””””▣▣ ””2““ in practice: support support 合≤ 1 Figure 4.5 Bending Deflection To evaluate A,one can,among other methods,use the Castigliano theorem W 高+r elastic energy contribution contribution from bending from shear △ oW energy deflection dF load where the following notations'are used for a beam of unit width: M=Moment resultant T=Shear stress resultant Ep=Modulus of elasticity of the material of the facings Ge Shear modulus of the core material (E）*Eex1×e:+e22 2 l(GS)=1/Gc(ec+2e)×1. Example:A cantilever sandwich structure treated as a sandwich beam (see Figure 4.6). Elastic energy is shown by +高r w=5 +高) See Equation 15.16 that allows one to treat this sandwich beam like a homogeneous beam. One can also use the classical strength of materials approach. 5 See Application 18.2.1 or Chapter 15. 2003 by CRC Press LLCTo evaluate D, one can, among other methods,4 use the Castigliano theorem where the following notations5 are used for a beam of unit width: M = Moment resultant T = Shear stress resultant Ep = Modulus of elasticity of the material of the facings Gc = Shear modulus of the core material Example: A cantilever sandwich structure treated as a sandwich beam (see Figure 4.6). Elastic energy is shown by Figure 4.5 Bending Deflection 4 See Equation 15.16 that allows one to treat this sandwich beam like a homogeneous beam. One can also use the classical strength of materials approach. 5 See Application 18.2.1 or Chapter 15. W 1 2 -- M2 · Ò EI ---------- dx Ú 1 2 -- k · Ò GS ------------T 2 dx Ú = + elastic energy contribution contribution from bending from shear D deflection ∂W ∂F = ------- energy load · Ò EI #Epep 1 ec + ep ( )2 2 ¥ ----------------------; k/· Ò GS 1/Gc ec + 2ep ¥ = ( ) ¥ 1. W 1 2 -- F2 ( )
– x 2 · Ò EI ------------------------ 0
Ú dx 1 2 -- k · Ò GS ------------F2 dx 0
Ú = + W F2 2 ----
3 3 · Ò EI -------------- k · Ò GS + ------------
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