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MECHANICS - CASE STUDY

    Introduction


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.
     
    Question

   

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

     
    Approach

   
  • 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.
     
   
 
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