Lesson 1 ARE Example

Added: 2026-05-31

[00:00:01]so now let's look at an example problem from a past are e and this problem may look a little intimidating at first with all of the equations and numbers but I'm going to give you some really helpful tips that will allow you to break this problem down into more simple digestible terms and keep in mind that these problems are meant to be solved very quickly and very rapidly so you need to be able to break them down into simple terms in order to get to the answer efficiently and use your time well over the course of the exam personally I think the number one lesson that you need to learn in order to succeed at the are is to learn how to use your time efficiently you need to have a plan of approach for each section of the exam and your plan of approach may not be exactly the same as mine but I'm going to show you what I would typically do When approaching specifically mathematical and analytical questions like these so for my Structural Engineers perspective this is how I would approach the are so first when solving seemingly complex problems The crucial first step is always to set expectations so what do you think the answer will be and this is crucial because it will allow you to verify your final answer as well as guide you as you take steps toward that final answer and also you need to think about what information do you need to justify a final answer and you may find that the information that you need to justify your answer is actually very little so the question may have all sorts of routes that you can take to the final answer but there may be shortcuts along the way that as long as you know this little bit of information that's enough to justify the final answer and you don't need to solve the rest of the problem through and indeed that's exactly what you'll find with this problem here so this problem States find the direction and magnitude of the resultant of the three concurrent forces shown Theta is the angle of the resultant measured clockwise from horizontal x-axis and they provide you with a diagram where you have three Force vectors one in the first quadrant here 30 degrees up from the x-axis with a magnitude of 80 pound Force the second pointing vertical along the y-axis with a magnitude of 90 pound Force and finally this Force F3 with an angle measured from the horizontal positive x-axis of 135 degrees and a magnitude of 120 pound Force and so that is our setup and we have four possible answers down below so what expectations can we set with this given scenario well we can see that all of the force vectors are in the first or second quadrant and so they are all pointing in the positive y direction so since all of these Force vectors are pointing in the positive y direction we know that their sum of their components must also be positive and therefore if we look at answer D which states that Theta will be zero which would mean that the resultant would lie along the horizontal axis and have a vertical component of zero we know from our expectations that d cannot be the answer so right off the bat we can eliminate d so now our choices are B C and A and let's try to visualize these three answers a has an angle of 86 degrees and so it would be somewhere there B has an angle 94 degrees so it would be past our vertical axis somewhere out here and lastly C is exactly 90 degrees and so it would lie along the vertical axis so if those are our three choices what information do we need in order to justify a decision well if we looked at the sum of the forces in the X if we found that that value were positive then that would mean that the answer is a because positive X is to the right and a would be pointing to the right if the sum of forces in the X were equal to zero that would mean that our answer would be C and the final resultant would be exactly vertical lastly if our sum of forces in the X where Less Than Zero that would mean that our answer is B therefore we need to know the sum of forces in the X to solve this problem and that's all we need to know to solve this problem so let's look at our sum of forces in the X Direction so starting with F1 we have cosine 30 degrees times 80 pound Force and it's cosine again because we complete the triangle here this is the adjacent side that we want and it's in the positive X Direction here so this will be a positive value next we have F2 which is pointing vertically so it has no X component or in other words we would have cosine 90 degrees times 90 pound force and that would be zero and finally we have rf3 which is defined by an angle of 135 so if we cut part of that off this 90 degrees here subtract that we would get 45 degrees and if we completed our triangle we would be solving for the opposite side of that angle so we'll choose sine 45 times 120 pound Force adding all that up we get negative 15.6 Which is less than zero so sum of f x is less than zero which means that answer B is the correct answer so note that we didn't have to set up this table to solve this problem we didn't need to solve for the Y component we didn't need to solve for the magnitude of the resultant and we didn't even need to solve for the angle all we needed to justify our answer is this that's it and we get the answer correct so if you were to follow this textbook example you would likely get yourself very confused it would take a long time you may even make some mistakes in your math and you may end up with the wrong answer but if you set expectations and you determine the critical information that you need to justify your answer you get to the answer more quickly and with greater accuracy so I would definitely encourage you as you are taking the are or preparing for the are to get into the habit of setting expectations for your answers and asking yourself what do I think the answer will be before I jump into the math and what information do I need to justify a final answer