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 A_{0} 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; А_{0} = 0.05 m^{2}.
Material properties:
Elastic modulus: E = 2·10^{7} tf/m^{2};
Moment of inertia: I = 5·10^{6} m^{4}.
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