The objective of a static analysis of a part or mechanism could be to determine if the kinematics of the body/mechanism will work for the application in which it is utilized. However, the strict kinematic analysis of a part or mechanism (and for the sake of simplicity I’m going to talk in the rest of this article about a single part or body, with the understanding that such can apply to a mechanism or complex assembly of parts as well) we need to consider whether the materials chosen to make-up said body can successfully sustain the internal forces caused by the loading. For that, we need to open a discussion on a subject widely known as Strength Of Materials.
But, as usual, I’m already well ahead of myself, as I’ve casually tossed-about some terms assuming we are all on the same page as to their definitions. As such, this will, once again, be a largely introductory piece.
Trust me, these posts will get far, far more interesting as we continue along. But walk before run, and all that.
At a very high conceptual level, consider some solid body – any will do. Forces applied to that body will cause said body to deform, regardless of how stiff or “strong” the body is. The deformations may be so small as to be imperceptible, but even a feather laying on a block of granite will cause nano-level deformations of said block. The deformation of the block will cause what is known as strain in the material, which, based on the physical properties of the material, will lead to a level of stress in that material.
Stress is, from a mechanics of materials perspective, precisely what it means for human physiology. It is a measure of the internal loads on the material within a body caused by some sort of external stimulus. And, just like humans, certain material are more capable of handling stress – they are stronger, in other words – than are others.
Strength of Materials aims at precisely the use of the macro-mechanical principles of stress and strain in (almost exclusively) solids. The engineering applications associated with this study include basic part design, failure avoidance, weight/mass optimization, and many others. Strength of Materials (which I’ll abbreviate as SoM for the duration) is a vitally important tool in the toolbox of mechanical designers and analysts.
To facilitate future discussions with regard to the details of SoM, we need, of course, to get some definitions out of the way. So please, indulge me. You’ll thank me later.
We can talk about a Force as being the push-or-pull which (according to Newton I) will want to change the state, or at least motion, of a body. Such motion will typically be in one or a combination of two forms:
Further, a force is a physical quantity that has several characteristics, such as…
- Magnitude (100-pounds, 10-kilonewtons, etc.)
- Direction (5-degrees counter-clockwise from the center-line)
- Sense (inward, outward, athwart, etc.)
- A point or location of application (2-cm axially from Joint A)
Among the types of forces we may consider include contact with another solid body (with or without friction), contact with fluids (wind, waves), or body forces associated with the environment (such as gravity). We call forces that act on a single point (or over a very small area in reference to the overall size of the body) to be concentrated forces. Similarly, forces acting over an area are called distributed forces (sometimes also called applied pressures), while line loads occur in the range between these two – over a line.
Note that the words force and load are used interchangeably.
Forces are vectors; we can quantify the direction and magnitude of a force in terms of the components of the vector describing the direction of the loads. Further, forces acting within the same area (point, line, surface) can be added according to the parallelogram rule. The inclination of the force is the angle described by it’s components, and the sense (inward, outward, tangential) is determined by the sign of the component vectors.
It should go without saying, but I’ll say it anyway, that you can use whatever coordinate system is convenient to describe your loads, so long as they are consistent across your entire body and all the forces acting upon it. For example, if it’s convenient to describe your loads and displacements in terms of cylindrical coordinates (opposed to the traditional rectilinear or rectangular) then knock yourself out – only do well to make sure you’re consistent across you’re entire body and not mixing messages (using one coordinate system some places, another in others).
You think this would never happen. I mean, who could possibly ever do this. All I can say is… spend a couple of days working Customer Support for an engineering software company and you’ll come to understand precisely why I took this little side-trip.
Further, we talk about forces as being internal or external – in that external forces are those exerted on the body, whereas internal forces are those generated within the body, typically as a result of external forces. If a body is in static equilibrium, all forces (internal and all external) on/in a body must sum to zero, identically. Internal forces are those that are manifested physically in quantities such as strain and stress.
With this background under our belt, I’ll jump into Force Triangles and other important statics fundamentals in our next post on this subject.