Materials: TestAS practice testlets

Engineers choose materials according to the demands of a component. Three properties are especially important for structures. Density determines how heavy a component of a given size is. Stiffness, measured by the modulus of elasticity E, describes how much a material deforms under load: a high modulus means little stretching. Strength describes the stress at which the material fails; for a tensile load, the tensile strength is the highest stress the material can bear.

stress σ = F ÷ A strain ε = σ ÷ E 1 MPa = 1 N/mm² 1 GPa = 1,000 MPa

For lightweight construction, as in aircraft, racing bicycles or cars, not only the properties themselves matter but their ratio to the density. The specific stiffness, E divided by the density, shows how stiff a component can be for a given mass; the specific strength, strength divided by density, shows how much load it can carry for a given mass. Steel is very stiff and strong but heavy; aluminium alloys are about one third as dense but also about one third as stiff, so their specific stiffness is similar to that of steel. Carbon-fibre-reinforced plastics (CFRP) combine low density with high stiffness and strength in the direction of the fibres, but they are expensive, difficult to recycle and much weaker across the fibres.

Other properties also matter: cost, resistance to corrosion, behaviour at high temperatures, ease of machining and joining, and environmental impact. Wood, for instance, has modest strength but low density, is renewable and easy to work, and its properties differ strongly along and across the grain. In practice, engineers also apply a safety factor: the permitted stress is the strength divided by a factor, for example 2, to allow for uncertainties in loads and material quality. In aircraft construction, where every kilogram counts, the safety factor is smaller but the checks on materials and structures are much stricter. Combining materials is also common: a bicycle may have a CFRP frame, aluminium wheels and steel spokes, each chosen for the demands of its part.

The table gives typical values; real values depend on the alloy, treatment and direction of loading.

In a liquid at rest, the pressure increases with depth, because each layer must carry the weight of the liquid above it. The additional pressure caused by a column of liquid of height h is called the hydrostatic pressure. It depends only on the depth, the density of the liquid and the gravitational acceleration, not on the shape or width of the container.

p = ρ·g·h F = p·A 1 bar = 100,000 Pa ρ(water) = 1,000 kg/m³

For water, the pressure increases by about 1 bar for every 10 m of depth. At the surface of the sea, the air already exerts a pressure of about 1 bar, so a diver at a depth of 10 m experiences an absolute pressure of about 2 bar, twice the pressure at the surface. Pressure gauges usually show the gauge pressure, the pressure above atmospheric pressure.

Water supply systems use hydrostatic pressure. A water tower stores water at a height above the houses it supplies; the height difference between the water level in the tower and a tap determines the water pressure at the tap when no water is flowing. Taps on higher floors therefore have lower pressure than taps on the ground floor. Tall buildings need pumps or intermediate tanks, because the pressure from the public supply is not enough for the upper floors.

Because pressure acts on every surface, large forces can arise on large areas. The force on a surface is the pressure multiplied by the area. Dams must be built thicker at the bottom than at the top, because the pressure of the water increases with depth. Submarine hatches and aquarium windows must be designed for the force of the water pressure, which can reach hundreds of thousands of newtons at great depths. When water flows, some of the pressure is lost through friction in the pipes, so the pressure at an open tap is lower than the static value calculated below.