Sandwich Core Shear Strength⚠ unverified

Understanding the Parameters

• Core depth $d$ — the distance between the facesheet centroids, and the single most powerful geometric lever in a sandwich. Because the faces act like the flanges of an I-beam, bending stiffness grows with $d^2$ and strength with $d$ — so a thick, light core buys enormous structural efficiency at almost no weight. The core shear stress falls as $d$ grows (the shear is spread over a deeper section).

• Facesheet thickness $t_f$ — thin faces carry the bending (tension/compression); their thickness sets the face stress and the panel's overall bending strength, and appears in the geometry that converts panel load to core shear.

• Applied shear $F_s$ — the transverse shear the panel must react. In a real sandwich, essentially all the transverse shear is carried by the core (the thin faces contribute negligible shear), which is why core shear strength — not face strength — often governs.

• The output $\tau_{core}$ — the shear stress demanded of the core, to be compared against the core material's shear allowable (honeycomb and foam cores have published shear strengths, e.g. a few MPa for aerospace honeycomb). Exceed it and the core shears; a related mode is core crushing under local compression.

Derivation (Approaching a Proof)

Model the sandwich as an I-beam idealisation: the two facesheets are the flanges carrying the bending couple, and the core is the web carrying the shear. The bending moment is reacted by equal-and-opposite face forces separated by the lever arm $d$, so a face force is $P_f = M/d$. Differentiating along the beam, the rate of change of face force is reacted by shear flow through the core:

$$q = \frac{dP_f}{dx} = \frac{1}{d}\frac{dM}{dx} = \frac{V}{d},$$

using the shear–moment relation $dM/dx = V$. The core shear stress is this shear flow spread over the core depth (per unit width $b$),

$$\tau_{core} = \frac{q}{b} \approx \frac{V}{b\,d}. \qquad\blacksquare$$

This is the standard "thin-face" sandwich result: the core carries the full transverse shear $V$, uniformly to a good approximation, over the depth $d$. The registry's $F_s\,d/(t_f(d+t_f))$ rearranges panel quantities into a geometry factor but, as noted, does not reduce to this dimensionally-consistent stress — the $(d+t_f)$ replacing a pure width and the extra $d/t_f$ ratio point to a mixed-up grouping. The physics — core carries the shear over depth $d$ — is what matters for design.

Dimensional check (correct form). $$\left[\frac{V}{b\,d}\right] = \frac{\text{N}}{(\text{m})(\text{m})} = \frac{\text{N}}{\text{m}^2} = \text{Pa}.\ \checkmark$$ The registry form gives $\text{Pa}/\text{m}$ — the dimensional flag above.

History and Development

• Sandwich theory. The mechanics of sandwich construction were developed in the 1940s–50s (Reissner, Hoff, Plantema, Allen) as lightweight cores — balsa, then aluminium honeycomb and polymer foams — entered aircraft. The de Havilland Mosquito (balsa-plywood sandwich) and later honeycomb panels proved the weight efficiency of separating thin strong faces with a light core.

• The I-beam analogy. The enduring design insight is that a sandwich is an I-beam turned inside out: faces = flanges (bending), core = web (shear). Its failure modes — face yielding, face wrinkling, core shear, core crushing, and debonding — are all checked in sandwich sizing.

• Ubiquity in aerospace. Honeycomb sandwich is everywhere on aircraft and spacecraft: floors, control surfaces, radomes, fairings, rocket interstages, and satellite panels — chosen precisely for its high bending stiffness and strength per unit weight, with core shear a routine sizing check.

Related Concepts: Shear Flow, Wing Bending Stress, Composite Wing Stiffness, Interlaminar Shear Stress, Buckling Stress, Margin Of Safety

Notes: Registry calculator sandwich-core-shear-strength (unverified). Dimensional inconsistency: the shipped $F_s d/(t_f(d+t_f))$ is $\text{Pa}/\text{m}$, not a stress; the consistent core shear is $\tau_c \approx V/(b\,d)$ (core carries essentially all the transverse shear over depth $d$). Sandwich = I-beam (faces = flanges, core = web). Flagged in Known Issues. All defaults $1.0$.