 How can we go about selecting a material for a given structural application before the entire structure is even designed? As we saw in an earlier video, our decisions necessitate us to make compromises between structural capability such as strength and stiffness, and design constraints such as weight and cost. So how can we go about doing this? In the early stages of design when we would begin to make decisions about the material to use, we do not have a detailed structural design for which we can perform detailed design calculations. Instead, we merely have a structural concept. This is best illustrated with an example. Imagine you want to design the upper skin panel of a new aircraft wing. From your knowledge of aircraft structures, you know that this wing skin panel will carry heavy compressive loads due to lift on the wing during flight, and tensile loads due to the weight of the wing and fuel within it while it is on the ground. For this case, we can even envision critical limits to its structural capability. We would need to design it such that we prevent fracture under tensile loading and buckling under compressive loading. But what will the wing skin panel look like? From our knowledge about aircraft structures, we know that a wing skin panel typically takes a form of a stiffened shell. That is, a relatively thin plate of material with reinforcing stiffeners. But at this stage of the design, even this is too detailed a configuration to consider. For the purposes of selecting a material, we can idealize the wing skin as a far more simple yet representative structure. A flat plate. So we now have idealized our structure as a flat plate and identified fracture and buckling as two limits to its structural capability. So how can we now go about weighing options against design constraints such as weight and cost? If we look at our limits on structural capability, fracture and buckling, we can identify engineering equations that relate the force at which this failure mode will occur to the material and geometry. For tension failure, fracture is limited by the ultimate stress of the material, so a flat plate of width B and thickness T will be able to carry a maximum force equal to the ultimate stress of the material multiplied by the cross-sectional area of the plate. We will call this a characteristic equation which relates a structural capability to the material properties and geometry. If we want to compare two materials for our design, we can use the characteristic equation. Let's say we want to compare an aluminum alloy to steel. We know these materials will have different ultimate strengths, so we can substitute in the values for these two materials in order to compare them. No matter what material we choose, we want to achieve the same structural capability, so f max will be the same for both materials. Similarly, the width of the plate will be the same as it is dictated by the size of the wing. So as a result, we would obtain two different thicknesses for the plate. The different thicknesses for these two materials combined with the different densities of the materials would mean that the weight of the aluminum and steel plates would be different for the same f max. So let's compare these weights. The weight is simply volume multiplied by density, so for our flat plate, weight would be equal to the width times the length times the thickness times the density. If we compare the weight of the aluminum to the weight of the steel, we would get the following expression. Substituting in the expression for thickness derived from our characteristic equation, we see that the comparison of weight reduces to a comparison of the ultimate strength of the material divided by the density of the material. We have now derived a material selection criterion that we can use to rank the efficiency of different materials in terms of our characteristic equation for tensile fraction and our constraint of weight. We can do a similar analysis for different constraints and characteristic equations. For instance, if we want to look at the material cost efficiency for tensile fracture, our selection criteria would reduce to the ratio of ultimate strength over the cost per unit volume of the material. Conversely, if we consider the case of buckling, which has the following characteristic equation, the selection criteria would reduce to a ratio of the cube root of a material stiffness divided by material density, or divided by material cost per unit volume depending on if weight or cost were the driving design constraints. There are many different characteristic equations for different structural capabilities and design constraints. So what does this mean for our wing skin example? We can take these four selection criteria and evaluate them for different materials. For our comparison, we will look at the four materials shown here in this table. You can pause the video here if you want to take note of the material properties before we insert them into our criteria and validate the math for yourself. After completing the math, we can come up with a table comparing these four materials with our different criteria. Remember, a higher value means that the material is more efficient at meeting the structural capability based on the particular constraint. So knowing this, we can highlight the materials that rank the highest and we see that steel comes out as the best in terms of cost constraints and composites on top in terms of weight constraints. So does this mean that these are the two best materials? Perhaps we should take a closer look. If we also highlight the worst materials in terms of cost and weight, we see that both steel and composites are also the worst materials. Steel is cheap but not so weight efficient, while composites are strong but not very cost efficient. This leaves the other two materials, aluminum and titanium. They are not the best in terms of weight and cost efficiency but they do a good job with both constraints. It should be no surprise then that aluminum and titanium are widely used in the aerospace industry. For the structural capabilities being evaluated here, actually aluminum is the most widely used material. Can you reason why this is based on the numbers provided here? The titanium is significantly less cost efficient while it is only marginally more weight efficient for fracture and actually less weight efficient for buckling. So for this particular application and these constraints, it seems that aluminum would be a good compromise in performance, weight and cost. You might have noticed that our final decision is not a calculated result. We had to apply what we call engineering judgment. We had to make a decision based on some quantitative results but there was no absolute correct answer. As an engineer we often have to make such decisions ourselves and be prepared to defend that choice based on sound reasoning, what we call engineering judgment.