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 M_M1, M_M2, M_M3, and bending moments at supports M_N1, M_N2, M_N3 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; 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 = 2.039·10⁷ tf/m²;

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

Yield strength: σ_Т = 26717 tf/m².

Boundary conditions:

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

Symmetry boundary conditions at right side.

Loads:

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:

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