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.
Loads:
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