Tools › Structures › Stability › Plate Buckling › Example
NACA TN 3781: simply supported plate under combined compression and shear, R_c + R_s² = 1
| Tool | Plate Buckling |
| Source | Gerard, G., and Becker, H. (1957). Handbook of Structural Stability, Part I: Buckling of Flat Plates. NACA Technical Note 3781, National Advisory Committee for Aeronautics, Washington, D.C. Combined compression and shear interaction, R_c + R_s² = 1. |
| Level | Professional |
Problem
The simply supported 20 × 10 × 0.1 in aluminum plate (E = 10 MSI, ν = 0.3) carries 100 lb/in of compression along its short edges together with 50 lb/in of shear. Find the critical loads of each component, the load factor at which the combination buckles and the total ratio to requirement.
Inputs to Enter
- a = 20 in, b = 10 in, t = 0.1 in; fixity S S S S; E_x = 10 MSI, ν_xy = 0.3
- N_x = −100 lb/in, N_xy = 50 lb/in; plastic correction off
Answers
- N_x,cr = 361.52 lb/in (k = 4)
- N_xy,cr = 573.92 lb/in (k_s = 5.35 + 4 (b/a)² = 6.35)
- Interaction R_c + R_s² = 1 solved for the load factor: λ = 3.3139 (hand 3.314), R_tot = 1/λ = 0.3018
- With compression reversed to +100 lb/in of tension: λ = 39.76 (tension relieves the shear)
- Energy-method check: at R_c = R_s = 0.5 the direct eigenvalue gives R_c + R_s² = 1 within 4 % (the TN 3781 curve is a fit of the exact solution)
Notes
Type the plate and the two loads (not the default case). The interaction is the handbook's published surface; the critical loads come from the closed-form coefficients, and the energy method solves the combined load directly.