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Question 3.15: Figure 3-22 repre.sents a print head for a computer printer....

Figure 3-22 represents a print head for a computer printer. The force F moves the print head toward the left against the ribbon, imprinting the character on the paper that is backed up by the platen. Draw the free-body diagram for the horizontal portion of the print head, along with the shearing force and bending moment diagrams.

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Objective     Draw the free-body diagram of the horizontal part of the print head in Figure 3-22. Draw the shearing force and bending moment diagrams for that part.

Given       The layout from Figure 3-22.
Analysis      The horizontal force of 35 N acting to the left is reacted by an equal 35 N horizontal force produced by the platen pushing back to the right on the print head. The guides provide simple supports in the vertical direction. The applied force also produces a moment at the base of the vertical arm where it joins the horizontal part of the print head.
We create the free-body diagram for the horizontal part by breaking it at its right end and replacing the removed part with the internal force and moment acting at the break. The shearing force and bending moment diagrams can then be drawn.

Results   The free-body diagram for the horizontal portion is shown below the complete sketch. Note that at the right end (section D) of the print head, the vertical arm has been removed and replaced with the internal horizontal force of 35.0 N and a moment of 875 N.mm caused by the 35.0 N force acting 25 mm above it. Also note that the 25 mm-moment arm for the force is taken from the line of action of the force to the neutral axis of the horizontal part. The 35.0 N reaction of the platen on the print head tends to place the head in compression over the entire length. The rotational tendency of the moment is reacted by the couple created by
R_1 and R_2 acting 45 mm apart at B and C.

Below the free-body diagram is the vertical shearing force diagram in which a constant shear of 19.4 N occurs only between the two supports.
The bending moment diagram can be derived from either the left end or the right end. we choose to start at the left end at A. there is no shearing force from A to B. and therefore there is no change in bending moment. From B to C. the positive shear causes an increase in bending moment from zero to 875 N.mm. Because there is no shear from C to D.

there is no change in bending moment, and the value remains at 875 N.mm. The counterclockwise-directed concentrated moment at D causes the moment diagram to drop abruptly, closing the diagram.

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