

View Full Document
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 G J δφ M x = 2 q A q := 2 A and ......
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}