Test 1.46. Square plate simply supported along the perimeter and subjected to a uniformly distributed load

Objective

To determine the maximum displacements and bending moments in a square plate simply supported along the perimeter and subjected to a uniformly distributed load p.

Reference

Strength, stability, and vibrations. Handbook in Three Volumes. Volume 1. Edited by I.A.Birger and Y.G.Panovko. — M.: Mashinostroyenie, 1968, pp. 532-535.

Problem statement

A square isotropic plate of constant thickness is simply supported along its perimeter and subjected to a uniformly distributed load p.

To determine: the maximum displacements and the maximum bending moments.

Design model

The design model is a beam grillage, slab.

Geometry

Slab side dimension a = 1,5 m
Plate thickness h = 0,01 m

Material properties

Modulus of elasticity Е = 2,0 * 10⁸ kPa
Poisson's ratio ν = 0,3

Boundary conditions

Hinged support of nodes along the contour out of the XOY plane (displacement w = 0).

Restraints are applied in the X, Y, and uZ degrees of freedom directions at the centre of the plate.

Loads

Load p = 10 kPa

Output data

Design model	Displacements w, mm
Bending moments Mx, kN*m/m	Bending moments My, kN*m/m

Analytical solution

In the analytical solution, the displacement w and the bending moments Mx and My at the centre of the plate are calculated using the following formulas:

w = 0,00406*(p*a⁴)/D, where
D = (E*h³)/(12*(1-ν));
M_x = M_y = 0,0479*p*a².

Comparison of calculation results