Answer to Question #172803 in Civil and Environmental Engineering for Kiara

Question

Two concentric springs, the central spring being 5 mm shorter than the outer spring, are to be loaded as shown. The outer spring consists of 40 turns of 15 mm diameter wire coiled on a mean diameter of 100 mm. The central spring, on the other hand, has 80 turns of 20 mm diameter wire coiled on a mean diameter of 80 mm. Use 83 GPa and 76 GPa for the shear modulus of the outer and the central springs, respectively. If the load P = 2 kN, determine the stress in the central spring and the displacement of the plate.

Answer 1

A force of 2 kN is acting on a circular rod with diameter 20 mm. The stress in the rod can be

σ = (20 10³ N) / (π ((20 10^-3 m) / 2)²)

  = 127388535*2 (N/m²) 

  = 127*2 (MPa)

= 381(MPa)

The change of length can be calculated by:

 dl = σ l_o / E

   = (381 10⁶ Pa) (2 m) / (83 10⁹ Pa) 

   = 0.00381 m

   = 3.81 mm