Determine the distance of application of the load:
A rigid bar of negligible weight transmits a load W to a combination of 3 springs as illustrated in Figure. The three springs are built of the similar material and are of equal diameters. They are of the similar length before loading. The number of coils in three springs are 10, 12 and 15 respectively, when the mean radii of coils are in the proportion 1 : 1.2 : 1.5 respectively. Determine the distance x such that the rigid bar remains horizontal after the application of the load.
Figure
Solution
As the springs are in parallel, Δ is simialr.
W_{1} + W_{2} + W_{3} = W ---------- (1)
G is similar, d is same.
R_{2} = 1.2 R_{1}
R_{3} = 1.5 R_{1}
n_{1} = 10; n_{2} = 12; n_{3} = 15
Δ= 64 W R^{3} n/ Gd ^{4}
⇒ W = Δ Gd ^{4}/64 R^{3 }n
W = K/ K R^{3} n
The FBD of bar illustrated in Figure
Now, taking moments around A,
W . x = W_{2} × l + W_{3} × 2l
⇒ 0.168 × x = 0.048 × l + 0.02 × 2l
∴ x = 0.52 l