TALAT Lecture 2301: Design of Members Example 8.3: Torsion constants for deck profile
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This 3-page document provides an example of calculating the torsion constants for a simplified aluminum bridge deck profile. It includes 18 nodes defining the profile's geometry with coordinates and thickness values. Calculations are shown for the cross-sectional area, first and second area moments, area within the mid-line, sum of length-to-thickness ratios, and finally the torsion constant and torsion resistance values for the profile. The example aims to demonstrate determining these properties for structural analysis of the deck under torsional loads.
TALAT Lecture 2301: Design of Members Example 8.3: Torsion constants for deck profile
- 1. TALAT Lecture 2301 Design of Members Torsion Example 8.3 : Torsion constants for deck profile 3 pages Advanced Level prepared by Torsten Höglund, Royal Institute of Technology, Stockholm Date of Issue: 1999 EAA - European Aluminium Association TALAT 2301 – Example 8.3 1
- 2. Example 8.3. Torsion constants for deck profile This example is a simplification of an aluminium profile used in a bridge deck. 0 110.5 1.5 6.5 Nodes, co-ordinates, 1 100 1.5 6.5 thickness 2 119.5 31.75 5.25 3 119.5 45.75 11 4 102.5 45.75 6.5 5 102.5 45.75 5 6 119.5 45.75 6.5 7 119.5 31.75 11 8 100 1.5 5.25 i 9 y 85.5 . mm z 1.5 . mm t 6.5 . mm 10 82.5 0 5 11 82.5 0 3.5 12 85.5 1.5 5 13 100 1.5 6.5 14 40 45.75 3.5 15 0 0 3.5 16 40 45.75 3.5 17 100 1.5 3.5 18 110.5 1.5 6.5 60 40 20 0 20 150 100 50 0 50 100 150 TALAT 2301 – Example 8.3 2
- 3. TALAT 2301 – Example 8.3 3
- 4. Nodes i 1 .. rows ( y ) 1 rows ( y ) 1 = 18 Area of cross ti . section 2 2 dAi yi yi 1 zi zi 1 elements Cross rows ( y ) 1 section A = 3.855 . 10 mm 3 2 area A dAi i =1 First rows ( y ) 1 dAi Sy moment Sy zi zi 1 . z gc of area. 2 A Gravity centre i =1 z gc = 24.932 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 = 1.468 . 10 mm 6 4 First rows ( y ) 1 dAi Sz moment Sz yi yi 1 . y gc of area. 2 A Gravity centre i =1 y gc = 0 m Second rows ( y ) 1 dAi yi . yi 1 . A . y gc moment 2 2 2 Iz yi yi 1 Iz Iz of area 3 i =1 I z = 2.33 . 10 mm 7 4 When calculating torsion constants the interior branches are omitted 13 Area within 0.5 . yi yi 1 . zi A v = 1.039 . 10 mm 4 2 mid-line Av zi 1 i =2 13 2 2 yi yi 1 zi zi 1 Sum of l/t Dn if t i > 0 . mm , ,0 Dn = 116.407 ti i =2 4 .A v 2 Torsion I v = 3.711 . 10 mm 6 4 constant Iv Dn I vc 3.713 . 10 . mm 6 4 Correct value incl. branches: i 0 .. 13 tm if t i > 0 . mm , t i , 100 . mm Torsion i resistance 2 . A v . min t m W v = 7.275 . 10 mm 4 3 Wv min t m = 3.5 mm TALAT 2301 – Example 8.3 4