
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 twomaterial 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, twomaterial,
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.




