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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 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:

Target value

Analytical solution

LIRA 10

Deviation, %

RA, tf

600

600

0.00

RВ, tf

900

900

0.00