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.
ϵs=ϵw
fbsEs=fbwEw
fbsfbw=EsEw
We let the moduli ratio be equal to n
n=EsEw
It will follow also that the equivalent wood stress of the transformed steel is
fb−wood equivalent=fbsn

From assumption no. (4): The loads carried by equivalent fibers are equal.
Pw=Ps
fbwAw=fbsAs
Aw=fbsfbw⋅As
Aw=EsEw⋅As
The equivalent area of steel in wood is
Aw=nAs
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