Answer
$R = 9.12 \times 10^{-3} m = 9.12 mm $
Work Step by Step
Required:
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 5560 N (1250 lbf), the flexural strength is 105 MPa (15,000 psi), and the separation between load points is 45 mm (1.75 in.).
Solution:
Rearranging Equation 12.7b to compute R:
$R = [\frac{F_{f} L}{σ_{fs} π}]^{1/3} = [\frac{(5560 N) 45 \times 10^{-3} m}{(105 \times 10^{6} N/m^{2}) π}]^{1/3} = 9.12 \times 10^{-3} m = 9.12 mm $
