**Design of sawn timber columns and compressive members**

**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}

**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}

**Example 4: Design of sawn timber column:**

Design data:

Floor area supported by column: A = 80 ft^{2}

Unsupported length of column, L = 10 ft

Hinge support at top and bottom of column

Design load:

Floor live load: W_{L} = 30 psf

Floor dead load: W_{D} = 10 psf

Superimposed dead load: W_{SD} = 5 psf

Timber: Southern pine, moisture less than 19%, used in normal room temperature.

Solution:

1. Select southern pine, 4″x4″ stud grade, d = 3.5 in

Actual cross section: A_{c} = 12.25 in2.

Allowable compressive stress parallel to grain: F_{c} = 975 psi

2. Calculate slenderness ratio: K_{e} = 1, L_{e} =K_{e}´L = 10 ft, L_{e}/d = 34 < 50

3. Calculate compressive stress with load duration factor

Load duration factor for dead load: C_{D} = 0.9

Load duration factors for live load: C_{D} = 1.0 (Use 1 per NDS)

Calculate Design load: P = [W_{D} + W_{SD}+ W_{L}]´A = 3600 lb

Column compressive stress, f_{c}=P/A_{c} = 293.8 psi

4. Calculate allowable stress without C_{p}.

C_{M}=1, C_{t}=1, C_{f}=1

F_{c}* = F_{c}´C_{M}´C_{t}´C_{F} = 975 psi

5. Calculate elasticity modulus

E’=E´CM´Ct = 1.4´10^{6} psi

6. Calculate F_{cE}

K_{cE}=0.3

F_{cE}= K_{cE}*E’/(L_{e}/d)^{2}= 357.3 psi

7. Calculate C_{p}

c = 0.8

C_{p} = 0.333

8. Calculate allowable compressive stress

F”_{c} = F_{c}*´C_{p} = 324.8 psi > f_{c}= 293.8 psi O.K.

**Example 5: Design of timber load bearing stud wall**

Design data:

Tributary width of floor supported by wall: B = 20 ft^{2}.

Unsupported height of stud wall, L = 10 ft

Hinge support at top and bottom of stud wall

Design load:

Floor live load: W_{L} = 30 psf

Floor dead load: W_{D} = 10 psf

Superimposed dead load: W_{SD} = 5 psf

Timber: Southern pine, moisture less than 19%, used in normal room temperature.

Solution:

1. Select southern pine, 2″x4″ stud grade at 16″ O.C. d_{1} = 3.5 in, d_{2} = 1.5 in, s = 16 in

Actual cross section: A_{c} = 5.25 in^{2}.

Allowable compressive stress parallel to grain: F_{c} = 975 psi

2. Calculate slenderness ratio:

K_{e} = 1, L_{ex} = K_{e}´L = 10 ft, L_{ex}/d_{1}=34 < 50

Provide blocking at mid-height in d_{2} direction

L_{ey}=K_{e}´(L/2) = 5 ft, L_{ey}/d_{2}=40 < 50 Govern

3. Calculate compressive stress with load duration factor

Load duration factor for dead load: C_{D} = 0.9

Load duration factors for live load: C_{D} = 1.0 (Use 1 per NDS 2001)

Calculate Design load: P = [W_{D} + W_{SD}+ W_{L}]´B´s = 1200 lb

Column compressive stress, f_{c}=P/A_{c} = 228.5 psi

4. Calculate allowable stress without C_{p}

C_{M}=1, C_{t}=1, C_{f}=1

F_{c}* = F_{c}´C_{D}´C_{M}´C_{t}´C_{F} = 975 psi

5. Calculate elasticity modulus

E’=E´C_{M}´C_{t} = 1.4´10^{6} psi

6. Calculate F_{cE}

K_{cE}=0.3

F_{cE}= K_{cE}*E’/(L_{e}/d)^{2}= 262.5 psi

7. Calculate C_{p}

c = 0.8

C_{p} = 0.252

8. Calculate allowable compressive stress

F”_{c} = F_{c}*´C_{p} = 246 psi > f_{c}= 228.5 psi O.K.

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