Fig. 1: Moment Capacity during the 3 stages of Lateral Torsional Buckling (L.T.B.)
What is Lateral Torsional Buckling (L.T.B.)?
Lateral Torsional Buckling (LTB) is a failure criteria for beams in flexure. The AISC defines Lateral Torsional Buckling as: the buckling mode of a flexural member involving deflection normal to the plane of bending occurring simultaneously with twist about the shear center of the crosssection. LTB occurs when the compression portion of a beam is no longer sufficient in strength and instead the beam is restrained by the tension portion of the beam (which causes deflection or twisting to occur).
The best analogy I can provide is a girl on a tightrope. As the rope gets longer and longer it will become more and more difficult for the girl to remain balanced (since the swing/twist of the wire will become greater and greater). This also makes sense empirically; without LTB then a beam would have the same flexural strength whether it stretched 10 feet or 100 feet.
The best ways to prevent Lateral Torsional Buckling are to:
 Adequately brace the beam laterally at small intervals
 Use a larger section size (this will increase your r_{y} which will increase the L_{p} shown in Figure 1 above)
How to find your LTB limits:
Three limits exist when solving for lateral torsional buckling (shown in Fig. 1 above):
 L_{b} < L_{p} which defines when a member is not subject to LTB
 L_{p} < L_{b} < L_{r} which defines when a member is subject to inelastic LTB
 L_{r} < L_{b} which defines when a member is subject to elastic LTB
where:
For Compact Cross Sections (most common):
Solving for L_{p}: L_p = {1.76{r_y}\sqrt{\frac{E}{F_y}}}

where:
r_{y} = The radius of gyration? about the weak axis of the cross section
E = The modulus of elasticity of the steel beam (e.g. 29000 ksi)
F_{y} = The yield strength of the steal beam (e.g. A36 has a yield strength of 36 ksi)
Solving for L_{r}: L_r = 1.95r_{ts}\frac{E}{0.7F_y}\sqrt{\frac{Jc}{S_xh_O}}\sqrt{1+\sqrt{1+6.76\left(\frac{0.7F_y}{E}\frac{S_xh_O}{Jc}\right)^2}}

where:
r_{ts}^{2} = \frac{\sqrt{I_yC_w}}{S_x} = \frac{I_yh_O}{2S_x}
I_{y} = The Moment of Inertia about the weak axis of the cross section (in^{4})
C_{w} = \frac{I_yh_O^2}{4} (for rectangular flanged doubly symmetric shapes)
S_{x} = Section Modulus? of the beam about the strong axis of the cross section (in^{3})
h_{O} = distance between flange centroids = d  t_{f} (in)
E = The modulus of elasticity of the steel beam (e.g. 29000 ksi)
F_{y} = The yield strength of the steal beam (e.g. A36 has a yield strength of 36 ksi)
J = torsional constant (in^{4})
c = 1 (for doubly symmetric Ishape) or \frac{h_O}{2}\sqrt{\frac{I_y}{C_w}} (for a channel)
C_{w} = warping constant (in^{6})
Note: For standard doubly symmetric Ishapes: r_{ts}, r_{y}, J, S_{x}, h_{O}, I_{y}, & C_{w} can all be found in Table 1 of the AISC 360 Steel Construction Manual^{[1]}. This makes these calculations much easier.
For NonCompact Cross Sections (uncommon):
Fig. 2: Moment Capacity vs. Unbraced Length
Solving for M_{p}' (noncompact section): M_p' = M_p  (M_p  0.7F_yS_x) \frac{\lambda  \lambda_p'}{\lambda_r  \lambda_p}

where:
M_{p} = The moment capacity with no LTB for a compact beam
F_{y} = The yield strength of the steal beam (e.g. A36 has a yield strength of 36 ksi)
S_{x} = Section Modulus? of the beam about the strong axis of the cross section (in^{3})
λ = \frac{b_f}{2t_f}
λ_{p} = the limiting slenderness for a compact flange (see AISC 360 Table B4.1) = 0.38\sqrt{\frac{E}{F_y}} (for flexure in the flanges of a rolled Ishape)
λ_{r} = the limiting slenderness for a noncompact flange (see AISC 360 Table B4.1) = 1.0\sqrt{\frac{E}{F_y}} (for flexure in the flanges of a rolled Ishape)
b_{f} = the base of the flange (in)
t_{f} = the thickness of the flange (in)
Solving for L_{p}' (noncompact section): L_p' = L_p + (L_r  L_p) \frac{M_p  M_p'}{M_p  M_r}

where:
L_{p} = The limit between no LTB and Inelastic LTB for a compact section
L_{r} = The limit between Inelastic LTB and Elastic LTB (ft)
M_{p}' = The moment capacity with no LTB for a noncompact beam
M_{p} = The moment capacity with no LTB for a compact beam
M_{r} = The moment capacity at the transition between inelastic and elastic LTB = 0.7F_{y}S_{x}
Solving for different Lateral Torsional Buckling cross sections
Solving for the capacity of a steel beam (and thus checking to see if the beam is in the inelastic or elastic lateral torsional buckling range) is shape dependent. Above you found how to find those limits. Below you will find how to design a member and find if LTB is present.
 Steel IBeam Lateral Torsional Buckling Design  Works for doubly symmetric IShaped members bent about their strong axis.
 Steel Channel Lateral Torsional Buckling Design
References:
 American Institute of Steel Construction), "Steel Construction Manual 13th edition", 2005
 This Section is thoroughly covered in Part 3 of the AISC Steel Manual and in Chapter F of the Specifications (AISC 360)
 Table B4.1 in the Specifications (AISC 360) has also been referenced to find λ_{p} & λ_{r}.