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TALAT Lecture 2301: Design of Members Example 6.7: Shear force resistance of orthotropic plate. Open or closed stiffeners

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This example provides calculations on shear force of members based on Eurocode 9.

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TALAT Lecture 2301: Design of Members Example 6.7: Shear force resistance of orthotropic plate. Open or closed stiffeners

  1. 1. TALAT Lecture 2301 Design of Members Shear Force Example 6.7 : Shear force resistance of orthotropic plate. Open or closed stiffeners 6 pages Advanced Level prepared by Torsten Höglund, Royal Institute of Technology, Stockholm Date of Issue: 1999  EAA - European Aluminium Association TALAT 2301 – Example 6.7 1
  2. 2. Example 6.7. Shear force resistance of orthotropicplate. Open or closed stiffeners Dimensions (highlighted) Plate thickness t 16.5 . mm t1 t fo 240 . MPa N newton Plate width b 1500 . mm fu 260 . MPa kN 1000 . newton 2200 . mm 70000 . MPa MPa 10 . Pa 6 Plate length L E w Stiffener pitch w 300 . mm a γ M1 1.1 2 If heat-treated alloy, then = 1 else ht = 0 ht ht 1 If cold formed (trapezoidal), then = 1 else cf. = 0 cf. cf 0 a) Open stiffeners Half stiffener pitch a = 150 mm Half bottom flange a2 50 . mm Thickness of bottom flange t2 10 . mm Stiffener depth h 160 . mm Half web thickness t3 4.4 . mm Half width of trapezoidal a1 0 . mm stiffener at the top Width of web a3 h a 3 = 160 mm Local buckling L L = 2.2 . 10 mm 3 Length of web panel a = 150 mm = 7.333 2 .a 2 .a 2 .a 2 2 L (5.97) kτ if > 1.00 , 5.34 4.00 . , 4.00 5.34 . k τ = 5.414 2 .a L L 0.81 . 2 . a . f o (5.96) λ w t E λ w 0.371 = kτ 0.48 Table 5.12 ρ v λ w ρ v = 1.295 fu Table 5.12 η 0.4 0.2 . η = 0.617 fo Table 5.12 ρ v if ρ v > η , η , ρ v ρ v= 0.617 fo ρ .b .t 1 . V w.Rd = 3.33 . 10 kN 3 (5.95) V w.Rd v γ M1 TALAT 2301 – Example 6.7 2
  3. 3. 5.11.6 Overall buckling, shear force 2 .t 1 .a 2 .t 2 .a 2 2 .t 3 .a 3 2 .t 1 .a 1 A = 7.358 . 10 mm 3 2 Cross sectional area A h 2 .t 2 .a 2 .h 2 .t 3 .a 3 . Gravity centre 2 e e = 37.054 mm A Second moment of area 2 h 2 .t 2 .a 2 .h 2 .t 3 .a 3 . A .e I L = 2.751 . 10 mm 2 2 7 4 IL 3 s if cf 1 , 2 . a 2 .a 3 . a 2 1 a2 , 2 .a s = 300 mm Rigidities of orthotropic plate E .I L ν 0.3 N . mm 2 B x = 6.42 . 10 9 Table 5.10 Bx 2 .a G E mm 2 .( 1 ν ) E .t N . mm 3 2 B y = 2.88 . 10 7 Table 5.10 By 12 . 1 2 mm ν G .t N . mm 3 2 H = 2.016 . 10 7 Table 5.10 H 6 mm Elastic buckling load 1 4 H L. B y η φ φ = 0.38 (5.83) (5.84) b Bx B x .B y η = 0.047 0.567 . φ 1.92 . φ 0.1 . φ 2.75 . φ .η 2 2 (5.82) kτ 3.25 1.95 k τ = 3.423 1 k τ .π 2 4 (5.81) V o.cr . B .B 3 V o.cr = 2.506 . 10 kN 3 b x y Buckling resistance b .t 1 .f o (5.120) λ ow λ ow 1.54 = V o.cr 0.6 (5.119) χ o χ o if χ o > 0.6 , 0.6 , χ o χ o 0.189 = 2 0.8 λ ow fo χ .o . t 1 . V o.Rd = 1.022 . 10 kN 3 (5.118) V o.Rd b γ M1 V Rd = 1.022 . 10 kN 3 V Rd if V w.Rd < V o.Rd , V w.Rd , V o.Rd TALAT 2301 – Example 6.7 3
  4. 4. b) Closed stiffeners Half stiffener pitch a = 150 mm Plate thickness t 1 = 16.5 mm Half bottom flange a 2 = 50 mm Thickness of bottom flange t 2 = 10 mm Stiffener depth h = 160 mm Web thickness t3 9 . mm Half width of trapezoidal a1 80 . mm stiffener at the top 2 2 width of web a3 a1 a2 h a 3 = 162.8 mm a4 a a1 a 4 = 70 mm Local buckling L L = 2.2 . 10 mm 2 .a 2 .a 1 3 Length of web panel am a m = 140 mm = 15.714 am 2 2 L am am (5.97) kτ if > 1.00 , 5.34 4.00 . , 4.00 5.34 . am L L k τ = 5.356 0.81 . a m . f o (5.96) λ w t E λ w 0.174 = kτ 0.48 Table 5.12 ρ v λ w ρ v = 2.76 fu Table 5.12 η 0.4 0.2 . η = 0.617 fo Table 5.12 ρ v if ρ v > η , η , ρ v ρ v= 0.617 fo ρ .b .t 1 . V w.Rd = 3.33 . 10 kN 3 (5.95) V w.Rd v γ M1 TALAT 2301 – Example 6.7 4
  5. 5. 5.11.6 Overall buckling, shear force 2 .t 1 .a 2 .t 2 .a 2 2 .t 3 .a 3 A = 8.88 . 10 mm 3 2 Cross sectional area A h 2 .t 2 .a 2 .h 2 .t 3 .a 3 . Gravity centre 2 e e = 44.415 mm A 2 h 2 .t 2 .a 2 .h 2 .t 3 .a 3 . A .e I L = 3.309 . 10 mm 2 2 7 4 Second moment IL of area 3 4. h. a 1 a 2 2 I T = 3.097 . 10 mm 7 4 Torsion constant IT 2 .a 1 2 .a 2 a3 2. t1 t2 t3 t2 4. 1 ν . a2 a 3 .a 1 .a 4 .h . 2 2 2 2 (5.79c) C1 C 1 = 3.076 . 10 mm 9 4 3 .a .t 1 3 E .t 3 B = 2.88 . 10 N . mm 7 B (5.79d) 12 . 1 2 ν a1 a2 2 a 4. a 1 a 2 .a 1 .a 4 . 1 2 a 1 .a 3 t 2 3 a2 a1 (5.79e) C2 . C 2 = 4.851 a 2 . 3 .a 3 4 .a 2 3 t1 Rigidities of orthotropic plate E .I L E N . mm 2 B x = 7.72 . 10 9 Table 5.10 Bx ν 0.3 G 2 .a 2 .( 1 ν ) mm 2 . B. a (5.79a) By 2 .a 1 .a 3 .t 1 . 4 .a 2 .t 3 a 3 .t 2 3 3 3 2 .a 4 a 3 .t 1 . 4 .a 2 .t 3 a 3 .t 2 a 1 . t 3 . 12 . a 2 . t 3 4 .a 3 .t 2 3 3 3 3 3 3 G .I T N . mm 2 B y = 3.929 . 10 7 6 .a mm (5.79b) H 2 .B 1.6 . G . I T . a 4 2 N . mm 1 2 1 . 1 H = 7.305 . 10 8 L .a .B 2 C1 mm π . 4 C2 4 L Elastic buckling load 1 4 H L. B y η φ φ = 0.392 (5.83) (5.84) b Bx B x .B y η = 1.326 0.567 . φ 1.92 . φ 0.1 . φ 2.75 . φ .η 2 2 (5.82) kτ 3.25 1.95 k τ = 6.52 1 k τ .π 2 4 (5.81) V o.cr . B .B 3 V o.cr = 6.311 . 10 kN 3 b x y TALAT 2301 – Example 6.7 5
  6. 6. TALAT 2301 – Example 6.7 6
  7. 7. Buckling resistance b .t 1 .f o (5.120) λ ow λ ow 0.97 = V o.cr 0.6 (5.119) χ o χ o if χ o > 0.6 , 0.6 , χ o χ o 0.345 = 2 0.8 λ ow fo χ .o . t 1 . V o.Rd = 1.861 . 10 kN 3 (5.118) V o.Rd b γ M1 TALAT 2301 – Example 6.7 7

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