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

Answer:

$R_{min} = 4.84\times 10^{-3} m$

Explanation:

Given data:

Applied force 750 N

Flexural strength is 105 MPa

separation is 50 mm = 0.05 m

flexural strength is given as

$\sigma_f = \frac{FL}{\pi R_{min}^3}$

solving for R so we have

$R_{min} = [\frac{FL}{\pi \sigma_f}]^{1/3}$

plugging all value to get minimum radius

$R_{min} = [\frac{750 \times 0.05}{\pi 105 \times 10^6}]^{1/3}$

$R_{min} = 4.84\times 10^{-3} m$