Reference:

Pisarenko G.S., Yakovlev A.P., Matveev V.V. Handbook on Strength of Materials. - Kyiv: Naukova Dumka, 1988.

Problem description:

The hinged beam with cross section area A₀ is loaded with a concentrated force F and a uniformly distributed pressure q. Determine the displacement w, angles of rotation θ, transverse forces Q, and bending moments M.

Problem sketch:

Type of created problem:

Plane frame (X, Z, UY).

Geometric characteristics:

L = 3 m; a = b = 1.5 m; А₀ = 14.2 сm²;

Moment of inertia: I_y = 244 сm⁴.

Material properties:

Elastic modulus: E = 2·10¹¹ Pa;

Poisson’s ratio: μ = 0.3.

Boundary conditions:

Point A: Z = 0;

Point B: X = Z = 0.

Loads:

F = 5 kN; q = 10 kN/m.

Model description:

The system is modeled by 10 general finite elements of spatial bar (FE type is 10). The number of nodes in the calculation scheme is 11.

Analytical solution:

Calculation results: