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

fbwood equivalent=fbsn

 

001-equivalent-sections.gif

 

From assumption no. (4): The loads carried by equivalent fibers are equal.
Pw=Ps

fbwAw=fbsAs

Aw=fbsfbwAs

Aw=EsEwAs
 

The equivalent area of steel in wood is

Aw=nAs