Objective
To determine the stress-strain state of a wall-beam subjected to bending by a uniformly distributed load.
Reference
Demidov S.P., Theory of Elasticity, Moscow, Vysshaya Shkola, 1979.
Problem statement
To determine the stress σ11 in the wall-beam at the faces, as well as at a distance of 0.4 m from them (points A, B, C, and D).
Design model
A uniformly distributed load of intensity q is applied to the upper face of the wall-beam.
|
|
|
|
|
Variant 1
|
Variant 2
|
Variant 3
|
Geometry
Thickness: l = 0,1 m
Length: 2L = 3,2 m
Height: h = 1,6 m
Material properties
Modulus of elasticity Е = 3 * 107 kPa
Poisson's ratio ν = 0,3
Boundary conditions
Vertical support along the side faces – restraints preventing displacement along the global Z-axis.
Loads
Uniformly distributed load: q = 500 kN/m.
Note
The problem is solved in a plane formulation (model type 2 – XOZ plane).
The model is generated with FE type 30 – arbitrary quadrilateral FE of 2D problem (wall-beam).
Variant 1:
FE mesh 2×4.
Nodes: 15. Elements: 8.
Variant 2:
FE mesh 4×8.
Nodes: 45. Elements: 32.
Variant 3:
FE mesh 8×16.
Nodes: 153. Elements: 128.
Output data
|
|
|
|
|
Variant 1
|
Variant 2
|
Variant 3
|
|
|
|
|
|
Variant 1
|
Variant 2
|
Variant 3
|
|
|
|
|
|
Variant 1
|
Variant 2
|
Variant 3
|
Analytical solution
J = bh3/12
Comparison of calculation results
Without additional side nodes:
| The unknown | Point | Analytical solution | LIRA-FEM | Error, % | ||||
| Var. 1 | Var. 2 | Var. 3 | Var. 1 | Var. 2 | Var. 3 | |||
| Stress σx, kN/m2 | А | -16070 | -11999 | -15457,89 | -15884,63 | 25,3329 | 3,809 | 1,1535 |
| В | -7045 | -5999,5 | -6720,937 | -6976,896 | 14,8403 | 4,5999 | 0,9667 | |
| С | 7090 | 5999,5 | 6751,063 | 6975,234 | 15,3808 | 4,7805 | 1,6187 | |
| D | 15925 | 11999 | 15127,71 | 15742,18 | 24,6531 | 5,0065 | 1,148 | |
With additional side nodes:
| The unknown | Point | Analytical solution | LIRA-FEM | Error, % | ||||
| Var. 1 | Var. 2 | Var. 3 | Var. 1 | Var. 2 | Var. 3 | |||
| Stress σx, kN/m2 | А | -16070 | -12589,25 | -15872,02 | -15996,21 | 21,6599 | 1,232 | 0,4592 |
| В | -7045 | -6291,6 | -6855,656 | -7014,763 | 10,6941 | 2,6876 | 0,4292 | |
| С | 7090 | 6303,7 | 6894,719 | 7016,448 | 11,0903 | 2,7543 | 1,0374 | |
| D | 15925 | 12601,35 | 15438,13 | 15829,75 | 20,8706 | 3,0573 | 0,5981 | |
Download verification test
If you find a mistake and want to inform us about it, select the mistake, then hold down the CTRL key and click ENTER.
Comments