 Register   #### TEST CASE 1.3 FLAT HINGED-ROD SYSTEM UNDER CONCENTRATED FORCE

Reference:

S. Rao, The finite element method in engineering, 4 ed, Elsevier science end technology books, 2004, p. 313.

Problem description:

The flat hinged-rod system consists of four inclined rods. The rods of the AC and BC have a common node (point C) and are hinged at support points, the rods CD and BC have a common node (point D). Concentrated force is applied to node D F. Determine the horizontal u and vertical w displacements of the common nodes C and D.

Problem sketch: Type of created problem:

Plane truss or beam-wall (X, Z).

Geometric characteristics:

Cross-sectional area of bars AC and BC: AAC = ABC = 2·10-4 m2;

Cross-sectional area of bars CD and BD: ACD = ABD = 1·10-4 m2.

Material properties:

Elastic modulus: E = 2·1010 Pa.

Boundary conditions:

Points A and B: X = Z = 0.

F­­ = 1000 N.

Model description:

The system is modeled by four finite elements of truss bar (FE type is 4). The number of nodes in the calculation scheme is 4.

Calculation results:

 Target value Analytical solution LIRA 10 Deviation, % uC, mm 0.26517 0.26517 0.00 wC, mm 0.08839 0.08839 0.00 uD, mm 3.47903 3.47903 0.00 wD, mm -5.60035 -5.60035 0.00