|
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.
|
|
|
|
|