Tools › Structures › Stability › Plate Buckling › Example
Timoshenko and Gere: simply supported plate in uniaxial compression, k = 4
| Tool | Plate Buckling |
| Source | Timoshenko, S. P., and Gere, J. M. (1961). Theory of Elastic Stability, 2nd ed. McGraw-Hill, New York. Art. 9.2, buckling of simply supported rectangular plates uniformly compressed in one direction. |
| Level | Undergraduate |
Problem
A simply supported aluminum plate 20 in long, 10 in wide and 0.1 in thick (E = 10 MSI, ν = 0.3) is compressed uniformly along its short edges by 100 lb/in. Find the buckling coefficient, the critical load per unit width and the margin of safety.
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, isotropic (E_y, G_xy blank); plastic correction off
- N_x = −100 lb/in (compression negative), other loads blank or zero
Answers
- D = E t³ / (12 (1 − ν²)) = 915.75 lb-in
- k = (m b/a + a/(m b))² minimised over m: k = 4.0 (m = 2 at a/b = 2)
- N_x,cr = 4 π² D / b² = 361.52 lb/in (hand 361.5)
- R_tot = 0.2766, M.S. = +2.615
- Energy method (Rayleigh-Ritz library): k = 4.000 at a/b = 1 and 2, 6.25 at a/b = 0.5 (within 0.02 % of the formula)
Notes
Not the tool's default plate (6 × 3 × 0.08 in with three loads); type the inputs above. The closed-form and energy methods agree on this case because the loaded edges are simply supported, where the handbook coefficient is exact.