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# TALAT Lecture 2301: Design of Members Example 8.2: Torsion constants for hollow cross section

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This example provides calculations on torsion of members based on Eurocode 9.

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### TALAT Lecture 2301: Design of Members Example 8.2: Torsion constants for hollow cross section

1. 1. TALAT Lecture 2301 Design of Members Torsion Example 8.2 : Torsion constants for hollow cross section 3 pages Advanced Level prepared by Torsten Höglund, Royal Institute of Technology, Stockholm Date of Issue: 1999  EAA - European Aluminium Association TALAT 2301 – Example 8.2 1
2. 2. Example 8.2. Torsion constants for hollow cross section a) Polygon b Half width b 50 . mm Half width of a a = 20.711 mm flat parts Thickness s 6 . mm 1 2 Nodes no., 0 b a s co-ordinates, 1 a b s thickness 2 a b s 3 b a s i 4 y b z a t s 5 a b s 6 a b s 7 b a s 8 b a s 50 0 Nodes i 1 .. rows ( y ) 1 z 0 0 Area of cross mm ti . section 2 2 dAi yi yi 1 zi zi 1 elements 50 Cross rows ( y ) 1 section 50 0 50 area A dAi y i =1 mm First rows ( y ) 1 dAi Sy moment Sy zi zi 1 . z gc of area. 2 A i =1 Gravity centre z gc = 1.704 . 10 15 mm Second rows ( y ) 1 dAi zi . zi 1 . A . z gc moment 2 2 2 Iy zi zi 1 Iy Iy of area 3 i =1 I y = 2.627 . 10 mm 6 4 rows ( y ) 1 Area within 0.5 . yi yi 1 . zi A v = 8.284 . 10 mm 3 2 mid-line Av zi 1 Check: i =1 ( 2 .b ) 2 .( b a ) = 8.284 . 10 mm 2 2 3 2 Sum of l/t rows ( y ) 1 4 .A v 2 2 2 yi yi 1 zi zi 1 Torsion Dn Dn = 55.228 Iv ti Dn constant i =1 I v = 4.971 . 10 mm 6 4 Torsion 2 . A v . min ( t ) W v = 9.941 . 10 mm 4 3 resistance Wv min ( t ) = 6 mm TALAT 2301 – Example 8.2 2
3. 3. TALAT 2301 – Example 8.2 3
4. 4. b) Symmetric hollow extrusion Half width b 50 . mm Indent c 10 . mm Half width of a 20 . mm flat parts Thickness s 6 . mm Nodes no., co-ordinates, 0 b a s thickness 1 b c a s 2 a b c s 3 a b s 4 a b s 5 a b c s 6 b c a s 7 b a s i 8 y b z a t s 9 b c a s 10 a b c s 11 a b s 12 a b s 13 a b c s 50 14 b c a s 0 15 b a s z 0 16 b a s 0 mm 50 50 0 50 Nodes i 1 .. rows ( y ) 1 y mm rows ( y ) 1 Area within 0.5 . yi yi 1 . zi A v = 7.2 . 10 mm 3 2 mid-line Av zi 1 i =1 rows ( y ) 1 2 2 yi yi 1 zi zi 1 Sum of l/t Dn Dn = 58.856 ti i =1 4 .A v 2 Torsion I v = 3.523 . 10 mm 6 4 constant Iv Dn 2 . A v . min ( t ) W v = 8.64 . 10 mm 4 3 Torsion Wv min ( t ) = 6 mm resistance TALAT 2301 – Example 8.2 4