고체역학 (Gere) — Axially Loaded Members: Problem 2.2-10

2.2-10 The device shown in the figure consists of a prismatic rigid pointer \(ABC\) supported by a uniform translational spring of stiffness \(k = 950 \text{ N/m}\). The spring is positioned at distance \(b = 165 \text{ mm}\) from the pinned end \(A\) of the pointer. The device is adjusted so that, when there is no load \(P\), the pointer reads zero on the angular scale. (a) If the load \(P = 11 \text{ N}\), at what distance \(x\) should the load be placed so that the pointer will read \(\theta = 2.5^\circ\) on the scale (see figure part a)? (b) Repeat part (a) if a rotational spring \(k_r = kb^2\) is added at \(A\) (see figure part b). (c) Let \(x = 7b/8\). What is \(P_{\text{max}}\) (N) if \(\theta\) cannot exceed \(2^\circ\)? Include spring \(k_r\) in your analysis. (d) Now, if the weight of the pointer \(ABC\) is known to be \(W_p = 3 \text{ N}\) and the weight of the spring is \(W_s = 2.75 \text{ N}\), what initial angular position (i.e., \(\theta\) in degrees) of the pointer will result in a zero reading on the angular scale once the pointer is released from rest? Assume \(P = k_r = 0\). (e) If the pointer is rotated to a vertical position (see figure part c), find the required load \(P\) applied at mid-height of the pointer that will result in a pointer reading of \(\theta = 2.5^\circ\) on the scale. Consider the weight of the pointer \(W_p\) in your analysis.