Expert Tips for Mastering Engineering Statics | Fall 2020

[Angry Citizen]

I'm a little nervous about this fall's statics class. It seems to be a lot more rigorous than my intro physics course, and I'm not sure I'm prepared. Does anyone have any pieces of advice on learning engineering statics?

 

[Pyrrhus]

Back when I was an undergrad in structural.eng, I remember Statics was a fun class based on two simple principles of static equilibrium. Learn those principles (sum of forces and sum of moments must be zero). In addition, learn the transport couple thm, the line of action rule, and varignon's thm. Other useful are steiner 2nd thm and the special equilibrium for 2 forces and 3 forces...

Actually, just make sure to understand the basics (statics is just linear algebra). You should be fine if you are comfortable with vectors.

 

[Angry Citizen]

Cool, thanks. I'll keep that in mind.

 

[nlsherrill]

As long as you are fine with physics 1, calc 2 material and how to take a cross product, you should be fine. I wouldn't say statics is linear algebra. The kind of LA you will encounter in that course is far less rigorous than what you will actually encounter in an LA class.

 

[Angry Citizen]

What should I know from linear algebra? I haven't taken a class in it yet.

 

[nlsherrill]

What should I know from linear algebra? I haven't taken a class in it yet.

Just vectors and linear equations(stuff that you learned in intro physics).

 

[Jokerhelper]

Just vectors and linear equations(stuff that you learned in intro physics).

Yup, basically.Angry Citizen, for vectors all you'll probably need know are getting the components, unit vectors, projections, cross and dot products. Of course, you'll also need to know how to add and subtract vectors, but that's pretty straight forward. I wouldn't worry if you haven't learned some of these things yet, because I'm sure you'll end up doing tons of examples and you'll get the hang of it. Also, any decent statics book will cover these things too.

Being able to solve systems of linear equations is probably one of the most important things in statics. When I took the course, I found that the concepts turn out to be easy (really, \sum\textbf{F} = 0 and \sum\textbf{M} = 0 sum up the entire course), but the thing is that you often have to solve for up to six unknowns in 3D systems using equations from these laws of motion.

 

[Angry Citizen]

Six equations in six unknowns? Yikes. I should finally get around to learning gauss-jordan, eh?

 

[clope023]

Six equations in six unknowns? Yikes. I should finally get around to learning gauss-jordan, eh?

Unnecessary in statics, you won't really be constructing matrices with the unknowns so no need to do any eliminating. When you get to trusses and the like you'll just be solving for all the interconnecting forces between all parts that make up the truss of the bridge, hence all the unknowns but with the method of sections/joints you'll probably use up to 6 sets of 2-3 equations for each section (2 forces in the x and y direction and the moments in the z direction).

 

[Angry Citizen]

I'm unfamiliar with any other method for solving equations with even half that many variables. Solve-and-replace generally only works for two equations in two unknowns, if my experience with Kirchoff's Laws is anything to go by.

Got a suggestion for another technique to learn? Let's just say my math education was ... spotty.

 

[Pyrrhus]

Sure, it is does not require the knowledge of linear algebra, but the subtopic of vector algebra.

You need to understand inner products (or dot product), and vectorial product (or cross product). The concept of determinant may help for the vectorial product, but you can also memorize a technique such as Cofactors or Sarrus rule.

All vectors in Statics are either in the plane (2 components) or in the space (3 components).

You should be fine. Just make sure you understand the basics right away.

I'll outline them again here.

Math Prereqs

1) Concept of Vector, and the algebra of Vectors. This includes the products, the norm or modulus of a vector, and how to normalize a vector (find unit vector along the direction of a vector)

2) Solving Simultaneous Equations, You may use Cramer's method or substitution, elimination or other methods.

Physics Concepts

3) Radius Vector or R - vector, Force Vectors, and Moment Vectors (This are usually represented by Double Arrows, and are normal to the surface where they act). Remember that also with moments and forces comes the convention of signs (which direction is positive and which is negative). Do note that moments are also called Couples in Statics.

4) The Static Equilibrium Equations. Sum of Forces, and Sum of Moments must be zero. Also, for forces partition, remember Newton's third law. Thus if you have a rigid body and you unhinge the forces on the separate FDB must be included in opposite directions.

Static Outline

5) The Line of Action principle for Force Vectors. You can slide the Force vector along its line of action without changing its effect on a rigid body (Note that this is not true in deformable bodies such as those you learn in Mechanics/Strength of Materials). Also, Moments are free vectors and can move to any points within the plane they act, as long as they are still normal to the plane. This is important to remember, many students completely ignore these basic principles.

6) Any system of Statics can be turned into a Resultant Force-Couple System. Thus, the whole idea of static is based that the resultant Force-Couple system is null. This is the transport-couple theorem. You can move a Force to any point outside of its line of action by introducing a couple to cancel the force moment effect.

7) The Parallel Axis Theorem or Steiner's 2nd Thm is useful for calculating Area Moments of Inertia. Do note that the definition of the moments to find centroids and inertia are important concepts to learn. This may require you to brush up on your Integral Calculus.

*8) If you put together these concepts, you can now know why a Truss if the forces apply on the nodes, it is assumed that the forces along the members must be acting on the same line of action. This is the 2 forces acting on a rigid body special equilibrium conditions. For the case of 3 forces, The forces must be concurrent. Look up Varignon's Thm. For rigid bodies connected with hinges, this is the principle where the solution method is derived along with Newton's 3rd Law.

Another last chapter I believe is moment with respect to an axis represent by a unit vector along the axis. Probably, there are other interesting chapters. However, I think it is best you are surprised by the course. Statics is one of my favorite courses along with Mechanics of Materials and Structural Mechanics while I was an undergrad.

 

[Jokerhelper]

Six equations in six unknowns? Yikes. I should finally get around to learning gauss-jordan, eh?

You would have to have some terrible luck (or more likely you did something wrong) if you ever happen to encounter an system of 6 equations with 6 unknowns in each equation. What will usually happen when you're dealing with a 3D system is that you'll have up to 6 equations to play around with (in most cases you won't need that many) and usually each equation will have 1 to 3 unknowns, sometimes even 4. A couple of equations will usually allow you to solve for 2 of the unknowns, and then would can plug those in your other equations to solve anything else.

I'm unfamiliar with any other method for solving equations with even half that many variables. Solve-and-replace generally only works for two equations in two unknowns, if my experience with Kirchoff's Laws is anything to go by.

Got a suggestion for another technique to learn? Let's just say my math education was ... spotty.

Actually, "solve-and-replace" or substitution gets you pretty far in statics. For example, say you have 3 equations with 3 unknowns, one of which happens to be a + b + c = 1. Now you can just rewrite a = 1 - b - c, and substitute for a in the other two equations. Now you have 2 equations with only 2 unknowns.
Also, using something like Gaussian elimination with a matrix just can be too messy sometimes, especially when you don't have "nice" numbers as it usually happens in statics. I don't think I ever used a matrix to solve a system or equations in statics.

 

[thegreenlaser]

^We never had to solve more than 4 equations on a test. I think we had one with 5 on one of the more difficult homework assignments, but our prof said that that if you can do 4-5 equations, you can do 6, it'll just take an annoyingly long time.

Don't worry about learning Gaussian elimination for solving systems of equations. I was already quite comfortable with that method before I started statics, and I think I used that method twice out of probably 100+ problems, mostly just to see how well it worked. Solve and replace is actually quite an effective method, especially when decimals are involved. I prefer matrices when there's integer values, but when you don't have nice numbers, the matrix can get pretty messy. Personally, I find that using matrices allows me to make a lot more mental shortcuts, but when nasty decimals are involved, that advantage disappears, and you're stuck following the algorithm. I From my understanding, the main advantage of matrices comes when you're using a computer. I can promise, though, whichever method you choose, you'll be 100x better at it when you finish the course

The key to doing well in statics was really just to do a ton of practice problems. The principles and concepts required are actually quite straight forward, but actually solving problems can be pretty challenging. Just do lots of practice questions, because you have to get really comfortable with reading a problem, figuring out what you need, and figuring out what the most efficient way to get that is. You really have to THINK in statics. A lot of people jump straight into a problem and end up doing a huge amount of math (which generally means more errors) when there's a much simpler way. You always want to figure out what the most efficient method of solving the problem is before you jump in. It can save you a lot of time and needless effort.