# Moduli Ratio

Ratio of modulus of elasticity of one material to the modulus of elasticity of another material. In equation, *n* = *E*_{1}/*E*_{2}.

## Beams with Different Materials

From assumption no. (3) in the previous page: The strains of any two adjacent materials at their junction point are equal.

$\epsilon_s = \epsilon_w$

$\dfrac{f_{bs}}{E_s} = \dfrac{f_{bw}}{E_w}$

$\dfrac{f_{bs}}{f_{bw}} = \dfrac{E_s}{E_w}$

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## Chapter 10 - 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*.

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