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By Howard G. Allen
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11. Wide and Narrow Beams It is convenient to assume in general that sandwich beams bend in a cylindrical manner; that is to say, there is no curvature in the j>z-plane (Fig. 1). This may well be the case if the load is applied through rigid mountings or if the beam is held down on its supports. I f the beam is narrow in the sense that the width b is less than the core depth c, the lateral expansions and contractions o f the faces in the j-direction (associated with the membrane stresses in the x-direction) may take place fairly freely without causing unduly large shear strains in the core in the j>z-plane.
3 (for c = d) and FIG. 11. Graph for the determination of Θ (equation ( 2 . 13b) (for Q = — W/2). In the expression for the maximum direct stress the first term represents the membrane stress in the faces, as predicted by ordinary bending theory. 1. EXTREME CASES FOR A SIMPLY-SUPPORTED BEAM W I T H A CENTRAL P O I N T L O A D Limiting values (ii) G (i) a θ ßl 0 0 0 oo (iii) t - 0 CO CO CO CO 1 1 Θ Τ" 1 1 0 1 1 0 1 3 Vi ^max ^max σ WL 2bd \ t 3 WL 4SEI WL 4SEIf 0 •4 3 3 WL c + 2t 4 21 WL 4SEI WL 4bdG W ~^2bd IJ WL c+2t 4 21 WL + ~4~ t 1 ~2/7'T be noted that this expression represents conditions at the point o f infinite curvature, c, in Fig.
A face may also undergo purely extensional deformation when it is subjected to a uniform tensile or compressive stress. When the sandwich bends as a whole (as in Fig. 5b) the faces partake of both kinds of deformation. 2). In addition to this, however, the local bending stiffness o f the faces has an effect on the shear deformation of the core. In Fig. 5c it is clear that if the faces and the core are to remain in contact, the faces are being called upon to bend to an infinite curvature at the centre o f the beam.
Analysis and Design of Structural Sandwich Panels by Howard G. Allen