A quick recap of strong & weak axis bending?
A beam's flexural capacities are broken into two main categories: strong axis bending and weak axis bending. Weak axis bending is about the axis that has the lower moment of inertial (normally considered the yy axis).
Weak axis bending is allowed a lower safety factor than strong axis bending since Lateral Torsional Buckling is not possible (since I_{x} is stronger than I_{y} LTB can't occur)
Note: These calculations work for Ishaped members and channels bent about their minor axis.
How to solve for Weak Axis Bending
The nominal strength of the beam (M_{n}) shall be the lower value of:
 Yielding (around the plastic moment)
 Flange Local Buckling)
1) Yielding
Yielding around the plastic moment is found by: M_n = M_p = F_yZ_y \le 1.6F_yS_y

where:
M_{p} = Plastic Moment
F_{y} = The Yield Strength of the Steel (e.g. 36 ksi, 46 ksi, 50 ksi).
Z_{y} = The plastic section modulus along the y or weak axis (can be found in the AISC 13th edition in Table 11) (in^{3})
S_{y} = The Section Modulus along the y or weak axis (similar to the plastic section modulus) (in^{3})
Important: Don't forget that M_{n} is the nominal moment which still needs to be divided by Ω_{b} (for ASD = 1.67) or multiplied by ϕ_{b} (for LRFD = 0.9) to find the design flexural strength.
2a) Flange Local Buckling (compact flanges)
For sections with compact flanges the yielding state will apply (as found in Section 1 above).
2b) Flange Local Buckling (noncompact flanges)
For sections with noncompact flanges: M_n = \left[Mp  M_p  0.7F_yS_y)\left(\frac{\Lambda\Lambda_{pf}}{\Lambda_{rf}  \Lambda_{pf}}\right)\right]

where:
M_{p} = Plastic Moment (solved in Section 1 above)
F_{y} = The Yield Strength of the Steel (e.g. 36 ksi, 46 ksi, 50 ksi).
S_{y} = The Section Modulus along the y or weak axis (similar to the plastic section modulus) (in^{3})
λ = \frac{b}{t} , where b = base of the beam & t = thickness of the flange
λ_{pf} = λ_{p} = the limiting slenderness ratio for a compact flange (From the AISC 360, Section B4)
λ_{rf} = λ_{r} = the limiting slenderness ratio for a noncompact flange (From the AISC 360, Section B4)
2c) Flange Local Buckling (slender flanges)
For sections with slender flanges: M_n = F_{cr}S_y

where:
F_{cr} = \frac{0.69E}{\left(\frac{b_f}{2t_f}\right)^2} , where b_{f} = the base of the flange, & t_{f} = the thickness of the flange.
S_{y} = The Section Modulus along the y or weak axis (similar to the plastic section modulus) (in^{3})
References
 American Institute of Steel Construction (AISC 360), "Steel Construction Manual 13th edition", 2005
 Weak axis bending is discussed in Section F6 of the specs.
 Table B4.1 in the Specifications (AISC 360) has also been referenced to find the compact and noncompact slenderness limits.
 Most of the required variables to solve the above complex equations (for standard sized beams) can be found in Table 1 of the manual.