Tools › Structures › Composites › Sandwich Panel › Example
Timoshenko and Woinowsky-Krieger Table 8: simply supported square plate under uniform load
| Tool | Sandwich Panel |
| Source | Timoshenko, S. P., and Woinowsky-Krieger, S. (1959). Theory of Plates and Shells, 2nd ed. McGraw-Hill, New York. Table 8, simply supported rectangular plate under uniform load, a/b = 1. |
| Level | Graduate |
Problem
A simply supported square plate of side a and flexural rigidity D (ν = 0.3) carries a uniform pressure q. Find the centre deflection, the centre bending moment and the largest edge shear force.
Inputs to Enter
- Square panel a = b = 20 in, uniform pressure q = 1 psi
- Isotropic facings; core shear stiffness set infinite (Kirchhoff limit) so the Navier series reduces to the thin plate; 30 series terms
Answers
- w_centre = 0.00406 q a⁴ / D (Table 8 coefficient 0.00406; reproduced within 0.2 %)
- M_x,centre = 0.0479 q a² at ν = 0.3 (Table 8 coefficient 0.0479; within 0.3 %)
- Q_x,max = 0.338 q a at the middle of an edge (Table 8 coefficient 0.338; within 2 %, the shear series converges as 1/N)
- With finite core shear stiffness the deflection grows by the shear term and the centre moment changes by less than 3 %
Notes
Library check (test_sandwich.php) of the panel-under-pressure solution in its thin-plate limit; on the tool the same limit is approached with a very stiff core. The coefficients are the book's tabulated series values, not a dimensioned textbook problem; the tool's default panel is its own case.