Chapter 12.3, Problem 49P

The machine below forms metal plates through the application of force.  Two toggles (ABC and DEF) transfer forces from the central hydraulic cylinder (H) to the plates that will be formed.  The toggles then push bar G to the right, which then presses a plate (p) into the cavity, thus shaping it.  In this case, the plate becomes a section of a sphere.  If the hydraulic cylinder can produce a maximum force of F = 10 kN, then what is the maximum P value (i.e. Pmax) that can be applied to the plate when θ = 35°?  Also, what are the compressive forces in the toggle rods in that situation?  Finally, what happens to Pmax and the forces in the rods as θ decreases in magnitude?

Determine the magnitude of the minimum force P needed to prevent the 20 kg uniform rod AB from sliding.  The contact surface at A is smooth, whereas the coefficient of static friction between the rod and the floor is μs = 0.3.

Determine the magnitudes of the reactions at the fixed support at A.