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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)
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).
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}
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
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.
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
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.