Test 1.53. Square panel under a uniformly distributed transverse load

Objective

To determine the bending moments at characteristic points of a square panel in a flat‑slab structure, rigidly connected to a column of circular cross‑section, under a uniformly distributed transverse load.

Reference

S.P.Timoshenko, S.Voynovsky-Kriger, Plates and shells, Moscow, LIBROKOM Publishing House, 2009, p. 287-289.

Problem statement

In a flat‑slab structure, a square panel rigidly connected to a column of circular cross‑section is subjected to a uniformly distributed transverse load q.

To determine the bending moments M_x and M_y at the characteristic points of the square panel in a flat-slab structure.

Design model

The design model is a beam grillage, slab. The finite element mesh of the panel in a flat‑slab structure is divided along the axes of the global coordinate system with a step of 0.05 m, except at the support contour, where the mesh is divided in the radial direction with a step of 0.05 m and in the circumferential direction with a step of 11,25⁰. Internal forces are to be determined along the axes of the global coordinate system.

Geometry

Thickness of the panel in a flat‑slab structure h = 0,1 m
Radius of the panel in a flat‑slab structure a = 2,5 m
Radius of the column cross‑section c = 0,25 m

Material properties

Modulus of easticity Е = 3*10⁷ Pa
Poisson's ratio ν=0,2.

Boundary conditions

Boundary conditions are ensured by applying restraints:
- Along Y and uX DOF — at the edge of the panel located along the X‑axis of the global coordinate system.
- Along X and uY DOF — at the edge of the panel located along the Y‑axis of the global coordinate system.
The rigid‑body node of the column is positioned at the centre of its cross‑section and is restrained in the direction of degree of freedom Z.

Loads

Uniformly distributed transverse load q = 100 N/m².

Output data

Design model

Deformed shape

Stress mosaic plot M_x, N*m/m

Stress mosaic plot M_y, N*m/m

Comparison of calculation results

For the analytical solution, the displacement w and the bending moments M_x and M_y at the plate centre under a uniformly distributed load can be calculated using the following formulas:

M = β*q*a²