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: W_{L} = 40 psf

Floor dead load: W_{D} = 10 psf

Superimposed dead load including mechanical and electric load, W_{SD} = 8 psf

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

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

Calculate Design load: W = [W_{D} + W_{SD}+ W_{L}]*s = 77.3 lb/f

Design moment: M = W*L^{2}/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 in^{3}, Modulus of inertia, I = 98.93 in^{4}.

Bending stress: f_{b} =M/S = 1388 psi

Try Southern pine No. 2, F_{b} = 1500 psi

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)

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

Since compressive edge is fully supported by plywood floor, C_{L} = 1

Repetition factor for joist: C_{r} = 1.15

Wet service factor: C_{M} = 1

Temperature factor: C_{t} = 1

Other factors not applicable

Allowable stress, F’_{b} = F_{b}*C_{D}* C_{L}* C_{r}* C_{M}* C_{t} = 1725 psi O.K.

Check deflection:

Elastic modulus: E = 1600000 psi*C_{M}* C_{t} = 1600000 psi

Deflection: D = 5*W*L^{4}/(384*E*I) = 0.75 in < L/240 O.K.

Check shear stress

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

Shear stress, f_{v} = V/bd = 46 psi

Conservatively assume shear stress factor, C_{H} = 1

Allowable shear stress, F_{v} = 90 psi * C_{D}* C_{M}* C_{t }*C_{H} = 90 psi O.K.

- Solved Example: Design of 3-3x12 Timber Beam with Southern Pine
- Solved Example: Design of 2x12 Timber Floor Joist with Douglas Fir-Larch
- Design of Sawn Timber Beams or Joists
- Solved Example: Design of Sawn Timber Column
- Solved Example: Design of Timber Load Bearing Stud Wall

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