Statics Solution Video By: William Rice, Mark Vogan, Jack Snell, and Robert Moss MAE /4/2010

The kinetic sculpture requires that each of the three pinned beams be in perfect balance at all times during its slow motion. If each member has a uniform weight of 2 lb/ft and length of 3ft, determine the necessary counterweights W 1,W 2, and W 3 which must be added to the ends of each member to keep the system in balance for any position. Neglect the size of the counterweights.

Approach We need to solve for W1 first since both the FBD’s of sections B and C have three unknowns associated with them where as section A only has 2 unknowns. After solving for W1 using the moment equation we can then solve for the force at point A, leaving us with only 2 unknowns in section B. Now we can apply the moment equation and sum of the forces equation to section B, giving us W2 and the reaction at point B. We can then repeat the last step to find the final weight. Note that the angles between the members are not needed because they cancel out in each of the moment equations. Also note that there are no forces acting in the X-direction.

SECTION A x y

SECTION B x y

SECTION C x y