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SLS 09: Four-sides simply supported plate under uniform load

Description

Length a =1m. Different ratio’s b/a are tested by changing the length of b in each model.

Material Modulus of elasticity E = 100 N/mm^2
Poisson’s ratio \nu= 0,3
Geometry Cross-section Thickness e=10 mm
Boundary conditions Along all edges Simply supported
Loads On the entire surface p=0.01 N/m^2
Mesh Maximum element size 0.10m
Minimum element size 0.00m

Results

Handcalculation
b/a
1.0 \alpha= 0.0443 \beta= 0.0479 \beta_1= 0.0479
2.0 \alpha= 0.0443 \beta= 0.1017 \beta_1= 0.0464
5.0 \alpha= 0.0443 \beta= 0.1246 \beta_1= 0.0375

    \[\delta_y=\frac{\alpha \cdot p \cdot a^{4}}{E \cdot e^3}\]

    \[M_{xx,max}=\beta \cdot p \cdot a^{4}\]

    \[M_{zz,max}=\beta_1 \cdot p \cdot a^{4}\]

Deformation \delta_y in Diamonds

Case Which result Independent reference Diamonds Difference
b=1m Deformation \delta_y 4.43mm 0,163mm -0.77%
Bending moment M_{xx} 0.479N/m/m 0.4818N/m/m 0.58%
Bending moment M_{zz} 0.479N/m/m 0.4818N/m/m 0.58%
b=2m Deformation \delta_y 11.06mm 10.993mm -0.61%
Bending moment M_{xx} 0.464N/m/m 0.4697N/m/m 1.23%
Bending moment M_{zz} 1.017/m/m 1.0214N/m/m 0.43%
b=5m Deformation \delta_y 14.1632mm 14.081mm -0.58%
Bending moment M_{xx} 0.375N/m/m 0.3794N/m/m 1.17%
Bending moment M_{zz} 1.246N/m/m 1.2451N/m/m -0.07%

References

  • Mécaniciens, S. F. D. (1990). Guide de validation des progiciels de calcul des structures: SSLS 24: plaque rectangulaire sur appuis simples avec chargement uniforme.
    Note: the modulus of elasticity and load imposed in the Afnor-example, felt outside the boundaries of Diamonds. As a work around, both parameters were multiplied by 10 and the results were recalculated accordingly.
  • Timoshenko, S., & Woinowsky-Krieger, S. (1959). Theory of plates and shells. McGraw-Hill Publishing Company.
  • Tested in Diamonds 2023r01.

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