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Solved Example: Design of 2x10 Timber Floor Joist with Southern Pine

Articles > Solved Example: Design of 2x10 Timber Floor Joist with Southern Pine

Question:

Design data:

Length of floor joist: L = 16 ft

Spacing of floor joist: s = 16 in.

Top of joist supported by plywood sheathing.

Design load:

Floor live load: WL = 40 psf

Floor dead load: WD = 10 psf

Superimposed dead load including mechanical and electric load, WSD = 8 psf

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

 

Solution:

Refer to Design of Sawn Timber Beams or Joists article for the concepts.

Calculate Design load: W = [WD + WSD+ WL]*s = 77.3 lb/f

Design moment: M = W*L2/8 = 2475 lb-ft

Try 2x10 joist

Nominal dimension, B = 2 in, D = 10 in

Actual dimension, b = 1.5 in, d = 9.25 in

Section modulus: S = 21.39 in3, Modulus of inertia, I = 98.93 in4.

Bending stress: fb =M/S = 1388 psi

Try Southern pine No. 2, Fb = 1500 psi

Load duration factor for dead load: CD = 0.9

Load duration factors for live load: CD = 1.0(Use 1 per NDS 2001)

The depth to width ratio based on nominal dimension, D/B = 5

Since compressive edge is fully supported by plywood floor, CL = 1

Repetition factor for joist: Cr = 1.15

Wet service factor: CM = 1

Temperature factor: Ct = 1

Other factors not applicable

Allowable stress, F’b = Fb*CD* CL* Cr* CM* Ct = 1725 psi       O.K.

Check deflection:

Elastic modulus: E = 1600000 psi*CM* Ct = 1600000 psi

Deflection: D = 5*W*L4/(384*E*I) = 0.75 in          < L/240 O.K.

Check shear stress

Maximum shear force. V = W*L/2 = 640 lb

Shear stress, fv = V/bd = 46 psi

Conservatively assume shear stress factor, CH = 1

Allowable shear stress, Fv = 90 psi * CD* CM* C*CH = 90 psi    O.K.


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