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To remain static, an entire structure, and each definable continuous part of it, must have a load pattern in equilibrium in all six degrees of freedom. (A load pattern includes all externally imposed forces, pressures or moments, body forces such as weight, internally generated loads due to the fit of parts, temperature differences or pre-stressing, and all necessary balancing reaction forces, pressures or moments applied at the supports.) However, loads in some directions may be trivial in comparison to the dominant cases. The loading may then be considered as having fewer dimensions, the structure needing simply to be appropriately "robust" in the other directions, having due regard for any vibration modes or instabilities involving other degrees of freedom. Load patterns may be essentially one, two, or three dimensional. They may be constant, variable or a mix of the two; applied at fixed points, or move around the structure. On spanning structures, for example, the support reactions and self weight loadings are fixed in position but the supported loads may move across the span in a random fashion. Load patterns may act virtually at a point (such as direct forces and moments), be distributed along a line as shear, or over an area as pressure, or be Œbodyš forces (such as weight) distributed throughout its volume. Generally, the structural design problem is made simpler if the number of dimensions of the loadings can be reduced, that is by moving loads, that is both their points of application and their lines of action, into a single plane or axis.

A static load case includes imposed loads, whose values, directions, and positions of application (perhaps within a range of movement) are specified, and the complementary support forces available, whose position and stiffnesses are known but whose values are determined as those necessary to balance the effects of the imposed forces. A set of all the load cases which the structure must withstand forms the overall load pattern. The flows analogy takes the imposed pattern as input points and the reactions as resulting output but that directionality normally has no physical meaning for static structures. 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 without performing any other structural function. The loads may then be considered as a few point loads on the scale of the whole structure. These local spanning structures, beams or plates, may then be designed in isolation. Loading may also result from environmental effects such as temperature or humidity changes, or be the result of in-built deliberate or unavoidable geometrical constraints (for example, prestressing, press fits, or in any redundant structure with ill fitting parts).

One Dimensional Loading

Here all load application and support points and all their lines of action lie on a single straight line. Loads may be tension, compression, shear along the load line, or any combination of these. (Torque about the axis is a special case not included here. Torsion carrying shafts for rotary power transmission are dealt with in MPT 6.1 and 6.2 on shaft design.) The forces acting along the line must be in balance. Tension and compression are simply opposite senses of direct load but are usually distinguished because the potential failure modes are different, compression loading tending to lead to buckling rather than the direct failure normal in tension.

Single Support

This implies that the support is at one end since an intermediate one effectively splits the structure into two virtually independent parts, though the loads in one part may help to offset the support reaction from the other.

Two or More Supports

Very few one dimensional loadings fall into this category, since two or more full supports would normally be redundant and the loading would depend on the fit between the structure and the spacing of the supports. More frequently one support provides all restraint in the loaded direction and another "prop" gives additional stability in other directions, by reducing the tendency to buckle, without affecting the major load pattern. Sometimes each will provide support in a different sense, for example, with two abutments and a structure closely fitted between, either end could provide all support depending on the total effect of the loading. Should there genuinely be two or several full supports, then their relative stiffness must be taken into account in order to determine the load distribution. If the level of redundancy is too high to do this, it must be reduced by relaxing some of the constraints or by designing the structure to selectively distribute loads, otherwise its structural behaviour cannot be easily determined.

Two dimensional Loading

Here all load application points and all the lines of action of those loads lie in a single flat plane, any torque loadings are about an axis perpendicular to the plane, appearing as "moments" on the structure. Supports may resist loading in any of the three degrees of freedom under consideration (i.e. forces in the plane and rotation about an axis perpendicular to the plane).

Single Support and Cantilevered Loading

A single pinned support may carry a two dimensional load pattern provided it is self stabilising. Almost inevitably this implies a "hanging" structure or some equivalent mechanism which is rotationally stable and self-balancing, only requiring a single supporting force.

A structure with a moment carrying support at one end, loaded transverse to its long axis, is called a cantilever. A linear structure is a cantilever beam. A deeper structure, either a truss or a panelled structure may also be regarded as a cantilever. Sometimes gaps are spanned with a cantilever from one side, an opposing pair, or a series of cantilevers from intermediate supports. These arrangements are structurally distinct from true spanning beams, since the major bending occurs at the supports, not under the load and there is no structural continuity between supports. The fundamental property of a cantilever is the ability of its supported end to react the imposed moments.

A "propped" cantilever lies between a true cantilever and a fixed end spanning beam. It receives additional transverse but not moment support at or near its outer end. It is somewhere between a true cantilever and a spanning beam.

2-D Spanning Loading

This is a very common form of 2-D loading, where two supports (or more than two on the same line) share loads applied transverse to the line between them by the spanning action of the structure, all loads and reactions being in the same plane. Most types of beam support this form of loading as do basic suspension bridges, arches, and many truss forms. Spanning structures do not necessarily carry loads only in a vertical plane, any connection between supports carrying loads across its axis in a single plane comes into this classification.

2-D complex loading

The general 2-dimensional load cases, with forces at different angles and various support conditions are more difficult to classify. Some, such as loads on rings or roof trusses have a form partly dependent on the shape of the structure itself, so cannot be fully specified initially, but will clarify as the structure evolves. Some may be considered as combinations of simpler cases. Most can only be considered on their individual merits. A number of frequently occurring cases are well covered by analytical methods, either specifically or in a simplified form. This allows early designs to be conveniently checked and refined, but the convenience of easy analysis should not be allowed to dictate the design, particularly in sensitive areas.

Three Dimensional Loading

Loads may be of any form act in any plane and be applied at any point in any direction. Similarly support point may resist loading in any of the six degrees of freedom. In practice overall support must be provided in any degree of freedom not otherwise balanced.

Point Loading

This occurs where all the forces act at virtually the same point. This apparently trivial situation occurs at joints or other points of contact, where an independent component, a structure in the simplest sense, transmits forces between other components or structures. It may be a pin (including a shear loaded bolt) or a ball (e.g. at the base of transmitter towers) or some other shape whose size is such that the distance between load and reaction points is small. Often its size is determined by the surface or cross section area necessary to transmit the loading, as in bolted, riveted, or adhesive joints. All of these cases are structural details, which will be dealt with in the appropriate guides.

One point support

This is the three dimensional equivalent of the cantilever. The support has to provide constraint in all six degrees of freedom, or any missing constraints must be compensated for by some appropriate balancing of the loading to eliminate the need for them.

As in the 2-dimensional case, a non-moment carrying support may occur where the load is self-stabilising (usually 'hanging').

Two Point Support

This is a hybrid cantilever/spanning loading, since loadings not passing through a line between the supports must be either self balancing (hanging) or reacted by at least one moment carrying support, as in the cantilever loadings described above. Load components passing through that line are shared between the supports as in the two dimensional spanning cases. Either support may resist moments in any direction. If both do then the structure is redundant.

Three Point Support

Three non-moment carrying points of support are the minimum necessary to completely fix a solid object. It is the simplest statically determinate support condition. One carries loads in all three directions, the second does not carry loads in the direction joining it to the first , and the third only carries loads in a direction perpendicular to the plane of all three.

This is used extensively in situations where undesirable distortion must be avoided, either of the object itself or of its supports, due to thermal expansion, deflection due to load or any other cause. The supported object is structurally isolated, apart from its support reactions, unaffected by relative distortions. Its other advantage is its lack of problems of fit during assembly or removal. Any other three point support with more constraints than this will become part of a larger load path constraining any relative distortion of its supports.

3-D Complex Loading

This is the general 3-D case covering all other types of loading and support combinations. Few general observations can be made except to note that experience shows that a few load cases tend to dominate the design requirements and most complex cases can be considered as a combination of several simpler cases.

Mode of Support

Supports are usually regarded as very stiff and fixed relative to each other in all degrees of freedom. Sometimes, with building foundations or when attaching to another structure for example, relative or absolute support stiffness in, or about, particular directions can be specified and incorporated into the design and analysis of the structure. If the supports can be configured so that the supporting loads are statically determinate, then problems of relative load path stiffness may be avoided and the structure will be easier to design. The following diagram shows some of the various configurations of individual support giving different degrees of load resistance. In addition there are linear shear and distributed force supports along a straight line and surface shear and pressure supports spread over surfaces. These may be uniform or variable depending on the circumstances, and hence give varying degrees of support. Typically this could be the edge connection of a shear panel, or the support provided by a large friction pad on a firm surface. In practice many of the variations between support types often result from deliberate differences in the relative stiffness of the support in the various degrees of freedom rather than specific mechanical devices, as shown in the one and two degree cases below.

Repeated Loads

When loads are repeatedly applied over many cycles (often many thousands) or in a random fashion, there may be a gradual accumulation of microscopic damage where stresses are locally high, which will eventually lead to failure even though no single load limits have been exceeded. This phenomenon is known as fatigue. It can often be avoided, or the expected life considerably extended, by careful attention to detail and, if necessary, by deliberately incorporating crack inhibiting features, such as holes, in vulnerable areas. Careful structural maintenance can also halt the progress of fatigue once it has begun. Fatigue will be covered in more detail in units dealing with situations where it is likely to occur. (See for example MPT 6.2 "Shaft With Fluctuating Loads")

Redundancy

Structural redundancy in static structures arises from two sources, parallel load paths within the structure itself and redundant support systems. Several of the latter have been identified earlier. They can be resolved into statically determinate systems by building additional freedoms into the individual supports or advantage can be taken by using the additional restraint to provide stability to a structural linkage mechanism. Thus a simple three pinned arch uses its abutments as if there were a structural member between them making a statically determinate system. (A full arch with no pins does the same but is redundant.) A measure of redundancy within the structure can be accommodated both in the design conception of the structure and in the analysis, but a very complex redundant structure becomes impossible on both counts and cannot be guaranteed to function as required without testing to back up any analysis. However, a regular pattern of redundancy may be amenable to analysis, and produce a robust structure able to continue functioning even after significant damage, yet still be very efficient. (See 'Mitchell' structures, section 7.)

In analysis, redundant structures are dealt with by assuming that loads are distributed within structures in proportion to the stiffness of the alternative paths. In reality, such distribution is often very sensitive to the accuracy with which parts fit together and to any changes in temperature patterns or other similar factors. (Most analytical methods, such as Finite Element Analysis, cannot allow for these effects since they are not easily quantified.) Thus redundancy in the structure itself (or in its support reactions as mentioned above) should be kept to a reasonable minimum. If necessary, a sensitivity analysis of small variations of length of redundant paths should be carried out and steps taken to move the sensitivity to less critical areas, increase the accuracy of manufacture, use joints which will take up any tolerance discrepancies on assembly, or use heat treatment or other methods of reducing residual stresses. If significant temperature differentials may occur between redundant load paths, then great care should be taken in the analysis of the extremes of thermally induced loading, and the effects should be reduced to manageable levels, or eliminated, by careful design.'

The design of a redundant structure is complicated by having to design for stiffness and strength simultaneously. For example, if there are two load paths and one is somewhat stiffer than the other, it will attract more load and hence its stress levels may be unacceptable. If it is strengthened to reduce the stresses, it will probably also become stiffer and hence attract yet more load which will in turn raise the stress levels again. They may now be more acceptable or be even higher than before! Thus a better approach would be to examine the stiffness of both paths to make the best use of the available materials. Stiffening the lightly loaded path will shift load away from the overloaded path, moving towards a better solution. This will probably be an iterative process.