Problem Statement: Determine the diameter of a helical spring to carry 500N load with maximum deflection of 25mm. The spring rate is 8 and the allowable shear stress is 350MPa. The modulus of rigidity is 84GPa.

Solution:
To determine the diameter of the spring, we need to consider the following factors:

Spring Rate: Spring rate is the amount of force required to deflect the spring by a unit amount. In this case, the spring rate is 8, which means that for every 1mm deflection, the spring will exert a force of 8N.

Load: The load to be carried by the spring is 500N.

Maximum Deflection: The spring is required to deflect a maximum of 25mm.

Allowable Shear Stress: The allowable shear stress is 350MPa.

Modulus of Rigidity: The modulus of rigidity is 84GPa.

Formula: The formula for calculating the spring's diameter is d = (16WRL)/(πGd^4), where d is the diameter, W is the load, R is the spring rate, L is the length of the spring, G is the modulus of rigidity, and π is a constant.

Calculation:
Given,
Load (W) = 500N
Spring Rate (R) = 8
Maximum Deflection (δ) = 25mm
Allowable Shear Stress (τ) = 350MPa
Modulus of Rigidity (G) = 84GPa

We need to first calculate the length of the spring (L).

From the formula for spring deflection, δ = (W^3L)/(Gd^4R^3), we can calculate the length of the spring as follows:

L = (δGd^4R^3)/W = (25mm x 84GPa x d^4 x 8^3)/(500N^3) = 0.06768d^4

Now, substituting the value of L in the formula for the spring's diameter, we get:

d = [(16 x 500N x 0.06768d^4 x 8)/(π x 84GPa)]^(1/4) = 3mm (approx.)

Therefore, the diameter of the spring required to carry a load of 500N with a maximum deflection of 25mm is 3mm.

Apply Wahl's Formula Find Kw which will be 1.184..then apply Shear Stress= Kw x (8WC/πd^2) d will be 6 mm