Structural Engineering & Statics
where the load goes
Series

Sandwich section — the series

2 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. Two faces, a couple, and a core that does none of it. A sandwich section 61.4 mm deep: two 0.7 mm faces separated by 60 mm of core. The bending is carried as a couple between the faces — 41 N/mm² of tension in one and compression in the other, over a lever arm of 60.7 mm — and the core carries a shear stress of 0.047 N/mm² and nothing else. The parallel-axis term is 98.8% of the section's second moment; the faces' own bending about their own centroids is 0.004% of it, and the core's is 1.2%. Separated by nothing at all the same two faces would be 2.3e+4 times less stiff.

    Two skins and the space between them

    A sandwich panel is a section made of a material that carries the bending and a material that carries none of it. The parallel-axis term is not a correction here — it is 98.8 per cent of the second moment — and the shear deflection is not a correction either.

    part 1 · sections
  2. How far a local load spreads, and what is nearest its limit. Along a steel-faced polyurethane cladding panel, 0.5 mm faces of 320 N/mm² steel on an 80 mm core crushing at 0.12 N/mm², from the middle of a strip load of 3.0 N per mm of width spread over 10 mm: the face's deflection over its value under the load, the core's compressive stress over its crushing strength, and the face's bending stress over its yield stress. The load spreads over a length set by the fourth root of the face's bending stiffness over the core's, 1/β = 20.5 mm; the deflection is 1.44 mm under the load and changes sign beyond 48 mm. The core is at 0.60 of its crushing strength and the face at 0.89 of its yield stress: this panel's face yields at 3.36 N/mm and its core crushes at 5.00.

    The face that dents and the core that crushes

    A sandwich panel carries bending as a couple between its faces, and that is a calculation about the whole panel. Put a local load on one face — a foot, a fixing, a dropped tool — and the face becomes a thin beam on a soft bed, spreading the load over a length the fourth root of their stiffnesses sets. Then either the face yields and dents, or the core crushes beneath it, and which comes first is decided by one thickness: below it the face gives, above it the core does, and a steel-faced roof panel is on the wrong side of it for anyone who walks on it.

    part 2 · sections

All series