Wood Column Stability Factor (C_P)

Fig. 1: Sawn lumber columns loaded from the overhead level

Column Stability Factor Explained:

The column stability factor is to ensure that weak-axis buckling or torsional buckling does not occur over non-laterally supported lengths. Note that this is similar to the beam stability factor except it deals with columns in compression, vs. beams in flexure.

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

• When the column (compression member) is supported throughout it's length, C_P can be assumed to be unity (1.0).

Otherwise the Column Stability Factor (C_P) must be solved out.

Solving for the column stability factor (C_P):

1. Start by solving for slenderness ratio:

Note: The slenderness ratio solved above should not exceed 50 (normal use), or 75 (during construction). If it does, then a larger member size should be chosen.

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

where:

3. Solve for F_c*:
F_c* is a reference compression design value which should be multiplied by all factors found here (for sawn lumber) except C_P.

For Sawn Lumber:

For Glued Laminated Lumber:

For Round Timber Poles/Piles?:

4. Solve for C_P:

where:

Note: It may be beneficial to solve for (F_cE/F_c*) initially.

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

Variations on design procedure:

• d (depth of the member) is used in place of radius of gyration (r) for rectangular beams. If other column shapes are used, d in the procedure above should be replaced with r\sqrt{12} where r is the radius of gyration?.

References:

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