By Howard G. Allen
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Extra resources for Analysis and Design of Structural Sandwich Panels
This has been assumed in the analysis o f beams in this chapter. The same argument does not apply to the local bending stresses in the faces; each face is a thin plate in cylindrical bending and the ratio o f stress to strain is strictly 2 E/(l — v ). However, these stresses and strains are o f secondary importance and it seems reasonable to adopt Ε throughout in order to avoid undue complication. I f the beam is wide (say b » c), the lateral expansions and contractions o f the faces in the ^-direction are severely restricted by the inability o f the core to undergo indefinitely large shear deformations in the ^z-plane.
The quantities M±, n>i, q\ may be obtained by integration and differentiation. 26) and the related quantities M 2 , w 2 , q2 again obtained by integration and differentiation. 2 The quantity a represents essentially the ratio o f the core shear stiffness to the local bending stiffness of the faces. The extent to which the faces modify the shear deformation of the core depends 2 partly on a and partly on the span, the effect being smaller at large 2 values o f a and at large spans. 28) EIfW2 = ^ .
T o discuss the nature o f this interaction between the bending stiffness o f the faces and the shear stiffness o f the core, consider first a sandwich with a core which is rigid in shear (G = « » ) and with a load qi per unit length. A deflection wi occurs in accordance with ordinary bending theory. This deflection is associated with a bending moment Mi and a shear force Qu the latter being given by: -Qi = Dw[" = £ ( / - / / ) < ' + £ / / < ' . 18) the modulus of elasticity o f the faces, / is the second moment o f area o f the faces about the centroid o f the sandwich and Ifis the sum o f the second moments o f area o f the faces about their own centroids.
Analysis and Design of Structural Sandwich Panels by Howard G. Allen