5.15 Circular slabs

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As noted earlier, zero deflection (w = 0) at the corner point of a hinged

slab implies that the gradient of the deflection surface is also zero, ∇w = 0.

Hence, if the edge of a hinged circular slab is approximated by an n-sided

polygon, then at n + 1 points on the boundary the slab is no longer able

to rotate, w,x = w,y = 0 (see Fig. 5.46). The strange thing is that the finer

Fig. 5.44. An FE program

replaces the wheel loads with

line loads, element loads, and

only the line loads = jumps in

the Kirchhoff shear between

the elements. The arrows

indicate the direction of the

line loads: ↓ = compressive

462 5 Slabs

Fig. 5.45. The bending moments generated by the truck

the subdivision becomes, the more the edge will appear to be clamped, and

therefore the error in the approximate solution increases, Babuˇskas paradoxon

[17].

The problem can be ameliorated by switching to a soft support w = 0, i.e.,

when the rotations are set free, w,x      = 0, w,y           = 0. Hence, a Reissner–Mindlin

plate should have less trouble with such slabs, but see [9].

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