Lumber Storage Shed Configuration

Top Grade Lumber company needs a new storage shed and have hired you to specify the longest span of the shed that be constructed using only 2x8 pieces of lumber. You have decided to use a "T" cross sectional beam by combining two 2x8 pieces of lumber (at the job site).

What is known:

• The roof needs to withstand a combined dead and live load of 60 lb/ft².
• The 2x8 "T" beams will be spaced 2 ft on center.
• The width of the shed, W, is not given and can be many more beams wide.
• Local building codes require a factor of safety of 2.0.
• The wood is Douglas Fir with a failure stress of 7,500 psi.
• Two 2x8s are securely glued and nailed together (shear stresses at joint do not have to be considered).
• Assume the beam is simply supported at each end by the wall structure.

What is the longest span, L, that can be safely used for the storage shed?

• Recall, actual lumber dimensions are not the same as the name (i.e. a 2x8 is not 2 inch by 8 inch). Use the Structural Shapes appendix to get actual size.
• The worst case is a center beam where it has to support the roof loading on both sides.
• The bending stress can be determined with
  
       
  
• The centroid of the "T" cross section needs to be found and then the moment of inertia of the combined beam can be calculated.