Question

2. 20 points: A plate of ductile cast iron [E = 200 GPa, v=0.38, alpha = 5.2x10degC) has a width a = 397 mm, a height b = 266 mm., and a thickness t = 33 mm. As shown in the figure, the plate is constrained between two rigid, perfectly smooth surfaces at an ambient temperature of 40°C. The plate is compressed by a constant normal stress Ox = 250 MPa. Assume that plane-stress conditions exist. Rigid Rigid (a) Determine the normal strain, Ey, and the average normal stress, y, at the ambient temperature. (b) Determine the normal strains, er, and the average normal stress, Oy, at a temperature of O'C (colder) (c) At what temperature will the average normal stress in the y direction be reduced to zero?

Answer 1

niven Q=397mm b=266 mm &= 200 GPa 2=0.38 x = 250 MPa t-33 mm d = 5.2x10-6 a) Ey = 0 oya vox = 38(-250) = 95 MPa b) Ey=0 9V +a (AT) = 0 sy-038 (-250) = -(AT) E oy +95 = - 512X166 (0-40) x 200x103. og = 41.6-95 oys - 53.4 MPa) &z= V (ou toy) +2 (AT) = -0.38 [-250-53-4]+ 5.2x10-6 (-40). = 0.57646X10-34 --208 X10-3 = 3.684 6 8 10 na F 200 x 10²4 d) Ey 20 og vor + 2 (DT) = 0 y = 0 &(ot) = x on AT = 0.38 × (-250) 5.2x10-6 x 200 x103 DT = -91.346 T2 - Ty = -91.346 +40 [= -51.346°c