Mechanics by J. P. Den Hartog

By J. P. Den Hartog

A great refresher quantity in addition to a classic introductory text, this book features hundreds of thousands of functions and layout difficulties that remove darkness from basics of trusses, loaded beams and cables, and similar components. contains 334 spoke back difficulties.

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First we note that the piston force P is transmitted without change to the crosshead B. Next we isolate the crosshead and stubs of the piston and connecting rods. The connecting rod, being a double-hinged bar without side loads, has a force along its center line only (page 23). The guides, being frictionless, exert on the crosshead only a force perpendicular to the guide (page 84). Thus there are three forces acting on the crosshead, originating from the piston, the rod, and the guide, of which one is known to be P and of which only the directions of the other two are known.

It is interesting to note the state of longitudinal tension of the beam. The portion between A and Ha Va has a compressive force Ha in it, while the right-hand part of the beam is free from compression. In case the roller support had been placed at A and the hinge support at B, the right-hand part of the beam would have been in tension Ha, and the left-hand part would have had no longitudinal force. In case of two hinge supports, all we could say is that the tension in the right-hand part is greater by the amount Ha than the tension in the left-hand part, but the longitudinal force in each part of the beam would have been indeterminate ("statically indeterminate").

We want to know the relation between P and M for a certain position designated by the angle a. First we note that the piston force P is transmitted without change to the crosshead B. Next we isolate the crosshead and stubs of the piston and connecting rods. The connecting rod, being a double-hinged bar without side loads, has a force along its center line only (page 23). The guides, being frictionless, exert on the crosshead only a force perpendicular to the guide (page 84). Thus there are three forces acting on the crosshead, originating from the piston, the rod, and the guide, of which one is known to be P and of which only the directions of the other two are known.

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