Problem 1 The stresses at a certain point in a cast iron machine part are Ox= 40 MPa, Oy= -50
MPa and Txy = 30 MPa (C. W). Determine analytically the safety factors
guarding against static failure according to the Coulomb-Mohr and
modified Mohr theories. The ultimate tensile and compressive stresses of the cast
iron are 150 MPa and 600 MPa respectively.

Awall of 0.5m thickness is to be constructed from a material which has average thermal conductivity of 1.4 w/mk. the wall is to be insulated with a material having an average thermal conductivity of 0.35 w/mk so that heat loss per square meter shall not exceed 1450 w. assume inner wall surface temperature of 1200°c and outer surface temperature of the insulation to be 15°c. calculate the thickness of insulation required.