Roarks Flat Plates

FlatPlate Quick v2.1.4 — Roark Table 11.4 flat-plate stress and deflection, every case, with FE-backed deflections and contour plots

Tagline: All 53 load cases of Roark's flat-plate table in one macro-free workbook — pick the case, enter the plate, read the stresses, deflection, margins and thickness sweep.

FlatPlate Quick implements Table 11.4 of Roark's Formulas for Stress and Strain (9th edition) — flat plates with straight boundaries and constant thickness — in a single formula-only Excel workbook with no macros, add-ins or external links. Choose the edge condition and load pattern from two drop-downs covering all 20 cases and 53 sub-cases: rectangular plates with every combination of simply supported, fixed and free edges, uniform, hydrostatic, partial, patch, concentrated, line and in-plane loading, the continuous plate on a post grid, the plate on an elastic foundation, and the skew, triangular and regular-polygon plates. Enter the dimensions, thickness, material and load in the blue cells, in US or SI units, and the sheet returns the bending stresses at every location Roark tabulates with their signs and coordinates, the edge reactions where Roark gives them, the maximum deflection, margins of safety against your allowable stress and deflection limit, and a thickness sweep that shows how the margins move across a range of plate thicknesses. A cell-grid sketch identifies the a and b dimensions and the load pattern for the selected case, and a link opens the original Roark figure. Coefficients are interpolated on Roark's own tables, out-of-range ratios are clamped with a visible warning, and the coefficient values in use are displayed alongside the results so every number can be traced back to the book.

Roark tabulates no deflection for 27 of the 53 sub-cases — the patch-loaded plate, the plate with one edge fixed and the opposite edge free, the three-edges-fixed families and the plate on posts — and most calculators simply leave those blank or show zero. FlatPlate Quick fills them from an independent finite-element solution of the same thin-plate problem, run on Roark's own aspect-ratio grid so it interpolates exactly like the handbook values. The solver was validated against every deflection coefficient Roark does publish, reproducing them to within 0.5 percent for the classical cases and 2 percent for the two-figure entries, and the results are clearly labelled as FE-derived on the Plate sheet so the distinction from handbook values is never in doubt. The same solution drives two live contour charts of deflection and top-face von Mises stress for the 40 rectangular sub-cases, scaled to the reported peaks, so you can see where the plate works hardest rather than reading a single number at a single point.

A Validation sheet re-evaluates all 53 sub-cases against an independent hand calculation at a built-in default input set — 205 checks, all passing — plus closed-form limit checks against the strip, circular-plate and square-plate solutions, and it can be re-run on any copy of the workbook to confirm nothing has been altered. A Technical Basis sheet documents where every number comes from, the FE method and mesh convergence, the full FE-versus-Roark comparison tables, and, unusually for a calculator, the places where the handbook tables themselves are inconsistent: the fixed-edge stress coefficients for cases 7, 9 and 10 that run a few percent below a converged solution and the reasons why, the corner values that are grid artefacts, a superposition failure in case 8d, and a probable column transposition in case 2d. Roark's values are retained throughout so results match the book; the documentation tells you how much weight the last few percent of a margin can carry.

Sheets are protected against accidental edits, with the password given in the Notes sheet for anyone who wants to look under the hood. Requires Excel 2010 or later; no VBA.