Objective
To verify the accuracy of calculations for the geometric properties of a solid pentagonal 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 pentagon, verify the accuracy of the calculated geometric properties.
Geometry
r = 10 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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| φ = 0 | |
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| It = 0,84781r4 | |
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| Wy = Iu/R |
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Comparison of calculation results
| Parameter | Theory | LIRA-FEM | Error, % |
| Area, A cm2 | 237,764 | 237,76 | 0,0017 |
| 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 | 4575,009 | 4575,012 | 0,0001 |
| Moment of inertia about the central V-axis, Iv cm4 | 4575,009 | 4575,012 | 0,0001 |
| Torsional moment of inertia, It cm4 | 8478,1 | 8480,222 | 0,025 |
| Radius of gyration about the principal Y1-axis, Ry mm | 43,865 | 43,865 | 0,0114 |
| Radius of gyration about the principal Z1-axis, Rz mm | 43,865 | 43,865 | 0,0114 |
| Section modulus about the principal Y1-axis, Wy cm3 | 457,501 | 457,501 | 0 |
| Section modulus about the principal Z1-axis, Wz cm3 | 481,045 | 481,045 | 0 |
| Perimeter, P mm | 587,785 | 587,79 | 0,0009 |
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