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Mechanical engineering general discussion FAQ

Structural Calculations

How do I construct Free Body Diagrams? by GregLocock
Posted: 22 Sep 12 (Edited 24 Sep 12)

/////DRAFT////// v0.03

Greg Locock

0) Assumption is that you are trying to solve a quasi static 2D system of forces moments and accelerations on one contiguous body, but the principle holds for 3D. For multiple bodies you will end up with multiple FBDs.

1) Identify the location and magnitude and direction of all forces and moments of interest. Usually these should only be the forces and moments acting ON the body. You could use just the forces the body is exerting on its constraints, but by convention we don't. The location of the point of application of a moment to a rigid body makes no difference.

2)Identify the accelerations of all 'large' inertias. Add D'Alembert pseudo forces (inertia * acceleration) to the centre of gravity in opposition to the accelerations. You may need to include pseudo moments due to rotational accelerations.

4)Sum all forces and pseudoforces in some obvious direction. Since the system is in equilibrium the total should be zero.

5)Sum all the forces and pseudoforces in some other direction that is not parallel to that in (4)(typically, but not necessarily, at right angles to it). Since the system is in equilibrium the total should be zero.

6)Take moments about a cunningly chosen location. Since the system is in equilibrium the total should be zero.

//At this point, if your system is well mannered, you should have a solvable solution//

If it is not fully defined you have to add additional constraints. Alternatively it may be over defined, for example, a car, sitting on four springs, is not solvable by the above, unless you know the profile of the road surface, and the lengths of the springs. That is called compatibility.

See also http://en.wikipedia.org/wiki/Free_body_diagram


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