Question 3.14: The bell crank shown in Figure 3-21 is part of a linkage in ...

Objective         Draw the free-body diagram of the horizontal part of the crank in Figure 3-21. Draw the
shearing force and bending moment diagrams for that part.
Given                 The layout from Figure 3-21.

Analysis Use the entire crank first as a free body to determine the downward force $F_2$ that reacts to the applied horizontal force $F_1$ of 80 lb by summing moments about the pin at O.
Then create the free-body diagram for the horizontal part by breaking it through the pin and replacing the removed part with the internal force and moment acting at the break.

Results We can first find the value of $F_2$ by summing moments about the pin at O using the entire crank:

$F_1.a = F_2.b$
$F_2 = F_1(a/b) = 80 \ lb( 1.50/2.00) = 60 \ 1b$

Below the drawing of the complete crank, we have drawn a sketch of the horizontal pai1, isolating it from the vertical part. The internal force and moment at the cut section are shown. The externally applied downward force $F_2$ . is reacted by the upward reaction at the pin. Also, because $F_2$ causes a moment with respect to the section at the pin, an internal reaction moment exists, where

$M = F_2.b = (60 \ lb)(2.00 \ in) = 120$ lb-in

The shear and moment diagrams can then be shown in the conventional manner. The result looks much like a cantilever that is built into a rigid support. The difference here is that the reaction moment at the section through the pin is developed in the vertical arm of the crank.

Comments        Note that the shape of the moment diagram for the horizontal part shows that the maximum moment occurs at the section through the pin and that the moment decreases linearly as we
move out toward point A. As a result, the shape of the crank is optimized, having its largest cross section (and section modulus) at the .section of highest bending moment. You could complete the design of the crank using the techniques reviewed in Section 3-15.