Objective
To verify the accuracy of calculations for the geometric properties of a solid octagonal cross-section.
Reference
A.A. Umansky, Design engineer’s handbook – calculation and theory, 1973, book 1.
Problem statement
For a solid cross-section in the shape of an octagon, verify the accuracy of the calculated geometric properties.
Geometry
r = 10 cm
|
|
|
|
Analytical model
|
Model in the 'Cross-section Design Toolkit' module
|
Note
The triangulation mesh size is 10 mm.
Analytical solution
|
|
| φ = 0 | |
|
|
| It = 1,25566r4 | |
|
|
| Wy = Wz = Iu/R | |
|
Comparison of calculation results
| Parameter | Theory | LIRA-FEM | Error, % |
| Area, A cm2 | 282,843 | 282,84 | 0,0011 |
| Rotation of the principal Y1-axis relative to the X-axis of the current coordinate system, φ ° | 0 | 0 | 0 |
| Moment of inertia about the central U-axis, Iu cm4 | 6380,718 | 6380,712 | 0,0001 |
| Moment of inertia about the central V-axis, Iv cm4 | 6380,718 | 6380,712 | 0,0001 |
| Torsional moment of inertia, It cm4 | 12556,6 | 12560,298 | 0,0294 |
| Radius of gyration about the principal Y1-axis, Ry mm | 47,496 | 47,5 | 0,0084 |
| Radius of gyration about the principal Z1-axis, Rz mm | 47,496 | 47,5 | 0,0084 |
| Section modulus about the principal Y1-axis, Wy cm3 | 638,072 | 638,071 | 0,0002 |
| Section modulus about the principal Z1-axis, Wz cm3 | 638,072 | 638,071 | 0,0002 |
| Perimeter, P mm | 612,293 | 612,29 | 0,0005 |
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