Design of Sawn Timber Columns and Compressive Members
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Timber columns are designed to resist 1) maximum compressive strength and 2) slenderness
Concepts and Formulas
Design requirements:

The slenderness ratio L_{e}/d for solid column shall not exceed 50 for service load and shall not exceed 75 for construction. L_{e}=K_{e}´L is effective length of column, Ke is slenderness ratio, L is unsupported length of column. For rectangular section, L_{e}/d shall be evaluated in both directions.

Maximum compressive stress, fc must not exceed allowable stress parallel to grain, F’_{c} = F_{c}*C_{D}*C_{M}*C_{t}*C_{F}*C_{p}
Where
F_{c} is allowable bending stress in NDS supplement.
C_{D} is load duration factor, (see beam design)
C_{M} is wet service factor, (use when moisture of timber is higher than 19%)
C_{t} is temperature factor, (when timber is used in temperature higher than 150°F)
C_{F} is size factor, (apply only to visually graded sawn lumber members, and to round timber bending members, not apply simultaneously with Cv for glued laminated timber)
C_{p} is column stability factor (see below)
Slenderness ratio, K_{e}
Column stability factor C_{p}
According to NDS 3.7.1, column stability factor shall be determined as

Fully supported laterally throughout its length, C_{p}=1.

Otherwise, C_{p} shall be calculated as
F_{c}*=Compressive design value in NDS tables multiplied by all other adjustment factor except C_{p},
F_{cE}= K_{cE}´E’/(L_{e}/d)^{2},
K_{cE}=0.3 for visually graded lumber and machine evaluated lumber, (note: K_{cE}=0.418 for machine stress rated lumber and glued laminated timber),
C=0.8 for sawn lumber, (note: c = 0.85 for round timber piles and 0.9 for glued laminated timber).
Design procedure for timber column and compressive members:

Select timber species and section.

Calculate slenderness ratio for both axes, L_{ex}/d_{x}, L_{ey}/d_{y}, where L_{ex}=L_{x}*K_{ex}, L_{ey}=L_{y}*K_{ey}. K_{ex} and K_{ey}, are slenderness ratios in x and y direction. L_{x} and L_{y} are unsupported length in x and y direction.

Determine maximum compressive stress, f”_{c}=P/A. P is column axial load. A is cross section area.

Determine allowable compressive stress, F_{c}*
F_{c}* = F_{c}´C_{D}´C_{M}´C_{t}´C_{F}
Where
F_{c} is allowable bending stress in NDS supplement.
C_{D }is duration factor,
C_{M }is wet service factor, (use when moisture of timber is higher than 19%)
C_{t} is temperature factor, (when timber is used in temperature higher than 150°F)
C_{F} is size factor, (apply only to visually graded sawn lumber members, and to round timber bending members, not apply simultaneously with C_{v} for glued laminated timber)

Calculate elastic modulus
E'=E´C_{M}´C_{t}
Where E is modulus of elasticity in NDS supplement

Calculate F_{cE}= K_{cE}*E'/(L_{e}/d)^{2}

Calculate C_{p}

Calculate allowable compressive stress,
F"_{c} = F_{c}*´C_{p}
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