statics 3d equilibrium problems and solutions

Statics 3d equilibrium problems and solutions how to#

For 3D rigid body equilibrium analysis, the most effective method of sum of force analysis is to add all the vectors in the free-body-diagram (FBD) and then solve for the reaction forces. Step 4 : Analyze the forces: Consider the reaction forcesĬalculate the reaction forces at point A using sum of force analysis in x,y,z direction. The force vectors will be used to calculate the reaction forces at point A. Step 3 : Compute the force vectors F_BC and F_BD, since their magnitude is now known. Point A is the only point suitable for taking the moment about as the system can only pivot about that point Set counter-clockwise moment to be positive. Step 3 : Take the moment about A to calculate the magnitude of F1 and F2.

Next, let's think of the wire connecting the point B and D

Statics 3d equilibrium problems and solutions how to#

Knowing how to do vector cross-product allows you to do the moment analysis with just one equation, instead of having to use 3 separate moment equations about the x,y, and z directions.

Before calculating for the tensional forces along the line of action BC and BD, the forces must be expressed as vectors for moment analysis at point A without having to do separate moment analysis about x,y,and z directions. The magnitude of tensional forces in each direction are used to calculate the reaction forces at point A, which is the ball-and-socket joint. We need to compute the unit vectors to analyze the magnitude of the tensional forces in x,y,z direction. You can use the equations of equilibrium to solve for the unknown reactions, and check your work. Now let's figure out the unit vector pointing from B to C. You can use these interactives to explore how the reactions supporting rigid bodies are affected by the loads applied. 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.

You can use three angles to determine the direction of a force in three dimensions.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.

Now, that is a bit of math there, but the important things to remember are: