Objective
To determine the stress‑strain state of a cantilever circular bar of constant cross‑section subjected to an out‑of‑plane concentrated load at the free end.
Reference
S. Timoshenko, Strength of materials, Part 1: Elementary theory and problem, 3ed, 1955; RJ Roark, Formulas for stress and strain, 4ed, New York, McGraw-Hill, 1965.
Problem statement
To determine displacement Y at the free end (point B), torsional moment Mx, and out‑of‑plane bending moment Mz for the cross‑section at central angle θ from the fixed end.
Design model
Cantilever circular bar of constant cross‑section subjected to an out‑of‑plane concentrated load at the free end.
|
|
|
|
Initial geometry of analytical model
|
Initial geometry of FE model |
Geometry
Radius of the arc of the longitudinal axis of the cantilever circular bar r = 1,0 m
Central angle of the arc length of the longitudinal axis of the cantilever circular bar θ = 90º
Outer diameter of the circular cross‑section of the bar de = 0,020 m
Inner diameter of the circular cross‑section of the bar dі = 0,016 m
Material properties
Modulus of elasticity for bars in the model Е = 2,0 * 1011 Pa
Loads
Vertical concentrated load F = 100 N
Note
Design model - model type 5, 6 DOF per node; 15 bar elements of FE type 10.
The boundary conditions are provided by applying restraints in the X, Y, Z, uX, uY, and uZ degrees of freedom (point A).
Nodes: 16.
|
Design and deformed models
|
Displacement Y (m) out of the plane of the bar
|
|
Diagram of torsional moments Mx, (N*m)
|
Out-of-plane bending moment diagram Mz, (N*m)
|
Comparison of calculation results
| Parameters | Analytical solution | LIRA-FEM | Error, % |
| Displacement along the Y-axis of the bar (point B), m | -1,34 | -1,34 | 0 |
| Torsional moment Mx (θ = 15º), N*m | -74,118 | -73,981 | 0,18 |
| Bending moment Mz, N*m | -96.593 | -96.591 | 0,002 |
Download verification test
If you find a mistake and want to inform us about it, select the mistake, then hold down the CTRL key and click ENTER.
Comments