TEST CASE 5.4 PLASTIC BENDING OF CLAMPED I-SECTION BEAM
Reference:
Volume 2. Verification examples from ANSYS Verification Manual. Moscow 2009. Example 23(VM134).
Problem description:
I-section beam is clamped at its end and loaded by uniform load q, as shown at figure below. Beam behavior is studied at load q_{1 }(plastic hinge appearance at supports), at load q_{2 }(plasticity appearance at span middle), and at load q_{3} (full plasticity). Determine deflections at span f_{1}, f_{2}, f_{3}, bending moments at span M_{M1}, M_{M2}, M_{M3}, and bending moments at supports M_{N1}, M_{N2}, M_{N3 }induced by loads q_{1}, q_{2}, q_{3 }respectively.
Problem sketch:
Type of created problem:
Spatial structure (X, Y, Z, UX, UY, UZ).
Geometric characteristics:
L = 3.6576 m; b = 0.254 m; h* = 0.26924 m; t_{w} = 0.00254 mm; t_{f} = 23.9141 mm.
*dimension h is given taking into account the fact that beam section is thin-walled
Material properties:
Elastic modulus: E = 2.039·10^{7} tf/m^{2};
Tangential elastic modulus after plasticity appearance: E_{Т} = 4.078·10^{6} tf/m^{2};
Yield strength: σ_{Т} = 26717 tf/m^{2}.
Boundary conditions:
Left side of beam: X = Y = Z = UX = UY = UZ = 0.
Symmetry boundary conditions at right side.
Loads:
q_{1} = 39.11 tf/m^{2}; q_{2} = 67.34 tf/m^{2}; q_{3} = 161.42 tf/m^{2}.
Model description:
System is modelled via 9 physically nonlinear finite elements of spatial bar (FE type is 510). Due to symmetry, only half of construction is considered. For nonlinear solution, iterative process is used (1000 iteration is performed).
Calculation results:
Target value |
ANSYS |
LIRA 10 |
Deviation, % |
f_{1}, mm |
-4.061 |
-4.0478 |
0.33 |
f_{2}, mm |
-9.12 |
-9.0447 |
0.83 |
f_{3}, mm |
-53.60 |
-52.998 |
1.12 |
M_{M1}, tf·m |
-43.601 |
-43.572 |
0.07 |
M_{M2}, tf·m |
-68.829 |
-69.145 |
0.46 |
M_{M3}, tf·m |
-172.499 |
-173.40 |
0.52 |
M_{N1}, tf·m |
21.801 |
21.797 |
0.02 |
M_{N2}, tf·m |
43.778 |
43.405 |
0.85 |
M_{N3}, tf·m |
97.436 |
96.412 |
1.05 |
Deflection value f_{1}, mm
Deflection value f_{2}, mm
Deflection value f_{3}, mm
Diagram of bending moments at load q_{1}, tf·m
Diagram of bending moments at load q_{2}, tf·m
Diagram of bending moments at load q_{3}, tf·m