Design of Sawn Timber Columns and Compressive Members

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Introduction

Timber columns are designed to resist 1) maximum compressive strength and 2) slenderness

 

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Concepts and Formulas

Design requirements:

1. 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.

2. 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

1. Fully supported laterally throughout its length, C_p=1.

2. 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:

1. Select timber species and section.

2. 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.

3. Determine maximum compressive stress, f”_c=P/A. P is column axial load.  A is cross section area.

4. 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)

5. Calculate elastic modulus

E'=E´C_M´C_t

            Where E is modulus of elasticity in NDS supplement

6. Calculate F_cE= K_cE*E'/(L_e/d)²

7. Calculate C_p

8. Calculate allowable compressive stress,

F"_c = F_c*´C_p

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Solved sample problems

 

• Design of Timber Load Bearing Stud Wall

• Solved Example: Design of Sawn Timber Column

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Read also

• Solved Example: Design of Sawn Timber Column
• Solved Example: Design of Timber Load Bearing Stud Wall
• Design of Sawn Timber Beams or Joists
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• Solved Example: Design of 3-3x12 Timber Beam with Southern Pine

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