LIRALAND

Test 1.55. Stress–strain state of a ring plate (subjected to a uniformly distributed transverse load) with hinged supports

Updated Jun 23, 2026 | Published Aug 28, 2025

Objective

To determine the stress-strain state of a ring plate of constant thickness (under a uniformly distributed transverse load) with hinged supports.

Reference

S.P.Timoshenko, Plates and shells. - Moscow: OGIZ, Gostekhizdat, 1948.

Problem statement

To determine the deflection w, the radial bending moment Mr and the tangential bending moment Mθ along the inner and outer edges of the plate.

Design model

A ring plate of constant thickness and with hinged supports is subjected to a uniformly distributed transverse load.

Initial geometry of analytical model

Initial geometry of FE model

Initial geometry of analytical model
Initial geometry of FE model

Geometry

Outer radius of plate R = 1,2 m
Inner radius of plate r = 0,6 m
Plate thickness h = 2,0 · 10-2 m

Material properties

Modulus of elasticity Å = 2,0 * 108 kPa
Poisson's ratio μ = 0,3

Loads

Uniformly distributed transverse load p = 10 kPa


Output data

Deflections w (mm)

Radial bending moments Mr (kN*m/m)

Tangential bending moments Mθ (kN*m/m)

Deflections w (mm)
Radial bending moments Mr (kN*m/m)
Tangential bending moments Mθ (kN*m/m)

Analytical solution

For the analytical solution, the deflection w, the radial bending moment Mr and the tangential bending moment Mθ along the inner edge of the plate can be calculated using the following formulas.

Comparison of calculation results

Parameter Along the inner edge of the plate Along the outer edge of the plate
Analytical solution LIRA-FEM Error, % Analytical solution LIRA-FEM Error, %
w, mm -8,93 -8,81 1,34 0,00 0,00 -
Mr, kN*m/m 0,00 0,13 - 0,00 0,249 -
Mθ, kN*m/m 3,46 3,41 1,45 1,57 1,65 5,10

Download verification test

Download

If you find a mistake and want to inform us about it, select the mistake, then hold down the CTRL key and click ENTER.

  • 20

Comments

Write