TEST CASE 5.2 HIGH-RIGIDITY BEAM ON FOUR HANGERS
Reference:
A.R. Rzhanitsyn, Structural Mechanics, Moscow, High School, 1982, p.179-181.
Problem description:
High-rigidity beam is suspended using four bars and loaded by force F at point B. Find the force value for situation, when plasticity appears in bars АА`, ВВ` and СС`. Find also vertical displacement w at point A when plasticity arises at each bar.
Problem sketch:
Type of created problem:
Plane frame (X, Z, UY).
Geometric characteristics:
L = 1 m;
Hanger area: А = 1·10-4 m2.
Material properties:
Stress values at points on the graph: σ1 = σ2 = -40000 tf/m2, σ3 = σ4 = 40000 tf/m2;
Deformation values at points on the graph: ε1 = -0.9, ε2 = -0.001905, ε3 = 0.001905, ε4 = 0.9.
Boundary conditions:
Points А`, В`, С` and D`: X = Z = UY = 0;
Point А: X = 0.
Loads:
F = 10 tf.
Model description:
System is modelled using 4 physically nonlinear general step finite elements of spatial bar (FE type is 210) for hangers and 3 general FE of spatial bar (FE type is 10) for beam. Hangers and beam are connected via hinges at points А`, В`, С` and D` respectively. For nonlinear problem solution, stepped load applying is performed.
Calculation results:
|
Target value |
Analytical solution |
LIRA 10 |
Deviation, % |
|
Fт.АА`, tf |
10.0 |
10.0 |
0.00 |
|
Fт.ВВ`, tf |
11.2 |
11.2 |
0.00 |
|
Fт.СС`, tf |
12.0 |
12.0 |
0.00 |
|
wA at Fт.АА`, mm |
-1.905 |
-1.905 |
0.00 |
|
wA at Fт.ВВ`, mm |
-2.667 |
-2.667 |
0.00 |
|
wA at Fт.СС`, mm |
-5.715 |
-5.715 |
0.00 |
Force value F at plasticity appearance in bar АА`, tf
Force value F at plasticity appearance in bar ВВ`, tf
Force value F at plasticity appearance in bar СС`, tf
Displacement value wA at plasticity appearance in bar АА`, mm
Displacement value wA at plasticity appearance in bar ВВ`, mm
Displacement value wA at plasticity appearance in bar СС`, mm
