Objective
To determine the deformed state of a rectangular wall-beam, rigidly supported at the sides, under the uniformly distributed load applied on the top surface.
Reference
A.Kalmanyuk, Analysis of wall-beams, Moscow, Gosstroyizdat, 1956.
Problem statement
A uniformly distributed load P is applied to the top surface of a rectangular wall‑beam, rigidly supported at the sides, in the plane of the wall‑beam along the Z‑axis.
To determine the displacement tensor components u(x, z) and v(x, z) in Cartesian coordinates for the mid‑surface of the wall‑beam in its plane.
Design model
The design model is a 2D plate model generated by the wall‑beam. The FE mesh is divided with a step of 0.08 m along the X and Z axes of the global coordinate system.
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Initial geometry
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Number of nodes
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Number of elements
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Geometry
Thickness of wall-beam h = 0,1 m
Span length of wall-beam a = 0,8 m
Height of wall-beam b = 1,6 m
Material properties
Modulus of elasticity Е = 2,65 * 106 Pa
Poisson's ratio ν=0,15
Boundary conditions
The boundary conditions are provided by applying restraints in the direction of:
- Z degree of freedom along the lateral side;
- X degree of freedom along the axis of symmetry.
Loads
A uniformly distributed load P = 500 N/m is applied to the top surface of a rectangular wall‑beam.
Note
The problem is solved in a plane formulation (model type 1).
Nodes: 231. Elements: 200.
Output data
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Design and deformed models
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Displacement u (m) along the span of the wall-beam
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Displacement v (m) along the height of the wall-beam
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Analytical solution
Displacement tensor components u(x, z) and v(x, z) in Cartesian coordinates for the mid‑surface of the wall‑beam in its plane can be computed as follows:
Comparison of calculation results
| Coordinates | Displacement u, m | Displacement v, m | |||||
| X | Z | Theory | LIRA-FEM | Error, % | Theory | LIRA-FEM | Error, % |
| 0 | 0 | -0,000719 | -0,000713 | 0,83 | 0 | 0 | - |
| 0 | 0,8 | -0,000220 | -0,000220 | - | 0 | 0 | - |
| 0 | 1,6 | 0,001468 | 0,001401 | 4,56 | 0 | 0 | - |
| 0,4 | 0 | -0,000508 | -0,000504 | 0,79 | -0,000672 | -0,000667 | 0,74 |
| 0,4 | 0,8 | -0,000148 | -0,000148 | 0 | -0,000950 | -0,000945 | 0,53 |
| 0,4 | 1,6 | 0,000780 | 0,000778 | 0,26 | -0,002032 | -0,002027 | 0,25 |
| 0,8 | 0 | 0 | 0 | - | -0,000950 | -0,000943 | 0,74 |
| 0,8 | 0,8 | 0 | 0 | - | -0,001326 | -0,001320 | 0,45 |
| 0,8 | 1,6 | 0 | 0 | - | -0,002510 | -0,002504 | 0,24 |
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