Issue 1 V1.07
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StructX > Resources > Statics > Plate Formulas

Assumptions and Limitations

Many components of structures may be logically idealized as laterally loaded, rectangular plates (or slabs). By identifying not only the loading condition but also the type of edge supports it is possible to use classical plate theory as one method to annalise a structure in smaller more manageable idealised sections. Classical plate theory assumes the following independent conditions:

  • The in-plane plate dimensions are large compared to the thickness.
  • Loads act transverse to the longitudinal axis and pass through the shear centre eliminating any torsion or twist.
  • Self-weight of the plate has been ignored and should be taken into account in practice.
  • The material of the beam is homogeneous and isotropic and has a constant Young's modulus in all directions in both compression and tension.
  • The centroidal plane or neutral surface is subjected to zero axial stress and does not undergo any change in length.
  • The response to strain is one dimensional stress in the direction of bending.
  • Deflections are assumed to be very small compared to the overall length of the beam.
  • The cross-section remains planar and perpendicular to the longitudinal axis during bending.
  • Membrane strains have been neglected.
  • Poisson's ratio has been assumed to be 0 unless stated otherwise in the notation section.

A note about bending moments: In structural engineering the positive moment is drawn on the tension side of the member allowing beams and frames to be dealt with more easily. Because moments are drawn in the same direction as the member would theoretically bend when loaded it is easier to visualise what is happening. StructX has adopted this way of drawing bending moments throughout.

Refer bottom of page for boundary conditions and loading Notation.

Supported Rectangular Plates with UDL

Supported Rectangular Plates with VDL

Supported Rectangular Plates with Point Load

Plate Icon Interpretation

Boundary Conditions and Loading Notation

The above plate icons show a series of letters representing the restraint conditions of the plate in question with the first letter dictating the support type on the left hand side followed by all the edges in a clockwise direction. The following notations have been used to describe the supports and loading conditions:

Notation

Additional Resources

  1. Lekhnit︠s︡kiĭ, S. G. Anisotropic Plates. New York: Gordon and Breach, 1968. Print.
  2. Mikhelson, Ilya. Structural Engineering Formulas. New York: McGraw-Hill, 2004. Print.
  3. Roark, Raymond J and Warren C Young. Roark's Formulas For Stress And Strain. New York: McGraw-Hill, 1989. Print.
  4. Timoshenko, Stephen and S Woinowsky-Krieger. Theory Of Plates And Shells. New York: McGraw-Hill, 1959. Print.