Wood Column Stability Factor Formulas and Calculator

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Wood Column Stability Factor Formulas and Calculator

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Structural Design Engineering Resources

The column stability factor is used when designing columns and is applied to the reference compression parallel to the grain design value. If the column is supported throughout its length to prevent lateral displacement in all directions, then CP = 1.0. Otherwise, CP is a function of the column's dimensions, design value in compression and modulus of elasticity as well as other variables.

When a compression member is supported throughout its length to prevent lateral displacement in all directions, C_p = 1.0.
The effective column length, l_e , for a solid column shall be determined in accordance with principles of engineering mechanics - see Eq. 3.
For solid columns with rectangular cross section, the slenderness ratio, l_e shall be taken as the larger of the ratios l_e1 /d₁ or l_e2 /d₂ (see Figure 1) where each ratio has been adjusted by the appropriate buckling length coefficient, K_e.
The slenderness ratio for solid columns, l_e /d, shall not exceed 50, except that during construction l_e /d should not exceed 75.

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The column stability factor shall be calculated as follows:

Eq. 1
C_p = ( 1 + ( F_cE / F_c^* ) / ( 2 · c ) ) - [ ( ( 1 + ( F_cE / F_c^* ) / ( 2 · c )² ) - ( F_cE / F_c^* ) / c ]^0.5

For a rectangular bending member of breadth, b, and depth, d, this becomes:

Eq. 2
F_cE = ( 0.822 · E_min' ) / ( l_e / d )²

Eq. 3
l_e = K_e · l

Where:

F_c^* = reference net bearing area compression design value parallel to grain multiplied by all applicable adjustment factors except C_p , psi
E_min' = reference and adjusted modulus of elasticity for beam stability and column stability calculations, psi
c = 0.8 or sawn lumber
c = 0.85 for round timber poles and piles
c = 0.9 for structural glued laminated timber, structural composite lumber, and cross-laminated timber
d = least dimension of rectangular compression member, in.
K_e = Table 1
l_e = effective length of compression member, in.

Figure 1 Simple Solid Column

Table 1

Bucking Configuration
Theoretical K_e value	0.5	0.7	1.0	1.0	2.0	2.0
Recommended design K_e(When ideal conditions approximated)	0.6	0.80	1.2	1.0	2.10	2.4
End condition code		Rotation fixed, translation fixed
		Rotation free, translation fixed
		Rotation fixed, translation free
		Rotation free, translation free

Source:

National Design Specification for Wood Construction