1st order linear - Simply supported orthotropic square slab

Tekla Structural Designer
2021
Tekla Structural Designer

1st order linear - Simply supported orthotropic square slab

Problem definition

Calculate the mid-span deflection of a 10m by 10m simply supported slab of 25mm thickness with 10N/m2 UDL applied to it. The material properties the slab were assumed to be as follow: Ex = 33.5 MPa, Ey = 33500 MPa, Gxy = 523 MPa, 𝜈x = 0.4000, and 𝜈y = 0.0004.


FEM model

A regular triangular finite element mesh is used with a mesh size of 0.25m.

Analytical solution

The deflection was calculated using the solution obtained by Timoshenko and Woinowsky-Kreiger. The solution uses Navier’s method, which employs the double trigonometric series equation:


where:

w - deflection,

a = b - side lengths

x and y - coordinates of the point of interest


Results

Value Analytical solution (mm) Solver result (mm) % Error
Mid-span deflection 29.799 29.795 0.01

Conclusion

A satisfactory convergence of the analytical and solver’s results was observed.

References

Timoshenko, S. and Woinowsky-Krieger, S. 1987. Theory of Plates and Shells. 2nd Edition. McGraw-Hill Book Company, Inc. New York, NY, USA.

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