TEST CASE 1.2 FLAT FARM UNDER CONCENTRATED FORCE
Reference:
S. Timoshenko, Resistance des materiaux, t.1, Bruxelles, Edition Polytechnique Beranger, 1963, p. 10.
Problem description:
A flat truss consists of two inclined bars of equal length, rigidity of cross section and sectional area А_{0}, located symmetrically about the vertical axis, hinged in a common node (point C) and hinged at the points of support (points A and B). A vertical force is applied to the joint node F. Determine the vertical displacement of the joint node w і longitudinal forces in the truss bars N.
Problem sketch:
Type of created problem:
Plane truss or beam-wall (X, Z).
Geometric characteristics:
L = 4.5 m; θ = 30°; А_{0} = 3·10^{-4} m^{2}.
Material properties:
Elastic modulus: E = 2.1·10^{11} Pa.
Boundary conditions:
Points A and B: X = Z = 0.
Loads:
F = 2.1·10^{4 }N.
Model description:
The system is modeled by two finite elements of truss bar (FE type is 4). The number of nodes in the calculation scheme – 3.
Analytical solution:
Calculation results:
Target value |
Analytical solution |
LIRA 10 |
Deviation, % |
N_{AC}, N |
21000 |
21000 |
0.00 |
N_{CВ}, N |
21000 |
21000 |
0.00 |
w_{C}, m |
-0.003 |
-0.003 |
0.00 |