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PROCEEDINGS OF THE TENTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING
Edited by: B.H.V. Topping
Numerical Results on the Buckling Strength of Stiffened Elliptic Paraboloidal Steel Panel Shutters
A. Zingoni+ and V. Balden*
+Department of Civil Engineering,
A. Zingoni, V. Balden, "Numerical Results on the Buckling Strength of Stiffened Elliptic Paraboloidal Steel Panel Shutters", in B.H.V. Topping, (Editor), "Proceedings of the Tenth International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 151, 2005. doi:10.4203/ccp.81.151
Keywords: stiffened steel panel, stiffened shell, steel shutter, elliptic paraboloid, buckling, bridge deck shuttering.
Steel panel shutters of double curvature, although costly to fabricate, may allow the casting of concrete bridge decks, walkways and floors over relatively large spans while avoiding the use of supporting scaffolding and other intermediate props. Long-span shutters are desirable when the ground below the deck cannot adequately support scaffolding, or the space below the deck carries traffic carriageways which should not be obstructed by scaffolding. This paper reports the results of a numerical study undertaken on the buckling behaviour of lightly stiffened elliptic paraboloidal steel panels intended for use as long-span shuttering for lightweight concrete bridge decks, walkways and floors.
Shutter units were considered to comprise a thin elliptic-paraboloidal shell of rectangular plan form of length a and width b (a>=b), the rise of the shell being h relative to the level of the midpoints of the sides of the paraboloid. The panel length a was fixed at 10m, while the width b was varied from 2m to 10m in steps of 2m (to cover aspect ratios b/a of 0.2, 0.4, 0.6, 0.8 and 1.0). Stiffening of the shell was achieved by welding steel strips onto the lower (i.e. inner) surface of the shell at a regular spacing in each of the two directions parallel to the edges of the rectangular plan form, to form an orthogonal pattern of stiffeners on the surface.
Two loading cases were considered, namely: (i) a uniform pressure p (force per unit area of the actual curved surface, acting normal to the shell surface at any given point); (ii) a vertical imposed loading of intensity q (force per unit area of the horizontal projection of the shell surface, acting vertically downwards at all points). The first loading simulates the pressure of the wet concrete, while the latter simulates the dead weight of the hardening concrete.
For each of the five aspect ratios adopted (b/a= 0.2, 0.4, 0.6, 0.8,1.0), four rise ratios (h/b=2.5%,5.0%,7.5%,10%) were considered, and a linear buckling analysis carried out using the FEM programme ABAQUS , to determine the lowest buckling loads (first mode solution) for the pressure loading and the gravity loading. To account for geometric non-linearities and material plasticity, a non-linear analysis employing a modified version of Riks' method  was also carried out. The modified Riks procedure allows the load displacement response to be traced in the post-buckling range of negative stiffness. The numerical comparisons show that for the lightly stiffened shallow elliptic paraboloidal steel panels in question, the linear buckling analysis predicts the first buckling load reasonably well for low aspect ratios (b/a=0.2 and b/a=0.4), but tends to considerably overestimate the buckling strength in the case of higher aspect ratios (b/a=0.8 and b/a=1.0).
It is observed that the load-carrying capacities between pressure and gravity loading is not too different (the difference generally not exceeding 10%), with pressure (i.e. loading normal to the shell surface) causing first buckling at a slightly lower load intensity than (vertical) gravity loading. Thus the initial conditions at the time of placement of concrete, when the concrete is at its most fluid and pressure effects prevail, govern the design of the shuttering.
For panel aspect ratios ranging from 0.2 to 1.0, and rise ratios ranging from 2.5% to 10%, the investigation quantifies the actual buckling strengths of the panels for specified shell thickness and stiffener proportions. It is shown that the buckling strength is strongly dependent on the rise of the panel (the higher the h/b ratio, the greater the load intensity the panel can carry) and the aspect ratio of its rectangular projection (the higher the b/a ratio, the smaller the load intensity the panel can carry).
Cut-off shallowness limits for structural viability (in terms of the ability to carry a specified minimum depth of wet concrete) are established for various panel aspect ratios. The overall conclusion is that edge-supported lightly stiffened steel panels in the form of shallow elliptic paraboloids are structurally viable as long-span shuttering units for lightweight concrete bridge decks, walkways and floors, provided that the correct aspect ratio and rise of the panel are chosen. Higher load-carrying capacities can be achieved in practice by using a thicker shell, more robust stiffeners and a denser network of stiffeners, while preserving the elliptic paraboloidal form.
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