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Solved Example: Design of 3-3x12 Timber Beam with Southern Pine

Articles > Solved Example: Design of 3-3x12 Timber Beam with Southern Pine

Question:

Design data:

Length of beam: L = 16 ft

Tributary width: s = 8 ft

Top of beam supported by floor joists at 16 in O.C.

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 = 464 lb/ft

Design moment: M = W*L2/8 = 14850 lb-ft

Use 3-3x12 nailed together with 12d nails at 12 in O.C. from both sides staggered.

Nominal dimension, B = 9 in, D = 12 in

Actual dimension, b = 7.5 in, d = 11.25 in

Section modulus: S = 158.2 in3, Modulus of inertia, I = 890 in4.

Bending stress: fb =M/S = 1126 psi

Try Southern pine No. 2, Fb = 1500 psi

The depth to width ratio based on nominal dimension, D/B = 1.33

Since compressive edge is supported by floor joist at 16 in O.C., CL = 1

Wet service factor: CM = 1

Temperature factor: Ct = 1

Load duration factor for dead load: CD = 0.9

Load duration factors for live load: CD = 1.0

Other factors not applicable

Allowable stress, F’b = Fb* CD*CL* CM* Ct = 1500 psi       O.K.

Check deflection:

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

Deflection: D = 5*W*L4/(384*E*I) = 0.48 in          < L/240 O.K.

Check shear stress

Maximum shear force. V = W*L/2 = 3840 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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