SEED Guides Selecting Structural Configuration < >
10. Designing the StructureA few structures almost seem to design themselves since the configuration produces an "obvious" shape. However most structures need some design effort to reach a satisfactory solution and a deliberate exploration of the less obvious routes may be fruitful in improving efficiency. Most areas of industry have their own approach to the types of structures, materials and manufacturing techniques common in that field. They have become popular because they have worked in the past and will probably be appropriate for most of the circumstances likely to arise. However, occasionally an unusual situation, change of circumstances or particularly critical situation makes a different approach worth considering.
Each load case should be examined carefully, with its associated safety factors, to ensure that it is realistic and that all its requirements are necessary. When load cases are combined to produce an extreme load case, great care should be taken to avoid applying all of the safety factors together to give an impossibly high loading. A little thought may well show that only one of the contributing cases could be at its worst state at any one time, or that such a combination of conditions would cause a failure elsewhere long before the piece in question becomes critical. A small change of geometry, or the easing of some other restriction will often make the load combination far less critical without compromising any other requirement.
The surface areas which are loaded may be small in comparison to the scale of the structure and hence be regarded as "point" loads in all but very local considerations. Where loads are distributed along a line or over a surface, some form of spanning structure may serve to concentrate them locally and hence they may again be considered as set of point loads on the scale of the whole structure. These local spanning structures, beams or plates, may then be designed independently. If the scale of the structure is such that loads cannot be considered as acting at a point (or even locally to a small load position where its area cannot be ignored), then the patterns of stress within the bulk of the solid must be considered directly. Design then becomes a matter of shaping the material in such a way that internal stresses do not exceed the capacity of the material, particularly where changes of the direction of stress flow concentrate the effects, and that the stiffness of the load paths remain adequate for the application. In these cases the design depends heavily on the specific case in hand, and very little general guidance can be given. The only exceptions are in basically simple situations such as pressure loading from inside or outside a simple container or from some cases of fluid dynamic loading. These will be dealt with in the separate guides covering those cases.
Linear Structures
Straight linear structures carrying one dimensional tension loads are the simplest design case. A calculation, of peak load / allowable stress, gives the minimum cross sectional area requirement for the whole length of the structure. Then, provided the end connections adequately distribute the load into the material, this cross section may be of any convenient compact shape to suit manufacturing, aesthetic, or other requirements. Compression introduces buckling instability and crushing into design considerations. Crushing is an equivalent failure to the simple tension case, i.e. a high stress causes a breakdown of local atomic bonding, but not necessarily at the same level of stress as the tensile case since the situation is complex. (Failure is often, in fact, a shear failure or even tensile due to the Poisson effects mentioned earlier.) A similar formula gives the required cross section area needed to avoid it. However, except for very short structures, crushing is unlikely to be the prime mode of failure. Buckling considerations, either for the whole structure or locally in relatively thin parts of the section, tend to dominate. Even at loads below the failure level, buckling modes can affect the stiffness of the structure and hence the way it performs its task. Where buckling loads dominate the design there is scope for ingenuity by increasing the section modulus, adding stiffening, or 'barreling' the section.
As the loading becomes more complex or the structure curves or bends, bending and shear must be accommodated by changing the section modulus and ensuring adequate connection between its parts. Constant section members are usually the cheapest to manufacture but rarely the most efficient. The competing choices between slender trusses, compact sections and shear plate beams must be carefully considered. Resistance to bending is increased be moving material away from the neutral axis, while retaining sufficient connection across the section to carry the accompanying shear. Thus I-sections and channels, trusses with larger top and bottom members, and equivalent shear panel structures should be examined for suitability. Where bending is in more than one direction, then the cross section must meet those requirements in all directions. A 'four cornered' section is often the most efficient route to a solution. As the cross section grows in comparison to the length, it may more properly be considered a planar or spacial structure (see below).
Another possibility is to use the curvature of the structure to reduce or remove the bending problems altogether. This is done with arches and suspended cables where the axis of the structure at all sections is tangential to the line of action of the support forces required at that point. Suspended cables or chains are flexible and will automatically take up the required shape. Arches must be built to have a sufficiently deep section so that the line of action always lies within it. The following Flow Chart summarizes linear structure design considerations. Other criteria may dictate the final form but these represent the minimum range necessary to meet the structural requirements.
Planar Structures
One dimensional loading on a flat planar structure is simply a wider version of the cases dealt with above and similar remedies apply. These are in essence very similar to the cases considered for straight linear structures, but with the option for much deeper designs. Those parts of the structure at a significant distance from the line of loading will play little part. Two dimensional in-plane loading on a flat planar structure is typical of many complete structures as well as the major parts of a high proportion of spacial structures. For example; bridges are frequently formed of two or more deep beams or plane trusses with the roadway supported on short beams spanning them; most modest sized building structures are a series of parallel load bearing walls or portal frames with floors spanning between them and a few connecting crosswalls to give lateral stability (and keep the wind out). In essence, many of these carrying spanning loads bear a similarity to the equivalent linear structure cases, but the loading and support points may be at different positions within the plane not confined to a single axis. Typical examples are shown below.
All other planar situations are curved, carry out of plane loads, or both. For out of plane loading or curved planes, bending and shear is induced within the depth of structure. This must be accommodated by moving material to the outer faces of the structure, with adequate connections, or by redirecting the loading within the curvature of the plane as membrane or arch action. The analogy with the linear structures is clear, the design problem has simply become more general.
Thin shell structures form another set of special cases since they are assumed to carry little out of plane bending or shear. They rarely form complete structures but are frequently components ranging from simple shear panels to complex hyperbolic roof structures. Often cylindrical shapes or domes may be considered as thin shells, but only if the loading is restricted to a limited range of cases. (Pressure vessels are special cases which will be dealt with in another unit.) Within the thin shell group are thin membranes which are assumed to be flexible enough to take up a shape where all the stresses are tensile. A number of tent like roof structures and pressurised enclosures have been constructed with such membranes as their major component.
Spatial Structures
One and two dimensional loading on a spacial structure can be dealt with by extension from the equivalent linear and planar situations. Many spacial structures can be broken down into an assembly of linear and planar components, which may be treated, for the purposes of design, almost independently, with some interactions at the connection points. Design analysis will then demonstrate the validity of this model and the sensitivity of the interactions. Only where there is a high level of interaction between such components, or where the solidity or complexity of the geometry will not allow such a model to be perceived, must the structure be considered as presenting a truly spacial design problem. Usually these can be divided into categories, one a relatively compact structure with loads imposed from the outside, the space it occupies may be circumscribed but has no internal obstructions, and the other a hollow structure probably with significant loads derived from masses carried within the structural envelope and spaces within or passing through the structure which must be left clear. The first type are usually specialist in form and therefore little general design advice can be given. The second represents wide range of structures ranging from domestic appliances, such as vacuum cleaners, to large buildings, such as theatres, which by reason of complexity cannot be broken down into structural components. Geometric constraints usually dictate the space available for structure. A rough model derived from these constraints can then be analysed and examined for deficiencies. Except in very simple cases, such structures should not be designed by the students and less experienced engineers for whom these Guides are intended.
General Remarks
The boundaries between these groups are blurred in that, say, a wider beam becomes a planar structure when there is significant variation in stress across its width. There are also compound structures which are combinations of any of the above in one assembly. Once the fundamental shape is known, the most convenient type can be determined. It may be a truss, frame, panelled frame or solid. Potential structural failure conditions arise from four main sources: