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Extra resources for Analysis and Design of Structural Sandwich Panels
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. The contribution o f the core to D is neglected. ) ' = T + - 2 - . 18) represents the shear force carried by the beam as a whole, supposing the faces to undergo only uniform extensions or contractions without bending locally.
V[ — 0 (Symmetry) c (iv) + EIwï+EI/wï. WL — = 2 C 3. vv'2 = 0 (Arbitrary) C2 , „ SANDWICH BEAMS 27 A s a result, the constants may be expressed as follows, C2 being still unknown : Wm C i - - y , WL. C3-—-g-, C 4 _ W. 32) In the part BC, with χ measured from B, the total shear force is zero. 30) are therefore valid provided the terms containing W a r e suppressed and new constants Βχ—Ββ are introduced to replace C\ — C%. There are four simple boundary conditions, as follows: ( v i ) X = 0, wi = 0 (Arbitrary) ( ν ϋ ) X = 0, w2 = 0 (Arbitrary) * (viii) X = L±, < = e + 4 = 0.
A s before, θ can be found from Fig. 11. 8. Beam with Four-point Loading (Antiplane Core and Thick Faces) A n ordinary homogeneous beam with four-point loading is illustrated in Fig. 14a. The central region is subjected to a constant bending moment — WLb and it therefore bends into a circular arc o f curvature +WLb/EL This fact is often used to determine the flexural rigidity EI of a simple beam, usually by measuring the deflections o f three different points in the central region. SANDWICH BEAMS 37 The method is also used to determine the flexural rigidity o f sandwich beams, on the assumption that because there is no shear force in the central region, there can be no shear deflection there and the deformation is one o f pure bending.