Objective
To verify the accuracy of calculations for the geometric properties of a solid square 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 a square, verify the accuracy of the calculated geometric properties.
Geometry
a = 40 cm
|
|
|
Model in the 'Cross-section Design Toolkit' module
|
Note
The triangulation mesh size is 10 mm.
Analytical solution
|
| A = a2 | Ay = Az = A/1,2 |
|
It = 0,1404*a4 |
|
|
Comparison of calculation results
| Parameter | Theory | LIRA-FEM | Error, % |
| Area, A cm2 | 1600 | 1600 | 0 |
| Shear area about the principal Y1-axis, Ay cm2 | 1333,3 | 1329,45 | 0,2888 |
| Shear area about the principal Z1-axis, Az cm2 | 1333,3 | 1329,45 | 0,2888 |
| Moment of inertia about the central U-axis, Iu cm4 | 213333,333 | 213333,333 | 0 |
| Moment of inertia about the central V-axis, Iv cm4 | 213333,333 | 213333,333 | 0 |
| Torsional moment of inertia, It cm4 | 359424 | 360094,019 | 0,1861 |
| Radius of gyration about the principal Y1-axis, Ry mm | 115,47 | 115,47 | 0 |
| Radius of gyration about the principal Z1-axis, Rz mm | 115,47 | 115,47 | 0 |
| Section modulus about the principal Y1-axis, Wy cm3 | 10666,6 | 10666,667 | 0,0006 |
| Section modulus about the principal Z1-axis, Wz cm3 | 10666,6 | 10666,667 | 0,0006 |
| Plastic section modulus about the principal axis Y1pl, Wply cm3 | 16000 | 16000 | 0 |
| Plastic section modulus about the principal axis Z1pl, Wplz cm3 | 16000 | 16000 | 0 |
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