Determine (a) the strain invariants; (b) the normal strain in the x′ direction, which is directed at an angle θ = 30° from the x axis; (c) the principal strains ε1, ε2, and ε3; and (d) the maximum shear strain.

Apiston-cylinder with a volume of 0.25 m3 holds 1 kg of air (r 0.287 k/kgk) at a temperature of 100 c. heat transfer to the cylinder causes an isothermal expansion of the piston until the volume triples. how much heat is added to the piston-cylinder?

At 12 noon, the count in a bacteria culture was 400; at 4: 00 pm the count was 1200 let p(t) denote the bacteria cou population growth law. find: (a) an expression for the bacteria count at any time t (b) the bacteria count at 10 am. (c) the time required for the bacteria count to reach 1800.

A12 mm diameter shaft runs in a plain cylindrical bush 30 mm long that is located in an 18 mm diameter hole in a housing. the shaft-inner bush fit is h8 f and the outer bush-housing fit is h7-p6. make a fully cimensioned sketch of the bush with tolerances. find the maximum and minimum clearance or interference for both fits on the inner and outer diameters of the bush