TEST CASE 5.3 STEEL THIN-WALLED CANTILEVER I-SECTION BEAM UNDER THE INFLUENCE OF CONCENTRATED BENDING MOMENT
Reference:
Analytical solution.
Problem description:
Steel thin-walled I-section beam is clamped at one side and loaded by external bending moment Мy at other side. Bilinear Prandtl stress-strain diagram for metal is used. Yield strength is σТ. Find deflection values at cantilever end f1, f2, f3 at bending loads Мy1, Мy2, Мy3 respectively.
Problem sketch:
Type of created problem:
Spatial structure (X, Y, Z, UX, UY, UZ).
Geometric characteristics:
L = 1 m; b = 0.2 m; h = 0.4 m; tw = 0.007 m; tf = 0.005 m.
Material properties:
Elastic modulus: E = 2.1·1011 Pa;
Yield strength: σТ = 250 MPa.
Boundary conditions:
At left side of a beam: X = Y = Z = UX = UY = UZ = 0.
Loads:
Мy1 = 1.3·105 N·m; Мy2 = 1.5·105 N·m; Мy3 = 1.65·105 N·m.
Model description:
System is modelled via 1920 4-noded physically nonlinear iterative finite elements of thin shell (FE type is 544). Concentrated bending moment is applied to absolutely rigid body, which includes nodes at right side of beam. For nonlinear solution, iterative process is used (2000 iteration is performed).
Analytical solution:
Calculation results:
|
Target value |
Analytical solution |
LIRA 10 |
Deviation, % |
|
f1, mm |
2.63789 |
2.6363 |
0.06 |
|
f2, mm |
3.21465 |
3.1872 |
0.85 |
|
f3, mm |
6.42931 |
6.2346 |
3.03 |
Deflection value f1, mm
Deflection value f2, mm
Deflection value f3, mm
