Reinforced Beams

Flexure formula do not apply directly to composite beams because it was based on the assumption that the beam was homogeneous. It is therefore necessary to transform the composite material into equivalent homogeneous section. To do this, consider a steel and wood section to be firmly bolted together so that they can act as one unit. Shown below are the composite wood and steel section and the corresponding equivalent in wood and steel sections.
 

The quantity n is usually taken as the ratio of the moduli of elasticity of stronger material to the weaker material. In the above case, n = E_s / E_w.
 

The use of the above concept is governed by the following assumptions:

1. The composite materials are firmly bonded together and act as a unit.
2. The strain and load capacities of each material remain unchanged.
3. The strains of any two adjacent materials at their junction point are equal.
4. The loads carried by equivalent fibers are equal.
5. The equivalent fibers must be at the same distance from the neutral axis as the original fibers.
6. The flexure formula can be applied only to the equivalent section.