Calculate deflection of a T304 stainless steel rod The diam

Calculate deflection of a T-304 stainless steel rod.

- The diameter of the rod is 0.625\".

- The Length of the rod is 8 in.

- The weight of the rod is 8.54 lbs

what is the deflection in the middle of the rod if rod is supported at both ends I need deflection when 20 lbs, 30lbs, and 40lbs of force is happening in the middle.

Solution

Solution:-

Given

L = 8 inch

Diameter of rod (D) = 0.625 inch

Weight of rod = 8.54 lbs

Let

E = 29 *10⁶ psi

I = /64* (0.625)⁴ = 0.00749 inch⁴

When force = 20 lbs apply on middle of rod

Total weight (w) = 20 + 8.54 = 28.54 lbs

Deflection() = wL³/(48EI)

= 28.54 * 8³/(48 * 29 * 10⁶ * 0.00749)

= 0.0014 inch   Answer

When force = 30 lbs Apply

Total weight (w) = 30 + 8.54 = 38.54 lbs

Deflection () = wL³/(48EI)

= 38.54 * 8³/(48*29*10⁶ * 0.00749)

= 0.00189   inch      Answer

When force = 40 lbs Apply on rod

Total weight (w) = 40 + 8.54 = 48.54 lbs

Deflection() = wL³/(48EI)

= 48.54* 8³/(48* 29*10⁶* 0.00749)

= 0.00238   inch     Answer