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Cb : The lateral-torsional buckling modification factor
E : Modulus of elasticity of steel = 29,000 ksi (200 000 MPa)
Fcr : Lateral-torsional buckling stress for the section as determined by analysis, ksi (MPa
Fy : Specified minimum yield stress of the type of steel being used, ksi
Its : Effective radius of inertia
J : Torsional constant
ho : Distance between the flange centroids, in. (mm)
Lb : Length between points that are either braced against lateral displacement of the compression flange or braced against twist of the cross-section, in. (mm)
Lp : The limiting laterally unbraced length for the limit state of yielding, in. (mm)
Lr: The limiting unbraced length for the limit state of inelastic lateral-torsional buckling, in. (mm),
Mmax : absolute value of maximum moment in the unbraced segment, kip-in. (N-mm)
MA : absolute value of moment at quarter point of the unbraced segment, kip-in. (N-mm)
MB : absolute value of moment at centerline of the unbraced segment, kip-in. (N-mm)
MC : absolute value of moment at three-quarter point of the unbraced segment, kip-in. (N-mm)
Mn : The nominal flexural strength
Mp : Plastic bending moment
ry : Radius of gyration about the y-axis
Sx : Elastic section modulus taken about the x-axis, in.3 (mm3)
Zx = Plastic section modulus about the x-axis, in.3 (mm3)
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| body | --uriencoded--$$ \normalsize M_n = F_%7Bcr%7DS_x \le M_p \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; (F2-3) $$ |
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| body | --uriencoded--$$ \normalsize |
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| \pi%5e2E%7D%7B \Big( \dfrac%7BL_b%7D%7Br_%7Bts%7D%7D\Big)%5e2 %7D \sqrt%7B1+0.078 \dfrac%7BJ_c%7D%7BS_xh_o%7D \Big(\dfrac%7BL_b%7D%7Br_%7Bts%7D%7D\Big)%5e2%7D \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; (F2-4) $$ |
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The lateral-torsional buckling modification factor, Cb, is calculated below.
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| body | --uriencoded--$$ \normalsize C_%7Bb%7D = \dfrac %7B12.5M_%7Bmax%7D%7D%7B 2.5M_%7Bmax%7D+3M_A+4M_B+3M_C%7D \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; (F2-4) $$ |
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Limiting laterally unbraced length for the limit state of yielding, Lp is calculated below.
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| body | --uriencoded--$$ \normalsize F_%7Bcr%7D = \dfrac %7BC_b \pi%5e2E%7D%7B \Big( \dfrac%7BL_b%7D%7Br_%7Bts%7D%7D\Big)%5e2 %7D \sqrt%7B1+0.078 \dfrac%7BJ_c%7D%7BS_xh_o%7D \Big(\dfrac%7BL_b%7D%7Br_%7Bts%7D%7D\Big)%5e2%7D \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; (F2- |
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