TEST CASE 1.1 PRISMATIC BAR WITH CLAMPED END LOADED AXLE DIRECTION
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 F_{1} and F_{2} 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 = 3·10^{7} tf/m^{2}.
Boundary conditions:
Points A and B: X = Z = UY = 0.
Loads:
F_{1} = 2F_{2} = 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:
Target value |
Analytical solution |
LIRA 10 |
Deviation, % |
R_{A}, tf |
600 |
600 |
0.00 |
R_{В}, tf |
900 |
900 |
0.00 |