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506.2.2 Lateral-Torsional Buckling 1. When L S Lp the limit torsional buckling does not apply. 2. When Lp L Ly Mn Cb 1p-(M₂-0.7FySx) 3. When Lb > Ly where Lb= Fer= Mn FerSx Mp C₁²E state of lateral- 1+0.078 s( −E)]< Length between points that are either braced. against lateral displacement of compression flange or braced against twist of the cross section, mm ≤Mp (506.2-2) Jc (Lb Sxhorts (506.2-3) (506.2-4) E modulus of elasticity of steel200,000 MPa Jc torsional constant, mm* Selastic section modulus taken about the x-axis, mm³ User Note: The square root term in Eq. 506.2-4 may be conservatively taken equal to 1.0. The limiting lengths Lp and Ly are determined as follows: E Jc L = 1.95rts 0.7Fy Sh where Lp = 1.76ry For a channel: C= 1+ 1+6.76 x 76 rts = E √√Cw Sx and For a doubly symmetric I-shape: c=1 holy 2√√Cw (506.2-5) 0.7F,S,ho (506.2-6) (506.2-7) (506.2-8a) (506.2-8b) where ho distance between the flange centroids, mm User Note: If the square root term in Eq. 506.2-4 is conservatively taken equal to 1, Eq. 506.2-6 becomes E Ly= TTT ts 0.7Fy Note that this approximation can be extremely conservative. For doubly symmetric I-shapes with rectangular flanges, and thus Eq. 506.2-7 becomes Lyh C₁= rts = lyho 25x Its may be approximated accurately and conservatively as the radius of gyration of the compression flanges plus one- sixth of the web: Tts == 12 b 1+ 1 ht,

506.2.2 Lateral-Torsional Buckling 1. When L S Lp the limit torsional buckling does not apply. 2. When Lp L Ly Mn Cb 1p-(M₂-0.7FySx) 3. When Lb > Ly where Lb= Fer= Mn FerSx Mp C₁²E state of lateral- 1+0.078 s( −E)]< Length between points that are either braced. against lateral displacement of compression flange or braced against twist of the cross section, mm ≤Mp (506.2-2) Jc (Lb Sxhorts (506.2-3) (506.2-4) E modulus of elasticity of steel200,000 MPa Jc torsional constant, mm* Selastic section modulus taken about the x-axis, mm³ User Note: The square root term in Eq. 506.2-4 may be conservatively taken equal to 1.0. The limiting lengths Lp and Ly are determined as follows: E Jc L = 1.95rts 0.7Fy Sh where Lp = 1.76ry For a channel: C= 1+ 1+6.76 x 76 rts = E √√Cw Sx and For a doubly symmetric I-shape: c=1 holy 2√√Cw (506.2-5) 0.7F,S,ho (506.2-6) (506.2-7) (506.2-8a) (506.2-8b) where ho distance between the flange centroids, mm User Note: If the square root term in Eq. 506.2-4 is conservatively taken equal to 1, Eq. 506.2-6 becomes E Ly= TTT ts 0.7Fy Note that this approximation can be extremely conservative. For doubly symmetric I-shapes with rectangular flanges, and thus Eq. 506.2-7 becomes Lyh C₁= rts = lyho 25x Its may be approximated accurately and conservatively as the radius of gyration of the compression flanges plus one- sixth of the web: Tts == 12 b 1+ 1 ht,

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
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If not given the value of JC and CW. Please provide what is the formula of JC and CW

 

Subject: Civil Engineering- Steel Design

 

506.2.2 Lateral-Torsional Buckling 1. When Lb Lp buckling does not apply. 2. When Lp <L≤ Lr Mn = Cb 3. Cb [Mp - (M₂ - 0.7F,Sx) When L > L, where Lb Fer = the limit state of lateral- torsional Mn FerSx Mp съпче (11) ² = = (Lb-Lp) Lr-Lp. 1+0.078 Length between points that are either braced against lateral displacement of compression flange or braced against twist of the cross section, mm Jc (Lb) Sxhorts ≤Mp (506.2-2) 2 (506.2-3) (506.2-4) E modulus of elasticity of steel = 200,000 MPa Jc torsional constant, mm* Sx elastic section modulus taken about the x-axis, mm³ User Note: The square root term in Eq. 506.2-4 may be conservatively taken equal to 1.0. The limiting lengths Lp and Ly are determined as follows: Lp = 1.76%'y E Jc L = 1.95rts 0.7Fy Sho where E F, For a channel: c C= y √TCw Sx S,ho 1+ + √ ₁ + 6.76 (0.75, 5₂ kg) ² E Jc and For a doubly symmetric I-shape: c=1 holy 2 (506.2-5) (506.2-6) (506.2-7) (506.2-8a) (506.2-8b) where ho = distance between the flange centroids, mm User Note: If the square root term in Eq. 506.2-4 is conservatively taken equal to 1, Eq. 506.2-6 becomes Ly = πrts Note that this approximation can be extremely conservative. E 0.7Fy For doubly symmetric I-shapes with rectangular flanges, and thus Eq. 506.2-7 becomes Iyh² 4 ris Iyho 2Sx Its == Its may be approximated accurately and conservatively as the radius of gyration of the compression flanges plus one- sixth of the web: b₁ htw 12 (1+6b₁tj)
Transcribed Image Text:506.2.2 Lateral-Torsional Buckling 1. When Lb Lp buckling does not apply. 2. When Lp <L≤ Lr Mn = Cb 3. Cb [Mp - (M₂ - 0.7F,Sx) When L > L, where Lb Fer = the limit state of lateral- torsional Mn FerSx Mp съпче (11) ² = = (Lb-Lp) Lr-Lp. 1+0.078 Length between points that are either braced against lateral displacement of compression flange or braced against twist of the cross section, mm Jc (Lb) Sxhorts ≤Mp (506.2-2) 2 (506.2-3) (506.2-4) E modulus of elasticity of steel = 200,000 MPa Jc torsional constant, mm* Sx elastic section modulus taken about the x-axis, mm³ User Note: The square root term in Eq. 506.2-4 may be conservatively taken equal to 1.0. The limiting lengths Lp and Ly are determined as follows: Lp = 1.76%'y E Jc L = 1.95rts 0.7Fy Sho where E F, For a channel: c C= y √TCw Sx S,ho 1+ + √ ₁ + 6.76 (0.75, 5₂ kg) ² E Jc and For a doubly symmetric I-shape: c=1 holy 2 (506.2-5) (506.2-6) (506.2-7) (506.2-8a) (506.2-8b) where ho = distance between the flange centroids, mm User Note: If the square root term in Eq. 506.2-4 is conservatively taken equal to 1, Eq. 506.2-6 becomes Ly = πrts Note that this approximation can be extremely conservative. E 0.7Fy For doubly symmetric I-shapes with rectangular flanges, and thus Eq. 506.2-7 becomes Iyh² 4 ris Iyho 2Sx Its == Its may be approximated accurately and conservatively as the radius of gyration of the compression flanges plus one- sixth of the web: b₁ htw 12 (1+6b₁tj)
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