Wide beam, or when is the beam a plate?
The bending stiffness of a beam with rectangular cross-section (h x b) is D=Eh3b/12 with E=Young's modulus. If the width b is large, the beam deflects like a plate, i.e. the bending stiffness is D=Eh3b/12(1--ν2). At what b is the effective Young's modulus E/(1--ν2) with ν=Poisson's ratio?
Thick membrane:
There is plane stress in a thin membrane with E, ν. For a thick membrane, plane strain is a better approximation with effective Young's modulus E/(1--ν2) and Poisson's ratio ν/(1--ν). At what thickness is plane strain a better approximation than plane stress?
Thick bar:
There is uniaxial stress in a bar under tension/compression. For a thick bar uniaxial strain is a better approximation with effective Young's modulus (1-ν)E/((1+ν)(1-2ν)). At what thickness does this hold? Thick bars are used for compression tests.
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