Statics

FBDs are trickier than you think, and they are the foundation of this entire course, so inspect the flipbook very carefully. It contains 1 loading diagram (image 1) and 5 FBDs (images 2 through 6).

Pay special attention to slide 6, which is the FBD of the monkey. You'll notice that the normal force was not drawn coincident with the center (centroid) of the monkey's mass. It is offset a bit to the right. This is because the FBD of the monkey is not symmetric. Don't worry about this too much right now. The key point is that each vector must be drawn in the exactly correct location -- and it is not necessarily at the center (centroid) of the object.

In Physics, your professors would lump all of the mass of an object (a baseball, a planet, a box on a ramp, etc.) into a single point. Graphically they would draw that as a solid dot, and then apply forces to that dot. This may have been called "particle equilibrium." In Statics, only the simplest systems can be modeled as a particle. We have to draw the actual geometry of the object or assembly of objects.

❏ Drawing as a mode of thinking

Statics is certainly based in principles from physics (mostly Newton's Laws), but its strongest connection may actually be to geometry. If you think back to your high school geometry class, you'll (hopefully) remember doing a lot of drawings.

In order to tackle Statics problems, we need to create good quality drawings. This takes time, but it is time well spent. The act of making good quality drawings, wherein the geometry and the vectors are drawn to scale, will help you think through the problem.

In Statics, the diagrams, figures, and plots are so important that many people value them more highly than a correct numeric answer.

❏ Some friendly advice

The more precisely you draw free-bodies, the more likely you'll be able to work problems quickly and accurately. I understand that some engineering students have internalized the perception that "they can't draw" or the stereotype that "engineers are people that are good at math, not drawing." 

I want to challenge you to keep a positive attitude about drawing. We can even rebrand it -- let's call it "visual communication."

You do not need to be an artist to succeed in Statics, but this course does present a valuable opportunity for honing your visual communication skills.

Please get in the habit of drawing the pictures/diagrams LARGER THAN YOU THINK IS NECESSARY. Your calculations will complement the information shown in the figure or diagram or plot.

For the early part of this course, we will focus on Statics problems that can be modeled in 2D. We will tackle 3D after mastering 2D (or planar) models.

Here is how we could express the (2D) E.o.E. in casual conversation:

"The sum of the forces in the x-direction must equal zero. The sum of the forces in the y-direction must equal zero. The sum of moments about any z-axis must equal zero. That is the definition of static equilibrium."

❏ Key points (for a 2D model):

• If all three E.o.E. are satisfied, then the body is in static equilibrium, and is studied in Statics.

• If any of the E.o.E. is not satisfied, then the body is in motion, and is studied in Dynamics.

• Generally, in a Statics course, we wish to use the E.o.E. to solve for unknown forces (and/or moments) that ensure static equilibrium. These unknowns can be thought of as reactions.

I want to draw your attention to one important detail from the flipbook. You can only draw a vector on a FBD when the body causing that force is not depicted as part of the free-body. 

In other words, if you were asked to depict the normal force between books B and C and tried to draw that on a FBD that consisted of the entire stack of books (A, B, and C), it would be a concept error. In order to reveal the force transferred between bodies B and C, you must disassemble the stack at that interface to reveal the normal force between B and C.

This problem can be modeled as a collinear force system. That means that all of the forces in the system share the same line of action.