Floor area supported by column: A = 80 ft2
Unsupported length of column, L = 10 ft
Hinge support at top and bottom of column
Floor live load: WL = 30 psf
Floor dead load: WD = 10 psf
Superimposed dead load: WSD = 5 psf
Timber: Southern pine, moisture less than 19%, used in normal room temperature.
Refer to Design of Sawn Timber Columns and Compressive Members article for concepts.
1. Select southern pine, 4"x4" stud grade, d = 3.5 in
Actual cross section: Ac = 12.25 in2.
Allowable compressive stress parallel to grain: Fc = 975 psi
2. Calculate slenderness ratio: Ke = 1, Le =Ke´L = 10 ft, Le/d = 34 < 50
3. Calculate compressive stress with load duration factor
Load duration factor for dead load: CD = 0.9
Load duration factors for live load: CD = 1.0
Calculate Design load: P = [WD + WSD+ WL]´A = 3600 lb
Column compressive stress, fc=P/Ac = 293.8 psi
4. Calculate allowable stress without Cp.
CM=1, Ct=1, Cf=1
Fc* = Fc´CM´Ct´CF = 975 psi
5. Calculate elasticity modulus
E’=E´CM´Ct = 1.4´106 psi
6. Calculate FcE
FcE= KcE*E’/(Le/d)2= 357.3 psi
7. Calculate Cp
c = 0.8
Cp = 0.333
8. Calculate allowable compressive stress
F”c = Fc*´Cp = 324.8 psi > fc= 293.8 psi O.K.