Forces

External loads are forces applied to or acting on a structure caused by the objects it is supporting such as a person sitting on a chair or a vehicle on a road bridge. This involves loads where physical contact is made.

The body load on a structure is a load without physical contact, e.g. a structure's own weight. In many cases the largest load acting on a structure is the weight of the structure itself. For example a large motorway bridges self-weight may be far larger than any of the other loads acting upon it.

Weight - The gravitational weight of a body is the force with which the Earth attracts the body. This force is proportional to the body's mass and depends on the location. Because the distance from the surface to the centre of the Earth decreases at higher latitudes, and because the centrifugal force of the Earth's rotation is greatest at the Equator, the observed weight of a body is smallest at the Equator and largest at the poles. The difference is sizable, about 1 part in 300. At a given location, the weight of a body is highest at the surface of the Earth; it diminishes with altitude and with the depth below the surface. For example, the weight of a body diminishes by about 0.1% if it is raised 3 km above the Earth's surface or taken 6 km below the surface. Weight also depends to a smaller but measurable degree on the density of the Earth's crust below the body. To emphasise that weight is a force it is expressed in the force unit Newton (N).

Mass - Isaac Newton said that the mass of a body is the measure of the quantity of matter the body contains. Quantity here does not mean volume. Mass can be thought of as the tendency of a body to resist the change in velocity caused by an external force. Mass is therefore said to be a measure of inertia. It has magnitude but not direction and is therefore a scalar quantity. The SI unit is the kilogram (kg).

A structure at rest (or one that is moving at a constant velocity) is said to be in equilibrium. This means that the forces acting on it just balance and have no resultant. In the case of a chair, for example, the downward force due to the combination of its own weight and that of the person sitting on it must be exactly balanced by the upward forces exerted by the floor.

A structure works by interpreting how external loads give rise to internal forces within the structural members. A static structure is in equilibrium, otherwise it would move, i.e. the forces acting upon it are equal in size and opposite in direction.

Tensile forces are pulling forces and compressive forces are pushing forces. Tensile loads tend to extend or stretch a structural member. Compressive loads tend to compress or shorten a structural member. Tensile and compressive forces must balance if the structure is to maintain equilibrium.

Stress – The force per unit area on a body that tends to cause it to deform. Tensile or compressive stress may be calculated given values for force and area.

Stress = force

Area

Strain – A measure of the extent to which a body is deformed when it is subjected to stress. Linear strain or tensile strain is the ratio of the change of length to the original length. Tensile or compressive strain may be calculated given values of the original dimension and the change in dimension.

Strain = Change of length

Original length

Evaluate the importance of forces in a design context.

The Strength and Stiffness of Structures

Deflection - Elastic movement or sinking of a loaded structural member, particularly of the mid-span of a beam.

Stiffness - The ratio of a steady force acting on a deformable elastic medium to the resulting displacement.

If an external load is applied to some part of a structure, that part will be deflected to some extent, depending on the size of the load and the stiffness of the structure.

The stiffness of a structure may be calculated given values for load and deflection.

Stiffness = Load

Deflection

A beam – is a bar, body or structure, with one dimension large compared with the other dimensions, whose function is to carry lateral loads (perpendicular to the large dimension) and bending movements. Many beams are horizontal and the loads they carry are weights acting vertically downwards.

Bending moment – The algebraic sum of all moments that are on one side of a cross section of a structural member. For example, in the illustration below diagramming a floor joist, a load on the joist tends to bend it at any particular cross section of the joist. At section A-A the bending moment is the reactive upward force of the left wall on the joist times the distance from wall to section A-A. At section B-B the bending moment is the upward reactive force of the left wall times the distance from wall to B-B plus (in the algebraic sense) the moment produced by the downward load acting at its distance from section B-B. The lower portion of the diagram shows the resultant bending moment at each cross section of the joist. A bending moment that bends a beam convex downward is positive, and that bends a beam convex upward is negative.

Bending moment on an end-supported joist with a concentrated load.

Moment arm - The load x distance from the pivot is called the "moment" about the pivot. The distance between the load and the pivot is called the "moment arm".

Factor of safety - The ratio between the breaking load on a member, appliance, or hoisting rope and the safe permissible load on it. Also known as safety factor. Structures are designed to take higher loads than those they are normally expected to support.

It is the designer’s responsibility to ensure that every component of a structure can withstand the forces acting on it. The first step is to decide on a safe stress for the material of the component. This is usually called the working stress and it is obtained by dividing the failure stress by a factor called the factor of safety. In examination questions, the factor of safety will be given whenever it is required and for practical design it will be specified in the code of practice.

The failure stress is obtained by experiment. If ’failure’ is taken to mean the onset of permanent strain then the yield point is used. In some circumstances failure is considered to be fracture and the ultimate strength is taken as the failure stress.

The value of the factor of safety will depend upon the type of loading to be expected. If the structure carries only static loads a low value such as two may be used. If there are suddenly applied or impact loads a higher value must be taken.

An alternative to using a factor of safety is to increase the load acting on a component by a load factor. In simple tension or compression it will not matter whether the factor is used to reduce the stress or increase the load but in complex loading cases the load factor and factor of safety methods lead to different results.

Factors of safety for steel structures will vary from about 3 for static loads to about 15 for impact loads or 20 where fluctuating loads may cause fatigue failure.

The factor of safety may be calculated where the values for design load and normal maximum load are given.

Factor of safety = design load

Normal maximum load

The concept of factor of safety may be applied to other areas of design. A factor of safety is simply a ratio of the quantitative value of a design (factor) divided by the normal maximum expected value, e.g. stiffness, fuel tank volumes, electrical resistance, engine acceleration.

Evaluate the importance of strength and stiffness in a design context.

Selecting an appropriate material.

The primary difficulties in selecting an appropriate material can be seen as lying in two areas:

· The gathering of information concerning suitable materials, their properties and cost,

· Developing an understanding of the service requirements.

Consideration of these two areas will allow the range of possible alternatives to be found. Then, to select from this group, the designer must identify other criteria, such as the material offering the lowest cost or the minimum weight, and explore the manufacturing implications of any particular alternative. Which material is selected may very largely determine the manufacturing route and there will be implications for the detailed design of the product form. The IB syllabus guide gives some information concerning available materials, but it is also useful to consult databooks and databases on materials and current journals. New options are constantly appearing.

Ways of determining the physical and mechanical properties of materials and the relationship between the test and service conditions is crucial. There is no point in using simple tensile test data if the components are subject to fatigue loads or temperatures which make creep a possibility. For example, the life of oil rigs will ultimately be determined by the rate of growth of fatigue cracks in sea water. In order to predict the rate of growth, small specimens were initially tested, but it was soon realised that the inaccuracies resulting from the scaling were too great. Larger-scale models were then tested, but ultimately it was felt necessary to build a fatigue test rig large enough to flex full-size legs. The important point to realise is that it is part of the designers’ responsibilities to ensure that the test data they use are valid. This may mean conducting special tests for measuring the wear resistance of fabrics or the frictional properties with specific lubrication conditions, or any other property of key interest, in the precise service conditions that we expect.

However, assuming that for a particular application, the data from a simple tensile test are valid, the table below shows how this information can be combined with another characteristic to simplify selection. In this case the density has been chosen to allow the material offering the lowest product weight for a given strength or the lowest product weight for a given stiffness to be identified.

Table combining some mechanical and physical properties

Similarly, if cost had been used instead of the density then the material giving the greatest strength or stiffness for the lowest cost could have been found.

As an example, consider the selection of a material for a car panel. If cost were the only criterion, then selecting the material with the highest stiffness- to-cost ratio would be the obvious choice. If weight were the only criterion then the material with the highest stiffness-to-density ratio would be chosen. Stiffness is likely to be more significant than strength because deflection (or sufficient rigidity) is likely to be seen by normal users as the important factor. However, racing drivers might well choose the material with the greatest strength-to-density ratio as they are probably even more concerned with weight than with the deflection of the bodywork.

Of course, all these statements concern simple mechanical properties. For car bodywork, as with most products, other aspects are potentially just as significant. In the case of car panels crash resistance, the effect of corrosion and the ease of quantity manufacture are vital matters. GRP and wood offer good strength properties, but have little toughness and hence offer very limited protection in crashes. It is therefore essential to have a chassis made of steel or a similarly tough material, when such materials are employed for vehicle bodywork. Any weight savings are therefore largely lost. Aluminium would offer both toughness and corrosion resistance, but requires specialist joining techniques and is therefore unsuitable for quantity production. It has, of course, long been used for sports cars, where typically it was TIG (or GTAW) welded, and on aircraft where it is riveted, welded or adhesively bonded.

There is no ’right’ material for vehicle bodywork: it all depends on the particular kind of vehicle. For example, a carefully sealed steel chassis is probably more adequate for all road cars, but with an off- road vehicle like a Land Rover, no undersealing can be guaranteed and hence the use of aluminium is justified despite the production difficulties.