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#### 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 cm2;

Coordinates of points 1: x1 = 0, y1 = 0, z1 = 0;

Coordinates of points 2: x2 = 0, y2 = 72, z2 = 0;

Coordinates of points 3: x3 = 96, y3 = 0, z3 = 0;

Coordinates of points 4: x4 = 48, y4 = 24, z4 = -72.

Material properties:

Elastic modulus: E = 2·107 Pa.

Boundary conditions:

Points 1, 2 and 3: X = Y = Z = 0.

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, % N1-4, N 10.39 10.39 0.00 N2-4, N 22.91 22.91 0.00 N3-4, N 31.18 31.18 0.00