Prerequisites

None

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Introduction to shell structures

OBJECTIVE/SCOPE

To qualitatively describe the main characteristics of shell structures and to discuss briefly the typical problems, such as buckling, that are associated with them.

SUMMARY

Shell structures are very attractive light weight structures which are especially suited to building as well as industrial applications. This lecture presents a qualitative interpretation of their main advantages. It also discusses the difficulties frequently encountered with such structures, including their unusual buckling behaviour, and briefly outlines the practical design approach taken by the codes.

1. INTRODUCTION

The shell structure is typically found in nature as well as in classical architecture [1]. Its efficiency is based on its curvature (single or double), which allows a multiplicity of alternative stress paths and gives the optimum form for transmission of many different load types. Various different types of steel shell structures have been used for industrial purposes; singly curved shells, for example, can be found in oil storage tanks, the central part of some pressure vessels, in storage structures such as silos, in industrial chimneys, and even in small structures like lighting columns (see Figures 1a to 1e). The single curvature allows a very simple construction process and is very efficient in resisting certain types of loads. In some cases, it is better to take advantage of double curvature. Double curved shells are used to build spherical gas reservoirs, roofs, vehicles, water towers, and even hanging roofs (see Figures 1f to 1i). An important part of the design is the load transmission to the foundations. It must be remembered that shells are very efficient in resisting distributed loads but are prone to difficulties with concentrated loads. Thus, in general, a continuous support is preferred. If it is not possible to have a foundation bed, as shown in Figure 1a, an intermediate structure such as a continuous ring (see Figure 1f) can be used to distribute the concentrated loads at the vertical supports. On occasions, architectural reasons or practical considerations impose the use of discrete supports.


As mentioned above, distributed loads due to internal pressure in storage tanks, pressure vessels, or silos (see Figures 2a to 2c) or to external pressure from wind, marine currents, and hydrostatic pressures (see Figures 2d and 2e) are very well resisted by the in-plane behaviour of shells. On the other hand, concentrated loads introduce significant local bending stresses which have to be carefully considered in design. Such loads can be due to vessel supports or in some cases, due to abnormal impact loads (see Figure 2f). In containment buildings of nuclear power plants, for example, codes of practice usually require the possibility of airplane crashes to be considered in the design. In these cases, the dynamic nature of the load increases the danger of concentrated effects. An everyday example of the difference between distributed and discrete loads is the manner in which a cooked egg is supported in the egg cup without problems and the way the shell is broken by the sudden impact of the spoon (see Figure 2g). Needless to say, in a real problem, both types of loads will have to be dealt with either in separate or combined states with the conceptual differences in behaviour ever present in the designer's mind.


Shell structures often need to be strengthened in certain problem areas by local reinforcement. A possible location where reinforcement might be required is at the transition from one basic surface to another; for instance, the connections between the spherical ends in Figure 1b and the main cylindrical vessel or the change from the cylinder to the cone of discharge in the silo in Figure 1c. In these cases, there is a discontinuity in the direction of the in-plane forces (see Figure 3a) that usually needs some kind of reinforcement ring to reduce the concentrated bending moments that occur in that area.


Containment structures also need perforations to allow the stored product (oil, cement, grain, etc.) to be put in, and extracted from, the deposit (see Figure 3b). The same problem is found in lighting columns (see Figure 3c), where it is general practice to put an opening in the lower part of the post in order to facilitate access to the electrical works. In these cases, special reinforcement has to be added to avoid local buckling and to minimise disturbance to the general distribution of stresses.

Local reinforcement is also often required at connections between shell structures, such as those that commonly occur in general piping work and in the offshore industry. In these cases, additional reinforcing plates are used (see Figure 3d), which help to resist the high stresses produced at the connections.

In contrast to local reinforcement, global reinforcement is generally used to improve the overall shell behaviour. Because of the efficient way in which these structures carry load, it is possible to reduce the wall thickness to relatively small values. The high value of the shell diameter to thickness ratios can, therefore, increase the possibility of unstable configurations. To improve the buckling resistance, the shell is usually reinforced with a set of stiffening members.

In axisymmetric shells, the obvious location for the stiffeners is along selected meridians and parallel lines, creating in this way a true mesh which reinforces the pure shell structure (see Figure 4a). On other occasions, the longitudinal and ring stiffeners are replaced by a complicated lattice (see Figure 4b), which gives an aesthetically pleasing structure as well as mechanical improvements to the global shell behaviour.

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