TEST CASE 1.5 SPATIAL HINGED-ROD SYSTEM UNDER THE ACTION OF CONCENTRATED FORCE
Reference:
F. P. Beer, E. R. Johnston Jr., D. F. Mazurek, P. J. Cornwell, E. R. Eisenberg, Vector Mechanics for Engineers, Statics and Dynamics, New York, McGraw-Hill Co., 1962, p. 47.
Problem description:
The three rods of the spatial system are hinged in a common node (point 4) and hinged in nodes 1, 2, 3. The support nodes are located in one horizontal plane, the common node is loaded with a concentrated force F. Determine the longitudinal forces N in each of the rods.
Problem sketch:
Type of created problem:
Spatial truss or solid array (X, Y, Z).
Geometric characteristics:
Cross-sectional area of bars: А = 3 cm^{2};
Coordinates of points 1: x_{1} = 0, y_{1} = 0, z_{1} = 0;
Coordinates of points 2: x_{2} = 0, y_{2} = 72, z_{2} = 0;
Coordinates of points 3: x_{3} = 96, y_{3} = 0, z_{3} = 0;
Coordinates of points 4: x_{4} = 48, y_{4} = 24, z_{4} = -72.
Material properties:
Elastic modulus: E = 2·10^{7} Pa.
Boundary conditions:
Points 1, 2 and 3: X = Y = Z = 0.
Loads:
F = 50 N.
Model description:
The system is modeled by three finite elements of truss bar (FE type is 4). The number of nodes in the calculation scheme is 4.
Analytical solution:
Calculation results:
Target value |
Analytical solution |
LIRA 10 |
Deviation, % |
N_{1-4}, N |
10.39^{} |
10.39 |
0.00 |
N_{2-4}, N |
22.91 |
22.91 |
0.00 |
N_{3-4}, N |
31.18 |
31.18 |
0.00 |