Objective
To verify the accuracy of calculations for the geometric properties of a solid semicircular 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 semicircular, verify the accuracy of the calculated geometric properties.
Geometry
d = 100 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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| Iu = 0,00686*d4 |
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zb = 0 |
Comparison of calculation results
| Parameter | Theory | LIRA-FEM | Error, % |
| Area, A cm2 | 3926,99 | 3926,73 | 0,0066 |
| Shear area about the principal Y1-axis, Ay cm2 | 3555,26 | 3364,73 | 5,3591 |
| Shear area about the principal Z1-axis, Az cm2 | 2991,99 | 2940,13 | 1,7333 |
| Moment of inertia about the central U-axis, Iu cm4 | 686000 | 685890,61 | 0,0159 |
| Moment of inertia about the central V-axis, Iv cm4 | 2454370 | 2454045,832 | 0,0132 |
| Torsional moment of inertia, It cm4 | 1859730 | 1859811,661 | 0,0044 |
| Radius of gyration about the principal Y1-axis, Ry mm | 132,169 | 132,16 | 0,0068 |
| Radius of gyration about the principal Z1-axis, Rz mm | 250 | 249,99 | 0,004 |
| Section modulus about the principal Y1-axis, Wy cm3 | 23819,444 | 23832,163 | 0,05 |
| Section modulus about the principal Z1-axis, Wz cm3 | 49087,4 | 49080,917 | 0,0132 |
| Y-coordinate of the shear centre, yb cm | 0 | 0 | 0 |
| Z-coordinate of the shear centre, zb cm | 4,244 | 4,243 | 0,0236 |
| Perimeter, P mm | 2570,796 | 2570,77 | 0,001 |
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