 Register   #### TEST CASE 1.6 HINGED BEAM, LOADED BY CONCENTRATED FORCE AND UNIFORMLY DISTRIBUTED PRESSURE

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: Iy = 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.

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:

 Target value Analytical solution LIRA 10 Deviation, % wL/2, mm -5.043 -5.043 0.00 θyB, rad 7.204×10-3 7.204×10-3 0.00 ML/2, kN×m 1.875 1.875 0.00 QA, kN 1.250 1.250 0.00 QB, kN -8.750 -8.750 0.00