고체역학 (Gere) — Axially Loaded Members: Problem 2.2-16

2.2-16 A uniform bar AB of weight $W = 25\text{ N}$ is supported by two springs, as shown in the figure. The spring on the left has a stiffness $k_1 = 300\text{ N/m}$ and natural length $L_1 = 250\text{ mm}$. The corresponding quantities for the spring on the right are $k_2 = 400\text{ N/m}$ and $L_2 = 200\text{ mm}$. The distance between the springs is $L = 350\text{ mm}$, and the spring on the right is suspended from a support that is a distance $h = 80\text{ mm}$ below the point of support for the spring on the left. Neglect the weight of the springs. (a) At what distance $x$ from the left-hand spring (figure part a) should a load $P = 18\text{ N}$ be placed in order to bring the bar to a horizontal position? (b) If $P$ is now removed, what new value of $k_1$ is required so that the bar (figure part a) will hang in a horizontal position under weight $W$? (c) If $P$ is removed and $k_1 = 300\text{ N/m}$, what distance $b$ should spring $k_1$ be moved to the right so that the bar (figure part a) will hang in a horizontal position under weight $W$? (d) If the spring on the left is now replaced by two springs in series ($k_1 = 300\text{ N/m}, k_3$) with overall natural length $L_1 = 250\text{ mm}$ (see figure part b), what value of $k_3$ is required so that the bar will hang in a horizontal position under weight $W$?