P13.55 WP A plate of ductile cast iron [E = 168 GPa; v = 0.32; a = 10.8 × 10<sup>-6</sup>/°C] has a width a = 420 mm, a height b = 250 mm, and a thickness t = 30 mm. As shown in Figure P13.53/54/55, the plate is constrained between two rigid, perfectly smooth surfaces at an ambient temperature of 20°C. The plate is compressed by a constant normal stress σ<sub>x</sub> = 300 MPa. Assume that plane stress conditions exist.
(a) Determine the normal strains ε<sub>x</sub> and ε<sub>z</sub> and the average normal stress σ<sub>y</sub> at the ambient temperature.
(b) Determine the normal strains ε<sub>x</sub> and ε<sub>z</sub> and the average normal stress σ<sub>y</sub> at a temperature of 150°C.
(c) At what temperature will the average normal stress in the y direction be reduced to zero?
✓ Answer
P13.55 (a) ε<sub>x</sub> = −1,603 με, ε<sub>z</sub> = 754 με, σ<sub>y</sub> = −96.0 MPa
(c) ε<sub>x</sub> = 250 με, ε<sub>z</sub> = 2,610 με, σ<sub>y</sub> = −332 MPa
(c) -32.9°C
