 Hello. Welcome to this Mechanics of Materials mini-lecture. My name is Calvin Ranz and today we're going to talk about stress. Now this isn't the type of stress you feel while studying for an exam, or the stress that builds up in you when you're going to ask out that special someone. Today we're actually going to talk about the stress that materials feel when we subject them to load. Let's get started. Consider a hanging weight system pictured here. We have a weight of mass m hanging from a rod that is rigidly connected at its other end. In this example, let's also neglect the weight of the rod and let's assume that the system is in static equilibrium. If we take a closer look at the center portion of that rod and cut it away and remove it from the system, we will recall from statics that we have to apply forces at either end to maintain equilibrium. In this case, we also know that the force is equal to the mass of the weight times the acceleration due to gravity. What else do we know about this force F? We know that it has the units of newtons. We also know that it's a vector quantity with both a magnitude and a direction. We know that acts at an infinitesimal point and the force has all forces is a resultant of an interaction. In this particular case, the interaction is between the acceleration due to gravity and the mass in the weight. The force is also a resultant of another interaction and that is what is actually happening on that cross-sectional surface. We know that it is physically impossible for us to have a force acting at an infinitesimal point. In reality, that force will be distributed over that cross-sectional area. We will call this distributed force stress and denote it by the Greek letter sigma. We also know that if we integrate that stress over that cross-sectional area, we get exactly the resultant force. So what else do we know about this new concept of stress? Well, it has the units of force per unit area because if we integrate it over an area, we will get force. It also is a vector quantity because it has both a magnitude and a direction associated with it and it acts at an infinitesimal point just like force. And what it actually represents is the intensity of a resultant force at a particular point. Looking at stress in this manner and looking at the units of stress, you might ask yourself, is stress just simply force divided by area? Well, not exactly. Stress is actually the intensity of a force and although force divided by area might actually be a nice approximation of what the stress distribution is in an actual case, stress is actually the limit of force divided by area as that area approaches zero. And the reason this is important is there may be some cases where you have higher stresses acting on a surface and in other areas lower, as shown on the right here, you could have a distributed level of stress. And this is important in materials, the performance of the materials and in the failure of materials where the average stress shown on the left might actually get you into trouble. I find it's easier for students to remember this danger of using an average stress assumption by using an analogy that relates a little bit more to what the students are experiencing now and that is the stress associated with the typical university course. Now if you look at what stress is for a student in a course, it's related to their studying, their rate of learning or accumulation of knowledge. That is the intensity whereas the resultant of a course is the overall knowledge to learn, the knowledge gained. So let's take a look at visually what the assumption of an average stress in the context of a university course would look like. If we plot the stress associated with learning over time or the duration of the course, you might assume that that stress is evenly distributed over the duration of that course. However, experience probably tells you that there are stress raisers during a course, midterm exams, assignment deadlines, final exams that really result in peak levels of stress. And those peak levels might actually cause the student to reach their breaking point and ultimately fail a course. The same thing can happen in materials. So please be careful when assuming an average stress level within a material.