 Computer - aided design (CAD)
Register   #### TEST CASE 5.1 HIGH-RIGIDITY BEAM ON HANGERS

Reference:

B.Halphen et J. Salencon, Elastoplasticité, Presses de l’ENPC.

Problem description:

High-rigidity beam is suspended using three bars and loaded by force Q at the BC centre of span. Find longitudinal internal force value N in bars АА`, ВВ` и СС`. Determine also vertical displacement w at point А, В and С.

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:

Elastic modulus of hangers before plasticity appearance: E = 2.1·1011 Pa;

Elastic modulus of hangers after plasticity appearance: EТ = 0.25·1011 Pa;

Elastic limit of hangers: σy = 400 MPa;

Axial stiffness of beam АС: (EA)AC = 1·1011 N·m2;

Bending stiffness of beam АС: (EIy)AC = 1·1011 N·m2.

Boundary conditions:

Points А`, В` and С`: X = Z = 0.

Q = (13/7)·σy·A.

Model description:

System is modelled using 3 physically nonlinear general step finite elements of spatial bar (FE type is 210) for hangers and 2 general FE of spatial bar (FE type is 10) for beam. For nonlinear problem solution, stepped load applying is performed (100 steps).

Calculation results:

 Target value Analytical solution LIRA 10 Deviation, % NАА`, kN 4.16 4.5151 8.54 NВВ`, kN 28.762 28.113 2.26 NСС`, kN 41.333 41.658 0.79 wA, cm -0.01995 -0.0215 7.77 wB, cm -0.13696 -0.13387 2.26 wC, cm -0.25397 -0.24623 3.05 Diagram of longitudinal forces N, kN Vertical displacements distribution w, cm