Question

A circular specimen of MgO is loaded using a three-point bending mode. Compute the minimum possible radius of the specimen without fracture, given that the applied load is 750 N (169 lbf), the flexural strength is 105 MPa (15,000 psi), and the separation between load points is 50.0 mm (1.97 in.).

Answer 1

`R_(min) = 4.84* 10^(-3) m`

Step-by-step explanation:

Given data:

Applied force 750 N

Flexural strength is 105 MPa

separation is 50 mm = 0.05 m

flexural strength is given as

`\sigma_f = (FL)/(\pi R_(min)^3)`

solving for R so we have

`R_(min) = [(FL)/(\pi \sigma_f)]^(1/3)`

plugging all value to get minimum radius

`R_(min) = [(750 * 0.05)/(\pi 105 * 10^6)]^(1/3)`

`R_(min) = 4.84* 10^(-3) m`