WikiEngineer :: Structural :: Steel Beam Weak Axis Bending

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 y-y 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 I-shaped 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_n = The nominal flexural strength (kip-in, lb-in, kip-ft, etc.)
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 1-1) (in³)
S_y = The Section Modulus along the y or weak axis (similar to the plastic section modulus) (in³)

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 (non-compact flanges)

For sections with non-compact flanges:

M_n = \left[M-p - M_p - 0.7F_yS_y)\left(\frac{\Lambda-\Lambda_{pf}}{\Lambda_{rf} - \Lambda_{pf}}\right)\right]

where:

M_n = The nominal flexural strength (kip-in, lb-in, kip-ft, etc.)
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) (in³)
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 non-compact 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:

M_n = The nominal flexural strength (kip-in, lb-in, kip-ft, etc.)
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) (in³)

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 non-compact 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.