Question

Derive the flexural rigidity of a sandwich beam whose breadth is b, which has a core of thickness c and skins of thickness t each. The distance between the centroids of the skins is d, the skin and core moduli are Es and Ec respectively.

Answer 1

To derive the flexural rigidity of a sandwhich beam,

breadth = b

Core of thickness = c

skin of thickness = t

the distance between the centroids of the skins is = d

skin and core moduli are E_s and E_c respectively

total thickness of the sandwich is d = c + 2t

The equivalent flexural rigidity (EI)_eq can be write as the sum of the flexural rigidity of the core and of the two faces.

(EI)_{eq =} E_c I_c + 2 E_s I_s

_{Where I is Moment of Inertia}

By using parallel axis theorem

(EI)_eq = ( E_c b c³ ) / 12 + E_s [( b t³ ) / 6 + ( b t d² ) / 2 ]

assumes that the skin’s thickness t is very much thinner than the thickness of the core c and that the Young’s modulus of the core is at least an order of magnitude smaller than that of the skins, the equation can be simplified as follows

Equivalent flexural rigidity (EI)_eq = E_s (b t d² ) / 2 .