In the case of sandwich beams, if the material of the faces has much larger modulus of elasticity than the material of the core, then it is ok to disregard the normal stresses in the core and assume that the faces resist all longitudinal bending stresses.

Question

BlackTom AI · Accepted Answer

In evaluating a statement about sandwich beams, it helps to separate the roles of the faces and the core in bending.
Option 1: True. The classic sandwich-beam theory states that when the face sheets have a much higher modulus of elasticity than the core, the faces predominantly carry the longitudinal bending stresses while the soft core mainly provides shear transfer and keeps the faces at a fixed separation. In this common regime (large E_f/E_c ratio), neglecting normal stresses in the core is a simplifying assumption that often yields good first-order results, because the core undergoes small axial strains while the faces experience the majority of the bending stress.
Option 2: False. Although the high-contrast condition just described makes it reasonable to minimize core normal stresses, it is not universally valid to completely disregard them. The core can still experience nonzero axial/normal stresses due to Poisson effects, geometric nonlinearity, bending-shear coupling, and any deviations from the idealized thin-face/low-density-core model. In some designs, especially where thicknesses are not extreme or where load paths induce significant core stiffness, neglecting core normal stresses can lead to error.

Therefore, the statement is conditionally correct under the common assumption of a very stiff faces / soft core with large E_f/E_c, but it is not an unconditional truth applicable to all sandwich-beam configurations. The key caveat is the ratio of moduli and the level of modeling accuracy required for the problem at hand.

In the case of sandwich beams, if the material of the faces has much larger modulus of elasticity than the material of the core, then it is ok to disregard the normal stresses in the core and assume that the faces resist all longitudinal bending stresses.判断题

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