 Computer - aided design (CAD)
Register   #### 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.

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