I modeled the deck as an equivalent simply supported bridge to estimate global bending and shear compliance. This retrospective September 2026 calculation uses a short, linear-elastic beam under a central load, not an as-built model of the metal assembly.
The model assumes a rigid base supporting the lower lands, idealized as simple supports at \(z=\pm30~\mathrm{mm}\). The equivalent section uses the remaining web thickness and subtracts the full slot envelope across the entire span.
The section properties and isotropic-surrogate shear modulus are:
\[
\begin{aligned}
A_g&=b_gh=1135.5~\mathrm{mm^2},\\
I_g&=\frac{b_gh^3}{12}\approx21290.6~\mathrm{mm^4},\\
G&=\frac{E}{2(1+\nu)}\approx740.7~\mathrm{MPa}.
\end{aligned}
\]
Reactions and nominal bending stress
\[
\begin{aligned}
R_A=R_B&=\frac{F}{2}=125~\mathrm{N},\\
M_{\max}&=\frac{FL}{4}=3750~\mathrm{N\,mm},\\
\sigma_{g,\max}&=\frac{M_{\max}(h/2)}{I_g}\approx1.321~\mathrm{MPa}.
\end{aligned}
\]
This is nominal bridge stress, excluding annulus and ligament-root concentrations—not a fixture strength rating.
Bending and shear deflection
The span-to-thickness ratio is only 4, so both bending and transverse shear contribute to midspan motion.
\[
\begin{aligned}
\delta_b&=\frac{FL^3}{48EI_g}\approx26.42~\mu\mathrm{m},\\
\delta_s&=\frac{FL}{4\kappa GA_g}\approx5.35~\mu\mathrm{m}.
\end{aligned}
\]
\[
\boxed{\delta_g=\delta_b+\delta_s\approx31.77~\mu\mathrm{m}}
\]
The bridge estimate is below the selected 50 µm screen, but does not resolve local annulus or ligament deformation. Its midspan motion differs from the FEA’s approximately 131 µm annular maximum; the lower bridge result alone does not establish full-fixture compliance.
Material comparison
With geometry, supports, and load held fixed, the same bending-plus-shear model gives:
These are analytical material comparisons using trial isotropic properties, not metal FEA or measurements of the built assembly.