Objective
To verify the accuracy of calculations for the geometric properties of a solid equilateral triangular 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 equilateral triangle, verify the accuracy of the calculated geometric properties.
Geometry
b = 40 cm
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Analytical model
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Model in the 'Cross-section Design Toolkit' module
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Note
The triangulation mesh size is 10 mm.
Analytical solution
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| yb = zb = 0 |
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| X0 = a/2 |
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Comparison of calculation results
| Parameter | Theory | LIRA-FEM | Error, % |
| Area, A cm2 | 692,82 | 692,82 | 0 |
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Moment of inertia about the central U-axis, Iu cm4 |
46188,021 | 46188,021 | 0 |
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Moment of inertia about the central V-axis, Iv cm4 |
46188,022 | 46188,022 | 0 |
| Torsional moment of inertia, It cm4 | 55425,625 | 55518,52 | 0,1673 |
| Radius of gyration about the principal Y1-axis, Ry mm | 81,649 | 81,65 | 0,0012 |
| Radius of gyration about the principal Z1-axis, Rz mm | 81,649 | 81,65 | 0,0012 |
| Section modulus about the principal Y1-axis, Wy cm3 | 2000 | 2000 | 0 |
| Section modulus about the principal Z1-axis, Wz cm3 | 2309,401 | 2309,401 | 0 |
| X-coordinate of the centroid in the current coordinate system, X0 mm | 200 | 200 | 0 |
| Y-coordinate of the centroid in the current coordinate system, Y0 mm | 115,47 | 115,47 | 0 |
| Y-coordinate of the shear centre, yb cm | 0 | 0 | 0 |
| Z-coordinate of the shear centre, zb cm | 0 | 0 | 0 |
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