Reference:

S. Timoshenko, Strength of Material, Part I, Elementary Theory and Problems, 3rd Edition, D. Van Nostrand Co., Inc., New York, NY, 1955, pg. 26, problem 10.

 Problem description:

The beam, clamped on two sides, is loaded with two concentrated forces F­­₁ and F₂ in the direction of the axis z. Determine the support reactions in the beam from the action of concentrated forces.

 Problem sketch:

Type of created problem:

Plane frame (X, Z, UY).

 Geometric characteristics:

L = 10 m; a = b = 0.3L m;

Cross section of the beam: 0.3 × 0.4 m.

 Material properties:

Elastic modulus: E = 3·10⁷ tf/m².

 Boundary conditions:

Points A and B: X = Z = UY = 0.

 Loads:

F­­₁ = 2F₂ = 1000 tf.

 Model description:

The system is modeled by 3 general finite elements of spatial bar (FE type is 10). The number of nodes in the calculation scheme – 4.

 Analytical solution:

Calculation results: