SLS 07: Thin cylinder under self-weight


Material Modulus of elasticity E =210 000N/mm^2
Poisson’s ratio \nu= 0.3
Density \rho=7850 kg/m^3
Geometry Cross-section Thickness e=2 mm
Boundary conditions At bottom edge R_y fixed
In point A R_x fixed
In point B R_z fixed
Loads Self-weight1 \gamma=78.5kN/m^3
Mesh Maximum element size 0.05m
Minimum element size 0.00m
1 The gravitational acceleration g equals 9.81m/s^2 in Diamonds. You cannot change it. In order to calculate with g=10.0m/s^2, the self-weight of steel was adjusted in Diamonds.



    \[\sigma_1(z)=\sigma_{zz}=\gamma \cdot z \rightarrow \sigma_1(2m)=78.5kN/m^3 \cdot 2m=0.157N/mm^2\]

    \[\Delta R(z)=\frac{\gamma \cdot \nu \cdot R \cdot z}{E} \rightarrow \Delta R(4m)=\delta_x(0m)=\delta_z(0m)=\frac{78.5kN/m^3 \cdot 0.3 \cdot 1m \cdot 4m}{210000N/mm^2}=0.000449mm\]

    \[\Delta y(z)=\frac{\gamma \cdot z^2}{2 \cdot E} \rightarrow \Delta y(4m)=\delta_y(4m)=\frac{78.5kN/m^3 \cdot (4m)^2}{2 \cdot 210000N/mm^2}=0.002990mm\]

Deformation \delta_y in Diamonds

Point Which result Independent reference Diamonds Difference
Y=2m stress \sigma_zz 0,157N/mm² 0,157N/mm² 0,00%
Y=0 Longitudinal deformation \delta_y 0,002990mm 0,002991mm 0,02%
Y=0 Radial deformation \delta_x and \delta_z 0,000449mm 0,000442mm -1,46%


  • Mécaniciens, S. F. D. (1990). Guide de validation des progiciels de calcul des structures: SSLS 09: cylindre mince sous son poids propre
  • Roark, R. J., & Young, W. C. (2002). Roark’s Formulas for Stress and Strain (7th edition, Table 13.1 case 1e). McGraw-Hill Companies.
  • Tested in Diamonds 2023r01.

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