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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