Ch 4. Beam Stresses Multimedia Engineering Mechanics Bending Strainand Stress BeamDesign Shear Stress Built-upBeams
 Chapter 1. Stress/Strain 2. Torsion 3. Beam Shr/Moment 4. Beam Stresses 5. Beam Deflections 6. Beam-Advanced 7. Stress Analysis 8. Strain Analysis 9. Columns Appendix Basic Math Units Basic Equations Sections Material Properties Structural Shapes Beam Equations Search eBooks Dynamics Statics Mechanics Fluids Thermodynamics Math Author(s): Kurt Gramoll ©Kurt Gramoll

 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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