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This month we look at the extreme approach to applying equivalent pressure distributions throughout a structure to achieve balance, avoiding any direct constraint boundary modeling and rigid body motion. This powerful technique is the best way of setting up some FEA models.

Fig. 5 shows an actuator crank. Vertical load of 100 lbf is applied to the flat surface, creating a moment about the pivot point. The vertical load is reacted by the pivot bearing. The moment created is reacted by a couple consisting of horizontal 125.67 lbf forces between the pivot point and actuator rod attachment point. This is typical free body diagram used to check the force balance in the system. Do a quick check yourself by making sure the vertical forces, horizontal forces and moment about the pivot all balance.

The vertical applied load shown in Fig. 5 is assumed distributed over the rectangular face. However, we could be more conservative and assume a line of action closer to the free edge, giving a larger moment arm. This was tried out with line of action at 25% of surface length versus original 50%, and new balancing forces calculated. The peak local stress is now 77,748 psi, which is acceptable.

The object under consideration in each part of this problem was circled in gray. When you are first learning how to draw free-body diagrams, you will find it helpful to circle the object before deciding what forces are acting on that particular object. This focuses your attention, preventing you from considering forces that are not acting on the body.

Each block accelerates (notice the labels shown for [latex] {\overset{\to }{a}}_{1} [/latex] and [latex] {\overset{\to }{a}}_{2} [/latex]); however, assuming the string remains taut, they accelerate at the same rate. Thus, we have [latex] {\overset{\to }{a}}_{1}={\overset{\to }{a}}_{2} [/latex]. If we were to continue solving the problem, we could simply call the acceleration [latex] \overset{\to }{a} [/latex]. Also, we use two free-body diagrams because we are usually finding tension T, which may require us to use a system of two equations in this type of problem. The tension is the same on both [latex] {m}_{1}\,\text{and}\,{m}_{2} [/latex].

of mass m at rest, scalar form[latex] T=w=mg [/latex]Conceptual QuestionsIn completing the solution for a problem involving forces, what do we do after constructing the free-body diagram? That is, what do we apply?

For a swimmer who has just jumped off a diving board, assume air resistance is negligible. The swimmer has a mass of 80.0 kg and jumps off a board 10.0 m above the water. Three seconds after entering the water, her downward motion is stopped. What average upward force did the water exert on her?

Larese, A., Rossi, R., Oñate, E. and Idelsohn, S.R. (2008), "Validation of the particle finite element method (PFEM) for simulation of free surface flows", Engineering Computations, Vol. 25 No. 4, pp. 385-425. 2b1af7f3a8