I want a full solution please. Problem 3.6 Figure 3.34 illustrates a bench exper

Question

I want a full solution please.

Problem 3.6 Figure 3.34 illustrates a bench experiment designed to test the strength of materials. In the case illustrated, an intertrochanteric nail that is commonly used to stabilize fractured femoral heads is firmly clamped to the Fig. 3.34 A bench test bench such that the distal am (BC) of the nail is aligned vertically. The proximal arm (AB) of the nail has a length a and makes an angle 0 with the horizontal. As illustrated in Fig. 3.34. the intertrochanteric nail is subjected to three experiments by applying forces EI (hori- zontal, toward the right), F2 (aligned with AB, toward A). and F3 (vertically downward). Determine expressions for the moment generated at point B by the three forces in tems of force magnitudes and geometric parameters a and 0. Answers: M aFl sin 0 (cw), M 0, M aF3 cos 0 (ccw).

Explanation / Answer

Moment is given by Force*distance, where force is the one that is acting perpendicular to the distance vector

In our case, the distance vector is along the rod that is along AB.

Moment due to F1:

Breaking F1 into two components, one along AB and one perpendicular to it,

the component of F1 along AB will be F1 cos(theta), while perpendicular to it will be F1sin(theta)

since for moment only perpendicular force matters

we get, M1 =F1sin(theta)*a

Since this force is trying to rotate the rod in clockwise fashion, so M1 is F1*a*sin(theta) clockwise

Moment due to F2:

since F2 is applied along AB, so there is no perpendicular component to our distance vector and hence M2 = 0

Moment due to F3:

Breaking F3 into two components, as in case of F1

=> perpendicular component as F1cos(theta)

hence M3 = F1*a*cos(theta), counterclockwise

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