A close coiled helical spring of round steel wire 10 mm diameter having 10 complete turns with a mean radius of 60 mm is subjected to an axial load of 200 N. Determine the deflection of the spring. C = 80 kN/mm2
Q4/ A helical spring made of steel wire with a diameter of 1 cm has 15 coils with a mean diameter of 10 cm. A 100 N axial load is applied to the spring. Calculate the: A. The maximum shear stress induced, B. The deflection, and C. Stiffened of the spring. Take the modulus of rigidity G= 8.16x10ʻ N/mm².
Determine the deflection of the spring. C = 80 kN/mm2
To determine the deflection of the spring, we can use Hooke's Law, which states that the deflection of a spring is directly proportional to the force applied to it.
First, we need to calculate the spring constant (k) using the formula:
k = (G * d^4) / (8 * D^3 * n)
Where:
- G is the shear modulus of the material
- d is the diameter of the wire
- D is the mean diameter of the spring (2 * radius)
- n is the number of turns
Given:
- Diameter of the wire (d) = 10 mm = 0.01 m
- Mean radius (r) = 60 mm = 0.06 m
- Number of turns (n) = 10
- Shear modulus (G) = 80 kN/mm^2 = 80 * 10^3 N/mm^2 = 80 * 10^9 N/m^2
Let's plug the values into the equation:
k = (80 * 10^9 N/m^2 * (0.01 m)^4) / (8 * (2 * 0.06 m)^3 * 10)
k = (80 * 10^9 N/m^2 * 10^-8 m^4) / (8 * 0.064 m^3 * 10)
k = 1.25 * 10^7 N/m
Now that we have the spring constant (k), we can calculate the deflection (x) using the formula:
x = F / k
Where:
- F is the applied axial load
Given:
- Applied axial load (F) = 200 N
Let's plug the values into the equation:
x = 200 N / (1.25 * 10^7 N/m)
x = 1.6 * 10^-5 m
Therefore, the deflection of the spring is 1.6 * 10^-5 m (or 16 μm).
You seem to just want us to do problems for you but give no indication of why you are having trouble.
https://www.quora.com/What-is-the-spring-constant-of-a-coil-spring-in-terms-of-its-physical-parameters
in particular:
The spring constant of a helical spring is given by,
k = G x d^4 / 8 x D^3 x n
Symbols
F = loading of spring
L_o = free spring length
L_s = solid length when gets pressed
k = spring constant
d = diameter of spring wire
D = mean spring diameter
G = modulus of elsticity
n = number of coils