Now let's figure out the unit vector pointing from B to C. ![]() ![]() Step 2 : Compute the directional vectors for Force along BC and BDįirst, let's think of the wire connecting the point B and C (NOTE : I put a mass with the shape of a circle just to simplify the drawing, but in real application this can be any other object like a sign) Determine the x, y and z components of the reaction at the ball-and-socket joint at A, and determine the tension in wires BC and BD. The most typical 3D supports that you run into during the midterm or exam are: ball and socket joints, fixed support, and roller (or equivalent)Īlways start the problems by drawing the Free-Body-Diagram and computing the directional vectors for the applied forcesĪdditionally, all the problem solving questions on the midterm and exam tends to be copy and pasted from the textbook, as it is easier for the professorsĪ pole has a mass of 100kg with the centre of mass at G. In order to be comfortable with any 3D supports without having to look back to the textbook (or your notes), practice solving the problems for all types of 3D supports in the first year Mechanics textbook But on the midterm or exam, you never know what type of 3D supports you will have to work with while you are most likely required to have them memorized. It is hard to memorize all the support reactions. There are a number of different supports for 3D rigid body equilibrium, as you saw. Interestingly enough, our legs are joined by a ball-and-socket joint to our hipbones. Examples of 3D rigid body equilibrium analysis in engineering include: reaction force and moment analysis of airplane wing during takeoff, calculating reactions on construction equipments during operationīall-and-socket joints are one of the most practical supports in mechanical systems engineering. However there are many engineering problems that require 3D rigid body equilibrium analysis. Since 3D rigid body equilibrium analysis is time consuming due to forces and moments in 3 dimensions, 2D rigid body equilibrium analysis is always preferred. However, the rigid body equilibrium concepts in 2D and 3D are no different, where the net force and moment in all directions must be equal to zero to maintain static equilibrium. The types of reaction supports from 2D rigid body equilibrium are not applicable to 3D rigid body equilibrium. Is it possible to automatically populate the coefficients in and from the equilibrium equation shown in Method-1 and -2?Īnother question is I’m interested in any recommendations to simplify my solution approach and / or apply best practices that others are using.3D rigid body equilibrium analysis involves calculating forces in the x,y, and z direction, as well as calculating moments about the x,y, and z axis. If I could get this approach (or something similar) to work it would be great because for more complex problems it would be very convenient to write equilibrium equations as a function of reaction load where represents Bxi + Byj + Bzk.Īlso, as mentioned, Method-3 works but I don’t really understand the utility of this method if I need to manually enter the numeric coefficients into and. I’m then trying to call function B in the moment equilibrium equation to simplify the form of the equation. ![]() In Method-2 I’m attempting to make the resultant loads Bx and By (the variables I’m solving for) variables within a function called B. I was able to get the correct result using Method-1 and Method-3 but I’m not able to get Method-2 to work. MathCAD document is attached (prepared in MathCAD Prime 3.0) and a scan of the sample problem that I’m working on is shown on the second page of the document. My goal is to understand the best way to do this type of analysis so that I can then scale it to more complex problems. I am new to MathCAD and am doing a simple static force equilibrium analysis.
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