Wood Beam Stability Factor (C_L)

Beam Stability Factor Explained:

The beam stability factor is to ensure that weak-axis buckling or torsional buckling does not occur over long non-laterally supported spans.

Situations when the beam stability factor is and is not necessary:

• If the depth of the member does not exceed it's width (d ≤ b), C_L can be assumed to be unity (1.0).
• When rectangular sawn lumber is braced in accordance with Section 4.4.1 of the NDS ^[1], C_L can be assumed to be unity (1.0).
• When the compression edge of a bending member is supported throughout it's length to prevent lateral displacement, and the ends have sufficient connections to prevent rotation, C_L can be assumed to be unity (1.0).
  • This will allow most floor and roof systems to be able to ignore the stability factor.

Otherwise the Beam Stability Factor (C_L) must be solved out.

Solving for the beam stability factor (C_L):

1. Start by solving for slenderness ratio, R_B :

Note: The slenderness ratio solved above should not exceed 50 (if it does choose a larger member size).

where:

2. Start by solving for the critical buckeling design value, F_bE :

where:

3. Solve for F_b*:
F_b* is a reference bending design value which should be multiplied by all factors found here except C_fu, C_v, and C_L.

For Sawn Lumber:

For Glued Laminated Lumber?:

4. Solve for C_L:

Note: It may be beneficial to solve for (F_bE/F_b*) initially.

5. Multiply C_L by your previously solved F_b* to get your actual bending stress:
Now lastly, multiply C_L by the F_b* you solved for in section 3 of this example to obtain F_b'. This is your allowable bending stress and you are now done.

References:

1. American Forest and Paper Association, "National Design Specification for Wood Construction", 2005
   • http://www.awc.org/pdf/WDF14-4-2005NDSarticle.pdf