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,
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
Related questions
Question
If not given the value of JC and CW. Please provide what is the formula of JC and CW
Subject: Civil Engineering- Steel Design
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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