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#### 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 q1 (plastic hinge appearance at supports), at load q2 (plasticity appearance at span middle), and at load q3 (full plasticity). Determine deflections at span f1, f2, f3, bending moments at span MM1, MM2, MM3, and bending moments at supports MN1, MN2, MN3 induced by loads q1, q2, q3 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; tw = 0.00254 mm; tf = 23.9141 mm.

*dimension h is given taking into account the fact that beam section is thin-walled

Material properties:

Elastic modulus: E = 2.039·107 tf/m2;

Tangential elastic modulus after plasticity appearance: EТ = 4.078·106 tf/m2;

Yield strength: σТ = 26717 tf/m2.

Boundary conditions:

Left side of beam: X = Y = Z = UX = UY = UZ = 0.

Symmetry boundary conditions at right side.

q1 = 39.11 tf/m2; q2 = 67.34 tf/m2; q3 = 161.42 tf/m2.

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, % f1, mm -4.061 -4.0478 0.33 f2, mm -9.12 -9.0447 0.83 f3, mm -53.60 -52.998 1.12 MM1, tf·m -43.601 -43.572 0.07 MM2, tf·m -68.829 -69.145 0.46 MM3, tf·m -172.499 -173.40 0.52 MN1, tf·m 21.801 21.797 0.02 MN2, tf·m 43.778 43.405 0.85 MN3, tf·m 97.436 96.412 1.05

Deflection value f1, mm

Deflection value f2, mm

Deflection value f3, mm

Diagram of bending moments at load q1, tf·m

Diagram of bending moments at load q2, tf·m

Diagram of bending moments at load q3, tf·m