Question

Q.8 [15] A research assistant for a materials science class has need to characterize the elastic behavior of a rectangular plate of Al2O3 known to have a flexural strength of 54.2 ksi, and flexural modulus of 23.1 x103 ksi. The length width and thickness of the plate are 10 in, 0.75 in and 0.325 in respectively. The student conducts a 3- point bend test by placing the plate between two rods 6 in apart. Determine (a) (b) The force required to fracture the plate The deflection of the plate at the point of fracture assuming only elastic deformation takes place.

Answer 1

For 3 point bend test Given L = 6 in d = 0.352 in b = 0.75 in For the figure, bending moment is maximum at the centre (M)_max = P/2 times L/2 = PL/4 Moment of Inertia, = I = bd^3/12 = 0.75 times (0.325)^3/12 = 2.1455 times 10^-3 in^4 we know that, sigma_max = m.y/I y = d/2 \r\n sigma_max = 3 PL/2bd^2 given strength , sigma_max = 54.2 kg 54.2 = 3 times p times 6/2 times (0.75)(0.325)62 p = 0.715 klb a) The force required to = 715.60 lb b) The occurs at the centre and maximum deflection is also at the centre delat_c = PL^3/48 EI = 0.7156 times 6^3/48 times 23.1 times 2.144^5 times 10^-3 delta_c = 0.0649 inches deflection is 0.0649 inches