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TEST CASE 4.3 CONSOLE BENDING

Reference:

L.D. Landau, E.M. Lifshitz. Course of Theoretical Physics. In 10 Volumes. Vol. VII. Theory of Elasticity – 4th edition. – М.: Nauka, 1987, p. 106.

 

Problem description:

Console bar with cross section area A0 is loaded by concentrated load F at its free end. Determine displacements u and w в at point В. Find also bending moment value M at point A.

 

Problem sketch:

Type of created problem:

Plane frame (X, Z, UY).

 

Geometric characteristics:

L = 10 m; А0 = 0.05 m2.

 

Material properties:

Elastic modulus: E = 2·107 tf/m2;

Moment of inertia: I = 5·10-6 m4.

 

Boundary conditions:

Point А: X = Z = UY = 0.

 

Loads:

F = 4 tf.

 

Model description:

The system is modeled via 100 geometrically nonlinear elements of tight bend bar (FE type is 309). Automatic selection of step of loading applying for nonlinear problem solution is used.

 

Calculation results:

Target value

Analytical solution

LIRA 10

Deviation, %

Point В

u, m

-3.29

-3.2898

0.006

Point В

w, m

-6.7

-6.7056

0.084

Point А

М, tf·m

26.8

26.857

0.213

 

Horizontal displacements distribution u, m

 

Vertical displacements distribution w, m

 

Diagram of bending moment M, tf·m