Homework 6

Coil spring:

Ex. 1) Determine the required number of coils and permissible deflection in a helical spring made of 1.6 mm diameter steel wire, assuming a spring index 6 and an allowable stress of 345 MN/m2 in shear. The spring rate is to be 1800 N/m. (G = 80 GPa)



d = 1.6 mm

C = 6

τs all = 345 MN/m2

k = 1800 N/m

G = 80 GPa










Find the force and deflection;



Ex.2) Design a coil spring to have a mean diameter of 125 mm and a spring rate of 72 kN/m. The total axial load is 8000 N and the allowable shear stress is 275 MPa. (G = 80 GPa)



D = 125 mm = 0.125 m

k = 72 kN/m = 72000 N/m

τs all = 275 MPa = 275 x 106 N/m2

F = 8000 N








By trail in

C = 5.5


Use 25 diameter wire



1) When a coil spring with a spring rate of 18 kN/m is compressed 30 mm, the coils are closed. The allowable shear stress is 345 MN/m2, the spring index C = 8, the ends are square and ground, and G = 83 GN/m2. Calculate the required wire diameter d, the required coil diameter D, and the closed length of the spring.



2) A compression coil spring has square and ground ends, and the spring material G = 80 GPa, and has the following dimensions:
- Coil outer diameter is 80 mm, Coil inner diameter is 60 mm

- Total coils is 10
- Coil closed length is 140 mm, and the free length is 250 mm
When the spring is loaded the operating length found to be 170 mm, Find the maximum stress on the spring wire.



3) Spring A has a spring rate of 15 N/mm, spring B has a spring rate of 10 N/mm, and spring C has a spring rate of 20 N/mm. Find the spring rate of the following arrangements.
a- Springs A, B and C are connected in series.
b- Springs A and B are connected in parallel, then connected with C in series.
c- Springs A, B and C are connected in parallel.