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MECHANICS - CASE STUDY

    Introduction


Beam Cross Section

 

A temporary beam is used to support an elevated stage at the local theater for a special production. The expected loading on the beam is 2 kN/m. The stage manager thinks a simple wood beam, 10 cm by 5 cm, will do just fine. But the consulting engineer thinks it needs more support and recommends rigidly attaching a 0.5 cm thick steel plate on the top and a 1.0 cm thick steel plate on the bottom.

What is known:

  • The stage span width is 5 m.
  • The beam loading is 2 kN/m.
  • The beam is constructed from two materials, Douglas Fir and Steel.
  • Young's modulus of the wood and steel is 12 GPa and 200 GPa, respectively.
  • The failure stress for the wood and steel is 50 MPa and 250 MPa, respectively.
     
    Question

   

What is the maximum bending stress in the steel and wood for the two-material beam? If the beam is only the wood, is it safe?

     
    Approach

   
  • Find the maximum moment.
  • Find the neutral axis (not at center since it is an unsymmetrical, two-material, composite beam).
  • Find the moment of inertia for both materials around the neutral axis.
  • Using the composite beam bending equations for two materials, find the bending stress in both the wood and the steel sections.
     
   
 
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