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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.

 

Loads:

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