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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 А0, 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°; А0 = 3·10-4 m2.

 

 Material properties:

Elastic modulus: E = 2.1·1011 Pa.

 

 Boundary conditions:

Points A and B: X = Z = 0.

 

 Loads:

F­­ = 2.1·104 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, %

NAC, N

21000

21000

0.00

N, N

21000

21000

0.00

wC, m

-0.003

-0.003

0.00