Superimposed or Built-up Beams

If a beam is composed of two or more thin layers placed on each other without any attachment, the separate layers would slide past each other and the total strength of the beam would be the sum of the strengths of the various layers. The strength of this beam is lesser than a solid beam having the same cross-sectional area.
 

Greatly Exaggerated Deformation of Built-up Beams

 

Neglecting friction between any two adjacent layers, the following relationships may be used:
 

$M = M_1 + M_2 + M_3$
 

$I = I_1 + I_2 + I_3$

 

Curvature, M / EI = constant
 

$\dfrac{M}{EI} = \dfrac{M_1}{E_1 I_1} = \dfrac{M_2}{E_2 I_2} = \dfrac{M_2}{E_2 I_2}$

 

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