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6.7: Plates versus Grillages

  • Page ID
    21751
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    Case (a). Two heavy stiffeners are subdividing the square plate shown in Figure (6.6.3) into four smaller square plates. An example of this type of design is the “hungry horse” deformation pattern of the ship hall, shown in Figure (6.6.2b).

    The point load is still applied at the intersection of both beams. The solution given by Equation (6.6.6) is still valid but now the beam stiffness is much higher than the plate bending stiffness, and the first term in Equation (6.6.6) can be neglected. The solution of two intersecting beam, each carrying half of the load is exact. The stiffness of the beam system is

    \[K|_{\text{two beams}} = \frac{P}{w_o} = \frac{12EI}{a^3} = \frac{EbH^3}{a^3} \]

    while the plate stiffness from Equations (6.6.3-6.6.4) is

    \[K|_{\text{plate}} = \frac{16 \pi D}{a^2} = \frac{16 \pi Eh^3}{12a^2(1 - \nu^2)} \frac{1+ \nu}{3 + \nu} \]

    Two intersecting beams form the simplest grillage

    The question is which of the two types of structures, plates or grillages are more weight efficient? So, let’s keep the volume of both types of structures the same and compare their stiffnesses.

    \[V_{\text{plate}} = V_{\text{beam}} \rightarrow ah = bH \]

    The ratio of stiffnesses, keeping the volume (weight) the same is

    \[\frac{K_{\text{beams}}}{K_{\text{plate}}} = 0.6 \frac{b}{a} \left(\frac{H}{h}\right)^3 = 0.6 \left(\frac{H}{h}\right)^3\]

    The stiffness of grillage is the same as that of the plate if \(H = 1.25h\). Stiffeners alone or their assemblages into a grillage can thus transmit considerable concentrated loads. They cannot resist distributed pressure. For that purpose plates or stiffened plates must be used.


    This page titled 6.7: Plates versus Grillages is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Tomasz Wierzbicki (MIT OpenCourseWare) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.